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.     

Uniqueness in remote sensing of the inherent optical properties of ocean water

We examine the problem of uniqueness in the relationship between the remote-sensing reflectance (Rrs) and the inherent optical properties (IOPs) of ocean water. The results point to the fact that diffuse reflectance of plane irradiance from ocean water is inherently ambiguous. Furthermore, in the 400 < lambda < 750 nm region of the spectrum, Rrs(lambda) also suffers from ambiguity caused by the similarity in wavelength dependence of the coefficients of absorption by particulate matter and of absorption by colored dissolved organic matter. The absorption coefficients have overlapping exponential responses, which lead to the fact that more than one combination of IOPs can produce nearly the same Rrs spectrum. This ambiguity in absorption parameters demands that we identify the regions of the Rrs spectrum where we can isolate the effects that are due only to scattering by particulates and to absorption by pure water. The results indicate that the spectral shape of the absorption coefficient of phytoplankton, a(ph)(lambda), cannot be derived from a multiparameter fit to Rrs(lambda). However, the magnitude and the spectral dependence of the absorption coefficient can be estimated from the difference between the measured Rrs(lambda) and the best fit to Rrs(lambda) in terms of IOPs that exclude a(ph)(lambda).     

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.     

Modeling the optical properties of mineral particles suspended in seawater and their influence on ocean reflectance and chlorophyll estimation from remote sensing algorithms

The optical properties of mineral particles suspended in seawater were calculated from the Mie scattering theory for different size distributions and complex refractive indices of the particles. The ratio of the spectral backscattering coefficient to the sum of the spectral absorption and backscattering coefficients of seawater, b(b)(lambda)/[a(lambda) + b(b)(lambda)], was analyzed as a proxy for ocean reflectance for varying properties and concentrations of mineral particles. Given the plausible range of variability in the particle size distribution and the refractive index, the general parameterizations of the absorption and scattering properties of mineral particles and their effects on ocean reflectance in terms of particle mass concentration alone are inadequate. The variations in the particle size distribution and the refractive index must be taken into account. The errors in chlorophyll estimation obtained from the remote sensing algorithms that are due to the presence of mineral particles can be very large. For example, when the mineral concentration is 1 g m(-3) and the chlorophyll a concentration is low (0.05 mg m(-3)), current global algorithms based on a blue-to-green reflectance ratio can produce a chlorophyll overestimation ranging from approximately 50% to as much as 20-fold.     

Measured and modeled radiometric quantities in coastal waters: toward a closure

Accurate radiative transfer modeling in the coupled atmosphere-sea system is increasing in importance for the development of advanced remote-sensing applications. Aiming to quantify the uncertainties in the modeling of coastal water radiometric quantities, we performed a closure experiment to intercompare theoretical and experimental data as a function of wavelength lambda and water depth z. Specifically, the study focused on above-water downward irradiance E(d)(lambda, 0+) and in-water spectral profiles of upward nadir radiance L(u)(lambda, z), upward irradiance E(u)(lambda, z), downward irradiance E(d)(lambda, z), the E(u)(lambda, z)/L(u)(lambda, z) ratio (the nadir Q factor), and the E(u)(lambda, z)/E(d)(lambda, z) ratio (the irradiance reflectance). The theoretical data were produced with the finite-element method radiative transfer code ingesting in situ atmospheric and marine inherent optical properties. The experimental data were taken from a comprehensive coastal shallow-water data set collected in the northern Adriatic Sea. Under various measurement conditions, differences between theoretical and experimental data for the above-water E(d)(lambda, 0+) and subsurface E(d)(lambda, 0-) as well as for the in-water profiles of the nadir Q factor were generally less than 15%. In contrast, the in-water profiles of L(u)(lambda, z), E(d)(lambda, z), E(u)(lambda, z) and of the irradiance reflectance exhibited larger differences [to approximately 60% for L(u)(lambda, z) and E(u)(lambda, z), 30% for E(d)(lambda, z), and 50% for the irradiance reflectance]. These differences showed a high sensitivity to experimental uncertainties in a few input quantities used for the simulations: the seawater absorption coefficient; the hydrosol phase function backscattering probability; and, mainly for clear water, the bottom reflectance.     

