Volume Scattering Function Research Articles

The optical volume scattering function: Temporal and vertical variability in the water column off the New Jersey coast

I present optical data collected offshore of the New Jersey coast at the Long Term Ecological Observatory LEO15 during the summer of 2001. The data were collected by using a LISST-100 instrument, which measured the volume scattering function (VSF) over the small-angle range 0.1‐208 (1.7‐340 milliradians) at 670 nm. The measurements only occasionally agree with the widely used data of Petzold. No simple correlation between surface or bottom forcing and the form of the VSF at this site was found. However, a systematic vertical variability as well as a temporal variability in the normalized VSF was observed. In particular, the departure from Petzold’s form appears to increase with increasing depth. Power-law forms of the time-averaged small-angle normalized VSF as a function of depth are given.

Optical properties of the particles in the Crimea coastal waters (Black Sea)

A field experiment was carried out in summer 2002 on an oceanographic platform near the coast of Crimea, in the Black Sea. For the first time, the spectral volume scattering function (VSF) was measured for a wide range of scattering angles (i.e., from 0.6 to 177.3 degrees) using a recently developed device. Our analysis revealed that the mineral particles are the primary component influencing the scattering and backscattering coefficient in the study area. The good correlation obtained between the backscattering coefficient bbp and the nonalgal particles absorption coefficient showed that the absorption efficiency of the mineral particles is high in the second half of the experiment. The ratio Chla/cp (where Chla is the chlorophyll a concentration and cp is the beam attenuation coefficient) did not correlate with the backscattering ratio and thus could not be used in this experiment as an alternative proxy to estimate the bulk composition of the particles. The spectral variation of bp (the scattering coefficient) and bbp (the backscattering coefficient) was less steep than what can be found in the open ocean waters. That was explained by the influence of the absorption on the scattering process, especially in the blue, as a consequence of the anomalous dispersion. The average backscattering ratio bp varied spectrally within 4%. Nevertheless, a high spectral variability of bp (around 30%) was observed suggesting that the use of a flat spectral variation is not accurate in coastal zones.

Numerical study of light scattering by a boundary-layer flow

Temperature inhomogeneities in free, isotropic turbulence have the effect of scattering light in near-forward angles. We investigate numerically modifications of free turbulence by a rigid wall and its effect on the propagation of light through turbulence. The wall is a 5 cm optical window placed at the leading edge of an instrument towed with speeds of 0.1 and 1 m/s in free turbulence. The turbulent flow field presents inhomogeneities of an embedded passive scalar (Pr = 7, temperature in water), which are modified by the boundary layer developing on the window. We find that the developing laminar boundary layer has a negligible effect on light scattering for the investigated geometry when considered in terms of the volume-scattering function (differential cross section). This indicates that the boundary layer is not an obstacle for optical measurements of turbulence.

Optical changes associated with cyanobacterial bloom termination by viral lysis

Optical changes that accompanied a collapse of the population of filamentous cyanobacteria from a shallow, eutrophic lake were studied in laboratory-scale enclosures (LSEs). The experimental conditions are known, from previous work on these systems, to cause a dramatic collapse of the dominant algal or cyanobacterial species, which in turn can be associated with viral activity. Within 2 weeks of continuous addition of nutrient-rich growth medium, near-complete collapse of the dominant population occurred over the span of a few days. The collapse was repeatedly and reproducibly observed and was primarily characterized by a marked increase in water transparency. Scattering of light decreased by ∼80%, absorption decreased by 20–80%. There was high similarity in optical changes between several experiments, carried out in different seasons. An increase of dissolved material and submicron-sized particles (SMP) that showed chlorophyll a (Chl a) absorption was observed during the collapse. The phycocyanin (PC): Chl a ratio and phaeopigment : Chl a ratio proved to be good indicators of the observed collapse. Reflectance spectra that were modelled using a constant volume-scattering function indicated that mass mortality of this magnitude can be detected in natural systems using current remote sensors.

Light scattering on oceanic turbulence

Turbulent inhomogeneities of fluid flow have the effect of scattering light in near-forward angles, thus providing an opportunity to use optics to quantify turbulence. Here we report measurements of the volume-scattering function in the range of 10(-7) to 10(-3) rad using a wave-front sensing technique. The total scattering coefficient b, due to scattering on turbulent inhomogeneities, is between 1 and 10 m(-1) under typical oceanographic conditions. The numerical calculations of turbulent volume-scattering functions compare well with the laboratory measurement. These results suggest that optical measurements at small angles are affected by turbulence-related scattering, and their effects can be well modeled with numerical calculations.

