Abstract
The ability to map the phase distribution and lateral coherence of an x-ray wavefront offers the potential for imaging the human body through phase contrast, without the need to deposit significant radiation energy. The classic means to achieve this goal is structured illumination, in which a periodic intensity modulation is introduced into the image, and changes in the phase distribution of the wavefront are detected as distortions of the modulation pattern. Two-dimensional periodic patterns are needed to fully characterize a transverse wavefront. Traditionally, the information in a 2D pattern is retrieved at high resolution by acquiring multiple images while shifting the pattern over a 2D matrix of positions. Here we describe a method to decode 2D periodic patterns with single-axis phase stepping, without either a loss of information or increasing the number of sampling steps. The method is created to reduce the instrumentation complexity of high-resolution 2D wavefront sensing in general. It is demonstrated with motionless electromagnetic phase stepping and a flexible processing algorithm in x-ray dark-field and phase contrast imaging.
Highlights
By introducing a periodic modulation in the intensity distribution of a wavefront, perturbations in the phase and lateral coherence of the wavefront become visible as distortions of the pattern and attenuation of its amplitude
P is the size of the squares, the H(r)s are the amplitudes of the harmonic oscillations, the w(r)s are the phase distortions of the harmonics in the X, Y and diagonal directions, and the Qj(r)s are applied instrumental phase shifts in the phase stepping process in the jth step
Johnswort (Hypericum calycinum) plant are imaged in the arrangement of Fig. 1A
Summary
By introducing a periodic modulation in the intensity distribution of a wavefront, perturbations in the phase and lateral coherence of the wavefront become visible as distortions of the pattern and attenuation of its amplitude. Proposed for astronomical telescopes, various embodiments span diverse areas such as adaptive-wavefront two photon microscopes [3], free-electron x-ray lasers [4], and diagnostic exams of the human eye [5]. Scattering reduces the lateral coherence of the wavefront, which is detectable as a drop in the visibility of the modulation pattern. X-ray scattering causes a diffuse background, or ‘‘fog’’, that degrades image quality in diagnostic exams. The ‘‘fog’’ can be quantified and removed through grid modulation of the beam [12,13]
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