Calculating BRDFs from surface PSDs for moderately rough optical surfaces

Harvey, James E.; Choi, Narak; Krywonos, Andrey; Marcen, J.

doi:10.1117/12.831302

Cited by 37 publications

(32 citation statements)

References 3 publications

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“…(22) approaches zero whereas the GHS Smooth obliquity factor in the denominator of Eqs. (23) does not.…”

Section: Inverse Scattering Problem: Predicting Surface Psds From Brdmentioning

confidence: 97%

Comparison of the GHS_Smoothand the Rayleigh-Rice surface scatter theories

Harvey¹,

Pfisterer²

2016

SPIE Proceedings

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The scalar-based GHS Smooth surface scatter theory results in an expression for the BRDF in terms of the surface PSD that is very similar to that provided by the rigorous Rayleigh-Rice (RR) vector perturbation theory. However it contains correction factors for two extreme situations not shared by the RR theory: (i) large incident or scattered angles that result in some portion of the scattered radiance distribution falling outside of the unit circle in direction cosine space, and (ii) the situation where the relevant rms surface roughness,  rel , is less than the total intrinsic rms roughness of the scattering surface. Also, the RR obliquity factor has been discovered to be an approximation of the more general GHS Smooth obliquity factor due to a little-known (or long-forgotten) implicit assumption in the RR theory that the surface autocovariance length is longer than the wavelength of the scattered radiation. This assumption allowed retaining only quadratic terms and lower in the series expansion for the cosine function, and results in reducing the validity of RR predictions for scattering angles greater than 60°. This inaccurate obliquity factor in the RR theory is also the cause of a complementary unrealistic "hook" at the high spatial frequency end of the predicted surface PSD when performing the inverse scattering problem. Furthermore, if we empirically substitute the polarization reflectance, Q, from the RR expression for the scalar reflectance, R, in the GHS Smooth expression, it inherits all of the polarization capabilities of the rigorous RR vector perturbation theory.

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“…(22) approaches zero whereas the GHS Smooth obliquity factor in the denominator of Eqs. (23) does not.…”

Section: Inverse Scattering Problem: Predicting Surface Psds From Brdmentioning

confidence: 97%

Comparison of the GHS_Smoothand the Rayleigh-Rice surface scatter theories

Harvey¹,

Pfisterer²

2016

SPIE Proceedings

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“…(9), then calculate the BRDF one point at an time by choosing an incident and a scattering angle, then implementing the FFTLog numerical Fourier transform algorithm [16,30] indicated symbolically in Eq. (14) below .…”

Section: Surface Scatter Effects At Suvi Wavelengthsmentioning

confidence: 99%

“…We have fit the measured metrology data with an ABC or K-Correlation Function of the following form [29][30] .…”

Section: Surface Scatter Effects At Suvi Wavelengthsmentioning

confidence: 99%

Effect of surface scatter upon the MTF of the solar ultra violet imager (SUVI) telescope

Harvey¹,

Choi

2013

Solar Physics and Space Weather Instrumentation V

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The solar UV imager (SUVI) is an extreme ultraviolet instrument that will fly on the Geostationary Operational Environmental Satellite (GOES)-R and-S platforms, as part of NOAA's space weather monitoring fleet. It will provide important information on solar activity and the effects of the Sun on the earth and the near-earth environment. This instrument will image the full solar disc in 6 EUV wavebands between 303.8 Å and 93.9 Å. A generalized Cassegrain telescope configuration is employed where six mirror sectors utilize multilayer coatings optimized for the six wavelengths of interest. An aperture shutter is used to select the appropriate sector for observations at a particular wavelength. A thinned, back-illuminated CCD sensor with 21m (2.5 arcsec) pixels resides in the telescope focal plane. The modulation transfer function (MTF) is usually considered to be the image quality criterion of choice for applications where fine detail in extended images needs to be specified or evaluated. However, the contractual image quality requirement was specified in terms of fractional ensquared energy for a variety of different wavelengths and square sizes. In this paper we will calculate and present MTF plots (as degraded by diffraction, geometrical aberrations, surface scatter effects and detector effects) for each of the SUVI wavelengths of interest. Surface scatter due to residual optical fabrication errors is a major factor limiting the performance at the shorter wavelengths, and the large detector size severely limits the performance at all SUVI wavelengths.

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“…It can be easily checked that in the BSDF from reference [3], proper normalization is not automatically achieved. Finally, the K-correlation model [15,16] is a physically-based BSDF obtained by inserting an analytical parametrization of the power spectral density (PSD) into the Rayleigh-Rice equation [10,16]. As can be checked numerically, this model is inherently normalized to the correct TIS.…”

Section: Roughness Of Optical Surfaces: Overview Of Existing Bsdf mentioning

confidence: 99%