Ocean inherent optical property estimation from irradiances

A method is evaluated for estimating the absorption coefficient a and the backscattering coefficient b(b) from measurements of the upward and downward irradiances E(u)(z) and E(d)(z). With this method, the reflectance ratio R(z) and the downward diffuse attenuation coefficient K(d)(z) obtained from E(u)(z) and E(d)(z) are used to estimate the inherent optical properties R(infinity) and K(infinity) that are the asymptotic values of R(z) and K(d)(z), respectively. For an assumed scattering phase function beta , there are unique correlations between the values of R(infinity) and K(infinity) and those of a and b(b) that can be derived from the radiative transfer equation. Good estimates of a and the Gordon parameter G = b(b)/(a + b(b)) can be obtained from R(infinity) and K(infinity) if the true scattering phase function is not greatly different from the assumed function. The method works best in deep, homogeneous waters, but can be applied to some cases of stratified waters. To improve performance in shallow waters where bottom effects are important, the deep- and shallow-measurement reflectance models also are developed.     

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.     

Comparison of the ocean inherent optical properties obtained from measurements and inverse modeling

A model developed recently by Loisel and Stramski [Appl. Opt. 39, 3001-3011 (2000)] for estimating the spectral absorption a(lambda), scattering b(lambda), and backscattering b(b)(lambda) coefficients in the upper ocean from the irradiance reflectance just beneath the sea surface R(lambda, z = 0(-)) and the diffuse attenuation of downwelling irradiance within the surface layer ?K(d)(lambda)?(1) is compared with measurements. Field data for this comparison were collected in different areas including off-shore and near-shore waters off southern California and around Europe. The a(lambda) and b(b)(lambda) values predicted by the model in the blue-green spectral region show generally good agreement with measurements that covered a broad range of conditions from clear oligotrophic waters to turbid coastal waters affected by river discharge. The agreement is still good if the model estimates of a(lambda) and b(b)(lambda) are based on R(lambda, z = 0(-)) used as the only input to the model available from measurements [as opposed to both R(lambda, z = 0(-)) and ?K(d)(lambda)?(1) being measured]. This particular mode of operation of the model is relevant to ocean-color remote-sensing applications. In contrast to a(lambda) and b(b)(lambda) the comparison between the modeled and the measured b(lambda) shows large discrepancies. These discrepancies are most likely attributable to significant variations in the scattering phase function of suspended particulate matter, which were not included in the development of the model.     

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.     

Uncertainties associated to measurements of inherent optical properties in natural waters

Monte Carlo simulations are used to explain and quantify the errors in inherent optical properties (IOPs) (absorption and attenuation coefficients) measured using the WET Labs AC-9 submarine spectrophotometer, and to assess correction algorithms. Simulated samples with a wide range of IOPs encountered in natural waters are examined. The relative errors on the measured absorption coefficient are in general lower than 25%, but reach up to 100% in highly scattering waters. Relative errors on attenuation and scattering coefficients are more stable, with an underestimation mainly driven by the volume scattering function. The errors in attenuation and scattering spectral shapes are small.     

Noise-robust stress intensity factor determination from kinematic field measurements

Stress intensity factors are often estimated numerically from a given displacement field through an interaction integral formalism. The latter method makes use of a weight, the virtual crack extension field, which is under-constrained by first principles. Requiring a least noise sensitivity allows one to compute the optimal virtual crack extension. Mode I and mode II specialized fields are obtained and particularized for a given displacement functional basis. The method is applied to an experimental case study of a crack in a silicon carbide sample, whose displacement field is obtained by a digital image correlation technique. The optimization leads to a very significant uncertainty reduction up to a factor 100 of the non-optimized formulation. The proposed scheme reveals additional performances with respect to the integral domain choice and assumed crack tip geometry, which are shown to have a reduced influence.     

Ocean optical source estimation with widely spaced irradiance measurements

A method was developed for determining the spatial distribution of a source from downward and upward irradiance measurements at a single wavelength in seawater of known optical properties. The algorithm uses measurements at two depths located an arbitrary distance apart and solves two nonlinear equations for two parameters that fit a globally exponential or linear source shape. Complex spatially dependent source shapes can be estimated from an irradiance profile by piecing together estimates from neighboring measurement pairs. Numerical tests illustrate the sensitivity of the algorithm to depth, measurement spacing, chlorophyll concentration, sensor noise, and uncertainty in the a priori assumed inherent optical properties. The algorithm works well with widely spaced measurements, moderate sensor noise, and uncertainties in the optical properties regardless of whether the assumed and true profiles are the same shape.     