Contribution of Raman scattering to water-leaving radiance: a reexamination

We have reexamined the contribution of Raman scattering to the water-leaving radiance in case 1 waters by carrying out radiative transfer simulations that combine the latest reported measurements of the absorption coefficient of pure water with direct measurements of the spectral variation of the Raman-scattering coefficient. The resulting contribution of Raman scattering is then compared with experimental measurements of the water-leaving radiance, and the fractional contribution of radiance produced by Raman scattering to the total radiance measured at a given wavelength is determined. The results show that (1) the contribution of Raman scattering to the water-leaving radiance in an ocean of pure seawater is as much as 50-100% larger than earlier predictions, and (2) the Raman contribution does not decay as rapidly with increasing concentrations of chlorophyllouslike pigments C as predicted earlier. In fact, the Raman fraction for C 8% at wavelengths of interest in ocean color remote sensing and therefore cannot be ignored in ocean color modeling.     

Low through channel loss wavelength multiplexer using multiple transmission volume Bragg gratings

We describe a wavelength multiplexer design that employs multiple transmission volume Bragg gratings written in the same region of a photosensitive glass having a through channel loss of < 0.5 dB. A two-channel multiplexer for wavelengths of lambda = 1310 and 1550 nm is demonstrated to test our design methods and assumptions. Agreement between simulation and experiment is within 0.2 dB at the peak diffraction efficiency. Grating apodization is used to reduce the interchannel cross talk from (13.5 +/- 0.5) to (41.5 +/- 8.5) dB, with an experimental through channel loss of (0.6 +/- 0.2) dB. Effects of angular dispersion on diffraction efficiency and grating spectral shape due to the finite diameter of the incident reading beam are also analyzed.     

Absorption and backscattering coefficients and their relations to water constituents of Poyang Lake, China

The measurement and analysis of inherent optical properties (IOPs) of the main water constituents are necessary for remote-sensing-based water quality estimation and other ecological studies of lakes. This study aimed to measure and analyze the absorption and backscattering coefficients of the main water constituents and, further, to analyze their relations to the water constituent concentrations in Poyang Lake, China. The concentrations and the absorption and backscattering coefficients of the main water constituents at 47 sampling sites were measured and analyzed as follows. (1) The concentrations of chlorophyll a (C(CHL)), dissolved organic carbon (C(DOC)), suspended particulate matter (C(SPM)), including suspended particulate inorganic matter (C(SPIM)) and suspended particulate organic matter (C(SPOM)), and the absorption coefficients of total particulate (a(p)), phytoplankton (a(ph)), nonpigment particulate (a(d)), and colored/chromophoric dissolved organic matter (a(g)) were measured in the laboratory. (2) The total backscattering coefficients, including the contribution of pure water at six wavelengths of 420, 442, 470, 510, 590, and 700 nm, were measured in the field with a HydroScat-6 backscattering sensor. (3) The backscattering coefficients without the contribution of pure water (b(b)) were then derived by subtracting the backscattering coefficients of pure water from the total backscattering coefficients. (4) The C(CHL), C(SPM), C(SPIM), C(SPOM), and C(DOC) of the 41 remaining water samples were statistically described and their correlations were analyzed. (5) The a(ph), a(d), a(p), a(g), and b(b) were visualized and analyzed, and their relations to C(CHL), C(SPM), C(SPIM), C(SPOM), or C(DOC) were studied. Results showed the following. (1) Poyang Lake was a suspended particulate inorganic matter dominant lake with low phytoplankton concentration. (2) One salient a(ph) absorption peak was found at 678 nm, and it explained 72% of the variation of C(CHL). (3) The a(d) and a(p) exponentially decreased with increasing wavelength, and they explained 74% of the variation of C(SPIM) and 71% variation of C(SPM), respectively, at a wavelength of 440 nm. (4) The a(g) also exponentially decreased with increasing wavelength, and it had no significant correlation to C(DOC) at a significance level of 0.05. (5) The b(b) decreased with increasing wavelength, and it had strong and positive correlations to C(SPM), C(SPIM) and C(SPOM), a strong and negative correlation to C(CHL), and no correlation to C(DOC) at a significance level of 0.05. Such results will be helpful for the understanding of the IOPs of Poyang Lake. They, however, only represented the IOPs during the sampling time period, and more measurements and analyses in different seasons need to be carried out in the future to ensure a comprehensive understanding of the IOPs of Poyang Lake.     

