Scattering and Coherence
Despite its ubiquity in human perception and technology, conventional physical models of light scattering are surprisingly primitive, often neglecting the fundamental wave nature of light. Applications including biomedical imaging and diagnosis, computer-graphic design, laser radar, and machine vision benefit from physical models of light scattering that account for wave effects.
From its early applications to radiation sources, coherence theory is currently being extended to the description of light scattering, providing more accurate predictions and discoveries of effects beyond the assumptions of conventional models.
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Coherence Versus Radiance Formulations of Surface Scattering, originally published in Polarization Science and Remote Sensing III, Proceedings of the SPIE, vol. 6682, 66820H-1-9, Sept 2007.
Abstract:
Surface scattering can be formulated in terms of coherence functions averaged over surface realizations. The resulting integrals for the average scattered intensity are superficially similar to those derived in conventional formulations like the Kirchhoff, Beckmann, and physical-optics models, but the coherence function is subject to some essential conditions, which are extensions of previously-derived conditions on the radiometric parameters of primary, partially-coherent sources and their propagated fields, that significantly influence the resulting scattered-intensity or BRDF solutions. The field approximation that leads to conventional radiance-like models is compared to a field approximation that leads to a particular coherence model of surface scattering, which is reviewed and verified against radiometric and atomic-force microscope (AFM) data due to a standard diffuse-gold reflector, representing apparently the first verified inverse reflectance solution for a non-contrived diffuse rough surface.
Coherence Solution for Bidirectional Reflectance Distributions of Surfaces with Wavelength-Scale Statistics, originally published in Journal of the Optical Society of America A, vol.23, pp. 314-328, February 2006.
Abstract:
The scalar bidirectional reflectance distribution function (BRDF) due to a perfectly-conducting surface with roughness and autocorrelation width comparable to the illumination wavelength is derived from coherence theory on the assumption of a random reflective phase screen and an expansion valid for large effective roughness. A general quadratic expansion of the two-dimensional isotropic surface autocorrelation function near the origin yields representative Cauchy and Gaussian BRDF solutions and an intermediate general solution as the sum of an incoherent component and a non-specular coherent component proportional to an integral of the plasma dispersion function in the complex plane. Plots illustrate agreement of the derived general solution with original bistatic BRDF data due to a machined aluminum surface, and comparisons are drawn with previously-published data in the examination of variations with incident angle, roughness, illumination wavelength, and autocorrelation coefficients in the bistatic and monostatic geometries. The general quadratic autocorrelation expansion provides a BRDF solution that smoothly interpolates between the well-known results of the linear and parabolic approximations.
Correlations among Angular Wave Component Amplitudes in Elastic
Multiple-Scattering Random Media, originally published in Physical
Review E, vol.65, 026614, February 2002.
Abstract:
The propagation of scalar waves through random media that provide multiple
elastic scattering is considered by derivation of an expression for the
angular correlation of the scattered wave amplitudes. Coherent wave transmission
is shown to occur through a mechanism similar to that responsible for
coherent backscattering. While the properties of the scattered wave are
generally consistent with radiative-transfer theory for sufficiently small
incident and scattering angles, coherent transmission provides corrections
to radiative-transfer results at larger angles. The theoretical angular
correlation curves are fit, by specifying the probability densities of
two random variables that correspond to material parameters, to measured
data of laser light scattering from various polymer microsphere suspensions.
Related content:
Imaging / A Coherent Approach to Image-Formation in Multiple-Scattering
Media
Related content: Optical
Determination of Field Angular Correlation for Transmission through Three-Dimensional
Turbid Media
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Comparison of Field Correlations in Multiply-Scattered Quasimonochromatic
Light, originally published in Applied Optics, vol.39,
pp.3978-83, August 2000.
Abstract:
An experiment is described that directly compares the degradations, with
the number of scattering mean free paths, of two field correlations that
may be used to form gates for imaging techniques in scattered light: the
correlation of the scattered wave with an unscattered reference wave and
the correlation of two wavevector components of the scattered wave itself.
Results for 20µm polymer spheres show that the latter correlation
is consistently larger well into the multiple scattering regime (up to
10 mean free paths) for wavevector separations less than at least 50mm-1
and that the two correlations tend to merge in this scattering regime
for larger wavevector separations.
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| Optical Determination
of Field Angular Correlation for Transmission Through Three-Dimensional
Turbid Media, originally published in Journal of the
Optical Society of America A, vol.16, pp.1040-48, May 1999.
Abstract:
A method is presented for measuring the correlation between the optical
fields scattered in different directions by an arbitrary three-dimensional
turbid medium. The field angular correlation function is obtained by processing
ensemble average intensity data, which are recorded experimentally by
a single-channel Shack-Hartmann wavefront sensor. Some general properties
of scattered light are expressed in terms of the field angular correlation
function, and the correlation function is measured for transmission through a suspension of microspheres under nonballistic transport conditions.
Related content: Correlations among Angular Wave
Component Amplitudes in Elastic Multiple Scattering Random Media
Related content: Imaging / A Coherent
Approach to Image-Formation in Multiple-Scattering Media
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