Influence of the angular shape of the volume-scattering function and multiple scattering on remote sensing reflectance

Scattering phase functions derived from measured (volume-scattering meter, VSM) volume-scattering functions (VSFs) from Crimean coastal waters were found to have systematic differences in angular structure from Fournier-Forand (FF) functions with equivalent backscattering ratios. Hydrolight simulations demonstrated that differences in the angular structure of the VSF could result in variations in modeled subsurface radiance reflectances of up to +/-20%. Furthermore, differences between VSM and FF simulated reflectances were found to be nonlinear as a function of scattering and could not be explained with the single-scattering approximation. Additional radiance transfer modeling demonstrated that the contribution of multiple scattering to radiance reflectance increased exponentially from a minimum of 16% for pure water to a maximum of approximately 94% for turbid waters. Monte Carlo simulations demonstrated that multiple forward-scattering events were the dominant contributors to the generation of radiance reflectance signals for turbid waters and that angular structures in the shape of the VSF at forward angles could have a significant influence in determining reflectance signals for turbid waters.     

Estimation of absorption and backscattering coefficients from in situ radiometric measurements: theory and validation in case II waters

A model that relates the coefficients of absorption (a) and backscattering (b(b)) to diffuse attenuation (K(d)), radiance reflectance (R(L)), and the mean cosine for downward irradiance (mu(d)) is presented. Radiance transfer simulations are used to verify the physical validity of the model for a wide range of water column conditions. Analysis of thee radiance transfer simulations suggest that absorption and backscattering can be estimated with average errors of 1% and 3%, respectively, if the value of mu(d) is known with depth. If the input data set is restricted to variables that can be derived from measurements of upward radiance (L(u)) and downward irradiance (E(d)), it is necessary to use approximate values of mu(d). Examination of three different approximation schemes for mu(d) shows that the average error for estimating a and b(b) increases to approximately 13%. We tested the model by using measurements of L(u) and E(d) collected from case II waters off the west coast of Scotland. The resulting estimates of a and b(b) were compared with independent in situ measurements of these parameters. Average errors for the data set were of the order of 10% for both absorption and backscattering.     

Modeling total and polarized reflectances of ice clouds: evaluation by means of POLDER and ATSR-2 measurements

Four ice-crystal models are tested by use of ice-cloud reflectances derived from Along Track Scanning Radiometer-2 (ATSR-2) and Polarization and Directionality of Earth's Reflectances (POLDER) radiance measurements. The analysis is based on dual-view ATSR-2 total reflectances of tropical cirrus and POLDER global-scale total and polarized reflectances of ice clouds at as many as 14 viewing directions. Adequate simulations of ATSR-2 total reflectances at 0.865 microm are obtained with model clouds consisting of moderately distorted imperfect hexagonal monocrystals (IMPs). The optically thickest clouds (tau > approximately 16) in the selected case tend to be better simulated by use of pure hexagonal monocrystals (PHMs). POLDER total reflectances at 0.670 microm are best simulated with columnar or platelike IMPs or columnar inhomogeneous hexagonal monocrystals (IHMs). Less-favorable simulations are obtained for platelike IHMs and polycrystals (POLYs). Inadequate simulations of POLDER total and polarized reflectances are obtained for model clouds consisting of PHMs. Better simulations of the POLDER polarized reflectances at 0.865 microm are obtained with IMPs, IHMs, or POLYs, although POLYs produce polarized reflectances that are systematically lower than most of the measurements. The best simulations of the polarized reflectance for the ice-crystal models assumed in this study are obtained for model clouds consisting of columnar IMPs or IHMs.     

Theory of equidistant three-dimensional radiance measurements with optical microprobes

Fiber-optic radiance microprobes, increasingly applied for measurements of internal light fields in living tissues, provide three-dimensional radiance distribution solids and radiant energy fluence rates at different depths of turbid samples. These data are, however, distorted because of an inherent feature of optical fibers: nonuniform angular sensitivity. Because of this property a radiance microprobe during a single measurement partly underestimates light from the envisaged direction and partly senses light from other directions. A theory of three-dimensional equidistant radiance measurements has been developed that provides correction for this instrumental error using the independently obtained function of the angular sensitivity of the microprobe. For the first time, as far as we know, the measurements performed with different radiance microprobes are comparable. An example of application is presented. The limitations of this theory and the prospects for this approach are discussed.     

