Analytical propagation model for underwater free-space optical communication through realistic levels of oceanic absorption and scattering.

Optical communications (OC) through water bodies is an attractive technology for a variety of applications. Thanks to current single-photon detection capabilities, OC receiver systems can reliably decode very weak transmitted signals. This is the regime where pulse position modulation is an ideal scheme. However, there has to be at least one photon that goes through the pupil of the fore optics and lands in the assigned time bin. We estimate the detectable photon budget as a function of range for propagation through ocean water, both open and coastal. We make realistic assumptions about the water's inherent optical properties, specifically, absorption and scattering coefficients, as well as the strong directionality of the scattering phase function for typical hydrosol populations. We adopt an analytical (hence very fast) path-integral small-angle solution of the radiative transfer equation for multiple forward-peaked scattering across intermediate to large optical distances. Integrals are performed both along the directly transmitted beam (whether or not it is still populated) and radially away from it. We use this modeling framework to estimate transmission of a 1 J pulse of 532 nm light through open ocean and coastal waters. Thresholds for single-photon detection per time bin are a few km and a few 100 m. These are indicative estimates that will be reduced in practice due to sensor noise, background light, turbulence, bubbles, and so on, to be included in future work.

Photon path distributions in optically thin slabs.

The probability distribution function of photon path length in a scattering medium contains valuable information on that medium. While strongly scattering optically thick media have been extensively studied, in particular, with resort to the diffusion approximation, optically thin media have received much less attention. Here, we derive the probability distribution functions for the lengths of singly- and twice-scattered photon paths in an isotropically scattering slab of optical thickness τ, for both reflected and transmitted photons. We show that, in the case of an optically thin slab, these photons dominate the overall response of the medium. We confirm that the second moment of the distribution deviates from the ballistic limit in the case of collimated illumination. Interestingly, we show that under diffuse illumination, the second moment of the distribution is dominated by unscattered transmitted photons, hence is proportional to lnτ, and independent of the phase function. Higher moments of order n (≥3) scale as Hnτn-2. When only reflected or transmitted photons are considered, the second moment scales as H2τ-1, whatever the illumination and viewing conditions. This provides direct access to τ. These theoretical results are extensively supported by Monte Carlo ray-tracing simulations. Extension to anisotropic scattering using these same simulations shows that the results hold, given a scaling factor for collimated illumination, and without any dependence on the phase function for diffuse illumination. These results overall demonstrate that the optical thickness of an optically thin slab can be estimated from the second moment of the distribution. Along with the fact that under diffuse illumination the geometrical thickness can be derived from the first moment of the distribution, this proves that the extinction coefficient of the medium can be estimated from the combination of both moments. This study thus opens new perspectives for non-invasive characterization of optically thin media either in the laboratory or by remote sensing.

Hyperspectral remote sensing of foliar nitrogen content.

A strong positive correlation between vegetation canopy bidirectional reflectance factor (BRF) in the near infrared (NIR) spectral region and foliar mass-based nitrogen concentration (%N) has been reported in some temperate and boreal forests. This relationship, if true, would indicate an additional role for nitrogen in the climate system via its influence on surface albedo and may offer a simple approach for monitoring foliar nitrogen using satellite data. We report, however, that the previously reported correlation is an artifact--it is a consequence of variations in canopy structure, rather than of %N. The data underlying this relationship were collected at sites with varying proportions of foliar nitrogen-poor needleleaf and nitrogen-rich broadleaf species, whose canopy structure differs considerably. When the BRF data are corrected for canopy-structure effects, the residual reflectance variations are negatively related to %N at all wavelengths in the interval 423-855 nm. This suggests that the observed positive correlation between BRF and %N conveys no information about %N. We find that to infer leaf biochemical constituents, e.g., N content, from remotely sensed data, BRF spectra in the interval 710-790 nm provide critical information for correction of structural influences. Our analysis also suggests that surface characteristics of leaves impact remote sensing of its internal constituents. This further decreases the ability to remotely sense canopy foliar nitrogen. Finally, the analysis presented here is generic to the problem of remote sensing of leaf-tissue constituents and is therefore not a specific critique of articles espousing remote sensing of foliar %N.

Multi sky-view 3D aerosol distribution recovery.

Aerosols affect climate, health and aviation. Currently, their retrieval assumes a plane-parallel atmosphere and solely vertical radiative transfer. We propose a principle to estimate the aerosol distribution as it really is: a three dimensional (3D) volume. The principle is a type of tomography. The process involves wide angle integral imaging of the sky on a very large scale. The imaging can use an array of cameras in visible light. We formulate an image formation model based on 3D radiative transfer. Model inversion is done using optimization methods, exploiting a closed-form gradient which we derive for the model-fit cost function. The tomography model is distinct, as the radiation source is unidirectional and uncontrolled, while off-axis scattering dominates the images.

Linearization of Markov chain formalism for vector radiative transfer in a plane-parallel atmosphere/surface system.

The Markov chain formalism for polarized radiative transfer through a vertically inhomogeneous atmosphere is linearized comprehensively with respect to the aerosol and polarizing surface properties. For verification, numerical results are compared to those obtained by the finite difference method. We demonstrate the use of the linearized code as part of a retrieval of aerosol and surface properties for an atmosphere overlying a black and Fresnel-reflecting ocean surface.

Markov chain formalism for polarized light transfer in plane-parallel atmospheres, with numerical comparison to the Monte Carlo method.

Building on the Markov chain formalism for scalar (intensity only) radiative transfer, this paper formulates the solution to polarized diffuse reflection from and transmission through a vertically inhomogeneous atmosphere. For verification, numerical results are compared to those obtained by the Monte Carlo method, showing deviations less than 1% when 90 streams are used to compute the radiation from two types of atmospheres, pure Rayleigh and Rayleigh plus aerosol, when they are divided into sublayers of optical thicknesses of less than 0.03.

