Paraxial diffusion-field retrieval

Abstract

Unresolved spatially-random microstructure, in an illuminated sample, can lead to position-dependent blur when an image of that sample is formed. For a small propagation distance, between the exit surface of the sample and the entrance surface of a position-sensitive detector, the paraxial approximation implies that the blurring influence of the sample may be modeled using an anomalous-diffusion field. This diffusion field may have a scalar or tensor character, depending on whether the random microstructure has an autocorrelation function that is rotationally isotropic or anisotropic, respectively. Partial differential equations are written down and then solved, in a closed-form manner, for several variants of the inverse problem of diffusion-field retrieval given suitable intensity images. Both uniform-illumination and structured-illumination schemes are considered. Links are made, between the recovered diffusion field and certain statistical properties of the unresolved microstructure. The developed theory -- which may be viewed as a crudely parallel form of small-angle scattering under the Guinier approximation -- is applicable to a range of paraxial radiation and matter fields, such as visible light, x rays, neutrons, and electrons.

arXiv commentNumerous very minor corrections and clarifications throughout, compared to the previous version

References in corpus (10)

• Theory and applications of free-electron vortex states
• Optical Mobius Strips in Three Dimensional Ellipse Fields: Lines of Circular Polarization
• Single-Image Geometric-Flow X-Ray Speckle Tracking
• X-ray Fokker--Planck equation for paraxial imaging
• Dark-field signal extraction in propagation-based phase-contrast imaging
• X-ray Multimodal Intrinsic-Speckle-Tracking
• X-ray phase-contrast imaging: a broad overview of some fundamentals
• On spatial resolution, signal-to-noise and information capacity of linear imaging systems
• Quantifying the x-ray dark-field signal in single-grid imaging
• Optimizing illumination patterns for classical ghost imaging

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