Derivation of realistic surface and particulate scatter transfer functions and their application to incoherent imaging of high-contrast fine-detail scenes

Previous research on optical surface scatter either assumed for the ACV (Auto-Covariance function) a simple analytical but unrealistic Gaussian form or depended on intensive numerical integrations. Measurements of polished optical surfaces indicate they accurately follow a simple inverse power law for the BSDF (Bi-directional Scatter Distribution Function) and the related PSD (Power Spectral Density) of their random height variations, i.e. they are fractal-like. By applying the appropriate limits to the scale-invariant (no intrinsic correlation length) PSD, a general analytic form for the corresponding ACV and STF (Surface or Scatter Transfer Function) can be derived. Combined with other Fourier-Bessel transform pairs, it’s possible to accurately simulate the effect of not only diffraction and aberrations such as defocus (via the system OTF or Optical Transfer Function) but also surface and particulate scatter on the incoherent imaging of highcontrast fine-detail scenes. Simple examples of Gaussian and point objects are first presented followed by application to digital cameras that require integrating the aerial image over each pixel’s active area. The needed subsampling for a camera with over ten million pixels (each only few microns in size) requires two-dimensional FFTs (Fast Fourier Transforms) of many gigabytes to accurately perform the detailed imaging calculations.