A New Method for the Measurement of the Optical Volume Scattering Function in the Upper Ocean

Abstract A new method to measure the optical volume scattering function (VSF) of seawater is presented. The VSF is a fundamental property used in the calculation of radiative transfer for applications as diverse as upper-ocean heating by solar radiation to laser ranging of the sea bottom. The approach differs from traditional ones and involves use of a special periscope prism that allows the direct determination of the VSF over a wide range of angles (0.6°–177.3°) with an angular resolution of 0.3°. Measurements taken in the laboratory using Barnstead International, Inc., Nanopure water, cleaned seawater, and known additions of defined scatterers indicate close correspondence between experimental data and theoretical simulations based on Mie theory over the angle range from 12° to 170°. Field deployments in the Atlantic Ocean continental shelf water are shown to produce high quality measurements of the VSF in the angle range from 0.6° to 177.3°; such observations have not been available before. The new da...

Irradiance inversion theory to retrieve volume scattering function of seawater.

An attempt to retrieve the volume scattering function (VSF) of source-free and no-inelastic-scattering ocean water is made from the upwelling irradiance Eu and downwelling irradiance Ed. It will be shown, from the radiative transfer equation, that the VSF of seawater can be calculated by the planar irradiances when the scattering phase function of the suspended particles in the backward direction and the molecular VSF are known. On the derivation of the hydrosol VSF, several optical properties such as the absorption coefficient a; the scattering coefficients of hydrosol, b, b(f), b(b) and those of the suspended particles, b(p), b(fp), b(bp); the beam attenuation coefficient c; the average cosines mu, mu(d), and mu(u); and the backscattering shape factor for the downwelling light stream, r(du), will also be obtained. On the derivation of those optical parameters, classical knowledge related to interrelationships between inherent optical properties and apparent optical properties and obtained with Monte Carlo numerical simulations is analytically verified. The present theory can be applied to surface waters and any wavelengths, except for waters and wavelengths with an extremely low b(b)/a ratio.

The volume scattering function of natural bubble populations

The volume scattering function (VSF) of natural bubble populations is (1) determined from Mie scattering theory, (2) measured by a newly designed volume scattering meter in the laboratory, and (3) inferred from field observations of the VSF. The laboratory measurements have confirmed our theoretical prediction in that (1) bubbles of sizes that have been recorded in situ in the surface ocean (>10 μm) show elevated scattering for angles between 60° and 80° and (2) the organic coatings on the bubble surface will increase the scattering in the backward hemisphere but little change the scattering in the forward directions, including the critical angles. An optimization analysis is applied to the measurement of the VSF in coastal waters, and the results suggest the potential existence of submicron bubbles that are coated with organic film. The bubble population thus determined, which has a negligible contribution to the total scattering (5%), accounts for 40% of the total backscattering that has been observed in situ. The extension of the bubble size distribution to smaller sizes than can presently be measured by direct techniques will alter the shape of derived phase function in general but will result in rather small changes to the backscattering ratio (<20%) as long as the slope of the size distribution is small, because most of the changes are in the forward (<10°) direction. However, the prominent peak in the VSF at the critical angle observed for larger bubbles is strongly reduced by the inclusion of the small sizes, and the backscattering ratio is increased by a factor of two for distributions that varies as the −4 power of size. Because these bubbles contribute strongly to scattering at large angles, these results have significant implications for the remote observation of the color of the sea.

Relationship of light scattering at an angle in the backward direction to the backscattering coefficient

We revisit the problem of computing the backscattering coefficient based on the measurement of scattering at one angle in the back direction. Our approach uses theory and new observations of the volume scattering function (VSF) to evaluate the choice of angle used to estimate b(b). We add to previous studies by explicitly treating the molecular backscattering of water (b(bw)) and its contribution to the VSF shape and to b(b). We find that there are two reasons for the tight correlation between observed scattering near 120 degrees and the backscattering coefficient reported by Oishi [Appl. Opt. 29, 4658, (1990)], namely, that (1) the shape of the VSF of particles (normalized to the backscattering) does not vary much near that angle for particle assemblages of differing optical properties and size, and (2) the ratio of the VSF to the backscattering is not sensitive to the contribution by water near this angle. We provide a method to correct for the water contribution to backscattering when single-angle measurements are used in the back direction (for angles spanning from near 90 degrees to 160 degrees ) that should provide improved estimates of the backscattering coefficient.