A temperature distribution study in cross sections of axially symmetric flames

A technique for determining temperature profiles and emissivities of combustion products in the cross section of a flame from experimentally measured spectral radiation intensities is considered. The optical electronic system used to investigate temperature fields is described, and results on the temperature distribution and emissivity of combustion products in the flame cross section obtained by the concentric zone method are given.Notation T temperature - I spectral intensity of radiation - radiation wavelength - absorption coefficient - a absorptivity - emissivity - l length - R radius Deceased.Kirov Polytechnic Institute, Kirov. Polytechnic Institute, Nizhnii-Novgorod, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 3, pp. 313–317, March, 1993.     

Semi-empirical correction algorithm for AC-9 measurements in a coccolithophore bloom

Values for the coefficients of absorption (a) and attenuation (c) obtained from AC-9 measurements in coccolithophore blooms do not provide satisfactory inputs for radiance transfer models. We have therefore modified the standard AC-9 scattering correction algorithm by including an extra term, F(lambda, lambda(r)), which allows for possible wavelength dependence in the scattering phase function. We estimated the magnitude of F(lambda, lambda(r)), which is unity in the standard algorithm, by adjusting the absorption and scattering values in Hydrolight radiance transfer calculations until the depth profiles of downward irradiance (E(d)) and upward radiance (L(u)) matched those measured in situ. The modified algorithm was tested with data from a phytoplankton bloom dominated by the coccolithophore Emiliania huxleyi, which occurred in the western English Channel in May 2001. In this paper, we only have sufficient data to adequately constrain the radiance transfer model in one wave band centered on 488 ma. A single value of F(lambda, lambda(r)) = 1.4 was found to produce satisfactory agreement between modeled and observed profiles at four widely spaced stations within the bloom. Measurements of the ratio of backscattering (b(b)) to total scattering (b) showed significant wavelength dependence at these stations.     

Molar absorptivities of glucose and other biological molecules in aqueous solutions over the first overtone and combination regions of the near-infrared spectrum

Molar absorptivities are measured for water, glucose, alanine, ascorbate, lactate, triacetin, and urea in the near-infrared spectral region at 37 degrees C. Values are based on the Beer-Lambert law and cover the first overtone (1550-1850 nm; 6450-5400 cm(-1)) and combination (2000-2500 nm; 4000-5000 cm(-1)) spectral windows through aqueous media. Accurate calculations demand accounting for the impact of water displacement upon dissolution of solute. In this regard, water displacement coefficients are measured and reported for each solute. First overtone absorptivities range from 2 to 7 x 10(-5) mM(-1)mm(-1) for all solutes except urea, for which absorptivity values are below 0.5 x 10(-5) mM(-1) mm(-1) across this spectral range. Molar absorptivities over the combination spectral region range from 0.8 to 3.2 x 10(-4) mM(-1) mm(-1), which is a factor of four to five greater than the first overtone absorptivities. Accuracy of the measured values is assessed by comparing calculated or modeled spectra with spectra measured from standard solutions. This comparison reveals accurately modeled spectra in terms of magnitude and position of solute absorption bands. Both actual and modeled spectra from glucose solutions reveal positive and negative absorbance values depending on the measurement wavelength. It is shown that the net absorbance of light is controlled by the magnitude of the absorptivity of glucose compared to the product of the absorptivity of water and the water displacement coefficient for glucose.     

Atmospheric correction of satellite ocean color imagery: the black pixel assumption

