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Monte carlo simulations as a tool to optimize target detection by AUV/ROV laser line scanners

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Monte carlo simulations as a tool to optimize target detection by AUV/ROV laser line scanners
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Montes, Martin Alejandro
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Shallow optically turbid waters
Underwater light model
Unmmaned underwater vehicles
Dissertations, Academic -- Marine Science -- Masters -- USF   ( lcsh )
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government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

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ABSTRACT: Monte Carlo simulations as a tool to optimize target detection by AUV/ROV laser line scanners Martin' Alejandro Montes ABSTRACT The widespread use of laser line scanners (LLS) aboard unmanned underwater vehicles in the last decade has opened a unique window to a series of ecological and military applications. Variability of underwater light fields and complexity of light contributions reaching the receiver pose a challenge for target detection of LLS under different environmental conditions. The interference of photons not originating at the target (e.g. water path, bottom) can often be minimized (e.g., time-gated systems) but not excluded. Radiative transfer models were developed to better discriminate noise components from signal contributions at the receiver for two continuous LLS: Real-time Ocean Bottom Optical Topographer (ROBOT) and Fluorescence Imaging Laser Line Scanner (FILLS).Numerical experiments using forward Monte Carlo methods were designed to explore the effects of diverse water turbidities and bottom reflectances on ROBOT and FILLS measurements. Interference due to solar light on LLS target detection was also examined. Reliability of radiative transfer models was tested against standard models (Hydrolight) and aquarium measurements. In general a green laser was the best all around choice to detect targets using both LLS sensors. Based on signal-to-noise (S/N) values, performance of ROBOT for target detection was greater (two-fold) than FILLS because of the lower contribution of path photons in ROBOT than FILLS. When ROBOT was located at 1 m above the target, path radiance contributions (noise) were reduced up to 25-fold in clear waters (0.3 mg m-3) with respect to turbid waters (5 mg m-3).Since ROBOT was more discriminative of bottom reflectance discontinuities (high-contrast transitions) than FILLS, algorithms are proposed to retrieve contrasting man-made targets such mines.
Thesis:
Thesis (M.S.)--University of South Florida, 2005.
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Includes bibliographical references.
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by Martin Alejandro Montes.
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Monte Carlo Simulations as a Tool to Optimize Target Detection by AUV/ROV Laser Line Scanners by Martn Alejandro Montes A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science College of Marine Science University of South Florida Major Professor: Kendall Carder, Ph.D. Frank Mller-Karger, Ph.D. Pamela Hallock-Muller, Ph. D. Date of Approval: August 24, 2005 Keywords: shallow optically turbid wa ters, underwater light model, unmmaned underwater vehicles Copyright 2005 Martn Alejandro Montes

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DEDICATIONS To my lovely daughter Sophia for providing th e strength I need in the most difficult moments…

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ACKNOWLEDGEMENTS I would especially like to thank my advi sor Dr. Kendall Carder, one of the sharpest scientists I have ever met, for his guidan ce, support, and patience. There are many good things I can say about Ken who was not only an excellent professional but also a great person. I won’t forget Flip (Philips Reinersman), my teacher in Monte Carlo simulations. He was always there to answer my ques tions and didn’t let me give up. Thanks to Dr. Frank Mller-Karger for his c onstructive criticism during my thesis work, and his generous support in difficult times. Thank you Dr. Pamela Hallock-Muller for helping me in connecting coral r eef topics to marine optics. Thanks to Ted Van Vleet for his perfect assistance in all academic issues; I have not words for his kindness. Thank you Dr. Robert Chen for fixing com puter logistical problems frequently. I also would like to thank my friends Jim Ivey, Jennifer Cannizzaro, Dan Otis, and David English for sharing moments and making the academic life more fun…

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i Table of Contents List of Tables iii List of Figures iv Abstract vi 1 Introduction 1 1.1 Classification of laser line scanners 9 1.1.1 Real-time Ocean Bottom Optical Topographer 10 1.1.2 Fluorescence Imagining Laser Line Scan 12 1.2 Artifacts of laser line scanners measurements 16 1.2.1 Adjacent effects 18 1.3 Line spread function components: Monte Carlo and other approaches 18 1.4 Radiomet ric entities and boundary interactions 21 1.5 Research Objectives 25 1.6 Hypotheses 26 2 Methods 27 2.1 Types of Monte Carlo schemes 27 2.2 Optimization of photon processing during Monte Carlo simulations 29 2.3 Basic steps of a forw ard-in-time realization 31 2.3.1 Ambient light model 31 2.3.2 Laser line scanner model 36 2.4 Checking reliability of Monte Carlo simulations 39 2.4.1 Monte Carlo simulations vs a light standard model (Hydrolight) 39 2.4.2 Monte Carlo simulations vs aquarium measurements 41 2.5 Simulating target detection in different environments 42 2.6 Software design, implementation and machine performance 48

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ii 3 Results 50 3.1 Validation of Monte Carlo simulations 50 3.2 Effect of different water turbidities 52 3.3 Effect of different bottom albedos 56 3.4 Effect of different laser wavelengths 58 3.5 Applications 63 3.5.1 Micr oenvironments with significant resuspensions 63 3.5.2 Coral reef ‘halo’ 69 4 Conclusions 72 References 78

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iii List of Tables Table 1.1 List of symbols and acronyms 3 Table 2.1 Inherent optical propertie s of MC validation experiments 41 Table 2.2 Parameters for LLS 2-D simulations 42 Table 2.3 Water optical components and sp ectral windows during 2-D simulations 43 Table 2.4 Monte Carlo algorithm efficien cy under different initial settings 49 Table 3.1 Curve fitting of true path radiance of modeled vs aquarium measurements 52 Table 3.2 Curve fitting parameters for different bottom albedo retrieval functions 70 Table 4.1 Summary of laser line scanne r performance for ta rget detection 74

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iv List of Figures Figure 1.1 Photon contributions to an underwater imager 5 Figure 1.2 Remotely operated vehicles and autonomous underwater vehicles 7 Figure 1.3 Classification system fo r underwater imagers (Jaffe, 1990) 9 Figure 1.4 Real-time Ocean Bottom Optical Topographer 11 Figure 1.5 Schematic for ROBOT scanning system 12 Figure 1.6 Fluorescence imaging laser line scanner (FILLS) 13 Figure 1.7 Topographic c onstraints of FILLS 14 Figure 1.8 Altitude effects on ROBOT footprint and signal arriving to detector 15 Figure 1.9 Artifacts of laser line measur ements due to bottom irregularities 17 Figure 1.10 Adjacency effects at the LLS receiver 19 Figure 1.11 Diagram of a basic spectrometer 21 Figure 1.12 Geometry of a solid angle 22 Figure 1.13 Partitioning of th e unit sphere in quads 23 Figure 2.1 Examples of Monte Carlo schemes 27 Figure 2.2 Comparison between forward and backwards Monte Carlo models 28 Figure 2.3 Variance reduction in Monte Carlo simulations 30 Figure 2.4 Flow chart of Monte Ca rlo simulation (ambient light) 32 Figure 2.5 Ray-tracing diagram of a typical 1-D Monte Carlo simulation 34 Figure 2.6 Flow chart of Mont e Carlo simulation (laser) 37 Figure 2.7 Fournier-Fora nd scattering functions 47 Figure 3.1 Validation of Monte Carlo simulations against Hydrolight 50 Figure 3.2 Validation of Monte Carlo simula tions against aquarium measurements 52 Figure 3.3 Effect of water tu rbidity on FILLS performance 53 Figure 3.4 Effect of water turb idity on ROBOT performance 54 Figure 3.5 Effect of bottom albedo on FILLS performance 56

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v Figure 3.6 Effect of bottom albedo on ROBOT performance 57 Figure 3.7 Effect of laser wave lengths on FILLS performance 59 Figure 3.8 Effect of laser wavelengths on ROBOT performance (‘clear water’) 60 Figure 3.9 Effect of laser wavelengths on ROBOT performance (‘turbid water’) 61 Figure 3.10 Target detecti on sensitivity as a functi on of laser wavelength 62 Figure 3.11 Variation of lase r signal in FILLS due to sunlight contributions 64 Figure 3.12 Effect of particle composition on FILLS performance 65 Figure 3.13 Effect of particle composition on ROBOT performance 66 Figure 3.14 Effect of particle-size di stributions on FILLS performance 67 Figure 3.15 Effect of particle-size di stributions on ROBOT performance 68 Figure 3.16 Bottom albedo algorith ms using ROBOT and FILLS 69

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vi Monte Carlo simulations as a tool to optim ize target detection by AUV/ROV laser line scanners Martn Alejandro Montes ABSTRACT The widespread use of laser line scan ners (LLS) aboard unmanned underwater vehicles in the last decade has opened a unique window to a series of ecological and military applications. Variabili ty of underwater light fields and complexity of light contributions reaching the receiver pose a challenge for target detection of LLS under different environmental conditions. The inte rference of photons not originating at the target (e.g. water path, bottom) can often be minimized (e.g., time-gated systems) but not excluded. Radiative transfer models were developed to better discriminate noise components from signal contributions at the receiver for two continuous LLS: Real-time Ocean Bottom Optical Topographer (ROBOT) and Fluorescence Imaging Laser Line Scanner (FILLS). Numerical experiments using forward M onte Carlo methods were designed to explore the effects of diverse water turbid ities and bottom reflectances on ROBOT and FILLS measurements. Interference due to sola r light on LLS target detection was also examined. Reliability of radiative transfer models was tested against standard models (Hydrolight) and aquarium measurements. In general a green laser was the best all around choice to detect targets using both LLS sens ors. Based on signal-t o-noise (S/N) values, performance of ROBOT for target detection was greater (two-fold) than FILLS because of the lower contribution of path photons in ROBOT than FILLS. When ROBOT was located at 1 m above the target, path radian ce contributions (noise) were reduced up to 25-fold in clear waters (0.3 mg m-3) with respect to turbid waters (5 mg m-3). Since ROBOT was more discriminative of bottom re flectance discontinuities (high-contrast transitions) than FILLS, algorithms are proposed to retrieve contrasting man-made targets such mines.

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1 1 Introduction Detection of underwater target s continues to be an area of active scientific interest due to the limitations imposed by the optical medium (e.g., turbidity). Submarine feature detection and recognition are important topics in several disciplines such as ecology (e.g., coral fluorescence), geomorphology (e.g., sedime nt bed forms), petroleum exploration, submarine communications (e.g., cable comp anies), and port security (Strand, 1995; Moore et al., 2000; Mazel et al., 2003). Micro-topographic mapping (Carder et al. 2003) is also useful in evaluating benthic habitats. The use of conventional lighting to im age objects in marine systems offers advantages in the field-of-view (FOV) (Table 1.1), multi-spectral content, and ease of implementation, but with a performance cost. Image degradation due to poor performance of underwater opti cal systems is caused by light attenuation and non-target light contribution (noise). Noise is mainly constituted by photons scattered along the optical path between the light source and the receiver. It has different origins (laser vs sunlight photons) and co mponents (backscattering vs forward scattering), and varies with optical environmental characteristic s and sensor geometry (Fig. 1.1). The challenge with which all under-water imaging systems must cope is to minimize noise to better resolve the target of interest (e.g., ma n-made objects, coral features). Another importan t constraint of underwater imagers is light attenuation throughout the optical medium. This effect can often be circumvented by increasing source power and/or changing dete ctor sensitivity. In spite of its relevance, this transferradiative problem is out of scope of the pres ent thesis. The widespre ad use of laser-based imagers in the last decade has allowed a sign ificant improvement on target detection with respect to those optical systems using non-coll imated light sources. Laser line scanners (LLSs) may overcome target-signal loss to the sensor since they can concentrate a significant flux of radiant ener gy in a small spot. Likewise, different LLSs configurations make possible noise-reduction by analyzing

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2 temporal and/or spatial variations of phot ons target-originated (Fournier et al., 1993; Caimi et al., 1998). Table 1.1: List of symbols and acronyms. Symbol Explanation Units FOV Field-of-view of the optical system receiver LLS Laser Line Scanner AVIRIS Airborne Visible-Infr ared Imaging Spectrometer Lidar Light detection and ranging UUV Uninhabited underwater vehicles AUV Autonomous underwater vehicles ROV Remotely operated vehicles MC Monte Carlo model ROBOT Real-time Ocean Bottom Optical Topographer FILLS Fluorescence Imagining Laser Line Scan system PMT Photo-multiplier tube UIR Minimum upper imaging range m LIR Lower imaging range m LSF Line-spread function IOP Inherent optical properties Source-detector angle rad Xdet Source-detector distance cm Receiver field-of-view angle rad azimuthal photon direction rad zenith photon direction rad Bottom reflectance or albedo Deflection angle of photon after collision rad Light wavelength nm Ad Collector area of receiver m2

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3 Table 1.1: List of symbols and acronyms (cont.). Symbol Explanation Units Solid angle sr r Radius of unit sphere m C Cloudiness shape factor of cardioidal distribution nw Index of refraction of water No Initial number of photons Q Radiant energy J s-1 L Spectral radiance without polarization W m-2 sr-1 nm-1 Ed Downwelling irradiance W m-2 Eu Upwelling irradiance W m-2 BDRF Bi-directional reflectance functions Qrs Unit sphere partition or quads d Lower unit hemisphere u Upper unit hemisphere l Optical path-length m optical thickness m Collision cross section m2 pdf Probability density function cdf Cumulative volume scattering function r Geometrical distance m c Beam total attenuation coefficient m-1 a Total absorption coefficient m-1 aw Total water absorption coefficient m-1 aph Specific absorption coefficient of phytoplankton m2 mg-1 chl chlorophyll a concentration mg m-3 bw Water scattering coefficient m-1 b Total scattering coefficient m-1

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4 Table 1.1: List of symbols and acronyms (cont.). Symbol Explanation Units bp Particle scattering coefficient m-1 bb Backscattering coefficient m-1 bbp Particle backscattering coefficient m-1 o Single-scattering albedo VSF Volume scattering function sr-1 m-1 fs Fraction of diffuse downwe lling irradiance to total downwelling irradiance laser divergence angle mrad cone Angle of the photon trajectory to the center line of FOV rad sun Solar zenith angle rad FF Fournier-Forand phase distribution sr-1 np Real part of particle index of refraction/nw Junge hyperbolic particle-size distribution

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5 Fig. 1.1: Photon contributions to an underwat er imager. Laser photons (black arrows), sunlight photons (grey arrows), direct photons (big arrows), diffuse photons (small arrows); = laser divergence angle, = source-detector angle, = receiver field-of-view angle. Notice that optical media above a nd below the sea-surface are not homogeneous due to time/space changes on atmospheric conditions and water properties. Clouds, aerosols and underwater turbidity patchiness change light field geometry, light intensities, and radiative components at the sensor. Main noise contributions reaching the optical system receiver are backscattering (small black arrows near the main laser beam) and forward-scattering of bottom-reflected photons (small grey arrows). Water (backscattering) and particles (forward-scat tering) are primarily responsible for photon collisions along the optical medium be tween the target and the receiver.