Light scattering by viral suspensions

Viruses represent one of the most abundant, ocean‐borne particle types and have significant potential for affecting optical backscattering. Experiments addressing the light‐scattering properties of viruses have heretofore not been conducted. Here we report the results of laboratory experiments in which the volume‐scattering functions of several bacterial viruses (bacteriophages) were measured at varying concentrations with a laser light‐scattering photometer using a He‐Ne and/or Argon ion laser (632.8 and 514.0 nm, respectively). Four bacterial viruses of varying size were examined, including the coliphages MS‐2 (capsid size 25–30 nm) and T‐4 (capsid size ∼100 nm), and marine phages isolated from Saco Bay, Maine (designation Y‐1, capsid size 50–80 nm) and Boothbay Harbor, Maine (designation C‐2, capsid size ∼110 nm). Volume‐scattering functions (VSFs) were fitted with the Beardsley‐Zaneveld function and then integrated in the backward direction to calculate backscattering cross section. This was compared to the virus geometric cross section as determined by transmission electron microscopy and flow‐field fractionation. Typical backscattering efficiencies varied from 20 × 10−6 to 1,000 × 10−6 . Data on particle size and backscattering efficiencies were incorporated into Mie scattering calcula‐tions to estimate refractive index of viruses. The median relative refractive index of the four viruses was ∼1.06. Results presented here suggest that viruses, while highly abundant in the sea, are not a major source of backscattering.

Instruments and methods for measuring the backward-scattering coefficient of ocean waters

The backward-scattering coefficient bb is an important optical property that plays a central role in studies of ocean-color remote sensing, suspended particle distributions, water clarity, and underwater visibility. We investigate the fixed-angle backscattering sensor approach for the application of measuring bb . Analysis shows that the sensor response to volume scattering can be expressed as the integral of the volume scattering function (VSF) over the backward angles (90 -180 degrees ) weighted by the sensor-response function. We present a procedure for determining the sensor-response function that contains all the information necessary to calibrate the sensor fully to measure the VSF at a nominal backscattering angle. It is shown that, for fixed-angle backscattering sensors,bb is most accurately estimated when the sensor-response function covers the middle range of backscattering angles, roughly 110 -160 degrees , where the shape of the VSF has the least variability. Backscattering at and near the end angles, namely, 90 degrees and 180 degrees , are least correlated with bb . We describe a variety of spectral backscattering sensors that we have developed, and we present their sensor-response functions.

Monte Carlo modeling of underwater-image formation: validity of the linear and small-angle approximations

<p>A Monte Carlo model has been used to compute a set of point-spread functions (PSF's) and modulation transfer functions (MTF's) that determine underwater-image quality in a range of different environments. The results have been used to analyze the range of application under which a linear-approximation theory holds. Conclusions of the study are that the linear-approximation theory Seems to hold quite well over a broad range of applications. The ramifications of the Wells small-angle-scattering theory that predicts the PSF from a knowledge of the volume-scattering function (VSF) are also considered.</p><p>Discrepancies are noted between a predicted and a computationally obtained MTF; these discrepancies increase with range. Therefore, the results of the simulations indicate that the small-angle-scattering theory is more valid at a limited number of attenuation lengths. The results of the simulations indicate that the theory is valid to approximately three attenuation lengths.</p>

