Variability of relationship between the volume scattering function at 180° and the backscattering coefficient for aquatic particles.

Properly interpreting lidar (light detection and ranging) signal for characterizing particle distribution relies on a key parameter, χp(π), which relates the particulate volume scattering function (VSF) at 180° (ßp(π)) that a lidar measures to the particulate backscattering coefficient (bbp). However, χp(π) has been seldom studied due to challenges in accurately measuring ßp(π) and bbp concurrently in the field. In this study, χp(π), as well as its spectral dependence, was re-examined using the VSFs measured in situ at high angular resolution in a wide range of waters. ßp(π), while not measured directly, was inferred using a physically sound, well-validated VSF-inversion method. The effects of particle shape and internal structure on the inversion were tested using three inversion kernels consisting of phase functions computed for particles that are assumed as homogenous sphere, homogenous asymmetric hexahedra, or coated sphere. The reconstructed VSFs using any of the three kernels agreed well with the measured VSFs with a mean percentage difference <5% at scattering angles <170∘. At angles immediately near or equal to 180°, the reconstructed ßp(π) depends strongly on the inversion kernel. χp(π) derived with the sphere kernels was smaller than those derived with the hexahedra kernel but consistent with χp(π) estimated directly from high-spectral-resolution lidar and in situ backscattering sensor. The possible explanation was that the sphere kernels are able to capture the backscattering enhancement feature near 180° that has been observed for marine particles. χp(π) derived using the coated sphere kernel was generally lower than those derived with the homogenous sphere kernel. Our result suggests that χp(π) is sensitive to the shape and internal structure of particles and significant error could be induced if a fixed value of χp(π) is to be used to interpret lidar signal collected in different waters. On the other hand, χp(π) showed little spectral dependence.

Re-examining the effect of particle phase functions on the remote-sensing reflectance.

Even though it is well known that both the magnitude and detailed angular shape of scattering (phase function, PF), particularly in the backward angles, affect the color of the ocean, the current remote-sensing reflectance (Rrs) models typically account for the effect of its magnitude only through the backscattering coefficient (bb). Using 116 volume scattering function (VSF) measurements previously collected in three coastal waters around the U.S. and in the water of the North Atlantic Ocean, we re-examined the effect of particle PF on Rrs in four scenarios. In each scenario, the magnitude of particle backscattering (i.e., bbp) is known, but the knowledge on the angular shape of particle backscattering is assumed to increase from knowing nothing about the shape of particle PFs to partially knowing the particle backscattering ratio (Bp), the exact backscattering shape as defined by ߘp(γ≥90°) (particle VSF normalized by the particle total scattering coefficient), and the exact backscattering shape as defined by the χp factor (particle VSF normalized by the particle backscattering coefficient). At sun zenith angle=30°, the nadir-viewed Rrs would vary up to 65%, 35%, 20%, and 10%, respectively, as the constraints on the shape of particle backscattering become increasingly stringent from scenarios 1 to 4. In all four scenarios, the Rrs variations increase with both viewing and sun angles and are most prominent in the direction opposite the sun. Our results show a greater impact of the measured particle PFs on Rrs than previously found, mainly because our VSF data show a much greater variability in Bp, ߘp(γ≥90°), and χp than previously known. Among the uncertainties in Rrs due to the particle PFs, about 97% can be explained by χp, 90% by ߘp(γ≥90°), and 27% by Bp. The results indicate that the uncertainty in ocean color remote sensing can be significantly constrained by accounting for χp of the VSFs.

Interpretation of scattering by oceanic particles around 120 degrees and its implication in ocean color studies.

Field observations and theoretical studies have found that the volume scattering functions (VSFs) of oceanic particles exhibit minimum variability at angles near 120°. However, its physical interpretation is still unknown. We find this minimum variability angle represents the intersection of two backscattering-normalized VSFs, one representing particles of sizes smaller than the wavelength of light and the other larger than the wavelength of light. This also suggests that the VSFs of oceanic particles at angles between 90° and 180°, which play a critical role in ocean color study, can be modeled by linear mixing of these two end members. We further validate this mixing model using measured VSFs in coastal and oceanic waters around the US and develop a two-component model predicting the backward shapes of the VSFs.

Using a multiwavelength LiDAR for improved remote sensing of natural waters.

This paper describes research to characterize the benefits of a multiwavelength oceanographic LiDAR for various water types. Field measurements were conducted to establish endmembers representative of both typical and extremely challenging natural conditions. Laboratory tests were performed using a prototype multiwavelength LiDAR in water tanks with optical conditions simulating both sediment-laden and biologically rich water types. LiDAR models were used to simulate the LiDAR signal from both field and laboratory experiments. Our measurements and models show that using a laser wavelength of 470-490 nm in the open ocean leads to an improvement factor of 1.50-1.75 compared to a 532 nm system. In more turbid areas using a laser wavelength of 560-580 nm leads to an improvement factor of 1.25. We conclude by demonstrating how using multiple LiDAR wavelengths can help detect and characterize constituents in the water column.