Derivatives of light scattering properties of a nonspherical particle computed with the T-matrix method.

Based on the T-matrix formalism, we analytically calculate derivatives of light scattering quantities by a nonspherical particle with respect to its microphysical parameters. Illustrative computations are performed for a spheroid, and the results agree with those obtained by finite differencing. The proposed formalism also predicts correctly derivatives for a sphere obtained by linearized Lorenz-Mie theory.

Markov chain formalism for vector radiative transfer in a plane-parallel atmosphere overlying a polarizing surface.

We report on a way of building bidirectional surface reflectivity into the Markov chain formalism for polarized radiative transfer through a vertically inhomogeneous atmosphere. Numerical results are compared to those obtained by the Monte Carlo method, showing the accuracy of the Markov chain method when 90 streams are used to compute the radiation from a Rayleigh-plus-aerosol atmosphere that overlies a surface with a bidirectional reflection function consisting of both depolarizing and polarizing parts.

Cloud Products from the Earth Polychromatic Imaging Camera (EPIC): Algorithms and Initial Evaluation.

This paper presents the physical basis of the EPIC cloud product algorithms and an initial evaluation of their performance. Since June 2015, EPIC has been providing observations of the sunlit side of the Earth with its 10 spectral channels ranging from the UV to the near-IR. A suite of algorithms has been developed to generate the standard EPIC Level 2 Cloud Products that include cloud mask, cloud effective pressure/height, and cloud optical thickness. The EPIC cloud mask adopts the threshold method and utilizes multichannel observations and ratios as tests. Cloud effective pressure/height is derived with observations from the O2 A-band (780 nm and 764 nm), and B-band (680 nm and 688 nm) pairs. The EPIC cloud optical thickness retrieval adopts a single channel approach where the 780 nm and 680 nm channels are used for retrievals over ocean and over land, respectively. Comparison with co-located cloud retrievals from geosynchronous earth orbit (GEO) and low earth orbit (LEO) satellites shows that the EPIC cloud product algorithms are performing well and are consistent with theoretical expectations. These products are publicly available at the Atmospheric Science Data Center at the NASA Langley Research Center for climate studies and for generating other geophysical products that require cloud properties as input.

Atmospheric Correction of Satellite Ocean-Color Imagery During the PACE Era.

The Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission will carry into space the Ocean Color Instrument (OCI), a spectrometer measuring at 5nm spectral resolution in the ultraviolet (UV) to near infrared (NIR) with additional spectral bands in the shortwave infrared (SWIR), and two multi-angle polarimeters that will overlap the OCI spectral range and spatial coverage, i. e., the Spectrometer for Planetary Exploration (SPEXone) and the Hyper-Angular Rainbow Polarimeter (HARP2). These instruments, especially when used in synergy, have great potential for improving estimates of water reflectance in the post Earth Observing System (EOS) era. Extending the top-of-atmosphere (TOA) observations to the UV, where aerosol absorption is effective, adding spectral bands in the SWIR, where even the most turbid waters are black and sensitivity to the aerosol coarse mode is higher than at shorter wavelengths, and measuring in the oxygen A-band to estimate aerosol altitude will enable greater accuracy in atmospheric correction for ocean color science. The multi-angular and polarized measurements, sensitive to aerosol properties (e.g., size distribution, index of refraction), can further help to identify or constrain the aerosol model, or to retrieve directly water reflectance. Algorithms that exploit the new capabilities are presented, and their ability to improve accuracy is discussed. They embrace a modern, adapted heritage two-step algorithm and alternative schemes (deterministic, statistical) that aim at inverting the TOA signal in a single step. These schemes, by the nature of their construction, their robustness, their generalization properties, and their ability to associate uncertainties, are expected to become the new standard in the future. A strategy for atmospheric correction is presented that ensures continuity and consistency with past and present ocean-color missions while enabling full exploitation of the new dimensions and possibilities. Despite the major improvements anticipated with the PACE instruments, gaps/issues remain to be filled/tackled. They include dealing properly with whitecaps, taking into account Earth-curvature effects, correcting for adjacency effects, accounting for the coupling between scattering and absorption, modeling accurately water reflectance, and acquiring a sufficiently representative dataset of water reflectance in the UV to SWIR. Dedicated efforts, experimental and theoretical, are in order to gather the necessary information and rectify inadequacies. Ideas and solutions are put forward to address the unresolved issues. Thanks to its design and characteristics, the PACE mission will mark the beginning of a new era of unprecedented accuracy in ocean-color radiometry from space.

Penile implants: a look into the future.

Inflatable penile prosthesis (IPP) has been around since the 1970's as a durable and one-time cure for erectile dysfunction (ED). For the past 40 years, many changes have been made to make the device better and currently IPP boasts a high percentage of long-term patient satisfaction. The next paradigm shift in IPP treatment for ED is upon us. Funding for ED related medications and devices has been a hot topic in health policy over the last 10 years. This suggests that the device must improve and patient advocacy and education must increase for IPP to remain as a viable solution for ED. In this paper, we conduct a literature search for innovations in IPP and argue that IPP must constantly improve to compete with oral, injectable, shockwave, and potentially gene therapies.

Lateral photon transport in dense scattering and weakly absorbing media of finite thickness: asymptotic analysis of the space-time Green function.

The asymptotic law for the radial distribution of radiance density from an isotropic point source placed in a slab of homogeneous absorbing and scattering material is obtained within the framework of diffusion theory. The exponential shape of the tail of the resulting Green function has been observed but was not theoretically explained until now. We derive formulas for both the steady-state and the time-dependent problems. The theoretical results are verified by comparison with Monte Carlo simulations.