Multiple polynomial regression method for determination of biomedical optical properties from integrating sphere measurements

We present a new, to our knowledge, method for extracting optical properties from integrating sphere measurements on thin biological samples. The method is based on multivariate calibration techniques involving Monte Carlo simulations, multiple polynomial regression, and a Newton-Raphson algorithm for solving nonlinear equation systems. Prediction tests with simulated data showed that the mean relative prediction error of the absorption and the reduced scattering coefficients within typical biological ranges were less than 0.3%. Similar tests with data from integrating sphere measurements on 20 dye-polystyrene microsphere phantoms led to mean errors less than 1.7% between predicted and theoretically calculated values. Comparisons showed that our method was more robust and typically 5-10 times as fast and accurate as two other established methods, i.e., the inverse adding-doubling method and the Monte Carlo spline interpolation method.     

Analysis of errors in thin-film optical parameters derived from spectrophotometric measurements at normal light incidence

A comparative analysis is made of the errors in deriving the optical parameters (n, refractive index; k, absorption coefficient; d, film thickness) of thin films from spectrophotometric measurements at normal light incidence. The errors in determining n, k, and d by the (TR(f)R(b)), (TR(f)R(m)), (TR(b)R(m)), (TR(f)), (TR(m)), and T(k = 0) methods are compared. It is shown that they are applicable to optical constants of thin films in the n > 1.5, k < 4.5, and d/lambda = (0.02-0.3) range, and their combinations make possible the determination of n and k to an accuracy of better than ?4%. To derive the optical constants in a wide spectral range with high accuracy and isolate the correct physical solutions reliably, one should apply all methods, using the relevant solutions with the lowest errors, as shown in this research, when determining the optical constants of As(2)S(3) and Sb(2)Se(3) films.     

Simultaneous determination of water-leaving reflectance and aerosol optical thickness from Coastal Zone Color Scanner measurements

We present an iterative algorithm for the simultaneous determination of water-leaving reflectances and aerosol optical thickness from the total outgoing radiances measured in the Coastal Zone Color Scanner (CZCS) visible and near-infrared channels. Numerical experiments were carried out to investigate the feasibility of the algorithm. The results show that the errors in determined water-leaving reflectance at 0.443 mum are approximately 10% in most cases. The errors in determined water-leaving reflectance at 0.55 mum are in the 4.05-7.2% range. The errors in the simultaneously determined aerosol optical thickness for all CZCS visible and near-infrared channels are less than approximately 10%.     

Uncertainties of inherent optical properties obtained from semianalytical inversions of ocean color

We present a method to quantify the uncertainties in the in-water constituent absorption and backscattering coefficients obtained from an inversion of remotely sensed reflectance (rrs). We first find a set of positive inversion solutions within a given uncertainty range around the values of the inverted rrs. The uncertainties of the solutions are then computed based on the statistics of these solutions. We demonstrate the uncertainty calculation algorithm using a specific semianalytic inversion model applied to both a field and a simulated data set. When the associated uncertainties are taken into account, the inverted parameters are generally within the uncertainties of the measured (or simulated) parameters, highlighting the success of the inversion and the method to obtain uncertainties. The specific inversion we use, however, fails to retrieve two spectral parameters within a usable range. The method presented is general and can be applied to all existing semianalytical inversion algorithms.     

Improved method for determination of optical constants of organic thin films from reflection and transmission measurements

A new technique for determining the optical properties of organic thin films is presented. A detailed evaluation of the accuracy of the determined optical constants has been performed, and the best combination of measured values yielding the smallest errors in the index of refraction for realistic experimental uncertainties has been found. The proposed method utilizes the fact that optical constants are smooth continuous functions, which reduces the possibility of encountering multiple solutions. The method consists of two steps. In the first step the optical constants at all wavelengths and the film thickness are determined. In the second step the thickness and the imaginary part of the index of refraction are kept fixed while we reevaluate the real part of the index of refraction by using a different objective function with improved sensitivity to the refractive index. After verifying that the proposed method is capable of an accurate estimation of optical constants, we determine the index of refraction data of vanadyl-phthalocyanine in the visible spectral range.     

