Clarification on generalized Lau condition for X-ray interferometers based on dual phase gratings

Abstract

To implement dual phase grating x-ray interferometry with x-ray tubes, one needs to incorporate an absorbing source grating. In order to attain good fringe visibility, the period of a source grating should be subject to a stringent condition. In literature some authors claim that the Lau-condition in Talbot-Lau interferometry can be literally transferred to dual phase grating interferometry. In this work we show that this statement in literature is incorrect. Instead, through an intuitive geometrical analysis of fringe formation, we derived a new generalized Lau-condition that provides a useful design tool for implementation of dual phase grating interferometry.OCIS codes: (110.6760) Talbot and self-imaging effects; (110.7440) X-ray imaging; (340.7440) X-ray imaging;(340.7450) X-ray interferometry.

Sample phase gradient and fringe phase shift in dual phase grating X-ray interferometry

“…The size of p 0 has a physical meaning in a different context. Namely, if a source grating were incorporated, then the periodicity of the source grating should be set to p 0 for achieving good fringe visibility [20].…”

Quantitative coherence analysis of dual phase grating x-ray interferometry with source grating*

“…[3,4,10,31] Similarly, a new generalized Lau condition was derived for dual phase grating interferometer equipped with a source grating. [28] The theoretical results have been validated by simulations and experimental results. [29] However, experimentally measured fringe visibility was no greater than 6.5%, which was too low for potential practical applications.…”

“…x ray source In order to employ x-ray sources of large focal spots, an absorbing source grating G0 is introduced into dual phase grating interferometers. [28,29] The source grating divides the tube's focal spot into an array of virtual line sources. Each of the mutually incoherent line sources can provide spatially coherent illumination of the phase gratings.…”

“…In recent years, dual phase grating x-ray interferometry has demonstrated its attractive advantages. [25][26][27][28][29][30] Two phase gratings are employed as beam splitters in a dual phase grating interferometer. The split beams transmitting through the phase gratings interfere with each other, creating distinct diffraction orders in the intensity fringe pattern.…”

“…The split beams transmitting through the phase gratings interfere with each other, creating distinct diffraction orders in the intensity fringe pattern. [27,28] The imaging detector just resolves the beat pattern of large periodicities, and makes other fine patterns a constant background. Compared to x-ray Talbot-Lau interferometers, the dual phase grating interferometers directly resolve intensity fringes without the need of an absorbing analyzer grating.…”