Wavelength dependence of the bidirectional reflectance distribution function (BRDF) of beach sands.

The wavelength dependence of the dominant directional reflective properties of beach sands was demonstrated using principal component analysis and the related correlation matrix. In general, we found that the hyperspectral bidirectional reflectance distribution function (BRDF) of beach sands has weak wavelength dependence. Its BRDF varies slightly in three broad wavelength regions. The variations are more evident in surfaces of greater visual roughness than in smooth surfaces. The weak wavelength dependence of the BRDF of beach sand can be captured using three broad wavelength regions instead of hundreds of individual wavelengths.

Airborne system for multispectral, multiangle polarimetric imaging.

In this paper, we describe the design, fabrication, calibration, and deployment of an airborne multispectral polarimetric imager. The motivation for the development of this instrument was to explore its ability to provide information about water constituents, such as particle size and type. The instrument is based on four 16 MP cameras and uses wire grid polarizers (aligned at 0°, 45°, 90°, and 135°) to provide the separation of the polarization states. A five-position filter wheel provides for four narrow-band spectral filters (435, 550, 625, and 750 nm) and one blocked position for dark-level measurements. When flown, the instrument is mounted on a programmable stage that provides control of the view angles. View angles that range to ±65° from the nadir have been used. Data processing provides a measure of the polarimetric signature as a function of both the view zenith and view azimuth angles. As a validation of our initial results, we compare our measurements, over water, with the output of a Monte Carlo code, both of which show neutral points off the principle plane. The locations of the calculated and measured neutral points are compared. The random error level in the measured degree of linear polarization (8% at 435) is shown to be better than 0.25%.

Significance of scattering by oceanic particles at angles around 120 degree.

Field observations and theoretical studies have shown that shapes of the volume scattering functions (VSFs) of oceanic particles in the backward directions, i.e., VSFs normalized by the total backscattering coefficient, exhibit a surprisingly low variability at angles near 120 degree, which is also confirmed by measurements of VSFs in coastal waters around the US. To investigate what this minimum variability angle (θ*) represents, we estimated mean values of the VSFs in the backward angles using four mean value theorems: mean value for integral, weighted mean value for integral, classic mean value for differentiation and Cauchy's mean value. We also estimated the angles corresponding to the minimum values of the VSFs. We found θ* to be very close to the angles representing the classic mean values for differentiation of the VSFs. The low variability is due to the fact that the classic mean values vary little with the composition and sizes of particles.

Order-of-scattering point spread and modulation transfer functions for natural waters.

The point spread and modulation transfer functions for natural waters are derived using the small-angle approximation to radiative transfer theory. The functional forms are expanded into a summation of terms that represent each order-of-scattering contribution to the total. The beam spread function is shown to be a product of an angle function that depends only on the phase function of the medium and a weighting factor that depends only on the optical properties and depth. The modulation transfer function is similarly shown as a product of a function depending only on the spatial frequency and a weighting function. These results are compared with Monte Carlo calculations using two different phase functions, with excellent agreement. The results suggest the small-angle approximation to be valid over a much larger angular range than previously thought.

Comparison of optically derived particle size distributions: scattering over the full angular range versus diffraction at near forward angles.

The volume scattering function (VSF) of particles in water depends on the particles' size distribution and composition as well as their shape and internal structure. Inversion of the VSF thus provides information about the particle population. The commercially available LISST instrument measures the scattering at near forward angles to estimate the bulk size distribution of particles larger than about 1 µm. By using scattering over the full angular range (0°-180°), the recently improved VSF-inversion method [X. Zhang, M. Twardowski, and M. Lewis, Appl. Opt. 50, 1240 (2011).] can characterize particles in terms of particle subpopulations, which are described by their unique size distribution and composition. Concurrent deployments of the Multispectral Volume Scattering Meter and the LISST in three coastal waters (i.e., Chesapeake Bay, Mobile Bay, and Monterey Bay) allowed us to compare the size distributions derived from these two different methods. We also obtained indirect validation of the results for submicrometer particles and for the composition of particles provided by the VSF-inversion method. For particle sizes ranging from 1 to 100 µm, the concentration was shown to vary over 10 orders of magnitude, and excellent agreement was found between the two methods with a mean relative difference less than 10% for the total size distributions. The inversion results also reproduced spectral variations in the shape of the VSF, although these spectral variations were not frequently observed in our study. The increased backscattering towards the shorter wavelengths was explained by the stronger influence of submicrometer particles affecting the backscattering. Based on published measurements of cell sizes and intracellular chlorophyll-a [Chl] concentrations over a wide range of phytoplankton species and strains, [Chl] was estimated for the inverted subpopulations that were identified as phytoplankton based on their refractive index and mean sizes. The estimated [Chl] agreed well with the fluorescence-based estimates in both magnitude and trend, thus reproducing a bloom event observed at a time series station.

Observation of non-principal plane neutral points in the upwelling polarized light field above a water surface.

Using a digital camera and linearly polarizing film, we have developed a method for observing neutral point locations in the natural light field of the atmosphere. Utilizing this method, we have observed neutral points in the upwelling light field above a water surface. We report the location of these neutral points and compare them to Monte Carlo simulations.