The assumption that values of water-leaving radiance in the near-infrared (NIR) are negligible enable aerosol radiative properties to be easily determined in the correction of satellite ocean color imagery. This is referred to as the black pixel assumption. We examine the implications of the black pixel assumption using a simple bio-optical model for the NIR water-leaving reflectance [rho(w)(lambda(NIR))](N). In productive waters [chlorophyll (Chl) concentration >2 mg m(-3)], estimates of [rho(w)(lambda(NIR))](N) are several orders of magnitude larger than those expected for pure seawater. These large values of [rho(w)(lambda(NIR))](N) result in an overcorrection of atmospheric effects for retrievals of water-leaving reflectance that are most pronounced in the violet and blue spectral region. The overcorrection increases dramatically with Chl, reducing the true water-leaving radiance by roughly 75% when Chl is equal to 5 mg m(-3). Relaxing the black pixel assumption in the correction of Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) satellite ocean color imagery provides significant improvements in Chl and water-leaving reflectance retrievals when Chl values are greater than 2 mg m(-3). Improvements in the present modeling of [rho(w)(lambda(NIR))](N) are considered, particularly for turbid coastal waters. However, this research shows that the effects of nonzero NIR reflectance must be included in the correction of satellite ocean color imagery.     

Bio-optical properties and ocean color algorithms for coastal waters influenced by the Mississippi River during a cold front

During the passage of a cold front in March 2002, bio-optical properties examined in coastal waters impacted by the Mississippi River indicated that westward advective flows and increasing river discharge containing high concentrations of nonalgal particles contributed significantly to surface optical variability. A comparison of seasonal data from three cruises indicated spectral models of absorption and scattering to be generally consistent with other coastal environments, while their parameterization in terms of chlorophyll (Chl) alpha concentration showed seasonal variability. The exponential slope of the colored dissolved organic matter (CDOM) averaged 0.0161+/-0.00054 nm(-1) and nonalgal absorption averaged 0.011 nm(-1) with deviations from general trends observed due to anomalous water properties. Although the phytoplankton specific absorption coefficients varied over a wide range [0.02 to 0.1 m2 (mg Chl)(-1) at 443 nm] being higher in offshore surface waters, values of phytoplankton absorption spectra at the Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) wave bands were highly correlated to modeled values. Particulate scattering characteristics were similar to observations for other coastal waters, while backscattering ratios were on average lower in phytoplankton-dominated surface waters (0.011+/-0.003) and higher in low Chl near-bottom waters (0.0191+/-0.0045). Average percent differences in remote sensing reflectance Rrs derived from modeled and in-water radiometric measurements were highest in the blue wave bands (52%) and at locations with more stratified water columns. SeaWiFS estimates of Chl and CDOM absorption derived using regional empirical algorithms were highly correlated to in situ data.     

Effect of suspended particulate and dissolved organic matter on remote sensing of coastal and riverine waters

We use remote sensing reflectance (RSR) together with the inherent optical properties of suspended particulates to determine the backscattering ratio b(b)/b for coastal waters. We examine the wavelength dependence of b(b)(lambda) and f(lambda)/Q(lambda) and establish the conditions when C(lambda) in RSR(lambda) approximately or = C(lambda)b(b)(lambda)/a(lambda) can be treated as a constant. We found that for case 2 waters, RSR was insensitive to the natural fluctuations in particle-size distributions. The cross-sectional area of the suspended particulate per unit volume, x(g), showed an excellent correlation with the volume scattering coefficient.     

Embedded centrosymmetric multilayer stacks as complete-transmission quarter-wave and half-wave retarders under conditions of frustrated total internal reflection

A centrosymmetric multilayer stack of two transparent materials, which is embedded in a high-index prism, can function as a complete-transmission quarter-wave or half-wave retarder (QWR or HWR) under conditions of frustrated total internal reflection. The multilayer consists of a high-index center layer sandwiched between two identical low-index films with high-index-low-index bilayers repeated on both sides of the central trilayer, maintaining the symmetry of the entire stack and constituting a QWR (Delta(t)=90 degrees or 270 degrees ) or HWR (Delta(t)=180 degrees ) in transmission. A QWR design at wavelength lambda=1.55 microm is presented that employs an 11-layer stack of Si and SiO(2) thin films, which is embedded in a GaP cube prism. The intensity transmittances for the p and s polarizations remain >99% and Delta(t) deviates from 90 degrees by <+/-3 degrees over a 100 nm spectral bandwidth (1.5< or =lambda< or =1.6 microm), and by < or =+/-7 degrees over an internal field view of +/-1 degrees (incidence angle 44 degrees < or = phi(0)< or =46 degrees inside the prism). An HWR design at lambda=1.55 microm employs seven layers of Si and SiO(2) thin films embedded in a Si cube, has an average transmittance >93%, and Delta(t) that differs from 180 degrees by <+/-0.3 degrees over a 100 nm bandwidth (1.5< or =lambda< or =1.6 microm) and by <+/-17 degrees over an internal field view of +/-1 degree . The sensitivity of these devices to film-thickness errors is also considered.     

