Advanced Optical Technologies Research and Development in Physical Optics

Scattering and Coherence

Conventional physical models of light scattering often neglect the fundamental wave nature of light, inevitably leading to inaccuracy. 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.

AOT has developed several coherence models of light scattering that have been verified against radiometric and materials data, including AFM data for rough surfaces. Applications including radiometric M&S and data analysis, computer-graphic design, and machine vision benefit from physical models of light scattering that account for wave effects. See the publications below or contact us for more information.

Extended-Range AFM Imaging for Applications to Reflectance Modeling, originally published in Reflection, Scattering, and Diffraction from Surfaces V, Proc. SPIE 9961, 99610R (2016).

A technique employing a 3D morphological image-registration algorithm is demonstrated for stitching together high-resolution surface images obtained with a commercial atomic-force microscope (AFM), producing 3D surface images up to 1mm long with lateral resolution ~ 100nm. These images can be applied to reflectance modeling by extracting surface parameters to be used as inputs for reflectance models, for instance the previously-published Coherence Model [BG. Hoover and VL. Gamiz, J. Opt. Soc. Am. A 23, 314 (2006)], which utilizes the surface roughness and autocorrelation derivatives in the large-roughness approximation. Surface moments estimated from extended-range AFM images demonstrate lower uncertainty at all frequencies and substantial reduction of sampling artifacts at low frequencies, enabling improved estimates of surface parameters. The autocorrelation of a nearly monoscale diffuse-gold surface is measured out to 800um separation, and the autocorrelation of a multiscale tin surface provides parameters that verify the Coherence Model fit to the measured quasimonostatic BRDF.

Coherence Model for Laser and Solar Scattering by Diffuse Metals, originally presented at Reflection, Scattering, and Diffraction from Surfaces III, SPIE Conf. OP316, 15 August 2012

Coherence Versus Radiance Formulations of Surface Scattering, originally published in Polarization Science and Remote Sensing III, Proc. SPIE 6682, 66820H-1-9 (2007).

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 23, 314-328 (2006).

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 65, 026614 (2002).

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.