Radiometric calibration of SeaWiFS in the near infrared

The radiometric calibration of the Sea-Viewing Wide-Field-of-View Sensor (SeaWiFS) in the near infrared (band 8, centered on 865 nm) is evaluated by use of ground-based radiometer measurements of solar extinction and sky radiance in the Sun's principal plane at two sites, one located 13 km off Venice, Italy, and the other on the west coast of Lanai Island, Hawaii. The aerosol optical thickness determined from solar extinction is used in an iterative scheme to retrieve the pseudo aerosol phase function, i.e., the product of single-scattering albedo and phase function, in which sky radiance is corrected for multiple scattering effects. No assumption about the aerosol model is required. The aerosol parameters are the inputs into a radiation-transfer code used to compute the SeaWiFS radiance. The calibration method has a theoretical inaccuracy of plus or minus 2.0-3.6%, depending on the solar zenith angle and the SeaWiFS geometry. The major source of error is in the calibration of the ground-based radiometer operated in radiance mode, assumed to be accurate to +/- 2%. The establishment of strict criteria for atmospheric stability, angular geometry, and surface conditions resulted in selection of only 26 days for the analysis during 1999-2000 (Venice site) and 1998-2001 (Lanai site). For these days the measured level-1B radiance from the SeaWiFS Project Office was generally lower than the corresponding simulated radiance in band 8 by 7.0% on average, +/- 2.8%.     

Retrieval of the scattering and microphysical properties of aerosols from ground-based optical measurements including polarization. I. Method

A method has been developed for retrieving the scattering and microphysical properties of atmospheric aerosol from measurements of solar transmission, aureole, and angular distribution of the scattered and polarized sky light in the solar principal plane. Numerical simulations of measurements have been used to investigate the feasibility of the method and to test the algorithm's performance. It is shown that the absorption and scattering properties of an aerosol, i.e., the single-scattering albedo, the phase function, and the polarization for single scattering of incident unpolarized light, can be obtained by use of radiative transfer calculations to correct the values of scattered radiance and polarized radiance for multiple scattering, Rayleigh scattering, and the influence of ground. The method requires only measurement of the aerosol's optical thickness and an estimate of the ground's reflectance and does not need any specific assumption about properties of the aerosol. The accuracy of the retrieved phase function and polarization of the aerosols is examined at near-infrared wavelengths (e.g., 0.870 mum). The aerosol's microphysical properties (size distribution and complex refractive index) are derived in a second step. The real part of the refractive index is a strong function of the polarization, whereas the imaginary part is strongly dependent on the sky's radiance and the retrieved single-scattering albedo. It is demonstrated that inclusion of polarization data yields the real part of the refractive index.     

Algorithms for ocean-bottom albedo determination from in-water natural-light measurements

A method for determining the ocean-bottom optical albedo R(b) from in-water upward and downward irradiance measurements at a shallow site is presented, tested, and compared with a more familiar approach that requires additional measurements at a nearby deep-water site. Also presented are two new algorithms for estimating R(b) from measurements of the downward irradiance and vertically upward radiance. All methods performed well in numerical situations at depths at which the influence of the bottom on the light field was significant.     

Effects of ocean surface reflectance variation with solar elevation on normalized water-leaving radiance

Effects of the ocean surface reflection for solar irradiance on the normalized water-leaving radiance in the visible wavelengths are evaluated and discussed for various conditions of the atmosphere, solar-zenith angles, and wind speeds. The surface reflection effects on water-leaving radiance are simply due to the fact that the radiance that is backscattered out of the water is directly proportional to the downward solar irradiance just beneath the ocean surface. The larger the solar-zenith angle, the less the downward solar irradiance just beneath the ocean surface (i.e., more photons are reflected by the ocean surface), leading to a reduced value of the radiance that is backscattered out of the ocean. For cases of large solar-zenith angles, the effects of surface irradiance reflection need to be accounted for in both the satellite-derived and in situ measured water-leaving radiances.     

Influence of the environment reflectance on the ultraviolet zenith radiance for cloudless sky

A three-dimensional Monte Carlo code is used to compute the ultraviolet zenith sky radiance; the code is validated by comparison with a successive-orders-of-scattering code. The amplifications of global irradiance, diffuse irradiance, and zenith radiance that are due to multiple reflectances between a snow-covered ground surface and the atmosphere are compared. For an inhomogeneous Lambertian surface, the contribution of the site environment is analyzed; it depends slightly on the atmospheric turbidity and on the surface reflectance distribution. However, in most cases one can expect approximately 12-15% of the reflected photon contribution to come from within 1 km about the observation site, 25-30% come from areas from 1 to 5 km from the site, 43-47% from 5 to 30 km, and still 10-15% reflected at larger distances. An average contribution function is proposed and used to compute an effective reflectance, which permits retrieval of the sky radiance within 2-4% with a one-dimensional model.     