The average cosine due to an isotropic light source in the ocean

The average cosine of the light field created by an isotropic point source (IPS) embedded in a homogeneous ocean is investigated with a Monte Carlo model. Two volume scattering functions (VSFs) are used in the model, taken from Petzold (1972), to compute the radiance distributions at various distances from the source. The simulated radiance distributions are compared with measurements of the point spread function made at Lake Pend Oreille, Idaho, during the 1992 optical closure experiment. An analytic model is presented for which is valid to at least 15 optical lengths from the source. The model shows that the mean light path, derived from , is a strong function of the single scattering albedo and the VSF. We found that errors in estimating the absorption coefficient by neglecting the increase in the mean light path, which is due to scattering, vary between 5% and 12% for nearly all natural waters. A mathematical proof is given that as the distance to the IPS goes to zero. An analytic expression is derived for close to a finite diffuse‐isotropic source which shows that approaches one as the distance decreases, but at extremely close distances, as the distance to the surface of the source goes to zero. At distances beyond one attenuation length, for finite sources small compared to an attenuation length, behaves essentially as it would for a point source. An asymptotic model for as a function of the single scattering albedo is given with coefficients that depend on the VSF. Model results and comparisons with measured PSFs reveal the surprising result that the light field from an embedded isotropic point source in the ocean does not exhibit asymptotic behavior as far as 15 attenuation lengths from the source.

Effect of volume-scattering function on the errors induced when polarization is neglected in radiance calculations in an atmosphere–ocean system: errata

Effect of volume-scattering function on the errors induced when polarization is neglected in radiance calculations in an atmosphere–ocean system: errata

Sensitivity of radiative transfer to small-angle scattering in the ocean: Quantitative assessment

It is shown that measurements of the absorption coefficient and the volume-scattering function for scattering angles ? 15° of ocean water are sufficient for predicting the transport of irradiance in the ocean. Thus, difficult-to-measure small-angle scattering is not necessary in many applications. Furthermore, the irrelevance of small-angle scattering suggests the irrelevance of the scattering coefficient and of the routinely measured beam-attenuation coefficient in many radiative-transfer problems. Finally, these observations provide a method for determining the adequacy of instruments in which small sampling volumes (~ few cm(3)) are analyzed when predicting irradiance attenuation and diffuse reflection for large volumes (~ 10-10(4) M(3)).

Effect of volume-scattering function on the errors induced when polarization is neglected in radiance calculations in an atmosphere–ocean system

We have developed a Monte Carlo program that is capable of calculating both the scalar and the Stokes vector radiances in an atmosphere-ocean system in a single computer run. The correlated sampling technique is used to compute radiance distributions for both the scalar and the Stokes vector formulations simultaneously, thus permitting a direct comparison of the errors induced. We show the effect of the volume-scattering phase function on the errors in radiance calculations when one neglects polarization effects. The model used in this study assumes a conservative Rayleigh-scattering atmosphere above a flat ocean. Within the ocean, the volume-scattering function (the first element in the Mueller matrix) is varied according to both a Henyey-Greenstein phase function, with asymmetry factors G = 0.0, 0.5, and 0.9, and also to a Rayleigh-scattering phase function. The remainder of the reduced Mueller matrix for the ocean is taken to be that for Rayleigh scattering, which is consistent with ocean water measurement.

Radiative transfer in the ocean: computations relating to the asymptotic and near-asymptotic daylight field

The asymptotic daylight field in a homogeneous ocean is, like the absorption (a), scattering (b), and attenuation (c) coefficients and the volume scattering function (VSF), an inherent optical property (IOP) of the medium. A simple relationship in the spirit of the van de Hulst similarity relationships is developed from which the diffuse attenuation coefficient K(infinity) of the asymptotic light field can be obtained from a, b, and the VSF with an error of < 2%. In this relationship, the shape of the VSF is characterized by its asymmetry parameter g, whereas omega(0) = b/c characterizes the other IOP's. The relationship applies approximately to other quantities as well, particularly tau(x), which is the optical depth at which the downwelling irradiance attenuation coefficient K(d) can be replaced by K(infinity) with an error no greater than x%. Computations of tau(5) and tau(10) are presented as a function of g, omega(0) and the incident light field, and it is shown that for overcast conditions K(d) can be within 5% of K(infinity) at depths at which the downwelling irradiance is greater than 50% of its value at the surface. Simulations of radiative transfer in verticall inhomogeneous waters reveal that for sufficiently large depth (z), the value of K(infinity)(z) determined from the asymptotic theory that uses the values of the IOP's at z is a good approximation to K(d)(z). Thus our results suggest that in addition to being a pedagogically interesting concept, the asymptotic theory may actually be useful in ocean optics research. The influence of inelastic processes (fluorescence and Raman scattering) on K(infinity) are briefly examined, and it is shown that for an ocean of pure sea water, i.e., no particles or fluorescent compounds, K(infinity)(lambda) approximately 0.02 m(-1) for lambda >/= 430 nm with little spectral variation.

