How many photons are needed to reconstruct random objects in coherent X-ray diffractive imaging?

Abstract

This paper presents an investigation of the reconstructibility of coherent X-ray diffractive imaging diffraction patterns for a class of binary random `bitmap' objects. Combining analytical results and numerical simulations, the critical fluence per bitmap pixel is determined, for arbitrary contrast values (absorption level and phase shift), both for the optical near- and far-field. This work extends previous investigations based on information theory, enabling a comparison of the amount of information carried by single photons in different diffraction regimes. The experimental results show an order-of-magnitude agreement.

X-Ray Near-Field Holography: Beyond Idealized Assumptions of the Probe

“…In this way, one can test the information content in the noisy 2d diffraction patterns and investigate the dependence of µ c on object contrast levels, the accepted error level, and the bitmap size. For the experimentally relevant case of weak phase contrast, applicable to most biological samples, NFH required lower dose than CDI for the optimum propagation distance (Fresnel number) [95]. However, apart from small oscillations of µ c as function of the distance, as expected based on the contrast transfer function (CTF), the results in the near field were almost identical to the far-field results [95].…”

“…For the experimentally relevant case of weak phase contrast, applicable to most biological samples, NFH required lower dose than CDI for the optimum propagation distance (Fresnel number) [95]. However, apart from small oscillations of µ c as function of the distance, as expected based on the contrast transfer function (CTF), the results in the near field were almost identical to the far-field results [95]. Hence, as far as the encoding of information is concerned, which can be tested by the ML approach, far-field CDI and near-field NFH seem, in principle to be roughly equal in dose efficiency.…”

“…Using µ we are able to tune our numerical experiment from the case "barely reconstructing" to "best object reconstruction". According to this parameter we generate test data of two phantoms (i) a cell, and (ii) a bitmap object (as in [95]), see Fig. 3.2.…”

“…Both phantoms are pure phase contrast objects, with phases φ x,y in the range [-1, 0] rad (cell), and φ x,y ∈ {0, −1} rad (bitmap). Note, that binary bitmaps with no correlations between pixels are to some extent amenable to analytical treatments and have been used before for in [94] (1d bitmap) and [95] …”

“…Accordingly, a critical fluence µ c can be defined above which the correct phantom (random bitmap) out of a selection of random bitmaps could be identified with a chosen tolerance (error) level and for given photon shot noise [95]. In this way, one can test the information content in the noisy 2d diffraction patterns and investigate the dependence of µ c on object contrast levels, the accepted error level, and the bitmap size.…”