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6 Other advantages of various LLSs are fine spatial resolution (mm), wider range of bottom types (e.g., patchy) compared to acoustic methods, night measurements (active sensors), 3-D mapping, and retr ieval of optical properties of the medium (Wells, 1969; Strand, 1997; Moore and Jaffe, 2002; Card er et al., 2003). The aforementioned capabilities make LLSs suitable to ‘ground tr uth’ remote sensing products in coastal waters. Remote sensing algorithms for bottom classification, in par ticular those obtained from airborne sensors (e.g., AVIRIS) (Lee et al., 2001), would also demand in situ validation that could be provi ded by LLS surveys (Costello, 1994). At present, passive sensors can only retrieve coarse bathym etry (Sandidge and Holyer, 1998), and are expected to be very influenced by contrasting features adjacen t to the FOV, such as when the bottom is not flat or has a patchy albedo distribution. In that regard, active sensors such as light detection and ranging (Lidar, Li ght detection and ranging) devices allow for a greater contrast of bottom characteristi cs. For instance, EAARL (Wright and Brock, 2002) uses a powerful laser source that al lows mapping at relatively high-spatial resolutions (spot circa 15 cm horizontal, and 7 cm vertical) from low-flying aircraft. Even with these advantages, airborne laser measurements also re quire calibration using finer resolution measurements such as provided by LLSs. The main stream of LLS studies concentrates on applications related with mine detection, coral reef health, wreckage mapping, microbathymetry, and bottom albedo characterization (S trand, 1997; Moore and Jaffe, 2002; Carder et al., 2003). The technological boom of LLSs is partly explained by the recent proliferation of unmanned underwater vehicles (UUVs) incl uding autonomous underwater vehicles (AUVs) and remotely operated vehicles (ROVs) at several marine science institutions in the United States (e.g., Scripps Instituti on of Oceanography, Woods Hole Oceanographic Institute, University of South Florida, Mont erey Bay Research Inst itute) (Fig. 1.2). LLSs aboard UUVs have lower cost with respec t to other platforms (e.g., ships and manned submersibles), can be positioned near the sea floor to measure distances, and may support other sensors (e.g., fluorometers, transmissomete rs). UUVs have proven to be effective in relatively shallow waters (<30 m) and can be deployed from relative small boats and managed as AUV arrays (Carder et al., 2001).

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7 Unlike ROVs (Fig. 1.2a), AUVs (Fig. 1.2b) can cover long ranges (60 km) in a relative short time (8 h) with high spatial resolution when near the bottom. Fig. 1.2: Remotely operated vehicles and aut onomous underwater vehicles developed or operated by the University of Sout h Florida. a) ROV, b) AUV. However, ROVs are, in general, eas ier to manipulate than AUVs. Although less common, LLSs can also be deployed from a lternative underwater platforms such as submarines (e.g., US Navy) and moorings (e .g., Monterey Bay Inst itute). The use of LLSs aboard UUVs introduces another set of va riables related with geometric settings (e.g., source-receiver distance, UUV altitude above the bottom) that must be accounted for to minimize noise reaching the LLS recei ver. Although noise of LLS measurements can be reduced, there is no single instrument ation capable of completely discriminating between target and ambient signal (noise) co ntributions. Solutions are partial (e.g., night surveys, time-gating, changes in source-detect or angle, fluorescence, shorter distance to

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8 the target even though footprin t is reduced) but not absolu te. Noise is determined by water (e.g., water scattering vs absorption), surface (e.g., sun altitude), and bottom (e.g., irregular vs flat areas) variability (Reinersman and Carder, 2004). Notice that ambient signal contribution to the total signal is also influenced by optical configuration of the LLS mounted to the UUV. Theoretically, total noise affecting target detection could be measured if all environmental conditions are known during each LLS survey. This approach would require a super optical system (LLS + various types of sensors) which is impractical and expensive because it must be used in defined field scenarios (e.g., there is an infinite combination of environmental conditions). Another complication is that ‘perfect sensors’ do not exist because optical sensors fail in very turbid waters (e.g., the instrument projects a shadow in very scattering waters) (Gordon and Ding, 1992). By searching a full solution to quantify noise, why not apply air-water radiative transfer models? Underwater light models have proven to be reliable tools to model arbitrary light fields and are potentially su itable to estimate different signal components arriving at the LLS receiver. One of the most popular numerical techniques among the light models is Monte Carlo (MC). Radia tive transfer simula tions using MC are consistent with other numerical sche mes (e.g., invariant embedding, eigenmatrix methods;Mobley et al., 1993). In atmospheric sc iences, MC has been applied to calculate light components (direct vs diffuse contributions) reaching airborne or satellite sensors (Reinersman et al., 1995; Miesch et al., 1999). In marine optics, MC have been mainly applied to study sensor shading effect s (Gordon and Ding, 1992; Piskozub, 2004) and bottom influence (albedo, slope) (Mobley and Sundman, 2003; Card er et al. 2003) on total signal at the receiv er. Although MC methods can model huge numbers of underwater ‘virtual’ light field scenarios w ithout necessary field measurements (Mobley et al., 1993), there have been no attempts to calculate the targ et signal and the effect of background medium signals on target identific ation of underwater laser line scanners using MC techniques. In the first part of this thesis, basic concepts about LLSs and light propagation are described. Methodological aspect s in developing MC models for two types of LLSs and design of numerical experiments are fully expl icit in the second part. In the third part, results of MC validations, environmental e ffects on signal-to-noise values at the LLS

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9 receiver, and LLS case studies are presente d. In the fourth pa rt, results on the performance of different types of LLS in various environmental scenarios (e.g., turbid vs clear waters) are discussed, and conclusions ar e summarized. The main intention of this thesis is to demonstrate how MC models can be used to optimize LLS measurements in water bodies with different light fields and bett er interpret the target signal arriving at the LLS receiver. Target detection resolution of two kinds of LLS sensors aboard UUVs is compared. 1.1 Classification of laser line scanners There are basically two kinds of LLS systems: conti nuous and short-pulse laser sources (Moore and Jaffe, 2002; Mazel et al., 2003) (Fig. 1.3). In general, improvement of image formation at the LLS receiver will depend on how much noise is reduced, and the strength of the power s ource (greater intensity produ ces better signal-to-noise). Fig. 1.3: Classification system for underwat er imagers (Jaffe, 1990). a) camera-light close, b) camera-light se parated, c) synchronous scan, and d) time gated. Notice the narrower illumination volume of laser-based sources compared to camera FOV (b-d).

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10 Based on attenuation lengths (1/beam attenua tion), performance of sensors with high-parallax geometry (source and detector ar e separated with a certain inclination) can easily double (>4) those obtained with an imaging system with minimum distance between source and receiver (~2) (Fig. 1.3a-b ). Better resolution in bi-static systems (source-receiver separated) w ith respect to conve ntional imagers is due to the lower influence of backscattered photons (‘veiling glow’) coming from the main laser beam (non-target contribution) into the FOV of the sensor. It is similar to the relatively high view angles of a truck driver viewing the ro ad in a snow storm. Scanning of bi-static optical systems usually involves a single-lin e projection method (f an-type laser with multiple beams) (Kaltenbacher et al., 2000) Push-broom or synchronous scan systems are also continuous LLS that may have paralla x geometry (Fig. 1.3c). In this case, noise due to forward scattered phot ons after target reflection (‘blur’) can be minimized by making smaller receiver FOV and volume illuminated by laser (one single laser beam) (Mullen et al., 1999). Scanning of synchronous optical systems is based on a single-point method (source and receiver are swept si multaneously perpendicular to the UUV direction). Unlike other imagers, synchr onous and Lidar (Fig. 1.3d) LLSs suffer power limitation because more energy must be focused in a smaller area (field-limited systems) to obtain greater S/N values. Noise in Lidar imagery is reduced when the camera system is activated at a precise time depending on the range of interest coll ecting light that has traveled a fixed delay and is relatively free of backscatter information (Fournier et al., 1993). Range-gated systems such as Lidar can al so be designed to classify target photons based on polarization filters (Morgan et al., 1997). According to a broader classification of LLSs, optical systems of Figure 1.3 can be grouped as structured illumination techniques (Bailey et al., 2003). Other met hods of target detection using lasers are multiple-line, color-coded, and gr ating projections (Gilbert, 1999). 1.1.1 Real-time Ocean Bottom Optical Topographer The Real-time Ocean Bottom Optical T opographer (ROBOT) (Carder et al., 2001, 2003) is a bi-static LLS consisting of a fan-b eam source and intensified camera receiver

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11 (University of South Florid a, Center of Ocean Technology, Kaltenbacher et al., 2000) (Fig. 1.4). Fig. 1.4: Real-time Ocean Bottom Optical To pographer. a) Diagram showing optical instrumentation, b) ROBOT components inside an AUV. The laser source is a fan-type, and the receiver is a CCD camera (Charged C oupled Device) with more than one pixel. An acoustic-Doppler sensor is located between the source and the receiver to record UUV speed. Source-receiver distance is adjust able (copyright Kaltenba cher et al., 2000). The CCD camera is an 8 x 10 mm array of 20 x 30 m pixels, and the source is a green laser Nad-YAG glass (double) (532 nm ) with a power of 0.5 W. FOV along UUV travel direction is 28.4, FOV across UUV tr avel direction (y-component) is 36.7, and is 1.5 milliradians. The typical resolution of th e system is 2 x 2 x 2 cm at 2 knots speed. The laser beam is split along the y-component, a nd its photons spread over an arc of 45. A schematic of the ROBOT scanning system is shown in Figure 1.5. Individual frames (topography lines) are assembled into a 3-D image in real time as the UUV passes over the object. Real measurements of ROBO T are made in 3-D using a laser fan-type system spread across the UUV travel direction, and a 2-D CCD array (Kaltenbacher et al., 2000). A single laser-beam is optically spread into a thin fan beam. Beam coverage is spread in one dimension completely and n eeds only be swept once in a perpendicular direction to obtain a complete im age of the area of interest.

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12 Fig. 1.5: Schematic for ROBOT scanning system A bi-static camera viewing light from a fan-beam laser reflected off the bottom and objects therein. The pixel with the brightest radiance per image column is saved as a meas ure of the object albe do, and the position of the pixel provides a measure of the range to the object. The spatial sequence of the columnar points creates the range profile shown as the ‘camera view’, and a temporal sequence of ‘camera views’ from video frames is used to build up 3-D images (after Kaltenbacher et al., 2000). 1.1.2 Fluorescence Imagining Laser Line Scan The Fluorescence Imagining Laser Line Scan system (FILLS) is a synchronous scan system that uses a laser point (small m illimeter-size spot) to il luminate an object, and a receiver with a very narrow (~ 0.573) FOV (U.S. Navy, Raytheon Electronic Systems Corps., Strand, 1997) (Fig. 1.6). FILLS has an Argon-Ion laser source at 488 nm and four separate photomultiplier receivers (1 -pixel resolution each) at 488 nm: blue (10 nm full width at half maximum spectral re solution), 520 nm: green, 580 nm: orange, 685 nm: red (Fig. 1.6a). FILLS has more interfer ence filters than ROBOT because it may

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13 work with scattering (488 nm) and fluor escence (>488 nm) channels. Each receiver consists of a rotating optical assembly (90 s can lines), a controllable aperture assembly, a photo-multiplier tube (PMT), a preamplifier and signal conditioning electronics, and an analog-to-digital converter. Each of the r eceivers’ rotating op tical assemblies are composed of four-faceted mirro rs that can be also fitted with polarization analyzers, which allow various aspects of the refl ected light field to be evaluated. Fig. 1.6: Fluorescence imaging laser line scanner: a) diagram showing optical instrumentation, b) scanning system (copyr ight Strand, 1997; Jaffe, 2005). Notice that FILLS receiver has only one wide pi xel that is scanned in time. FILLS can also be used create color imag es using a laser source with a different combination of gases (Argon/Krypton). RGB outputs in red (647 nm), green (515 nm)

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14 and blue (488 nm) can be collected at range s up to one order of magnitude greater with respect to those obtained with ambient light illumination. The power consumption of the sensor is ~7.5 kW (~8,000X more energy is used compared to ROBOT because of the tiny viewing spot and integration time). FI LLS geometry partially compensates for the inefficient parallax (light source and rece iver are very close each other, ~25 cm separation) of FILLS measurements. Unlike ROBOT, FILLS also can avoid scattering noise due to the medium by detecting fluor escence (target is detected at longer wavelengths than those used for excitatio n). Nevertheless, the use of fluorescence provides other light interferences such as sunlight near the surface during daylight hours (Mobley, 1994) and bioluminescence (Widde r, 2002) during night surveys. In FILLS, source and receiver are moved concurrently during each scan using a sophisticated mechanical system (Fig. 1.6b). Likewise, imag e gathering and processing time is more complex in FILLS compared to ROBOT. The smaller source-detector angle in FILLS (~2) compared to ROBOT (up to 45) makes FILLS measurements close to the target difficult because the minimum upper imaging range (UIR) is constrained to 15 feet (Fig. 1.7). Fig. 1.7: Topographic constrai nts of FILLS. UIR = upper imaging range, LIR = lower imaging range, = source-detector angle.

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15 The upper and lower (14.6 m) imagining range limits are adjusted to bracket the range to the sea floor. At 7 m above the botto m, the area illuminated by the source has a 7 mm diameter, the target seen at the receiver is 25.46 cm, and the swath is circa 10 m (8 m usable). Although ROBOT has a lesslimited minimum on the upper imaging range, changes in range affect its s canning width (further from the object the larger the area) in the same way as other multiple-beam LLSs. Also a smaller source-detector angle and the single pixel of FILLS do not allow topographic mapping of the seafloor or bottom objects. Because the signal/noise decreases as the optical path betw een the detector and the target increases (Fig. 1.8) FILLS must be more sensitive than ROBOT by increasing the power source and using a high-gain receiver (e.g., PMT). Fig. 1.8: Altitude effects on ROBOT footprin t and signal arriving to detector: a) UUVZ = 1 m, b) UUVZ = 5 m. Unlike Xdet, source-detector angl es are similar in a) and b). Notice that at greater UUV altitudes above the target mo re pixels in the far-ra nge are particularly affected by the backscattering component and larger the target seen by the sensor.