Light backscattering efficiency and related properties of some phytoplankters

By using a set-up that combines an integrating sphere with a spectroradiometer LI-1800 UW, the backscattering properties of nine different phytoplankters grown in culture have been determined experimentally for the wavelengths domain ν = 400 up to 850 nm. Simultaneously, the absorption and attenuation properties, as well as the size distribution function, have been measured. This set of measurements allowed the spectral values of refractive index, and subsequently the volume scattering functions (VSF) of the cells, to be derived, by operating a scattering model previously developed for spherical and homogeneous cells. The backscattering properties, measured within a restricted angular domain (approximately between 132 and 174°), have been compared to theoretical predictions. Although there appear some discrepancies between experimental and predicted values (probably due to experimental errors as well as deviations of actual cells from computational hypotheses), the overall agreement is good; in particular the observed interspecific variations of backscattering values, as well as the backscattering spectral variation typical of each species, are well accounted for by theory. Using the computed VSF, the measured backscattering properties can be converted (assuming spherical and homogeneous cells) into efficiency factors for backscattering ( Q bb ) . Thhe spectral behavior of Q bb appears to be radically different from that for total scattering Q b. For small cells, Q (λ) is practically constant over the spectrum, whereas Q b(λ) varies approximately according to a power law (λ −2). As the cell size increases, Q bb conversely, becomes increasingly featured, whilst Q b becomes spectrally flat. The chlorophyll-specific backscattering coefficients ( b b ∗ appear highly variable and span nearly two orders of magnitude. The chlorophyll-specific absorption and scattering coefficients, a ∗ and b ∗ , are mainly ruled by the interspecific variations in cellssize ( D) and intracellular pigment concentration ( C i) (actually by the variations of the product DC i). Though b b ∗ is involved in the modelling of the diffuse reflectance of waters, the impact of its actual variation is greatly limited because typical b b ∗ values, even at their maximum (10 −3 m 2 mg −1), are very low. This result confirms that living algae have a negligible influence on the backscattering process by oceanic waters; other particles (bacteria, detritus, etc.) associated with algae are mainly responsible for this process.

Diffuse reflectance of oceanic waters: its dependence on Sun angle as influenced by the molecular scattering contribution

A spectral model of the inherent optical properties (absorption and scattering coefficients a and b, respectively) of oceanic case 1 waters with varying chlorophyll concentrations C is operated. It provides the initial conditions for Monte Carlo simulations aimed at examining the diffuse reflectance directly beneath the surface R and its variations with the solar zenith angle zeta. In most oceanic waters, molecular scattering is not negligible, and molecular backscattering may largely exceed backscattering. The variable contributions (depending on C and wavelength) of water molecules and particles in the scattering process result in considerable variations in the shape of the volume-scattering function. R(zeta) is sensitive to this shape. From the simulations, R (which increases as zeta increases) appears to be linearly related to cos zeta, with a slope that is strongly dependent on eta(b), the ratio of molecular backscattering to particle backscattering. The value of the single-scattering albedo (?= b/a + b) has a negligible influence on the R(zeta) function provided that ? < 0.8, a condition that is always fulfilled when dealing with oceanic case 1 waters. Practical formulas for R(zeta) are proposed. They include the influence of the diffuse sky radiation. The history of each photon and the number of collisions it experiences before exiting have been recorded. These histories and also a probabilistic approach allow the variations of R with cos zeta, eta(b), and ? to be understood.

Dependence of the diffuse reflectance of natural waters on the sun angle

Through Monte Carlo simulation, the variation of the diffuse reflectance of natural waters with sun angle is found to be dependent on the shape of the volume scattering function (VSF) of the medium. It is shown that single scattering theory can be used to estimate the reflectance—sun angle variation given the VSF—and, conversely, the VSF over a limited range of scattering angles can be estimated from measurements of the variation of the reflectance with sun angle. The complex variation of reflectance with the incident illumination and surface roughness can be reduced to the variation of a single parameter: the downwelling distribution function in the absence of scattering. These observations are applicable to all but the most reflective of natural waters.