Ptychographic X‐ray speckle tracking

• Published in: Journal of applied crystallography Vol. 53; no. 3; pp. 760 - 780
• Main Authors: Morgan, Andrew J., Quiney, Harry M., Bajt, Saša, Chapman, Henry N.
• Format: Journal Article
• Language: English
• Published: 5 Abbey Square, Chester, Cheshire CH1 2HU, England International Union of Crystallography 01-06-2020; Blackwell Publishing Ltd
• Subjects: Algorithms; Approximation; Holograms; Holography; Image reconstruction; in‐line projection holography; Laser beams; Mathematical analysis; Metrology; phase retrieval; ptychography; Robustness; Tracking; Wave fronts; wavefront metrology; X‐ray speckle tracking; X-ray speckle tracking; phase retrieval; in-line projection holography; ptychography; wavefront metrology
• ISSN: 1600-5767; 0021-8898; 1600-5767
• DOI: 10.1107/S1600576720005567

A method is presented for the measurement of the phase gradient of a wavefront by tracking the relative motion of speckles in projection holograms as a sample is scanned across the wavefront. By removing the need to obtain an undistorted reference image of the sample, this method is suitable for the metrology of highly divergent wavefields. Such wavefields allow for large magnification factors that, according to current imaging capabilities, will allow for nanoradian angular sensitivity and nanoscale sample projection imaging. Both the reconstruction algorithm and the imaging geometry are nearly identical to that of ptychography, except that the sample is placed downstream of the beam focus and that no coherent propagation is explicitly accounted for. Like other X‐ray speckle tracking methods, it is robust to low‐coherence X‐ray sources, making it suitable for laboratory‐based X‐ray sources. Likewise, it is robust to errors in the registered sample positions, making it suitable for X‐ray free‐electron laser facilities, where beam‐pointing fluctuations can be problematic for wavefront metrology. A modified form of the speckle tracking approximation is also presented, based on a second‐order local expansion of the Fresnel integral. This result extends the validity of the speckle tracking approximation and may be useful for similar approaches in the field.
A method for the simultaneous measurement of a wavefront's phase and the projection hologram of an unknown sample is presented. This method relies on an updated form of the speckle tracking approximation, which is based on a second‐order expansion of the Fresnsel integral.