Apparent and inherent optical properties of turbid estuarine waters: measurements, empirical quantification relationships, and modeling

Spectral measurements of remote-sensing reflectance (Rrs) and absorption coefficients carried out in three European estuaries (Gironde and Loire in France, Tamar in the UK) are presented and analyzed. Typical Rrs and absorption spectra are compared with typical values measured in coastal waters. The respective contributions of the water constituents, i.e., suspended sediments, colored dissolved organic matter, and phytoplankton (characterized by chlorophyll-a), are determined. The Rrs spectra are then reproduced with an optical model from the measured absorption coefficients and fitted backscattering coefficients. From Rrs ratios, empirical quantification relationships are established, reproduced, and explained from theoretical calculations. These quantification relationships were established from numerous field measurements and a reflectance model integrating the mean values of the water constituents' inherent optical properties. The model's sensitivity to the biogeochemical constituents and to their nature and composition is assessed.     

Cartilage thickness measurements from optical coherence tomography

We describe a new semiautomatic image processing method for detecting the cartilage boundaries in optical coherence tomography (OCT). In particular, we focus on rabbit cartilage since this is an important animal model for testing both chondroprotective agents and cartilage repair techniques. The novel boundary-detection system presented here consists of (1) an adaptive filtering technique for image enhancement and speckle reduction, (2) edge detection, and (3) edge linking by graph searching. The procedure requires several steps and can be automated. The quantitative measurements of cartilage thickness on OCT images correlated well with measurements from histology.     

Temperature field calculation from body deformation measurements

A method is considered for solution of the converse thermoelasticity problem of finding the temperature field on the basis of measurements of deformations at certain points of the body.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 2, pp. 281–285, August, 1980.     

Spectral parameters of inherent optical property models: method for satellite retrieval by matrix inversion of an oceanic radiance model

Inherent optical property (IOP) spectral models for the phytoplankton absorption coefficient, chromophoric dissolved organic matter (CDOM) absorption coefficient, and total constituent backscattering (TCB) coefficient are linear in the reference wavelength IOP and nonlinear in the spectral parameters. For example, the CDOM absorption coefficient IOP a(CDOM)(lambda(i)) = a(CDOM)(lambda(ref))exp[-S(lambda(i)- lambda(ref))] is linear in a(CDOM)(lambda(ref)) and nonlinear in S. Upon linearization by Taylor's series expansion, it is shown that spectral model parameters, such as S, can be concurrently accommodated within the same conventional linear matrix formalism used to retrieve the reference wavelength IOP's. Iteration is used to adjust for errors caused by truncation of the Taylor's series expansion. Employing an iterative linear matrix inversion of a water-leaving radiance model, computer simulations using synthetic data suggest that (a) no instabilities or singularities are introduced by the linearization and subsequent matrix inversion procedures, (b) convergence to the correct value can be expected only if starting values for a model parameter are within certain specific ranges, (c) accurate retrievals of the CDOM slope S (or the phytoplankton Gaussian width g) are generally reached in 3-20 iterations, (d) iterative retrieval of the exponent n of the TCB wavelength ratio spectral model is not recommended because the starting values must be within approximately +/-5% of the correct value to achieve accurate convergence, and (e) concurrent retrieval of S and g (simultaneously with the phytoplankton, CDOM, and TCB coefficient IOP's) can be accomplished in a 5 x 5 iterative matrix inversion if the starting values for S and g are carefully chosen to be slightly higher than the expected final retrieved values.     

Fundamental limitations on the accuracy of simultaneous measurements of optical field parameters

Based on the semiclassical theory of photoelectric detection of radiation and information theory, we have studied the fundamental limits on the accuracy of simultaneous measurements of optical field parameters. Within a one-dimensional four-parameter and a two-dimensional seven-parameter gaussian model with a background and for Poisson photocounting statistics, we consider the limiting and conditional minimum variance matrix bounds on estimates of the radiation parameters. We use numerical methods to study the effect of background illumination, noise counts, dimensions and position of the measurement region relative to the center of the field when detecting radiation using photosensitive arrays with different numbers of elements.     

Dust optical properties retrieved from ground-based polarimetric measurements

We have systematically processed one year of sunphotometer measurements (recorded at five AERONET/PHOTONS sites in Africa) in order to assess mineral dust optical properties with the use of a new polarimetry-based algorithm. We consider the Cimel CE318 polarized sunphotometer version to obtain single-scattering albedo, scattering phase matrix elements F(11) and F(12) for dust aerosols selected with Angstr?m exponents ranging from -0.05 to 0.25. Retrieved F(11) and F(12) differ significantly from those of spherical particles. The degree of linear polarization -F(12)/F(11) for single scattering of atmospheric total column dust aerosols in the case of unpolarized incident light is systematically retrieved for the first time to our knowledge from sunphotometer measurements and shows consistency with previous laboratory characterizations of nonspherical particles.