Use of a Fabry-Perot interferometer to isolate pure rotational Raman spectra of diatomic molecules

We propose to use a Fabry-Perot interferometer (FPI) as a comb frequency filter to isolate pure rotational Raman spectra (PRRS) of nitrogen molecules. In making the FPI's free spectral range equal to the spectral spacing between the lines of nitrogen PRRS, which are practically equidistant, one obtains a device with a comb transmission function with the same period. However, to match the FPI transmission comb completely with the comb of nitrogen PRRS lines one should tune the wavelength of the radiation used to excite the PRRS of nitrogen exactly to the position of any minimum in the FPI transmission comb. Thus to achieve this task for the case of nitrogen PRRS one must take the FPI's free spectral range Dnu(f)= 4B(N(2)) and the wavelength of the exciting radiation such that (1/lambda(exc)) = 4B(N(2))(k + 1/2), where B(N(2)) is the rotational constant of the nitrogen molecule and k is an arbitrary integer number. In this case all (odd and even) pure rotational Raman lines of nitrogen will pass through the FPI while the line of exciting radiation is being suppressed. Additionally, a FPI cuts out the spectrally continuous sky background light from the spectral gaps between the PRRS lines.     

In vivo measurements of the wavelength dependence of tissue-scattering coefficients between 760 and 900 nm measured with time-resolved spectroscopy

We present in vivo values for the optical transport coefficients (mu(a), mu(s)?) of the adult human forearm, calf, and head from 760 to 900 nm measured with time-resolved spectroscopy. The accuracy of the method is tested with tissue-simulating phantoms. We obtain mu(s)?(lambda) approximately 1.1 - (5.1 x 10(-4) lambda) mm(-1) (forearm), 1.6 - (8.9 x 10(-4) lambda) mm(-1) (calf), and 1.45 - (6.5 x 10(-4) lambda) mm(-1) (head), where lambda is measured in nanometers. At 800 nm we obtain mu(a) = 0.023 +/- 0.004 mm(-1) (forearm), 0.017 +/- 0.005 mm(-1) (calf), and 0.016 +/- 0.001 mm(-1) (head). Our values differ substantially from published in vitro data. In particular, our transport coefficients for the adult head are substantially lower than previously reported values for adult human cerebral matter and pig skull cortical bone measured in vitro.     

Localized surface plasmon resonance biosensor using silver nanostructures fabricated by glancing angle deposition

Glancing angle deposition was used to produce approximately 150-nm-thick silver nanoparticle films, which were evaluated as localized surface plasmon resonance (LSPR) biosensors. The films have a strong extinction peak around 368 nm in air due to LSPR. As the refractive index of the surrounding environment is increased, the extinction peak red-shifts with a linear dependence. The films were functionalized with 11-amino-1-undecanethiol and rabbit immunoglobulin G (rIgG) to allow for the detection of anti-rIgG binding. Binding of biomolecules to the nanoparticle surface increases the local refractive index and results in a red-shifting of the extinction peak. The wavelength shift at varying concentrations of anti-rIgG was measured and fit to the Langmuir isotherm. This yielded approximate values for the saturation response, Delta lambda max = 29.4 +/- 0.7 nm, and the surface confined binding constant, Ka = (2.7 +/- 0.3) x 10(6) M(-1). The response to nonspecific binding was also investigated.     

Polarization-maintaining optical fibers with low dispersion over a wide spectral range

The total dispersion characteristics of the doubly clad Panda (or bow-tie) fibers have been investigated. It is shown that the contribution of the photoelastic effect to the total dispersion becomes of the order of several psec/km x nm in the 1.5-1.7-microm wavelength region. By careful adjustment of the cutoff wavelength, the total dispersion is reduced to within +/- 1 psec/km x nm over the 1.38-1.70-microm wavelength region for the HE(11)(x) mode and 1.38-1.68 microm for the HE(11)(y) mode, respectively.