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16 However under this configuration, path ra diance is also incr eased. Hence, FILLS can operate farther away from the target wh en turbidity is low; otherwise fluorescent mode is the only alternative. Farther from the target, FILLS measurements are less prone to sea-bottom impacts due to AUV/ROVs botto m irregularities. In terms of construction and operation, ROBOT is cheaper (~$ 30,000 US) than FILLS (>$1 million US) because of the simplicity of ROBOT mani pulation and optical components. 1.2 Artifacts of laser line scanners measurements In general terms, artifacts of LLS meas urements are caused by background light (noise) and topographic effects. The first category was alread y discussed, and it is related to the influence of non-target photons (s unlight and laser-derived) on total signal generated at the LLS receiver The second category is connect ed with distortions of LLS measurements caused by targets with non-uni form reflectance or shape. For optical triangulation systems (e.g., ROBOT), the accuracy of the range data depends on proper interpretation of imaged light reflections (Mundy and Porter, 1987; Buzinski et al., 1992). The most common approach to locate a poi nt on a laser line scan is to find the ‘center’ of each cross-scan power distributi on of reflected light. Re latively simple (e.g., mean, median, peak; Soucy et al., 1990) or co mplex (e.g., space-time analysis ; Kanade et al., 1991) statistical methods are used to define the ‘center’ of the spot illuminated. The first family of statistical measures is cu rrently used in contin uous lasers, whilst the second is commonly a tool in shortpulse lasers. LLS imaging involves projecting a light sour ce in an oftenturbid medium. A line spread (LSF) or point spread (PSF) functi on can be used in describing the spatial distribution of scattered phot ons in 2 and 3-D, respectively. In general, LSF/PSF are Gaussian-type functions that describe how scattered photons are or dered across a line or over a plane. Maximum signal is expected wher e the laser spot (main laser beam) hits the target surface and lower photos densities tend to be found toward the edges of the fieldof-view of the sensor. Notice that fan-type LLSs (e.g., ROBOT) have more than one laser beam hitting the surface and consequently must deal with multiple LSF/PSFs and ranges. LSF or PSF Shapes change due to surface refl ectance discontinuities non-flat surfaces,

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17 and partial occlusion of light beams (Fig. 1.9) In Figure 1.9, the LLS receiver is treated as one-dimensional orthographic, the illumina nt has a Gaussian cross-section, and the laser divergence is zero. By c onvention, laser beam divergence or width is the distance between the beam center and the e-2 point (~13.5%) of the irradiance profile. Notice in Figure 1.9 that estimated ranges could lie outsi de the limits of the target. One possible strategy for reducing these bottom effects is to decrease the width of the laser beam. However, there is a limit to collimate a Ga ussian beam due to diffraction effects (e.g., lobes of Bessel function; Bickel et al., 1985). Fig. 1.9: Artifacts of laser line measurements due to bottom irregularities: a) reflectance discontinuity, b) corner, c) shape discontinuity with respect to illumination, d) sensor occlusion (copyright Curle ss and Levoy, 1995); bottom albedo 1> 2. Shape of line spread function is plotted behind the receiver.

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18 Although not represented in Figure 1.9, FILLS and ROBOT measurements can also be affected by speckle, a random interf erence pattern (Maul, 1985) that has been found when the target surface is sufficiently rough with respect to the laser wavelength (Baribeau and Rioux, 1991). In general, topogr aphic artifacts are more notorious when the sensing system is 3-D (e.g., ROBOT), a nd corrections become more sophisticated (e.g., 3-D shading or fanni ng; Moore et al., 2000). 1.2.1 Adjacent effects Distortions on target detec tion not only are present when there are irregularities within the FOV of the sensor but also when those irregularities ar e outside the FOV but relatively close to it (patch is larger than F OV). In this case, ‘adjacency or edge effects’ are produced when adjacent light scatters in to the FOV affecting the image formation (Fig. 1.10). Edge effects have a dual contribution of photons to the sensor (backscattered and forward scattered), and are very pronoun ced in sloping or albedo patchy bottoms (Mobley and Sundman, 2003). Studies regarding underwater adjacency effects are recently new compared to those carried out in atmospheric/terrestrial sciences (Reinersman et al., 1995; Miesch et al., 1999), even though the theoretical principl es are the same and the case studies comparable (e.g., saw-tooth bottom vs linear dunes, cloud-shadow vs seagrass bed patch) (Reinersman et al., 1998; Miesch et al., 1999; Carder et al., 2003; Mobley and Sundman, 2003). 1.3 Line spread function components: Monte Carlo and other approaches The analysis of LSF/PSF curves is vital to know the LLS performance and understand the importance of noise contributions to the target signal. At the LLS receiver there are two important photon contributions: re flected direct target and path radiance.

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19 Fig. 1.10: Adjacency effects at the LLS receive r. FOV configuration belongs to ROBOT, patchy bottom is represented with black and white rectangles, a box-like bottom featured is mounted close to the far-range of dete cted area, ambient and laser light photons (arrows) are simultaneously interacting. Stronge st signal is coming from the illuminated spot (grey oval). Additional light contribu tions from pixels surrounding FOV of receiver are determined by bottom reflectance hete rogeneities and topographic distortions. The first signal component has the maxi mum probability (LSF/PSF can be seen as a probability density function) and coincided with target center (i.e., spot illuminated by the main laser beam). At both sides of the main peak, noise contributi on is expected to be greatest, especially over far-range viewing pixels if source-receiver separation is significant. Therefore, more symmetric LSF/PSF could be obtained in those sensor configurations with minimum parallax. Near-range pixels of the LLS receiver may capture target and path radiance due mainly to multiple-scattering (forward scattered photons before and after bottom reflection). Th e far-range pixels of FOV are expected to have the most degraded signal because path radiance is the highest. In these pixels,

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20 backscattering (single-scattered photons from the main laser beam) increase path radiance contributions with respect to target counts. Regarding the probabilistic nature of LSF/PSF functions, proba bilistic methods such as MC ray-tracing models arise as a feasible solution to improve target detection by un-mixing noise and target si gnal contributions reaching the LLS sensor. MC methods can also help to examine the effect of each environmental factor (e.g., cloud coverage, stratification of water opti cal components) or instrument setting (e.g., UUV depth, source-detector angle) on LLS signal/noise variability. In general, MC solutions are based on radiative transfer equations in conjunction with their boundary conditions (Mobley, 1994). MC can be applied to any water body, even those with changing boundary conditions and inherent optical propert ies (IOPs) in three spatial dimensions. Although computationally ineffi cient with respect with ot her numerical methods (e.g., invariant embedding, eigen-matrix methods) (Mobley, 1994), MC is the unique choice when light fields in 3-D or other high dimensional cases need to be modeled. For instance, invariant embedding methods (e.g., Hydrolight software, Sequoia Scientific Inc.) are quick for solving 1-D radiance tr ansfer equation (Mobley and Sundman, 2001). However, effects of irregular bottoms on li ght fields are easily treated by using MC approaches (Carder et al., 2003; Mobley and Sundman, 2003). MC methods have been already tested for solving adjacency problems observed in coupled atmospheric/terrestrial problems (Miesch et al., 1999) and involving airborne sensor s (e.g., AVIRIS; Reinersman et al., 1995). Adjacency effects derived from this approach are comparable to the background/target signal contributions of the LLS problem exposed in the present study. As a final comment, it is important to differentiate MC methods from illumination and bi-directional reflectance models. I llumination models do not include light interaction with the medium between the light source and the target (i.e., assume that light travels in vacuum). Moreover, photon interactions are modeled using Markov-chain, random-walk techniques, that imply dependency between collisions with only one branch per event (Jensen, 2001). In bi-directional refl ectance models, bi-directional reflectance functions (BDRF) describing surface reflectan ce for all combinations of incident and reflected angles are used (Mobley et al., 2003; Zaneveld and Boss, 2003). An important limitation of BDRF is that they are speci fic and must be known (e.g., based on canopy

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21 geometric models) or measured a priori (e.g., ooid sand) to proceed with radiative calculations. Both illumination and bi-directi onal reflectance models can be coupled to MC simulations if radiance transfer throughout the water column is part of the model (Pattanaik and Mudur, 1992; Pa ringit and Nadaoka, 2001). 1.4 Radiometric entities and boundary interactions In a general form, spectral radiance (L) without polarization can be defined as: L = power/{[proj ected area] [solid angle] [wavelength interval]} = Q/{[ t] [ Ad cos ] [sin d d ] [ d ] } (W m-2 sr-1 nm-1) (1) where power is the radiant energy Q in Joules or number of photons (e.g., 1 green photon at 550 nm = 3.6 10-19 J) arriving at the detector surface per unit of time, Ad is the effective area of the collector or A (full area) projected onto a plane perpendicular to the beam direction (Fig. 1.11). Fig. 1.11: Diagram of a basic spectrometer. The photons have a specific energy Q and are traveling right to left. Light baffles delimit photon energy from a specific solid angle to a discrete diffuser plate, and after being sp ectrally filtered, photons are collected over the detector surface (copyright Mobley, 1994).

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22 The solid angle = sin d d is a measure of angularity in three dimensions (Fig. 1.12). Values of can also derived from A/r2, where A is an infinitesimal area patch on a spherical surface with a size inversely proportional to the square of the radius of the sphere (r). Notice that L varies with location, time, direction, and wavelength and is the primary building block for deriving ot her radiometric defin itions. For instance, spectral downward plane irradian ce is expressed as follows: Ed = 0 2 0 2 / L |cos | d (2) Fig. 1.12: Geometry of a solid angle: r is the radius of the unit sphere, A is the projected area patch delimited by the solid angle ; increases downward from 0 to whilst values augment anti-clockwise from 0 to 2 The term cos corrects for the projected colle ctor area normal to the photons heading toward the collector from the source of interest. Partition of the unit sphere into quadrilateral domains or quads implies a di rectional discretizati on and consequently a finite number of solid angles (Fig. 1.13). Cr iteria for quad partitions are determined by

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23 the geometry of the problem (i.e., more reso lution is emphasized at those angles where more photons are expected). In some cases, a polar cap (~5) is used (Mobley, 1994) for natural conditions even though this partition might not be convenient when the sun is positioned at relatively small zenith angles The partition used in this thesis was consistent with a grid of 180 ( ) by 360 ( ) bins per unit hemisphe re, thus solid angles were not necessarily equal for different quads Directional resoluti on is constrained due to computing time and memory space requirements that increase when quad resolution is augmented (e.g., 1 x 104 more computer effort if part ition is one order of magnitude greater). Fig. 1.13: Partitioning of the unit sphere in qua ds. In this specific example there are 5 bands and 10 bands per hemisphere (upper hemisphere = u, lower hemisphere = d). The arrow at the right indicates the directi on of upwelling radiance th at is leaving trough quad Qrs with a solid angle, rs. Notice the polar caps in bo th hemispheres (Q5) and the order of labeling of quads. A stream of photons traveling throughout a medium different from a vacuum will undergo attenuation in a stochastic way due to absorption and scatte ring. Therefore, each photon will have a probability of some collision within an opt ical path-length interval ( l ):

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24 p ( l ) = el (3) where p ( l ) is the probability density function (pdf) of collision of any individual photon, and is the collision cross section. If the total number of photons (No) is specified in Equation 3, then we obtain an expression for the whole beam. As p decreases with the optical path-length, fewer photons remain alive and a higher pr obability of collision results. A useful way to describe probability of photon extinction with l <= L is the cumulative volume scattering function (cdf): P ( l ) = 0Lp* ( l ) d l = 1el (4) where p* is p normalized by No, and P ( l ) varies between 0 a nd 1. The limits of integration in Equation 4 are bounded between 0 and L instead – and + as required by the method of forced collisions (Marchuk et al., 1980). Given that optical attenuation length 1/c, also known as optical thickness ( ) or free path length, is related to geometrical distance ( r = cos l / c where c is the beam total attenuation coefficient of the medium and r / cos is also known as path length), a random collision point can be found within the interval l + dl based on a random number ( R ) generated between 0 and 1 using an uniform pdf: r = -{cos /c } ln(1 -R ) (5) Once a photon encounters an extinction even t, the probability that a photon will be scattered is parameterized w ith the single-scattering albedo ( o) that is equivalent to the fraction of c accounted for by th e total scattering coefficient ( b) with respect to c ( o = b/c ). Although the collision po int is randomly assigned, photons entering the water column are not scattered equally in all direc tions or following an isotropic distribution. Instead, water constituents (water, partic les) introduce asymmetries on radial photon trajectories. Scattering functi ons are commonly applied to de scribe the redi stribution of photons in different directions:

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25 P ( ) = 2 0 2 0 2 / f *( ) d (6) where P now is a cumulative volume scatteri ng function (cdf), which depends on angles and f (sr-1) is a normalized volume scatteri ng function (phase function = VSF/ b ) if the interaction happens in the water column, or a normalized bottom albedo function (e.g., Lambertian) if the photons are scatte red by the bottom. Again by definition, the integral of Eq. 6 is always equal to 1 and can also be understood as the joint probability due to (1/2 ) and changes. Derivation of P ( ) is crucial for obtaining random directions by inversion that in some cases cannot be achieved anal ytically ex cept using numerical methods (e.g., Petzold or Kopelevich VSF; see Mobley 1994). When a collision occurs in the medium, one way of choosing VSF’s (e.g., Rayleigh or molecular vs Petzold or particulate) is to determine the relative contribution of each type of scattering to b ( bw/ b vs bp/ b ) such that the sum of VSF relative probabilities is equal to 1. As a final ste p, a random number between 0 and 1 weighted by the scattering type decides what kind of s cattering was present during that event. For bRayleigh/ b = 0.3, for example, if 0
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26 2. Obtain a protocol to calculate optim um LLS parameters based on different environmental conditions. 1.6 Hypotheses A) Target detection using FILLS is more a ffected by path radiance than using ROBOT, especially in turbid waters. Small laser sour ce-detector angles of FILLS (<2) make the signal detection less sensitive because of pa rticle backscattering contributions from photons going into the detector and forward-sc atter spread of laser photons. In turbid waters more particles enha nce these two contributions. B) ROBOT can be used over a wider range of distances to the target than FILLS especially in turbid waters. Source-detector angular proximity is an impediment when FILLS needs to be used at relati vely short distances from the ta rget (“target is detected in the water”). ROBOT can better adjust to such differences due to the variable sourcedetector angle. In addition, background noise caused by laser beam divergence is expected to be more significan t in FILLS due to larger targ et-detector ranges required. C) LLS with wavelengths within the red band (e.g., 620 nm) are less influenced by ambient light than green wavelengths in rela tive deep waters (>3 m). Water absorption increases toward longer wavelengths and is more significant after 700 nm. Sunlight contribution to red photons in the water colu mn is removed by the surface layer (<5 m) except for a small photon fraction derived from solar-stimulated fluorescence. Therefore only red photons provided by a near-bottom LLS would survive at greater depths. Moreover, a relatively short target range is expected due to wate r absorption itself. These hypotheses, if proven, will strengthe n the relative value of ROBOT relative to FILLS for many bottom-mapping tasks as it has already been demonstrated that ROBOT is capable of 3-dimensional mappi ng of topography (e.g Ca rder et al., 2003).