Information content of point radiance measurements in turbid media: implications for interstitial optical property quantification

Motivated by a recent report by Dickey et al. [Phys. Med. Biol. 46, 2359 (2001)], who demonstrated optical property retrieval by using relative radiance measurements at a single position, we investigate the uniqueness of relative radiance measurements for quantifying the optical properties of turbid media by studying the solutions of the diffusion and P3 approximations of the Boltzmann transfer equation for a point source. Using the P3 approximation, we investigate the potential of radiance measurements for optical property recovery by examining the optical property response surface for point radiance information. We further derive first-order similarity relations for relative point radiance measurements and use these expressions to examine analytically the effects of noise on optical property retrieval over a wide range of optical properties typical of biological tissue. Finally, optimal experimental configurations are studied and explicit conditions for uniqueness derived that suggest potential strategies for improving optical property recovery. It is expected that point radiance measurements will prove valuable for both on-line treatment planning of minimally invasive laser therapies and optical characterization of tissues.     

General theory of three-dimensional radiance measurements with optical microprobes

Measurements of the radiance distribution and fluence rate within turbid samples with fiber-optic radiance microprobes contain a large variable instrumental error caused by the nonuniform directional sensitivity of the microprobes. A general theory of three-dimensional radiance measurements is presented that provides correction for this error by using the independently obtained function of the angular sensitivity of the microprobes.     

An inherent-optical-property-centered approach to correct the angular effects in water-leaving radiance

Remote-sensing reflectance (R(rs)), which is defined as the ratio of water-leaving radiance (L(w)) to downwelling irradiance just above the surface (E(d)(0?)), varies with both water constituents (including bottom properties of optically-shallow waters) and angular geometry. L(w) is commonly measured in the field or by satellite sensors at convenient angles, while E(d)(0?) can be measured in the field or estimated based on atmospheric properties. To isolate the variations of R(rs) (or L(w)) resulting from a change of water constituents, the angular effects of R(rs) (or L(w)) need to be removed. This is also a necessity for the calibration and validation of satellite ocean color measurements. To reach this objective, for optically-deep waters where bottom contribution is negligible, we present a system centered on water's inherent optical properties (IOPs). It can be used to derive IOPs from angular R_rs and offers an alternative to the system centered on the concentration of chlorophyll. This system is applicable to oceanic and coastal waters as well as to multiband and hyperspectral sensors. This IOP-centered system is applied to both numerically simulated data and in situ measurements to test and evaluate its performance. The good results obtained suggest that the system can be applied to angular R(rs) to retrieve IOPs and to remove the angular variation of R(rs).     

Physics-Based Visualization of Dense Natural Clouds. II. Cloud-Rendering Algorithm

We discuss the representation of aerosol-scattering properties, boundary information, and the use of these results in line-of-sight rendering applications for visualization of a modeled atmosphere based on a discrete ordinates three-dimensional radiative-transport method. The outputs of the radiative-transfer model provide spatial and angular distributions of limiting path radiance, given an input density distribution and external illumination conditions. We discuss the determination of the direct attenuated radiance, integrated path radiance, and background radiance for each pixel in the rendered scene. Orthographic and perspective projection approaches for displaying these results are described, and sample images are shown.     

Assessment of a bidirectional reflectance distribution correction of above-water and satellite water-leaving radiance in coastal waters

Water-leaving radiances, retrieved from in situ or satellite measurements, need to be corrected for the bidirectional properties of the measured light in order to standardize the data and make them comparable with each other. The current operational algorithm for the correction of bidirectional effects from the satellite ocean color data is optimized for typical oceanic waters. However, versions of bidirectional reflectance correction algorithms specifically tuned for typical coastal waters and other case 2 conditions are particularly needed to improve the overall quality of those data. In order to analyze the bidirectional reflectance distribution function (BRDF) of case 2 waters, a dataset of typical remote sensing reflectances was generated through radiative transfer simulations for a large range of viewing and illumination geometries. Based on this simulated dataset, a case 2 water focused remote sensing reflectance model is proposed to correct above-water and satellite water-leaving radiance data for bidirectional effects. The proposed model is first validated with a one year time series of in situ above-water measurements acquired by collocated multispectral and hyperspectral radiometers, which have different viewing geometries installed at the Long Island Sound Coastal Observatory (LISCO). Match-ups and intercomparisons performed on these concurrent measurements show that the proposed algorithm outperforms the algorithm currently in use at all wavelengths, with average improvement of 2.4% over the spectral range. LISCO's time series data have also been used to evaluate improvements in match-up comparisons of Moderate Resolution Imaging Spectroradiometer satellite data when the proposed BRDF correction is used in lieu of the current algorithm. It is shown that the discrepancies between coincident in-situ sea-based and satellite data decreased by 3.15% with the use of the proposed algorithm. This confirms the advantages of the proposed model over the current one, demonstrating the need for a specific case 2 water BRDF correction algorithm as well as the feasibility of enhancing performance of current and future satellite ocean color remote sensing missions for monitoring of typical coastal waters.     

