X-ray ptychography using randomized zone plates

Abstract

We have developed a randomized grating condenser zone plate (GCZP) that provides a µm-scale probe for use in x-ray ptychography. This delivers a significantly better x-ray throughput than probes defined by pinhole apertures, while providing a clearly-defined level of phase diversity to the illumination on the sample, and helping to reduce the dynamic range of the detected signal by spreading the zero-order light over an extended area of the detector. The first use of this novel x-ray optical element has been demonstrated successfully for both amplitude and phase contrast imaging using soft x-rays on the TwinMic beamline at the Elettra synchrotron.

Single-frame far-field diffractive imaging with randomized illumination

“…The first ingredient is Band-Limited Random (BLR) illumination, a variety of structured illumination which has been explored in the context of ptychographic imaging [14][15][16][17][18]. Our choice to use this illumination arises from the longstanding observation that the reliability of a phase retrieval problem is typically improved by the presence of high-frequency phase structures [19].…”

Shaping coherent x-rays with binary optics

“…For the case of a synchrotron-based experiment, the diffraction efficiency of a zone plate can be on the order of 2 -40 percent, depending on experimental needs and fabrication capabilities [29][30][31]. An estimate of absolute efficiency for the case of the bandwidth limited random ptychography zone plate would then be given by the product of the relative efficiency and the diffraction efficiency, approximately 0.8 -16 percent, which is well within experimentally acceptable limits [17,18]. In the case of an XFEL experiment, assuming the use of a diamond-based zone plate where efficiencies have been shown to be on order of 2-13 percent [32], for pure diamond -diamond/Ir zone plates, respectively, implementation of a similar zone plate for XFELs would yield absolute efficiencies of approximately 0.8-5.2 percent, also within experimentally acceptable limits.…”

“…Given a desired illumination, various parameters such as duty cycle, harmonic order, and zone placement are adjusted to vary both the amplitude and phase of the wavefront at the lens. These binary diffractive optics can then be used to generate arbitrary structured illumination optimized for a variety of applications such as holography [11], imaging [12][13][14][15], interferometry, ptychography [16][17][18][19][20], and other coherent multiplexing experiments.…”

Fixed Point Analysis of Douglas--Rachford Splitting for Ptychography and Phase Retrieval

“…We use a randomly phased probe with the unknown transmission function µ 0 (n) = |µ 0 |(n)e iθ(n) where θ(n) are random variables and |µ 0 |(n) = 0, ∀n ∈ M 0 . Randomly phased probes have been adopted in ptychographic experiments [32,34,38,41].…”