Neutral points in an atmosphere-ocean system. 2: Downwelling light field.

We use a Monte Carlo code that calculates the complete Stokes vector to predict the degree of polarization in the complete observable solid angle at any level in an atmosphere-ocean system. Using the Stokes vector components, we can find the positions of neutral points in a simulated plane-parallel atmosphere-ocean system for various conditions. We examine the locations and behavior of these neutral points for an observer placed directly above and beneath the air-water boundary and show how their positions are influenced by different atmospheric and oceanic conditions.

Flow-through integrating cavity absorption meter: experimental results.

We report experimental results from a flow-through integrating cavity absorption meter. The operating range of the device is from 0.004 m(-1) to over 80 m(-1) of absorption. Absorption coefficients have been measured with 8% or less change in the presence of over 200 m(-1) of scattering in the medium. The instrument signal has been shown to be independent of flow rate up to 20 liters/min and thus independent of turbulence. This large operational range along with the ability to measure absorption independently of adverse scattering affects allows the instrument to be utilized in a wide range of environmental conditions.

Polarized light in coastal waters: hyperspectral and multiangular analysis.

Measurements of the underwater polarized light field were performed at different stations, atmospheric conditions and water compositions using a newly developed hyperspectral and multiangular polarimeter during a recent cruise in the coastal areas of New York Harbor - Sandy Hook, NJ region (USA). Results are presented for waters with chlorophyll concentrations 1.3-4.8 microg/l and minerals concentrations 2.0- 3.9 mg/l. Angular and spectral variations of the degree of polarization are found to be consistent with theory. Maximum values of the degree of polarization do not exceed 0.4 and the position of the maximum is close to 100 masculine scattering angle. Normalized radiances and degrees of polarization are compared with simulated ones obtained with a Monte Carlo radiative transfer code for the atmosphere-ocean system and show satisfactory agreement.

An underwater light attenuation scheme for marine ecosystem models.

Simulation of underwater light is essential for modeling marine ecosystems. A new model of underwater light attenuation is presented and compared with previous models. In situ data collected in Monterey Bay, CA. during September 2006 are used for validation. It is demonstrated that while the new light model is computationally simple and efficient it maintains accuracy and flexibility. When this light model is incorporated into an ecosystem model, the correlation between modeled and observed coastal chlorophyll is improved over an eight-year time period. While the simulation of a deep chlorophyll maximum demonstrates the effect of the new model at depth.

Comparison and validation of point spread models for imaging in natural waters.

It is known that scattering by particulates within natural waters is the main cause of the blur in underwater images. Underwater images can be better restored or enhanced with knowledge of the point spread function (PSF) of the water. This will extend the performance range as well as the information retrieval from underwater electro-optical systems, which is critical in many civilian and military applications, including target and especially mine detection, search and rescue, and diver visibility. A better understanding of the physical process involved also helps to predict system performance and simulate it accurately on demand. The presented effort first reviews several PSF models, including the introduction of a semi-analytical PSF given optical properties of the medium, including scattering albedo, mean scattering angles and the optical range. The models under comparison include the empirical model of Duntley, a modified PSF model by Dolin et al, as well as the numerical integration of analytical forms from Wells, as a benchmark of theoretical results. For experimental results, in addition to that of Duntley, we validate the above models with measured point spread functions by applying field measured scattering properties with Monte Carlo simulations. Results from these comparisons suggest it is sufficient but necessary to have the three parameters listed above to model PSFs. The simplified approach introduced also provides adequate accuracy and flexibility for imaging applications, as shown by examples of restored underwater images.

Design and analysis of a flow-through integrating cavity absorption meter.

We present a design for a flow-through integrating cavity absorption meter. This instrument, in principle, is capable of measuring the spectral optical absorption coefficient of natural waters in situ independently of scattering effects. Monte Carlo simulations are used to determine the design parameters and evaluate instrument performance. We investigate both detector response and the distribution of radiant energy inside the instrument and present empirical equations describing these quantities as a function of the absorption coefficient. The effects of changing the instrument geometry are illustrated. Finally, we discuss the effects of scattering on the instrument performance and verify that they are negligible for natural waters.

Mueller matrix imaging of targets in turbid media: effect of the volume scattering function.

Detecting objects in turbid media by use of just radiance signals has been a subject of study for many years. The use of Mueller matrix imaging methods has only recently been used as a tool for target detection. We will show not only that can targets still be detected by Mueller matrix methods even after their detection has escaped normal radiance schemes but also that their surface features can also still be distinguished. We will also show how the shape of the volume scattering function as well as the target and medium albedo strongly influences various elements of the Mueller matrix. One of the more interesting features of Mueller matrix imaging is that the diagonal elements are sensitive to perturbations in the environment surrounding the target. This implies that targets can be detected far beyond their geometric cross section. The methods presented here will have applications to submersible object detection, remote sensing in the atmosphere, and the detection of inhomogeneities in tissue.