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27 2 Methods 2.1 Types of Monte Carlo schemes Selecting the right MC model is largely determined by the specific geometry of the problem (Fig. 2.1). Fig. 2.1: Examples of Monte Carlo schemes: a) forward approach applied to 2-D geometry, the light source (S) is the sun and the receiver (D) is an infinite plane collecting down-welling photons for Ed calculation; b) backwards approach where photons follow an inverse path from S (d etector is now the so urce of photons) to D (ultimately the sun). For instance, if the sola r zenith angle changes th en the receiver must be changed in the same way to be consistent with the incident light field geometry. In the backward approach, S can be a point. In both MC cases sunlight is the only source involved and radiometric quantities at depth –Z.

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28 In a forward MC approach, tracking of photon trajectories be gins at the source (e.g., laser, sun) (Fig. 2.1a) whilst in a backward MC approach photons are launched from the receiver (Fig. 2.1b). This ‘back wards MC’ approach is possible using the reciprocity principle of Helmholtz (Case, 1957) that allows back-tracing the photon history. Another remarkable difference between these two MC schemes is the way radiometric quantities are calculated. For in stance, computation of upwelling irradiance applying forward methods requires that the to tal weights collected at the detector be normalized by the initial number of photon (No) entering the system. On the other hand, backwards normalization implies that each photon leaving the surface is weighted by a geometric factor (e.g., 1/(1+2/3 C )) proportional to the angular di stribution of the incident radiance of the original problem (Fig. 2.2). Fig. 2.2: Comparison between forward and b ackwards Monte Carlo models: a) forward basic tracing, b) backwards tr acing, B = sea-surface boundary, nw = water index of refraction, and is the deflection angle of the photon after suffe ring a collision. In both cases the detector (D) is a plane. Unlike L1, L2 is an upwelling photon observed at a specific point along the surface boundary.

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29 Backward MC is more computationally efficient than forward MC because the number of photons wasted duri ng each simulation is smaller (No is not too large). As the detector size decreases the num ber of incident photons must be increased to maintain high signal-to-noise ratios in the forward MC approach, and becomes infinite if the receiver is a point. Therefore, backward techniques are more statistically appropriate than forward methods to determinate radiometric va lues at specific points in the space. However when the source is a point, back ward MC hold no advantage over forward methods. For this reason, a forward approach was chosen in this thesis to solve LLS problems. Interestingly, backward and forwar d MC methods can also be combined and coupled with radiance atmospheric models. 2.2 Optimization of photon processing during Monte Carlo simulations Regarding the probabilistic origin of Monte Carlo models, accuracy of MC radiometric outputs relies on the number of initial photons launched and photon interactions throughout the optical medium. Several modeling solutions are used for variance reduction of estimated radiometric quantities: partial extin ction of a photon in each collision, wrapping of phot on trajectories in lateral boundaries, and generation of daughter rays (Fig. 2.3) (M archuk et al., 1980; Kirk, 1981; Reinersman and Carder, 2004). All of these techniques have in comm on a key statement: ‘save photons as much as possible’ in order to reduce error on final calculations. The accuracy of the estimates is proportional to the square root of the number of photon used in the simulation (Mobley et al., 1993). Spatial dimensions of the light field mode led can modify uncertainty of estimated radiometric quantities. For instance, radiance tr ansfer computations are more precise in a smaller element of space if optical components of the medium remain constant and initial number of photons is sufficiently large. Reinersman and Carder (2004) studied this problem using a hybrid model that combines radiance transfer equation with an iterative relaxation algorithm (finite-element method). Briefly, the 3-D spatial domain is divided into cubes and planes (bounda ries) and solution convergence is tested (light fluxes

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30 between elements is constant) for different No, grid resolution of planes, and partitions of cubes. Fig. 2.3: Variance reduction in Monte Carlo simulations. The illustration depicts a 2-D problem (component y extends indefinitely) where the top facet is the surface boundary, the bottom facet corresponds to the bottom boun dary. In this case, surface and bottom relief are flat. Elements of the diagram: 1) wrapping of photons leaving the lateral boundaries where the entrance or exit point of an incident ray to the surface is represented with a solid circ le. 2) partial attenuation of the photon when it encounters a collision point (solid star) where the original weight in this location is not totally extinct but its weight is reduced by single-scattering albedo or th e scattering probability. 3) generation of secondary rays (D) from the main ray (M) where the sphe re at the collision point indicates the 3-D direc tionality of main and daughter rays. After a collision, paths followed by each daughter ray are dictated by the VSF of the medium.

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31 Reinersman and Carder (2004) also highlighted the importance of water components (e.g., the more turbid, the more incident photons are needed) and their temporal dynamic (e.g., more resolution near the sea-surface) as additional factors controlling the ideal minimum resolution to re produce realistic ambi ent light fields. The use of finite element meshes applied to MC with complex geometries have also been reported for solving problems related with heat transport (Farmer and Howell, 1994). Likewise, techniques for improving the speed of Monte Carlo programs can be found elsewhere (Maltby and Burn s, 1991; Henson et al., 1996). 2.3 Basic steps of a forw ard-in-time realization An instructive way of viewing the ray-tr acing process for a forward MC is as follows: 1) determine position and direction of photon; 2) determine optical distance to the boundary; 3) find a random collision or even t point along that boundary; 4) check if photon is still alive after the co llision; 5) assign a new dire ction for the scattered photon that survived the collision using a phase func tion; 6) repeat until all photons are analyzed (circa of 1 x 106 initial photons is a reliable photonpacket size to typically start a simulation). 2.3.1 Ambient light model A flow chart of a 1-D MC (monte1d_ma in2.cpp, hereafter MC1D) is shown in Figure 2.4. Since the model is plane-parallel, the water body is infinite in horizontal extent and there are not horizontal varia tions of IOPs or of boundary conditions. In spite of the one-dimensionality, MC1D photon tracking geometry is 3-D. Further assumptions of the model include linear interac tions of light with ma tter, no internal light sources except the sun, only multiple and el astic scattering (e.g., fluorescence and Raman scattering not allowed), and Lambertian bottom reflection.

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32 Fig. 2.4: Flow chart of Monte Carlo simulati on (ambient light). Noti ce that algorithm is structured with two stacks for main and daughter rays: No = number of incident photons, df = fraction of diffuse light, Hbottom = bottom depth.

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33 In short, the Setup routine fixes the initial weight (Wo) of photons to one (sum of the weights is the source power and equal to 1 W m-2), the total number of photons (1-5 x 106), the IOPs of the water column including the index of refraction of water, and the number of layers along the vertical (homogeneous vs stratified columns). In the same routine, a Set_counters sub-routine place seve ral receivers into th e water and at the boundaries (surface and bottom). The next stage in the MC code (Sta rtup()) is related to light transfer calculations above and acro ss the sea-surface. Atmospheric radiance distribution at the sea-surface for direct (sun) and diffuse (sky) incident photons was parameterized as: fs = Eod (sky)/{Eod (sky)+Eod (sun)} (7) where fs is the fraction of diffuse downwelling irradiance to to tal downwelling irradiance including those collimated beams coming from the sun (Eod(sun)). The diffuse component in this thesis is treated as a cardioidal distributi on (Mobley, 1994), thus axially symmetric incident geometry results (no isotropic fields): L( ) = Lo+LoC cos s (8) where L is equal to Lo, the radiance of the horizon, when the angle with respect to zenith ( s) is equal to 90 (cos( /2) = 0). Notice that C accounts for cloudiness conditions and has a value of 2 for overcast skies. Computation of incident-ray geometry is condensed in three functions: radiance_fill, radiance_search, and surface_cal c_dir. The first one makes a 2-D array using cardioidal distribution, cdf values, and their corresponding values; the second one selects cdf for each diffuse ray based on a random sorting of the cardioidal ; and the third one determines directionality of each direct ray. MC1D continues calculating the loss of Wo after hitting the air-sea in terface due to Fresnel reflect ion as it is clarified in Figure 2.5. Refracted photons are stored in a main stack that is called every time the

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34 function “Process” detects photon extincti on (photon weight smaller than a predetermined threshold such as 10-6). The transmitted portion of Wo (Wi = 1-Wor) is going downward (geometric distance is negative), and it is attenuated by two factors: water optical thickness and absorption at the bottom boundary. The f unction “Before_Collision” of MC1D determines the optical path attenuation of Wi between the initial position and the boundary (Wb). If Wb is greater than the mini mum weight to survive (>10-12) (Wmin) the function “Daughter ()” is called. Fig. 2.5: Ray-tracing diagram of a t ypical 1-D Monte Carlo simulation: = bottom reflectance, incident weight at the surface (Wo), weight after fresnel reflection (Wi), weight at the boundary (Wb), weight after si ngle-scattering (Ws), weight at collision point (Wc), collision point (star), optical thickness ( ), lb and lc are path lengths, Wwr and Wbr are reflected weights. Recall weights are reduced on average as c *distance.

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35 In this case, the photon trajectory is down ward and a daughter ray is going to be generated at the bottom boundary. A further weight decrease from Wb to Wbr due to bottom interaction (Wbr = Wb = bottom albedo) follows, and if Wbr is still alive, a daughter ray with bottom flag is originated and stored in a daughter stack. This daughter ray has a new direction obtai ned from a Lambertian cdf: PLambertian = 20 2/cos sin d = sin2 = 1 (9) Here is calculated from a random number between 0 and 1 ( 1), and is computed with a second random number as 2 2. Notice that for a Lambertian surface, the radiance is reflected equally in to all directions even though th e probability of leaving the surface is maximal at /4 (solid angle varies inversely with area projected). Every time the function “After_Co llision” is called, Wi is reduced to Wc at the collision point (Wc = Wi-Wb). Later, single-scattering ( o = b / c b = total scattering coefficient) diminishes Wc to Ws (Ws = o Wc), and a new direction is chosen randomly for Ws depending on the interaction type (water vs particle). The fraction of sca ttering due to water and particles with respect to b determines whether the ray is go ing to be deflected according to Rayleigh or Petzold VSFs. The calling of “B efore_Collision/After_Collision” continues until Ws <10-6. The photon weight going to the sea-surface can suffer total (internal reflection) or partial reflection (Fresnel) (Wwr). In the latter case, part of the main ray leaves the sea surface (Ww), and it is counted as water-leaving ra diance. The reflected part is rotated ( r = ) and stored as another daughter ray with a surface flag if Wwr > Wmin. As described before, Wc of an upwelling ray is later diminished due to water (Rayleigh phase) or particle (Petzold phase) collision, and a new direction is assigned to Ws or future Wi. It is important to mention that photons traveli ng horizontally are s lightly deflected ( 1 x 1012 rad) with a random upward or downward di rection. In order to perform radiometric

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36 calculations (e.g., irradiance and radiance va lues) two functions were implemented, “Update_wo ()” and “Update_wb (),” that successively sum Wi and Wb to each counter (receiver) distributed along the ve rtical on their way up or down. A final comment is connected to 2-D a nd 3-D ambient light geometries. Although ray-tracing is similar to MC1D, additional complexities come out due to ray position updating in more spatial dimensions. This procedure is done for x and y vector components based on polar coordinates: X_new = r cos sin Y_new = r sin sin (10) Radiometric quantities are calculated for in finite rectangles (2-D) or cubes (3-D), and IOPs may change along x and y directions Geometry of plane receivers (e.g., CCD) also adapts to the spatial dimensionality of the problem (e.g., in zx-dimensions we have an infinite detector along y). Sea-surface inci dent light now arrives at segments (2-D) or pixels (3-D) (collimated beams must be di stributed among the number of surface bins), and extra boundaries are re quired for photons crossing YBmin and YBmax if the problem presents three-dimensions. 2.3.2 Laser line scanner model A computing program derived from a 2-D version of monte1d_main2.cpp (AmbientPetzold2d.cpp) was written to analy ze laser photon contributions at the ROBOT and FILLS receivers (hereafter LaserPetzo ld2d.cpp) (Fig. 2.6). Below are the main modifications of MC1D code to incorpor ate LLS’s geometries: 1) a Set_Detector() function fixes the receiver parameters; 2) an extra boundary correspond ing to the detector plane is amalgamated inside the Calc_boun () and Interaction() routines; 3) photons crossing lateral boundari es are totally absorbed (i.e ., boundaries are not periodic in Wrapp_photon2()); 4) photons within the receiver’s FOV may be detected (cone_vision()) and are flagged depending if they are derived from target (Direct_target_to_de tector()) or optical medi um (water + particles) (Weight_to_detector3()) collisions.

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37 Fig. 2.6: Flow chart of Monte Carlo simulati on (laser). The 2-D LLS model simulates a single beam across the x-component. No = number of incident photons, Hbottom = bottom depth, = bottom albedo, = laser divergence angle, W’s are photon weights, Lc and Lb are optical path-lengths between the initial point and the co llision point, and the initial point and the boundary, respectively.

