## Abstract

For a particle population with known size, composition, structure, and shape distributions, its volume scattering function (VSF) can be estimated from first principles through a governing relationship, the Fredholm linear integral equation of the first kind. Inverting the Fredholm equation to derive the composition and size distribution of particles from measured VSFs remains challenging because 1) the solution depends on the kernel function, and 2) the kernel function needs to be constructed to avoid singularity. In this study, a thorough review of the earlier and current inversion techniques is provided. An inversion method based on nonnegative least squares is presented and evaluated using the VSFs measured by a prototype volume scattering meter at the LEO-15 site off the New Jersey coast. The kernel function was built by a compilation of individual subpopulations, each of which follows a lognormal size distribution and whose characteristic size and refractive index altogether cover the entire ranges of natural variability of potential marine particles of the region. Sensitivity analyses were conducted to ensure the kernel function being constructed is neither singular nor pathological. A total of 126 potential subpopulations were identified, among which 11 are common in more than half of the inversions and only five consistently present ($>90\%$ of measurements). These five subpopulations can be interpreted as small colloidal type particles of sizes around $0.02\text{\hspace{0.17em}}\mathrm{\mu m}$, submicrometer detritus-type particles (${n}_{r}=1.02$, ${r}_{\text{mode}}=0.2\text{\hspace{0.17em}}\mathrm{\mu m}$), two micrometer-sized subpopulations with one relatively soft (${n}_{r}=1.04$ and ${r}_{\text{mode}}=1.6\text{\hspace{0.17em}}\mathrm{\mu m}$) and the other relatively refringent (${n}_{r}=1.10$ and ${r}_{\text{mode}}=3.2\text{\hspace{0.17em}}\mathrm{\mu m}$), and bubbles of relatively large sizes (${n}_{r}=0.75$ and ${r}_{\text{mode}}=10\text{\hspace{0.17em}}\mathrm{\mu m}$). Reconstructed PSDs feature a bimodal shape, with the smaller peak dominated by the colloidal subpopulations and the larger particles closely approximated by a power-law function. The Junge-type slope averages $-4.0\pm 0.2$, in close agreement with the well-known mean value of $-4.0$ over the global ocean. The distribution of the refractive index suggested a dominance of particles of higher water content, also in agreement with earlier results based on the backscattering ratio and attenuation coefficients at the same area. Surprisingly, the colloidal-type subpopulations, which have often been operationally classified as “dissolved” and neglected for their scattering, exhibit significant backscattering with contributions of up to 40% over the entire backward angles.

© 2011 Optical Society of America

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