Source size and temporal coherence requirements of coded aperture type x-ray phase contrast imaging systems

Peter R T Munro,Konstantin Ignatyev,Alessandro Olivo,Robert D Speller

doi:10.1364/oe.18.019681

Abstract

There is currently much interest in developing X-ray Phase Contrast Imaging (XPCI) systems which employ laboratory sources in order to deploy the technique in real world applications. The challenge faced by nearly all XPCI techniques is that of efficiently utilising the x-ray flux emitted by an x-ray tube which is polychromatic and possesses only partial spatial coherence. Techniques have, however, been developed which overcome these limitations. Such a technique, known as coded aperture XPCI, has been under development in our laboratories in recent years for application principally in medical imaging and security screening. In this paper we derive limitations imposed upon source polychromaticity and spatial extent by the coded aperture system. We also show that although other grating XPCI techniques employ a different physical principle, they satisfy design constraints similar to those of the coded aperture XPCI.

Highlights

Phase sensitive x-ray images have a significantly higher quality than conventional absorption based x-ray images
The signal detected by each detector pixel is calculated by integrating the intensity of x-rays transmitted by G2 onto the pixel. This may be expressed mathematically for each pixel as: The Illuminated Pixel Fraction (IPF) may be calculated as: It has been shown previously [11] that the contrast of a CAXPCI system increases as the IPF decreases and so it is an important metric for such systems
We have derived two metrics, γt and γs, which can be used to characterise the effect of source temporal coherence and size, respectively, upon the performance of a CAXPCI

Summary

Introduction

Phase sensitive x-ray images have a significantly higher quality than conventional absorption based x-ray images. One category is characterised by the use of an analyzer crystal whose rocking curve is used to generate intensity modulation from small angular deviations of photons [5] This technique requires a highly collimated, monochromatic beam and so is most practically performed using synchrotron radiation. The third category may be broadly described as grating interferometry which employs a combination of phase and transmission gratings to perform wavefront sensing All manifestations of this technique make use of Talbot's self imaging phenomenon and impose restrictions on source coherence in order that the diffracted orders of the grating interfere. The objective of this paper is to analyse the requirements placed upon the source temporal coherence and size such that satisfactory pixel edge illumination may be achieved This is done by deriving general equations for the field which results from diffraction by G1 for a realistic x-ray source. We demonstrate the salient differences between the CAXPCI method and interferometric grating based techniques

Calculation of the field intensity incident upon the detector

Analysis

Discussion and conclusions