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38 Unlike AmbientPetzold2d.cpp where the light source is the sun and incident rays (diffuse + direct) are crossing the seasurface along the x-component boundary, the photons in LaserPetzold2d.cpp are injected from a specific bin along the x-component. Along the y-component, 2-D laser MC models assu me an infinite target and receiver. As suggested by Mobley and Sundman (2003), la teral boundaries were se t according to the horizontal scale of variation of IOPs (more variability narrower the model window). In general, values of c ranged between 0.22 and 1.5 m-1, and these turbidities corresponded with attenuation lengths between 0.7 and 5 m. Th erefore, a water patch size of six meters was established for all LLS runs. Briefl y, LaserPetzold2d.cpp starts launching No initial photons with an individual we ight (Wi) equal to 1 from a source located at distance UUVz (altitude above the bottom of UUV) from the target and a position Xi along the UUV direction. The photons are deviated randomly from the original light pencil due to the specific laser divergence of each LLS sour ce. In Process2(), initial photons pulled out from the main stack begin inte racting with the boundaries (s urface, bottom and detector). Photons hitting a non-target bottom are disti nguished from those hi tting a target-bottom using flags. Moreover, photon collisions w ithin the FOV are selectively flagged from those occurring outside the FOV. Notice that events going to the detector boundary do not produce daughter rays (photons are totally absorbed at th e receiver plane). Ordering (20 bins per target length or FOV) and coun ting of weights reaching the LLS receiver are effectuated with Order_Detector() and Ra diance_Detector () routines, respectively. Determination of optical path-length (Lb) and photon weight at the boundary (Wb) is complicated by the fact of an additiona l boundary (the LLS receiver). A similar consideration was also made for calculati ng the optical path length (Lc) and photon weight (Wc) at the collision point. Therefor e, Get_layer_limits() and Strato_collision() functions were modified accordingly to incl ude interactions of light with the LLS detector plane. In After_Collision2() function, weights within the detector cone of vision have a forced collision with in the water column and Wei ght_to_detector3() is called if Wb is greater than a minimum weight. Usi ng law of cosines, the angle of the photon trajectory to the center line of the LLS FOV is computed ( cone). A scattering angle

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39 relative to the LLS receiver is calculated as the difference between the original direction of the ray and cone. Then, cos (scattering_angle) is used to obtain the probability distribution function of the corresponding VSF (previously selected using a random number and bp/ b ). The weight going to detector (W d) is obtained as the product between Wc, phase scattering function, and Values of are computed using the area of the detector, the detector plane inclination a nd the distance between the collision point and the center of the receiver. The remaining phot on weight not going to the detector (Ww = Ws-Wd) continues interacting un til it is extinct. When the photon hits the target and the remaining weight after bottom reflection (W rd) is above the minimum weight to be absorbed (Wmin), the function Direct_target_t o_detector3 () is called. Part of Wrd is the target weight contribution going to the receiver, a nd is calculated as the product between Wrd, probability (phase distri bution function) derived from a Lambertian radiance, and The probability of a target weight going to the LLS receiver will be a function of the angle formed between the vertical and the cen ter of the receiver. Unlike FILLS, this angle can be modified in ROBOT along the UUV di rection. The remaining portion of Wrd is oriented in a new random direction accord ing to a Lambertian radiance distribution. Weight forcing (i.e., every time a photon collides with the target or is within the FOV of the LLS receiver) is a popular and useful technique (e.g., Lidar models) because it increases the number of rays re aching the sensor and improves considerably the statistical robustness of Monte Carlo outputs. 2.4 Checking reliability of Monte Carlo simulations 2.4.1 Monte Carlo simulations vs a light standard model (Hydrolight) In order to verify MC outputs, a series of comparisons were made against the now-standard one-dimensional model Hydrolight 4.2 (Mobley and Sundman, 2001) and MC1D. Hydrolight is a radiative transfer numerical model that computes radiance distributions and derived quantities for natural water bodies. In brief, this model solves the time-independent radiative transfer equati on (light fields change in milliseconds) using invariant imbedding methods. Unlik e the simplified MC version MC1D,

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40 Hydrolight may simulate elastic scattering and a non-flat surface boundary (e.g., effect of capillary waves). Neither MC1D nor Hydroli ght are able to com pute light polarization effects. Notice that Hydrolight estimations are more accurate than standard field instrumentation if all inpu t variables and parameters are exact, because it has no measurement error in the numerical data MC1D performance was tested against Hydrolight for calculation of irradiances above the sea-surface, at the water surface and within the water column. MC1D-Hydrolight estimations of vertical attenuation coefficients of di ffuse down-welling (Kd) and upwelling (Ku) light were also evaluated: Kd( ) = -d{ln[Ed(z)]}/dz (11) Ku( ) = -d{ln[Eu(z)]}/dz (12) where Ed and Eu are down-welling and upwelling i rradiances and dz is the depth difference between irradiance measurements (Smith and Baker, 1984). Differences between MC1D and Hydrolight models we re compared using log RMS (root mean square) (Carder et al., 2004) differences. The para meters for each MC1D realization were as follows: initial number of surface incident photons = 5 x 106; = 532 nm, C = 0, and fs = 21%. The Solar zenith angle ( sun) was 29.5 and matched in cident light conditions corresponding with a water body situated at 27 latitude, during a typical summer day (31 July), and illuminated at 10 am local standard time at 0 degrees longitude. Specifications of MC1D inherent optical properties were similar to “ABCONST“ version of the Hydrolight sub-model: propertie s were driven by chlorophyll a concentrations of 0.3 and 5.0 mg m-3. Notice that particle VSF is implicit in backscattering-to-scattering ratio or backscattering efficiency ( bb/ b ) values every time Hydrolight runs are modified. Total absorption ( a ) and particle scattering ( bp) coefficients were derived from Equations 3.27 and 3.4, respectively, of Gordon and Morel ( 1983) and Mobley (1994). Likewise based on Mobley (1994), water absorption ( aw) coefficient and specific absorption coefficient of phytoplankton ( aph *), and water scattering coefficient ( bw) were obtained from Tables 3.7 and 3.8, respectively (from More l, 1974; Prieur and Sathyendranath, 1981). Optical characteristics of the waters under study ar e presented in Table 2.1. Bottom reflectance

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41 ( ) was 15% for the clear water case and 5% for the turbid case. Since fewer photons are needed in shallower waters to have enough pr ecision in estimated radiometric quantities, bottom depth in all MC1D-Hydrolight comparisons was 10 m. Also, relatively shallow water columns avoided longer computer runs. Table 2.1: Inherent optical properti es of MC validation experiments: = 532 nm, sunlight wavelength, chl = chlorophyll a concentration (mg m-3), = bottom albedo, aw = 0.05172 m-1 and bw = 0.0218 m-1 are absorption and scattering coefficient of water, respectively, apH = 0.4624 m2 mg-1, specific phytoplankton ab sorption coefficient, wo = single scattering albedo or to tal scattering coefficient ( b ) to beam attenuation ( c ) ratio, bp/b = particle sca ttering efficiency, bb/b = backscattering efficiency. chl a b c wo bp/b bb/b 0.3 0.15 0.0648 0.1470 0.2171 0.6872 0.9854 0.025272 5.0 0.05 0.1667 0.8391 1.0058 0.8342 0.9974 0.019376 2.4.2 Monte Carlo simulations vs aquarium measurements The experimental setup consisted of transmittance laser measurements using ROBOT across a 0.6-m square aquarium. The aquarium volume was filled with a solution containing diatomaceous earth. This optical medium, characterized by highscattering values ( c = 1.07 m-1), is ideal to collect true backscattering data (multiple scattering is dismissed). The laser source ( = 532 nm) was located perpendicular at 0.5 m from a non-reflective target (paper sheet with almost zero reflectance) and the receiver was set behind the target and facing the lase r beam. MC simulations were designed with bottom albedo and chl absorption equal to ze ro, thus water was the principal light absorber (diatomite particles do not abso rb photons), and scattering was produced by particles and water molecules. LSF curves we re generated using photons tallied all over

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42 the target along the x-compone nt. In order to validate MC runs, non-linear regression using fifth-order Gaussian functions were applied to experimental data. 2.5 Simulating target detection in different environments Detection capability of ROBOT and FILLS measurements in water bodies with different turbidities, particle assemblages, and bottom albedos, spectral variations for different sunlight conditions and LLS settings (distance to the bottom, source-detector angle) were evaluated (Table 2.2). Table 2.2: Parameters for LLS 2-D simulations: chl = chlorophyll a concentration (mg m3), = bottom albedo, = laser wavelength (nm), sun: zenith angle (), UUVZ = UUV altitude above bottom (m), = source-detector angle (), Xdet = source-detector distance (cm). Notice that laser footprint (mm) is very small compared to receiver FOV (cm). Water column depth was in all cases 10 m. ROBOT FILLS chl 0.3, 5.0 0.3, 5.0 0, 0.05, 0.15, 0.30 0, 0.05, 0.15,0.30 400, 532, 620 400, 532, 620 sun 8.7, 29.5, 68.8 8.7, 29.5, 68.8 UUVZ 1, 5,7 7 20, 30 2 Laser footprint 1.5, 7.5 7 Xdet 57, 182 25.4 FOV 58, 269 26 Receiver CCD, 400 x 333 pixels PMT, 1 wide pixel

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43 For LLS receivers with multiple pixels (R OBOT), S/N values were calculated as target/path radiance using the middle pixel of the target. In one-pixe l detectors (FILLS), only one integrated target/path radiance or total/path radiance was computed from the model. Simulations were performed for sh allow waters (bottom depth = 10 m) one representing clear offshor e water (chl = 0.3 mg m-3), the other more turbid water (chl = 5 mg m-3) characteristic of ports and estuarie s such as Tampa Bay (Table 2.3). Table 2.3: Water optical components and spec tral windows during 2-D simulations: chl = chlorophyll a concentration (mg m-3), = laser wavelength (nm), aw and bw are absorption and scattering coefficients of water (m-1), respectively, ap and bp are absorption and scattering coefficients of particles (m-1), respectively, apH = chlorophyllspecific phytoplankton absorption coefficient (m2 mg-1), wo = single scattering albedo or ratio of total scattering coefficient ( b ) to beam attenuation coefficient ( c ), bp/b = particle scattering efficiency (particle/t otal scattering). The number of initial main photons was 5 million for each run. chl aw bw ap bp apH c wo bp/b 0.3 400 0.018 0.00750.052 0.196 0.687 0.273 0.744 0.963 532 0.052 0.00220.013 0.145 0.462 0.217 0.687 0.985 620 0.310 0.00130.008 0.126 0.276 0.446 0.286 0.990 5.0 400 0.018 0.00760.323 1.119 0.687 1.467 0.768 0.993 532 0.052 0.00220.115 0.839 0.462 0.996 0.847 0.997 620 0.310 0.00130.051 0.722 0.276 1.084 0.667 0.998 In relatively clear waters, total light attenuation is largest at = 620 nm since water itself is the main absorber. The singl e-scattering albedo is greater at shorter wavelengths ( = 400 nm) where water absorption is the smallest. Conversely, particle scattering efficiency peaks relative to molecular scattering at longer ’s because of the

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44 smaller molecular scattering values. In relative ly turbid waters, total light attenuation is strongest at blue wave lengths and maximum wo values are shifted to green ’s. Similar to low-chl waters, particle scattering effi ciency peaks at longest wavelengths. Bottom reflectance values encompassed a wi de range of benthic substrates such as sea-grass beds ( = 5%) and sandy sediments ( = 30%). Given the heterogeneity of substrates to be measured during LLS missi ons, intermediate bottom brightness (mixed end members) values were part of the simulations. A totally absorbing bottom ( = 0%) was of interest because it allows true path radiance calculation. In nature, this type of bottom is associated with anoxic pool patches. Since range measurements using LLSs are influenced by bottom reflectance, bottom albedo retrieval algorithms were de veloped for a real case of bottom albedo discontinuity (coral reef ‘halo’) assuming a flat target. The coral reef ‘halo’ is a band of nearby sand between the base of the reef and the outlying be ds of seagrass, and it is mainly formed by echinoid ( Diadema antillarum ) grazing activity duri ng nighttime hours (Ogden et al., 1973). Change of ‘halo’ diameter has been attributed to impact due to human activities such over-fishing and introduction of new diseases (Lessios, 1988). For ROBOT, three kinds of S/N indices were proposed to construct LSFrelationships: 1) (Wmax-Wmin)NEAR or signal difference between photons collected at the middle pixel of receiver (Wmax) and in the near range, 2) (Wmax-Wmin)FAR or signal difference between photons collected at the middle pixel of receiver and in the far range, and 3) Wmax. Regarding the lack of pixels in FILLS (only one-wide pixel is collecting the whole signal at a single instant in time), total signal reachi ng the detector was analyzed. Linearity of bottom-albedo-retieval algorithm s was also explored by fitting second-order parabolic models. To study solar altitude effects on LLS signals, three solar zenith angles ( sun = 8.7, 29.5, 68.8) corresponding to morning, noon and evening conditions of a typical cloud-free day of summer in Tampa Bay were selected. The remaining atmospheric parameters (e.g., C fs) were similar to those proposed for validating MC1D. The effect of different pa rticle assemblages on S/N va lues of ROBOT and FILLS receivers was studied consideri ng case studies with variable particle composition (organic

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45 vs inorganic) and size (small vs large). Regarding the relationship between volume scattering functions and particle optical characteristics, a sp ecific VSF (Fournier-Forand), which depends on the real part of index of refraction (np) and the slope of the Junge hyperbolic particle-size distribution ( ), was selected from the literature (Fournier and Forand, 1994). Fournier-Forand phase function ( FF) is (Fournier and Jonasz, 1999): FF ( ) = [1/(4 (1)2v)] [ v (1)-(1v) + [ (1v)v (1) sin-2( /2)]] + [(1v 180)/(16 ( 180-1) v 180)] (3 cos2 -1) (13) where v = (3)/2, = [4/(3(np-1)2)] sin2( /2) (14) Recall that is the linear slope of the hyperbolic cumulative distribution function in loglog space (Junge, 1955). By integrating (11) over 2 steradians in the backward direction, the particle backscattering e fficiency can be obtained: ~ bbp= (190 v +1-0.5 (190 v))/((190) 90 v) (15) 90 and 180 are evaluated at the scattering angle = 90 and = 180, respectively. Caution is advised in appl ying this model in areas wh ere phytoplankton or detritus are strong light absorbers because the imag inary part of the index of refraction (absorption) starts having a significant effect on VSF (> 5% error, Twardoswki et al., 2001) and has been ignored. Likewise, deviations of the model can be expected if biology dominates physics (turbulence) in term of changing the slope of bulk particle-size distribution (non-Jungian slopes, e.g., red-tide phytoplankt on blooms, an abundant swarm of calanoid copepods). Notice that each value of the index of refraction ( m = np + i np’) is also composed of an imaginary part (np’) related to absorption char acteristics of particles.

