Quantitative diffraction-enhanced x-ray imaging of weak objects

Abstract

Theoretical aspects of quantitative diffraction-enhanced imaging of weak objects are considered using the Fourier optics approach. The amplitude and phase transfer functions are introduced by analogy with the well-known case of in-line (holographic) imaging. The inverse problem of the reconstruction of the phase and amplitude of the incident wave from recorded images is solved in the case of non-absorbing objects and objects consisting of a single material and in the general case of objects with uncorrelated refraction and absorption characteristics. A comparison is given between the solutions to the inverse problem obtained using the new formalism and the geometric-optics approximation.

A quantitative, non-interferometric X-ray phase contrast imaging technique

“…These assumptions, and the mathematical form of Eqs. (7), lead us to form the sum and difference of these two quantities as: (8) (9) Note that Eq. (8) is equivalent to a conventional absorption image and an identical result could be obtained by integrating the X-ray intensity over the equivalent region of the sample aperture.…”

“…Using this technique, contributions to image contrast due to the phase and absorption are able to separated. Furthermore, researchers have developed algorithms for quantifying the phase shift using various simplifying approximations [8][9][10][11]. This method requires a beam of high spectral purity and small angular divergence thus limiting it to synchrotron sources or monochromated laboratory sources [2,12].…”

Development of phase-contrast X-ray imaging techniques and potential medical applications

“…The complimentary behaviour of the refraction and absorption images is an advantage of the DEI technique in determining the extension of tumour growth. The spatial resolution of synchrotron-based DEI imaging has already reached the order of micrometers [33], which is several orders of magnitude higher than that of conventional CT or magnetic resonance imaging (MRI). However, this high resolution will be difficult to achieve in vivo because of dose limitations.…”

In-line Hard X-ray Holography for Biomedical Imaging

“…The estimated coherence volume for DEI is about 10 −18 m 3 , therefore this method can be only implemented with very high brilliance x-ray source such as synchrotron or freeelectron laser x-rays source. The reported spatial resolution was in the range of a few micrometers (Nesterets et al, 2004). Another limitation of this method stems from the fact that the x-ray beam emerging from the analyzer is vary narrow (typically no more than 1 mm height) with its width not exceeding 10 cm.…”