Analytical solution of radiative transfer in the coupled atmosphere-ocean system with a rough surface

Using the computationally efficient discrete-ordinate method, we present an analytical solution for radiative transfer in the coupled atmosphere-ocean system with a rough air-water interface. The theoretical formulations of the radiative transfer equation and solution are described. The effects of surface roughness on the radiation field in the atmosphere and ocean are studied and compared with satellite and surface measurements. The results show that ocean surface roughness has significant effects on the upwelling radiation in the atmosphere and the downwelling radiation in the ocean. As wind speed increases, the angular domain of sunglint broadens, the surface albedo decreases, and the transmission to the ocean increases. The downward radiance field in the upper ocean is highly anisotropic, but this anisotropy decreases rapidly as surface wind increases and as ocean depth increases. The effects of surface roughness on radiation also depend greatly on both wavelength and angle of incidence (i.e., solar elevation); these effects are significantly smaller throughout the spectrum at high Sun. The model-observation discrepancies may indicate that the Cox-Munk surface roughness model is not sufficient for high wind conditions.     

Ocean source and optical property estimation from explicit and implicit algorithms

We solve an inverse problem of ocean optics for estimating spatially dependent absorption and scattering coefficients and for determining sources such as fluorescence, bioluminescence, or Raman scattering. The solution requires in situ measurement of the downward and upward plane irradiances and scalar irradiances and a priori estimation of the angular shape of the volume scattering function. Both an explicit algorithm and an implicit one are developed from new two-stream radiative-transfer equations that utilize an asymptotic radiance approximation to close the set of equations. A comparison of numerical tests for the two algorithms is given.     

Self-consistent approach to the solution of the light transfer problem for irradiances in marine waters with arbitrary turbidity, depth, and surface illumination. I. Case of absorption and elastic scattering

A self-consistent variant of the two-flow approximation that takes into account strong anisotropy of light scattering in seawater of finite depth and arbitrary turbidity is presented. To achieve an appropriate accuracy, this approach uses experimental dependencies between downward and total mean cosines. It calculates irradiances, diffuse attenuation coefficients, and diffuse reflectances in waters with arbitrary values of scattering, backscattering, and attenuation coefficients. It also takes into account arbitrary conditions of illumination and reflection from the bottom with the Lambertian albedo. This theory can be used for the calculation of apparent optical properties in both open and coastal oceanic waters, lakes, and rivers. It can also be applied to other types of absorbing and scattering medium such as paints, photographic emulsions, and biological tissues.     

Ocean optics estimation for absorption,backscattering, and phase function parameters

We propose and test an inverse ocean optics procedure with numerically simulated data for the determination of inherent optical properties using in-water radiance measurements. If data are available at only one depth within a deep homogeneous water layer, then the single-scattering albedo and the single parameter that characterizes the Henyey-Greenstein phase function can be estimated. If data are available at two depths, then these two parameters can be determined along with the optical thickness so that the absorption and scattering coefficients, and also the backscattering coefficient, can be estimated. With a knowledge of these parameters, the albedo and Lambertian fraction of reflected radiance of the bottom can be determined if measurements are made close to the bottom. A simplified method for determining the optical properties of the water also is developed for only three irradiance-type measurements if the radiance is approximately in the asymptotic regime.     

Estimation of the total uncertainty of sky-radiance measurements in field experimental conditions: implications for the aerosol single-scattering albedo

We compare the spectral sky radiance measured by three ground-based optical radiometers during the second Aerosol Characterization Experiment (ACE-2) to estimate the total uncertainty of the radiance in field experimental conditions. The propagation of this uncertainty on the column-integrated aerosol single-scattering albedo omega0 at 868 nm is investigated. The radiance measurements are affected by a systematic gain uncertainty of less than 2% in the visible spectral region and within 6% in the near-IR region. Correcting the measured radiance by a systematic uncertainty reduces the dispersion of the omega0 from 0.07 to 0.03. Besides, the total relative uncertainty of the radiance measurements in field experimental conditions is within 4% at any wavelength. The corresponding uncertainty delta omega0 is 4% for an aerosol optical thickness of 0.2.     

Radiometric characterization of ultrahigh radiance xenon short-arc discharge lamps

Xenon short-arc discharge lamps exhibit ultrahigh radiance with substantial emission beyond the visible, primarily in the near infrared. Their radiance distributions are spatially and angularly inhomogeneous due to both the structure of the plasma arc and the infrared radiation from the electrodes. These characteristics are favorable for high-irradiance biomedical and high-temperature reactor applications that exploit both visible light and infrared radiation. For the affiliated optical designs, full-spectrum radiometry, rather than just visible photometry, is needed and not extensively available. We present experimental measurements for the spectral, spatial, and angular distributions of such 150 W lamps and relate the consequences for such novel applications.