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Scattering of Directional Light
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Abstract
Backlight scattering of directional light is mainly a coherent single event effect, considered so far to be a diffusive, multi-event effect. Diffusive scattering must lead to non-uniform images that obey Lambert's Cosine scattering law. However, there are no object images, neither celestial, nor terrestrial, that comply with the law. Observed images are all nearly uniform. The uniformity is a direct outcome of single event scattering. Uniform images of the full moon have been discussed, so far, as diffusive events. Similar images of other bodies have not been discussed. Single event scattering is automatically coherent since a single electromagnetic source wave stimulates all the scattering dipoles. The coherence is responsible to the "Opposition Effect", enhancement of 180 degrees back-scattering by constructive interference. Opposition enhancement has been considered so far as a separate effect from image uniformity.
Coherent single event scattering may be separated from non-coherent scattering noise, by interference methods, in order to observe objects such as asteroids, with better resolution or at a higher distance, or to observe bodies within scattering media as in biological tissues.
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A novel shadowing and coherent-backscattering model is utilized in the analysis of the single-scattering albedos and phase functions, local surface roughness, and regolith porosity of specific lunar mare regions imaged by the AMIE camera (Advanced Moon micro-Imager Experiment) onboard ESA SMART-1 mission. Shadowing due to the regolith particles is accounted via ray-tracing computations for densely-packed particulate media with a fractional-Brownian-motion interface with free space. The shadowing modeling allows us to derive the scattering phase function for a ~100-mum volume element of the lunar mare regolith. The volume-element phase function is explained by coherent-backscattering modeling, where the fundamental single scatterers are the wavelength-scale particle inhomogeneities or the smallest fraction of the particles on the lunar surface. The phase function of the fundamental scatterers is expressed as a sum of two Henyey-Greenstein terms, accounting for increased backward scattering as well as increased forward scattering. Based on the modeling of the AMIE lunar photometry, we conclude that most of the lunar mare opposition effect is caused by coherent backscattering within volume elements comparable in size to typical lunar particles, with only a small contribution from shadowing effects.
Introducing planetary photometry as a quantitative remote sensing tool, this handbook demonstrates how reflected light can be measured and used to investigate the physical properties of bodies in our Solar System. The author explains how data gathered from telescopes and spacecraft are processed and used to infer properties such as the size, shape, albedo, and composition of celestial objects including planets, moons, asteroids, and comets. Beginning with an overview of the history and background theory of photometry, later chapters delve into the physical principles behind commonly used photometric models and the mechanics of observation, data reduction, and analysis. Real-world examples, problems, and case studies are included, all at an introductory level suitable for new graduate students, planetary scientists, amateur astronomers and researchers looking for an overview of this field. An introductory text on planetary photometry, providing an accessible overview of the field and a foundation for more advanced texts Assumes little specific background knowledge, providing readers new to the field with the knowledge and tools they need to use this technique in practice Many concepts and equations are derived from first principles, promoting a deeper understanding of the theory of planetary photometry.
Principles of classical electricity and magnetism are briefly considered
along with aspects of scattering theory, light mixing spectroscopy,
interferometry, photon-counting fluctuations, and experimental methods.
Attention is given to the laser, the optical system, the photon-counting
technique, questions of current detection, the Fabry-Perot
interferometer, and problems of data analysis. Principal applications in
laser light scattering include phase transitions, reaction kinetics, and
velocity of fluid flow. Studies of the dynamics of macromolecules are
discussed, taking into account basic particle scattering theory, the
translational diffusion coefficient, the rotational diffusion
coefficient, the depolarization ratio, and aspects of electrophoresis
and light scattering.
The electromagnetic scattering properties of Solar System regoliths are commonly interpreted using the lunar regolith as a prototype. Hence, a thorough understanding of the reflectance of lunar soil is essential to remote sensing planetary studies. We have measured the linearly and circularly polarized reflectances of samples of lunar soil in order to better understand the nature of the lunar opposition effect. Several independent observations show that the zero-phase peak is caused by both shadow hiding and coherent backscatter in roughly equal amounts. Any radiative transfer model for planetary regoliths must take this dual nature into account. The transport mean free path for photons in the lunar regolith is about 1 μm, which is much smaller than the mean particle size.
Recent experiments have confirmed that coherent effects in the multiple scattering of light affect the angular dependence of the intensity reflected by disordered media. By considering the constructive interferences between time-reversed paths of light in a semi-infinite medium, we analyze the experimental line shape of the albedo within the diffusion approximation and explain the observed effects of polarization.
On Lambertian spheres
- V T Toth
Toth, V.T. (2019) On Lambertian spheres,
https://www.vttoth.com/CMS/physics-notes/336-on-lambertian-spheres
Opposition Effect (Seeliger effect) | Aerial video examples
- J Flies
Flies, J. (2017) Opposition Effect (Seeliger effect) | Aerial video examples,
https://www.youtube.com/watch?v=c0MRM8ViXdQ
Space Image Library: Saturn during Opposition
- B Murray
Murray, B. (2005) Space Image Library: Saturn during Opposition
https://www.planetary.org/space-images/opposition-surge-of-saturns-rings
On the web: December 2020. Revised September 2022