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46 Values of np can be derived using Van de Hulst simplifications of Mie theory for non-absorbing spheres (Van de Hulst, 1946) which require knowledge about scattering efficiencies, particle cross s ectional areas, and number of pa rticles (Carder et al., 1972). Values of can be obtained from particle-size distributions in the ocean: N ( D ) = No ( D / Do)(16) where N ( D ) is the number of particles per un it of volume per unit of size bin ( D ), No is the density of particles at Do or a reference particle diameter (e.g. 1 micron). For the purpose of LLS simulations, four cases studies of particle assemblages were investigated: TYPE I = medium-size-organic (np = 1.02, = 3.6), TYPE II = medium-size-inorganic (np = 1.26, = 3.6), TYPE III = large-size-mixed-composition (np = 1.10, = 3.1), and TYPE IV = small-size-mixed-composition (np = 1.10, = 4.0). For hyperbolic slopes less or equal to 3.6, ~ bbpvalues are approximately independent of (Twardoswki et al., 2001). Therefore, np values are expected to have a significant effect on TYPE I and TYPE II assemblages due to changes in ~ bbp. A constant np which is similar to that estimated for a Petzold VSF, was used to evaluate the effect of particlesize changes on FF ( ), and consequently in LSF’s formed at the FILLS and ROBOT receivers. In order to minimize absorption effects and maximize S/N, a bright bottom ( = 0.3), low water turbidity (chl: 0.3 mg m-3), and a green laser (532 nm) were chosen for all numerical experiments. The use of a green la ser is also particularly advantageous to reduce changes on np due to absorbing pigments. To make ROBOT less influenced by bottom-reflected photons and more sensitive to variations in light distribution along the optical path between the receiver and target an altitude above the bottom of 5 m was set instead of 1 m. Considering a light field structured according to a FF VSF, random scattering directions were generated by c onstructing a cumulative volume scattering distribution function based on Equations 11, 12 and 13. Hence, the new cdf and pdf corresponding to Fournier-Forand VSF were inserted in After_collision2() and

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47 Weight_to_detector3() functions of modified LaserPetzold2. cpp (see Fig. 2.6). Examples of different FF’s and cdf’s for particles with diffe rent indices of refraction (real part) and size distribution are shown in Figure 2.7. Fig. 2.7: Fournier-Forand scatte ring functions: a) Particle pha se function, b) Cumulative volume scattering function of V SF for particles with differe nt indices of refraction (np, real part) and Junge slopes ( ) as a function of the scattering angle. TYPE I = mediumsize-organic (np = 1.02, = 3.6, dotted line), TYPE II = medium-size-inorganic (np = 1.26, = 3.6, solid line), TYPE III = large-size-mixed-composition (np = 1.10, = 3.1, dash line), TYPE IV = small-size-mixed-composition (np = 1.10, = 4.0, dash-dot line).

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48 Type I and TYPE III populations have a mo re important forward-scattering lobe than populations II and III due to their larger size or lower refractive index (Fig. 2.7a). On the other hand, TYPE II and IV were curv es that presented a significant fraction of backscattering relative to the total scattering. Indeed, these cases co rresponded with very small particles or with particles charact erized by the largest index of refraction. Based on their cumulative volume scatte ring functions, 50% of total scattering was concentrated between 0.06 (TYPE III) and 0.5 (TYPE IV) (Fig. 2.7b). Values of ~ bbp for each kind of partic le population were: 2.479 10-3 (TYPE I), 5.568 10-3 (TYPE II), 1.779 10-3 (TYPE III), 5.45 10-2 (TYPE IV). A practical appli cation of target detection in waters with variable resuspension and particle composition is presente d in the results. For ROBOT, only those runs with UUVZ = 7 m were analyzed to e nhance the effect of water constituents and minimize bottom effects on LSF formed at the receiver. To make more comparable environmental effects on target detection performance between LLSs, numerical experiments were also performed using a hypothetical FILLS receiver with multiple pixels. Likewise, to avoid S/N differences caused by dissimilar UUVz ranges, additional ROBOT runs were initia lized with an altitude above bottom of 7 m. Notice that the area seen by an LLS de tector (FOV) is variable in ROBOT with respect to FILLS because source-detector and distance above the target are constant in FILLS. 2.6 Software design, implementation and machine performance During MC1D development, code structure was optimized using templates derived from C++ Standard Template Libr ary. For instance, daughter rays generated through ray-tracing were manipulated using st ack templates already specified in stack.h. Code re-use and encapsula tion (classes) are among the most popular programming techniques to make time-efficient algorith ms in a more compact way. Introduction of pointers as input arguments of functions was minimized to avoid system stability

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49 problems during simulations. Some examples of MC1D performance based on simulation times obtained with a Pentium 4 machine ( 2.8 Ghz, Dell inc.) ar e shown in Table 2.4. In general, longer runs were those w ith relatively highl y reflective bottoms, shallow water columns, low chl values, and characterized by a larger number of daughter rays. Increase of water column structur e was also among those factors affecting negatively on computing efficiency in each real ization. This effect is variable depending on the number of layers along the vertical and their relative turb idity. The C++ Linux environment used for MC1D simulations did no t have a graphic interface, and the output was visualized using high-level languages such Matlab. It is intended in the near future to write new MC distributions based on Borl and C++, TKC or PDL (Perl). Likewise, parallel-programming methods (Message Passi ng Interface, MPI) will be implemented to speed up every run in more time-consuming runs (e.g., 3-D light models with irregular bathymetry). Table 2.4: Monte Carlo algorith m efficiency under different initial settings: chl = chlorophyll a concentration (mg m-3), Hbottom = bottom depth (m), = bottom albedo, NDAU = number of daughter rays resulting at the end of the run (interactions) 103, TRUN = simulation running time (min); No = 1 x 104 photons, fs = 0.21, sun = 29.5 , and sun = 0. chl Hbottom NDAU TRUN (secs) 0.3 10 0.05 587,650 0.4 10 0.30 1,962,687 1.22 0.3 10 0.15 1,149,505 0.69 5.0 10 0.15 472,276 0.67 0.3 3 0.15 579,907 0.76 0.3 20 0.15 1,788,929 0.43

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50 3 Results 3.1 Validation of Monte Carlo simulations Comparisons between MC1D and Hydrolig ht irradiance outputs for a water column of 10 m, No = 5 x 106 photons and an incident irradiance of 1 W m-2 are presented in Figure 3.1. Fig. 3.1: Validation of Mont e Carlo simulations agains t Hydrolight. Downwelling (Ed) and upwelling (Eu) irradiances are plotted as a function of depth (Z). a) and c) chl = 0.3 mg m-3, b) and d) chl = 5 mg m-3, MC1D (solid circles), Hydr olight (empty circles).

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51 Notice the increase of upwelling ph otons with depth in clear ( = 0.15) with respect to turbid ( = 0.05) waters. At low wate r turbidities (chl = 0.3 mg m-3), the proportion of photons above the sea surface (w ater leaving + fresnel reflected photons) was quite similar (< 1% difference) in MC1D (Eu0+ = 0.0529 W m-2) and Hydrolight (Eu0+ = 0.0536 W m-2) models. In turbid wa ters (chl = 5 mg m-3), the relative difference was circa 2.5% (MC1D Eu0+ = 0.0470 W m-2, Hydrolight Eu0+ = 0.0482 W m-2). Simulations in clear water for Ed and Eu showed a difference between MC1D and Hydrolight of 1.04 and 1.31% RMSlog, respec tively. Maximum error was found near the bottom for both radiometric estimates (up to 2%). Differences of Ed and Eu between MC1D and Hydrolight models were examined using one random ‘seed’, thus irradiance comput ations are expected to have the largest error compared with those estimates based on statistics of many runs. In general, correspondence between MC1D and Hydrolight for Ed and Eu values was poorer in more turbid waters (chl = 5 mg-3). Error in upwe lling irradiances (RMSlog ~4.04%) was greater than computed fo r downwelling irradiances (R MSlog ~2.86%). In both Ed and Eu estimations, larger differences were obtai ned with depth (~5%). Agreement between MC1D and Hydrolight estimates of vertical attenuation coefficients was also very remarkable. Differences in Kd for clear waters (~1.1%) were smaller than those for turbid waters (~1.4%). However, Ku values of MC1D were closer to Ku values of Hydrolight in turbid waters (~2.2%) compared to clear waters (~5.6%). Reliability of MC1D to estimate a radiom etric quantity was also confirmed when MC1D and aquarium measuremen ts of ROBOT line spread f unction were compared (Fig. 3.2).The greatest differences between experi mental and modeled transmitted data were observed near the middle pixel (~0-3 cm). A fifth-order Gaussian in each kind of data evidenced a more important radial spreading of photons (coefficient B in Table 3.1) in the LSF generated with aquarium measurem ents. This is to be expected since np for diatomaceous earth (silica frustules in aquari um) were higher than modeled values using the average Petzold phase f unction of Mobley (1994).

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52 3.2 Effect of different water turbidities The variation of total signal and sign al contributions in FILLS and ROBOT receivers are represented in Figures 3.3 to 3.5. Fig. 3.2: Validation of Mont e Carlo simulations against aquarium measurements. Aquarium measurements (empty circles) vs Monte Carlo simulations (LaserPetzold2d.cpp). Only data 10 cm away (a rea seen by the receiver is 33 cm) from the target center is plotte d to emphasize those points w ith the largest variability. Table 3.1: Curve fitting of tr ue path radiance of modeled vs aquarium measurements. The statistical Gaussian model is: Y = YO + A x exp(-0.5 x abs((X-XO)/B)C), where X is the distance from the target center XO and Y is the estimated number of photons reaching X bin and normalized to the target middle pixel. Aquarium MC YO 0.0092 0.0091 A 1.030 0.989 B 0.0057 0.0041 C 1.0 1.0 XO 0 0

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53 Fig. 3.3: Effect of water turb idity on FILLS performance: a) Hypothetical LSF for path radiance (solid triangles) and ta rget contributions (empty triangles) in clear waters (left axis). Total path radiance (solid line) and ta rget (dotted line) inte grated weights in one pixel (right axis), b) Total signal in clear (solid circles) and turbid (empty circles) waters (left axis). Total integrated weights in one pi xel in clear (solid line) and turbid (dotted line) waters (right axis). Distance to the target = 7 m, = 0.3, and = 532 nm. For FILLS, the path radiance contribution in clear waters was circa eight times larger than target contribution (Fig. 3.3a, right axis). Path ra diance is enhanced in the farrange of the FOV and was manifested as a bulge in the LSF shape (Fig. 3.3a, left axis). At high turbidities ( c ~ 1), the total signal reaching the receiver suffered a drastic flattening (Fig. 3.3b, left axis). In Figure 3.3b (right axis), to tal weights collected within

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54 one pixel of FILLS’ receiver (~25 cm) in low-chl waters were more than 400 times greater than those tallied in turbid waters (optical depth is re duced five-fold). Not surprising, path radiance in turbid waters re presented a larger fr action (99%) of total signal with respect to that cal culated for clear waters (89%). In Figure 3.4 is depicted the influence of turbidity on LSF of the ROBOT se nsor at two altitudes above the target. Not surprisingly, performance based on S/N valu es was overwhelmingly superior in ROBOT (clear waters, S/N = 253.4) with respect to FILLS (S/N<1). Fig. 3.4: Effect of water turb idity on ROBOT performance. UUVZ = 1 m, = 30 and Xdet = 182 cm. a) path radiance (solid tr iangles) and target c ontributions (empty triangles) in clear waters. b) total signal in clear (solid circles) and turbid (empty circles) waters. Panels c) and d) idem as a) and b) but UUVZ = 5 m, = 20 and Xdet = 57 cm. For all runs, = 0.3 and = 532 nm. Notice that total signal in turbid waters is negligible (S/N<1) when ROBOT altitude is 5 m above the target.

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55 Part of this difference was caused by UUVZ differences between FILLS and ROBOT. Therefore, an additional set of r uns with ROBOT at 7 m above the bottom was carried out and still supported a better target detection using a bi-static configuration (S/N ROBOT 2*S/N hypothetical FILLS) instead of a synchronous optical system (data not illustrated). In turbid waters, image quali ty generated by ROBOT was degraded with respect to clear waters but signalto-noise was above 1 (S/N = 13.4). In spite of the larger interaction between the laser beam and the bottom at UUVZ = 1 m (Fig. 3.4a-b), path radian ce contribution was a minor term with respect to the target photons. This fact emphasizes the superiority of a bi-static optical arrangement for target detection compared with FILLS. Path radian ce in ROBOT at 1 m altitude accounted for a smaller fraction in the middle pixel observ ed by the receiver. However, non-target contribution dominates the signal observed to the left of the peak (Fig. 3.4a). As expected, a larger FOV in ROBOT with resp ect to FILLS (ROBOT has a much smaller FOV per pixel than FILLS, which has only one large pixel), integrat ed path radiance along the target radius was la rger in ROBOT. Nevertheless in ROBOT, path radiance per single pixel was insignificant to the right of the laser beam. Th is value can be subtracted from the peak-value pixel to provide a m easure of the target radiance. Note that integrating the forward-scattered radiance (multiple-scattering component of path radiance) with the peak radiance for the right side provides a first estimate of half the target brightness if corrections for path attenuation (~ a + bb X where X is side scattering beyond the FOV and may be 2 or 3). In turbid waters, target-o riginated weights were more homogenously distributed over the FOV of ROBOT (Fig. 3.4b). This broa der pattern of LSF was also connected with less total signal at the r eceiver compared with simulations in clear waters due to path radiance increase with turbidity. In general te rms, as the target contribution dominates total signal in clear waters, path radi ance contribution does in turbid waters. As ROBOT altitude above the target increa ses five-fold, detection capability in clear waters decreases 45 times (S/N = 5.6) (Fig. 3.4c) and the target is no l onger seen in turbid waters (Fig. 3.4d). Likewise, path radiance contribution increases at longer distances from the bottom and modifies greatly the basi c Gaussian shape of LSF (asymmetry more

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56 evident in the far-range). Up to five times the loss in total signal was calculated when ROBOT has a UUVz of 5 m and source-detector angle of 20 (Fig. 3.4b, d). 3.3 Effect of different bottom albedos LSF’s for path radiance and total signal are modeled for FILLS and ROBOT in Figure 3.5 and Figure 3.6 as a function of bottom reflectance variations. Fig. 3.5: Effect of bottom albedo on FILLS perf ormance: a) path radiance of hypothetical multiple-pixel sensor (left axis), = 0.05 (solid rectangles), = 0.15 (solid circles), and = 0.30 (solid triangles), integrated weights over one wide pixel (right axis) are indicated with a constant value for = 0.05 (dotted line), = 0.15 (thin solid line), and = 0.30 (thick solid line). b) total signal, = 0.05 (empty rectangles), = 0.15 (empty circles), and = 0.30 (empty triangles). For all runs, chl = 0.3 mg m-3 and = 532 nm.

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57 A general increase of path radiance weights with bottom albedo was observed in all LLS sensors simulations (Fig. 3.5a, Fig. 3.6a -b), and preferentially in the far-range of each receiver. Likewise, path radiance c ontribution in the near-range of FOV was consistently greatest in those runs with smallest FOV values and longest ranges from the target. Note that target weights reaching the LLS receivers were also higher with brighter bottoms (Fig. 3.5b, Fig. 3.6c-d). Fig. 3.6: Effect of bottom albedo on ROBOT pe rformance: a-b) path radiance for UUVZ = 1 (left panel) and 5 m (right panel), = 0.05 (solid rectangles), = 0.15 (solid circles), and = 0.30 (solid triangles). c-d) total signal for UUVZ = 1 (left panel) and 5 m (right panel), = 0.05 (empty rectangles), = 0.15 (empty circles), and = 0.30 (empty triangles). For all runs, chl = 0.3 mg m-3 and = 532 nm. In general, path radiance was relatively more important than target contribution for darker bottoms. For instance, the fracti on of non-target weight s in FILLS decreased

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58 from 93 to 89% as the LLS was moving from a seagrass type of bottom to a sandy substrate. Therefore, the net signal at the receiver of FILLS increased slightly as the UUV moved from bottoms with low reflectance ( = 0.05, S/N = 0.89) to bottoms with intermediate reflectance ( = 0.15, S/N = 1.33). Curiously, the detection ability deteriorates over even brighter bottoms (S /N = 1.22), perhaps because of increased bottom-reflected photons scattered into the se nsor by the medium. For different albedos, path radiance contributions to LSF of FILLS (hypothetical CCD) and ROBOT (UUVz = 5 m) were very similar in the near-ra nge viewing direction (Fig. 3.5a, Fig. 3.6b). Interestingly, path radiance contribution when ROBOT was situated very close to the target was comparable between a mixe dsubstrate bottom with intermediate reflectance and a sandy bottom ( = 0.3) (Fig. 3.6a). S/N values of ROBOT with a UUVz of 1 m were heavily influenced by botto m type (Fig. 3.6c). Approximately a 50% improvement on detection was calculated for a 3-fold change of bottom albedo from darker to brighter values. When ROBOT wa s positioned at 5 m above the bottom, target detection performance was not significantly affected by botto m albedo differences (S/N ~ 5.6) (Fig. 3.6d). 3.4 Effect of different laser wavelengths Variation of target detecti on capability of LLSs with li ght source characteristics is described below. Likewise, the relative impo rtance of sunlight interference on laser measurements for a specific wavelength is al so investigated. Before presenting how LSF is affected by spectral change s of the laser source, one s hould identify ‘transparency windows’ (i.e. spectral regions where minimum light attenuation is expected) (Table 2.3). Although the importance of different optical constituents to light attenuation vary between ‘clear’ and ‘turbi d’ waters, values of c are consistently lower at 532 nm than at 400 or 620 nm. When chl = 0.3 mg m-3, the primary light attenuation component is water as a consequence of significant light scatte ring at 400 nm and absorption at 620 nm. As

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59 the water becomes more turbid due to ch l increases, phytoplankton absorption at blue wavelengths accounts for a considerable fraction of c In FILLS, path radiance contributions over the 1-pixel receiver was largest at 620 nm (~96%) whilst the minimum was obtained using a green laser (~90%) (Fig. 3.7). Fig. 3.7: Effect of laser wavelengths on FILLS performance: a) path radiance of a hypothetical multiple-pixel se nsor (left axis), for = 400 nm (solid rectangles), = 532 nm (solid circles), and = 620 nm (solid triangles); in tegrated weights over one-wide pixel (right axis) are indicated with a constant value for = 400 nm (dotted line), = 532 nm (thin solid line), and = 620 nm (thick solid line). b) total signal, for = 400 nm (empty rectangles), = 532 nm (empty circles), and = 620 nm (empty triangles). For all runs, chl = 0.3 mg m-3 and = 0.15.

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60 In general, spectral differences on path radiance contributions were more defined in those spatial bins distant from the ta rget center. An excep tion was found during ROBOT simulations (UUVz = 1 m) (Fig. 3.8a) where path radiance spikes at 400 nm and 532 nm were concentrated at 0 and 10 cm from the target cente r and towards the farrange of the LLS receiver. In general terms, LSF shape for total signal was quite similar for a laser source of 400 and 620 nm in both sensors (Fig. 3.7b, Fig. 3.8c-d). Fig. 3.8: Effect of laser wave lengths on ROBOT performance (‘clear water’): a-b) path radiance for UUVZ = 1 (left panel) an d 5 m (right panel), = 400 nm (solid rectangles), = 532 nm (solid circles), and = 620 nm (solid triangles). c-d) total signal for UUVZ = 1 (left panel) and 5 m (right panel), = 400 nm (empty rectangles), = 532 nm (empty circles), and = 620 nm (empty triangles). For all runs, chl = 0.3 mg m-3 and = 0.15. In turbid waters, only ROBOT simulati ons 1 m above the target evidenced S/N values above one (Fig. 3.9). At = 400 nm, the path radiance contribution was larger adjacent to the target center whilst propor tion of background photons increased to the

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61 edge of the image produced by ROBOT when the laser source used corresponded to longer wavelengths (Fig. 3.9a). Shorter wave lengths had the highest path radiance contribution to total signal (up to 90% at 10 cm of the target center in the far-range of the ROBOT receiver) (Fig. 3.9b). Fig. 3.9: Effect of laser wave lengths on ROBOT performance (‘turbid water’). Similar to Figure 3.8 but chl = 5.0 mg m-3, = 0.15 and UUVZ = 1 m. In terms of target detection sensitivity, green had the best overall performance in both LLS sensors even though a red source can slightly more sensitively discriminate bottom objects in eutrophic wa ters (S/N in ROBOT = 7.15, UUVZ = 1 m) (Fig. 3.10). However, some interference might be expected due to solar-pumped fluorescence of phytoplankton and perhaps other targets (e.g., macroalgae, seagrass ). For ROBOT, a green laser was particularly advantageous near the bottom where the net signal was

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62 amplified up to 4 times (S/N at 532 nm = 164.5) with respect to the blue channel (S/N at 400 nm = 40.5) (Fig. 3.10a). Fig. 3.10: Target detection sensitivity as a function of laser wavelength: a) ROBOT measurements in clear (chl = 0.3 mg m-3, UUVz = 1, 5 m) and turbid (chl = 0.3 mg m-3, UUVz = 1 m) waters and three laser source wavelengths (400, 532 and 620 nm)(S/N is computed as the ratio between target and path radiance photons in the middle pixel of the target). b) FILLS, only simulati ons in clear waters had S/N>1, S/N is derived as the ratio between total signal and path radiance contributions at the LLS receiver.

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63 A blue laser source definite ly was not a suitable option for LLS measurements in clear or turbid waters with respect to the pa th radiance contributions above discussed. For all wavelengths tested, ROBOT was superior ability in distinguishing targets over FILLS. Interestingly, S/N values were comparable between ROBOT UUVZ = 5 m (chl = 0.3 mg m-3) and ROBOT UUVZ = 1 m (chl = 5 mg m-3). Path radiance was greater than target photons when ROBOT was situated at 5 m above the bottom in turbid waters. In ROBOT (UUVZ = 1 m), level of detection in turbid waters was reduced as much as 30fold compared with that measured in clear waters. The laser simulations described above assume night-time conditions (i.e., the only light source is the laser). Solar illumination during diurnal surveys introdu ces an additional photon comp onent at the LLS receiver. For the sake of simplicity, sunlight interfer ence was analyzed for the one-pixel sensor (FILLS) as a function of sun altitude a nd spectral composition (Fig. 3.11). Values on Figure 3.11 represent maximum estimations becau se initial photon quantities were 1 and 0.4 W for solar and laser sources, respectivel y. In general, ambi ent path radiance contribution with respect to laser target signal increases as the sun approaches the zenith (Fig. 3.11a). This trend is less pronounced at higher turbidities because the underwater light field becomes more diffuse. Moreover, fo r a fixed solar altit ude above the horizon, FILLS detector collects a greater proportion of sunlight photo ns when the water is more turbid. As expected, FILLS measurements us ing a green laser were highly affected by sunlight photons due to its proximity to th e sea-surface (Fig. 3.11b). Likewise, sunlight interference on laser measurements decrease s for brighter targets (see Fig. 3.11a-b, sun = 29.5, = 532 nm). At 620 nm, the influence of solar photons on LLS signal was minimal. 3.5 Applications 3.5.1 Microenvironments with si gnificant resuspension UUV missions using laser line scanners may encounter waters with different proportions of organic and mineral particles or even different particle spectra (e.g., variations of particle assemblage s within the bottom boundary layer).

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64 Fig. 3.11: Variation of laser si gnal in FILLS due to sunli ght contributions : a) Proportion of sunlight/laser photons at the receiver of LLS (one-wide pixel) as a function of sun zenith angle and water turbidity, chl = 0.3 mg m-3 (empty rectangles, left axis), chl = 5.0 mg m-3 (solid rectangles, right axis), = 0.30 and = 532 nm. b) Spectral contributions of laser and sunlight com ponents at the LLS receiver, = 0.15, chl = 0.3 mg m-3, and sun = 29.5. In all cases C = 0 and fs = 21%. Signal modifications at the FILLS receiver associated with waters of different indices of refraction (real part ) are depicted in Figure 3.12.

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65 Fig. 3.12: Effect of particle composition on FI LLS performance: a) path radiance of hypothetical multiple-pixel se nsor (left axis) for TYPE I (circles) and TYPE II (rectangles) particle populati ons; integrated weights over on e wide pixel (right axis) are indicated with a constant value for TYPE I ( dotted line) and TYPE II (solid line) particle populations. b) total signal for TYPE I (c ircles) and TYPE II (re ctangles) particle populations. In all cases UUVZ = 7 m, = 532 nm, = 0.3, and chl = 0.3 mg m-3. In general for a CCD-like receiver, path radiance of FILLS was more concentrated near the target center for organic-enriched (np = 1.02) than for mineralenriched particle populations (np = 1.26) (Fig. 3.12a). Notic e that the original FILLS detector cannot discriminate photon distributions around the illuminated spot because it

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66 has only one viewing pixel resolution. Nontarget photons reaching the detector were more than 2-fold greater in TYPE I than in TYPE II waters, and thei r contribution to total integrated signal was higher in TYPE I (~ 80.6%) than in TYPE II (~64.4%) waters (Fig. 3.12b). Similar to FILLS, path radiance photons of ROBOT LSF increased as long as the index of refraction of partic les increased (Fig. 3.13a). Fig. 3.13: Effect of particle composition on ROBOT performance: a) path radiance for TYPE I (circles) and TYPE II (rectangles) part icle populations. b) total signal for TYPE I (circles) and TYPE II (rectangles) pa rticle populations. In all cases UUVZ = 7 m, = 532 nm, = 0.3, and chl = 0.3 mg m-3. However, path radiance was a smaller fraction of total signal in ROBOT with respect to FILLS (Fig. 3.13b). Consequently, S/N values of ROBOT were circa 8-fold greater than FILLS. Slope of to tal signal estimated from the target center to the far-range

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67 FOV edge was more variable in ROBOT th an in FILLS (hypothetical CCD) (Fig. 3.12b, Fig. 3.13b). Likewise, a greater vari ation of S/N values due to np (~25%) changes was estimated for ROBOT (~50%) than for FILLS (~16%), probably due to finer pixel resolution. Variation of LSF with different sized particle dist ributions at the receiver of FILLS is presented in Figure 3.14. Fig. 3.14: Effect of particle-si ze distributions on FILLS performance: a) path radiance of hypothetical multiple-pixel sens or (left axis) for TYPE III (circles) and TYPE IV (rectangles) particle populati ons; integrated weights over on e wide pixel (right axis) are indicated with a constant value for TYPE III (dotted line) and TYPE IV (solid line) particle populations. b) total signal for TY PE III (circles) and TYPE IV (rectangles) particle populations. In all cases UUVZ = 7 m, = 532 nm, = 0.3, and chl = 0.3 mg m-3.

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68 In FILLS, total path radiance integrated ove r a one-pixel receiver was circa 2-fold larger when runs were made with large pa rticle populations (Fig. 3.14a). In far-range pixels of a hypothetical CCD, large-particle populations ( = 3.1) had a greater path radiance contribution than sm all-particle populations ( = 4.0). Nevertheless, non-target weights of smaller-sized particles were larger in near-range pixels (Fig. 3.14a). This effect was not evident in LSF of total si gnal (Fig. 3.14b). Likewise, relatively small particle assemblages affected more drasti cally the shape of path radiance LSF by inflicting a flattening on weights collected al ong the receiver viewi ng direction. For nearrange pixels of ROBOT (UUVZ = 5 m), there was not a significant path radiance difference between particles assembla ges with different size (Fig. 3.15a). Fig. 3.15: Effect of particle-si ze distributions on ROBOT perfor mance: a) path radiance for TYPE I (circles) and TYPE II (rectangles) particle popu lations, b) total signal for TYPE I (circles) and TYPE II (rectangles ) particle populations. In all cases UUVZ = 7 m, = 532 nm, = 0.3, and chl = 0.3 mg m-3.

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69 Similar to FILLS, the performance of ROBOT for detecting targets in environments with relatively small particle populations was superior to those cases where coarser particle populations dominate (Fig. 3.15b). However due to the greater path radiance contribution in FILLS (>62%), FILLS had a noisier (~2-fold) signal than ROBOT (S/N~43). Overall, cha nges in particle spectra (~29 % variation of Junge slope) had a more significant influence on S/N values of ROBOT (~12%) than on FILLS (~8%). 3.5.2 Coral reef ‘halo’ In Figure 3.16 is simulated an LLS trans ect across a theoreti cal ‘halo’ surrounding a coral patch. Fig. 3.16: Bottom albedo algorithms for LLS s: a-c) ROBOT, clear water, UUVZ = 1 m (circles) and 5 m (rectangles); turbid water, UUVZ = 1 m (triangles), parabolic model (dotted lines). d) FILLS, clea r water (circles), linear model (dotted line). In all cases = 532 nm. Unlike FILLS, signal indices for ROBO T are path radiance corrected. Note the non-zero intercept for FILLS.

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70 Notice that there is a range of reflect ance values as the UUV is passing over sandy sediments (inner part of the ‘halo’, = 0.3), mixed-bottom types (transition boundary, = 0.15), and dark substrates such sea-gr ass beds (outer part of the ‘halo’, = 0.05). For ROBOT at 1 m above the target, th e slope between path radiance-corrected signal and bottom albedo was greater for clear than for turbid waters (Fig. 3.16a-c, Table 3.2). Table 3.2: Curve fitting parameters for di fferent bottom albedo retrieval functions. ROBOT model: y1 = a0 + a1 X + a2 X2, a0 = 0, where y stands for Wmax-Wmin (near) (first row), Wmax-Wmin (far) (second row), and Wmax (third row). FILLS model: y2 = m1 X + b1, where y2 is the total si gnal at the sensor. ROBOT1: UUVZ = 1 m, chl = 0.3 mg m-3, ROBOT2: UUVZ = 5 m, chl = 0.3 mg m-3, ROBOT3: UUVZ = 1 m, chl = 5 mg m-3. In FILLS chl is 0.3 mg m-3. Between parentheses is one standard error. Values a2 must be divided by 1,000. All models explained above 99% variability of simulated data. Coefficient ROBOT1 ROBOT2 ROBOT3 FILLS a1 8.084 (0.033) 6.038 (0.406) 8.295 (0.006) 1.438 (0.017) 0.778 (0.165) 1.800 (0.006) 3.283 (0.363) 2.484 (0.384) 3.346 (0.367) a2 1.29 (1.19) 3.95 (0.63) -33.2 (13.3) 49.1 (14.8) -4.09 (6.03) -27.6 (14.0) 1.31 (0.24) 0.51 (0.22) -34.2 (13.4) m1 10.97 (0.140) b1 49.44 (2.746) ROBOT detection was also less influe nced by changes of bottom reflectance when LLS measurements were obt ained at larger distances (UUVZ = 5 m) from the target. In general, parabolic functions we re the most satisfactory models for ROBOT -

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71 LSF curves whilst linear regressions seemed to explain better FILLS curves. Overall, the Wmax-Wmin (far) algorithm provided the mo st linear ROBOT results (smallest 2nd-order term) for the different water and observa tional conditions, although Wmax-Wmin (near) was most linear for 1m, clear-water settings. Unlike ROBOT, FILLS fits were not forced through the zero value because it is not possible to estimate and eliminate path radiance in the original sensor from LLS measurements. However, path radian ce in FILLS could be estimated at = 0 because the intercept was significantly different from zero (P<0.035, t-Student = 18). For this particular exercise, estimated FILLS path ra diance may contribute to total signal between 10 ( = 0.30) and 50% ( = 0.05).

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72 4 Conclusions As a preliminary step before mode ling laser-line-scanner performance for detecting underwater targets, a 1-D Mont e Carlo model was built and validated. The elemental pieces to construct the one-dimen sional MC were derived from the model originally proposed by Reinersman and Card er (2004). Similar to MC1D, HyMOM (3-D Hybrid Marine Optical Model, Monte Carlo) was validated against Hydrolight using the same type of waters with low (0.3 mg m-3) and high (5.0 mg m-3) chlorophyll a concentrations (i.e., a wide range of wate r transparencies). When irradiances were analyzed, RMSlog differences between MC1D a nd Hydrolight for clea r and turbid waters were comparable to those found between Hy MOM and Hydrolight irradiances (chl: 0.3 mg m-3, Ed = 0.98%, Eu = 1.28%; chl: 5 mg m-3, Ed = 2.36%, Eu = 3.63%). Similar to underwater irradiances, comparisons between Eu 0+ values calculated by MC1D and Hydrolight also showed less agreement in tu rbid waters than in clear waters. More uncertainty in less transparent waters is pr imarily related to the increase of variance caused by fewer photons reaching the detector and the need for more photons to maintain the same signal-to-noise ratio. General co mparisons of various Monte Carlo models against Hydrolight were reported by Mobley et al. (1993) for 1-D scenarios, with MC methods suffering in comparison at very deep ocean depths and in upwelling radiance or irradiance comparisons at any depth due to signal -to-noise considerations. Comparisons of L values between MC1D and Hydrolight models were not made because the way these two models are specif ied varies in many aspects (Reinersman and Carder, 2004). For instance, the unit sphe re in MC1D is partitioned into 100 bins whilst Hydrolight considers 10 quads over 85 and polar ca ps of 5. Furthermore, the direct solar beam is distributed from 29o to 30 in MC1D and from 25o to 35 in Hydrolight.

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73 Although MC1D has better directional resolu tion than Hydrolight, more variance (less photon weights are tallie d) is expected in final ra diance estimates using MC1D. Angular-bin resolution differences between MC 1D and Hydrolight also affects internal sub-surface reflections and could also account fo r differences of radiance values for these two models (Reinersman and Carder, 2004). As suggested by Reinersman and Carder (2004), the above variations on algorithm stru ctures may also explain the differences observed between MC1D and Hydro light for irradiance estimations. Based on MC1D, a 2-D Monte Carlo model was successfully implemented in this work to model target detection and the eff ect of various oceanogra phic conditions on S/N values of two continuous laser line s canners: ROBOT and FILLS. These optical instruments are currently in use and were first conceived to fa cilitate the identification of mine-like contacts and to address environmen tal issues such as mapping of coral reefs (Strand et al., 1996; Strand, 1997; Kaltenbach er et al., 2000). Likewise, ROBOT and FILLS are ideal systems to automatically de tect and classify objects of interest in clustered bottoms (e.g., coral reefs) where acoustic techniques fa il. They represent cheaper and more accurate solutions than human recognition of diverse and numerous underwater targets. ROBOT and FILLS have been designed for different purposes. ROBOT allows morphologic characterization of bottom featur es in 3-D whilst FILLS is not able to retrieve bottom ‘shape’ even though it may detect simultaneous fluorescence signatures (inelastic scattering) at va rious wavelengths. Robustness of 2-D LLS models was tested by comparing modeled and measured (aquarium experiments) line spread functions. The model imitated very well the shape of ROBOT LSF and it was able to capture geometric characteristics such as the bi-static configur ation between the source and the receiver (see Figure 3.2). A typical feature in all simulations (m ore pronounced in hypothetical FILLS) was the asymmetric LSF with more photon weight concentrated in far-range pixels with respect to the sensor viewing direction. This e ffect was likely relate d to its greater path radiance contribution with respect to total signal. Those pixels closer to the sensor have a minor backscattering component originating from the main laser beam, thus path radiance is reduced compared to those pixels situat ed beyond the target. In near-range pixels,

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74 multiple scattering off the target (forward s catter and then target reflectance or vice versa) is the largest path radiance component. Simulations in 2-D clearly confirmed th at ROBOT and FILLS are useful optical devices for target detection in clear waters and for highly -reflective bottoms. Thus, it is not surprising that most oceanographic stud ies using LLSs have been planned in clear tropical waters with sandy bottoms such t hose found in the Bahamas Islands (e.g., FILLS, Mazel et al., 2003). For diffe rent environmental conditions (e.g., turbidity) and UUV altitudes above the target, ROBOT produced a sharper image than FILLS due to parallax that reduces contributions due to backscatte red photons (Table 4.1). For instance at 7 m above the target, ROBOT efficiency to recogn ize objects was two-fold superior to FILLS. Also notice the S/N degradation caused by a gr eater path radiance in turbid waters for FILLS may represent 100% of the signal reaching the sensor. Table 4.1: Summary of laser line scanner SNR performance for target detection. chl = mg m-3, S/N calculated as target/path radian ce contributions. ROBOT1, ROBOT2 and ROBOT4 have UUVZ of 1, 5 and 7 m, respectively. chl ROBOT1 ROBOT2 ROBOT4 FILLS 0.3 253.4 5.6 2.0 1.2 5.0 10.46 <1 <1 <1 As was demonstrated, far-range viewing photons at the receiver of ROBOT can be subtracted from the signal with the largest target contribution (cen tral pixel of CCD) to remove much of the path ra diance contribution. Hence, noise due to underwater optical variability in ROBOT measurements may be f iltered in real-time. Assuming a flat bottom within the ROBOT FOV and after path radiance correcti on, LSFs would still experience changes that can be interpreted by differen ces as bottom reflectivity changes (bottom albedo retrieval capability).

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75 Unfortunately, in situ path radiance measurements c ould not be derived analyzing FILLS signals unless this original sensor is further sub-divided into multiple pixels (see above hypothetical CCD) similar to the ROBOT receiver. FILLS, using a one-pixel FOV, sees simultaneously photons coming from th e target and the propa gation medium. Thus, the only way to estimate which fraction of th e total FILLS signal is caused by non-target photons is by modeling path radiance using known (measured) IOPs and apparent optical properties. Even doing that, -LSF relationships found in this work suggest that ROBOT is more discriminative of bottomalbedo discontinuities than FILLS. Simulations analyzing spectral effect s on S/N values at the LLS receiver consistently showed that a green laser is th e best all-around choice to detect targets in marine waters. In turbid waters, target discrimination using red ( = 620 nm) and green ( = 532 nm) laser sources was comparable. In estuarine waters red lasers are widely used (Moore et al., 2000) whilst in shallow reef systems (typically oligotrophic and transparent waters) a green source is more recommended for nocturnal work (Carder et al., 2001). LLS measurements during daylight hours (e.g., night-time schedule is full for inspection of ships hulls) ar e sometimes mandatory even though the effect of solar illumination on target detection can be detrimental. For instance, the mapping of light fields under ships can take place during daylight hours since ambient down-welling irradiance can be 3.5 orders of magnitude smal ler than at the sea surface (Reinersman et al., 2004). MC results from this work indicated th at the greatest interference of ‘green’ sunlight photons on total signal reaching th e LLS receiver occurs around noon when no ship is present to block ambient photons reaching the bottom. Thus, longer laser wavelengths ( = 620 nm) and mid-morning/mid-evening measurements would be the most suitable choice when the target to be detected lay in open areas (e.g., no objects shading the target) and near the bottom, if night-time surveys are not possible, water turbidity is relatively high, and detection range is comparably short (strong attenuation of ambient red wavelengths due to water itself). In that regard, an alternativ e solution to get rid of ‘g reen’ photons is the use of fluorescence channels in FILLS, although sola r-induce bottom fluorescence would also be present. The FILLS excitation channel does not match the spectral filter of the

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76 receiver, so path-scattered laser photons are not ‘seen’ by fluorescence detectors. However, fluorescence measurements may also encounter difficulties such as interference due to solar-pumped variations (excitation energy of sun changes as FILLS is moved away from the sea-surface) and phytoplankton fluorescence contributions. For the same water turbidity, bottom re flectance and detection wavelength, LLS signals can also be affected by changes in particle size distribu tion and composition. For instance, LLS measurements in high-ener gy environments (e.g., exposed beaches, shallow coastal waters highly influenced by wind) would be modifi ed by aggregation and breakup of particle aggregates (Milligan, 1995). Simulations considering measurements of FILLS and ROBOT in waters with different particle assemblages were assessed using a forward method of inversion of the VSF. The Fournier-Forand pha se scattering function allowed the generation of artificial VSFs c onsidering contrasting cases of particle assemblages with various origins (mineral vs organic) or size dist ributions. In general, both mineral-dominant and small-size particle populations produced a flattening of LSF obtained at the LLS receiver (e.g. less fo rward and more side and back scattering. Likewise, they allowed a better LLS performance because path radiance of larger organic particles preferentially scattered in the forward direction with respect to small mineral particles, thus noise (mostly forward-s cattered photons before and after bottom reflection) was concentrated in the neighborhood of the targ et center. In that regard, source-receiver inclination of ROBOT make s ROBOT measurements less vulnerable to path radiance than FILLS in environments with larger, organic-enriched particles. The real part of the index of refraction of particles, np, had the largest effect on total signal variability because of the greater dependency of particle backscattering efficiency on np (Mobley et al., 2002). In nature np and (Junge size-distribution parameter) bulk properties result from a compli cated matrix of particles that makes more diffuse the idea of defined particle populati ons. For instance, transparent exopolymers in marine snow increases np as bacteria with slighter higher np (1.04-1.07) attach to it (Costello et al., 1995). Likewise relatively dehydrated organic particles may result in larger np values (e.g., fecal pellets of copepods) (Twardowski et al., 2001). Since Mie theory assumes sphere-type particles, an a dditional complication is introduced when non-

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77 spheres (spheroids) are meas ured (~ 30% deviation from the maximum scattering) (Herring, 2002). The study of the bottom bounda ry layer (BBL) has recently become a favorite natural lab to test different np and models (see Boss et al., 2001) and represents the ideal place to investigate LLS models in connection with different particle assemblages. In this scenario, np increases near the bottom due to more inorganic particles, and has the opposite trend because of the greater abundance of larger particles near the sea bed (more vertical mixing ener gy). In the other hand, fi ne organic particles with low settling velocities are dominant fu rther from the BBL (Boss et al., 2001). Therefore, np and effects on FILLS/ROBOT line spread function could crosscompensate, and no differences in LSF shap e would be expected due to changes of particle populations along th e path between the AUV and the target. Furthermore, since ROBOT was more sensitive to np changes ( ~ bbp variability accounted mainly by np) than FILLS, FILLS would be a better option to target detections in waters with drastic changes in ~ bbp (e.g., changes on BBL thickness, channel-sh allow transitions in an estuary). Choosing the most convenient laser line scanner (ROBOT vs FILLS) will depend on the application and in what environments these systems will be deployed. The main limitations of FILLS are: a) relatively large interference of elastic path radiance (larger noise per pixel at the recei ver), b) lack of 3-D mappi ng, and no underway bottom albedo retrievals, and c) the larger cross-track spatial resolution of detector. However, ROBOT is more influenced by solar photons and must be reconfigured to perform inelastic measurements (fluorescence). MC models pr oposed in this work answer many questions regarding target detection capab ilities of each kind of LLS st udied and for different types of waters or meteorological conditions. Nevert heless, further refinements will be required to explore inelastic-based signa ls (e.g., fluorescence in FILLS) 3-D receivers and targets, and the effect of multiple laser beams (e .g., fan-type lasers such ROBOT) on LSF. Likewise, no major advances for LLS m odels would be possi ble without field measurements.

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ABSTRACT: Monte Carlo simulations as a tool to optimize target detection by AUV/ROV laser line scanners Martin' Alejandro Montes ABSTRACT The widespread use of laser line scanners (LLS) aboard unmanned underwater vehicles in the last decade has opened a unique window to a series of ecological and military applications. Variability of underwater light fields and complexity of light contributions reaching the receiver pose a challenge for target detection of LLS under different environmental conditions. The interference of photons not originating at the target (e.g. water path, bottom) can often be minimized (e.g., time-gated systems) but not excluded. Radiative transfer models were developed to better discriminate noise components from signal contributions at the receiver for two continuous LLS: Real-time Ocean Bottom Optical Topographer (ROBOT) and Fluorescence Imaging Laser Line Scanner (FILLS).Numerical experiments using forward Monte Carlo methods were designed to explore the effects of diverse water turbidities and bottom reflectances on ROBOT and FILLS measurements. Interference due to solar light on LLS target detection was also examined. Reliability of radiative transfer models was tested against standard models (Hydrolight) and aquarium measurements. In general a green laser was the best all around choice to detect targets using both LLS sensors. Based on signal-to-noise (S/N) values, performance of ROBOT for target detection was greater (two-fold) than FILLS because of the lower contribution of path photons in ROBOT than FILLS. When ROBOT was located at 1 m above the target, path radiance contributions (noise) were reduced up to 25-fold in clear waters (0.3 mg m-3) with respect to turbid waters (5 mg m-3).Since ROBOT was more discriminative of bottom reflectance discontinuities (high-contrast transitions) than FILLS, algorithms are proposed to retrieve contrasting man-made targets such mines.
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