![]() When a laser beam is transmitted through a diffractive optical element (DOE), it can be transformed into an almost arbitrary light pattern in the observation plane. The diffractive elements that produce these complex light patterns must be designed and fabricated in a sophisticated way. Examples include viewfinder patterns, arrangements of multiple lines or circles that can be used for three-dimensional (3-D) surface measurements, and patterns that represent rulers or scales. The obtained value is larger than the pixel size because of the combined contributions of the detector resolution (2.2 μm) and the aberration and mechanical instability of the beamline optics.Diffractive optical elements can be used to generate complex light patterns with precisely defined dimensions in a specified plane. 3(d), is 3.8 μm, as determined by the angular unrolled method reported in Ref. The spatial resolution, measured by the smallest resolvable line pair in the Siemens star pattern in Fig. The spatial resolution of the CMMI method is significantly better than that for the SSXI and SGXI methods thanks to the use of the maximum-likelihood reconstruction algorithm and the coded mask. 3, where (a) is obtained by the SSXI method using the coded mask, (b) is from the SGXI measurement using a checkerboard π / 2 grating with a pattern period of 3.4 μm at the same location as the coded mask, and (c) is from the CMMI method with the enlarged image shown in (d) using the same measured images by the SSXI method. The reconstructed phase results are shown in Fig. The spatial resolution of the CMMI method was demonstrated by measuring a resolution standard composed of SU-8 epoxy resist as a phase sample and comparing it with those of the SGXI and the correlation-based SSXI method. 1(a) and 1(b) is 1 and 20 s, respectively. The resolution of the detector system is estimated to be 2.2 μm, following Ref. The effective pixel size of all recorded images is 0.65 μm. The detector system used in both setups consisted of a 100 μm thick LuAG:Ce scintillator, a 10 × objective lens, and an Andor Neo sCMOS camera. 34 The related distances are Δ z = 134 mm, Δ s = 75 mm, and d = 790 mm, yielding a geometric magnification of M c = 4.8 for the coded mask and M s = 7.5 for the sample at the detector plane. 1(b), the focused beam was created by a polymeric compound refractive lens at a photon energy of 20 keV. For the setup with geometric magnification as shown in Fig. The related distances are Δ s = 134 mm, d = 310 mm, and the source-to-sample distance L = 34 m. 1(a) setup, the x-ray energy was set to 14 keV by the beamline's Si(111) double-crystal monochromator. The CMMI method was experimentally verified at the 1-BM beamline of the Advanced Photon Source in Argonne National Laboratory (USA). While the phase sensitivity and spatial resolution of both SGXI and SSXI are limited by the size of the reference pattern, they can be improved by phase-stepping 4,22 or speckle-scanning, 9 respectively, at the expense of a significant increase in the data acquisition time and the sample's absorbed radiation dose. Traditional SSXI techniques cannot, however, be easily calibrated because of the randomness of the speckle generator, which is usually a piece of sandpaper or membrane filter. 20,21 For SGXI, reference-free measurements can be realized through a calibration procedure if the grating pattern is known and well-characterized. 17,18 However, to achieve higher phase sensitivity, SGXI methods require either setups with multiple gratings, 19 or a complicated calibration procedure to correct the grating fabrication and other systematic errors. Single-shot grating-based x-ray imaging (SGXI) and single-shot speckle-based x-ray imaging (SSXI) have been widely applied to biomedical imaging 14–16 and wavefront sensing.
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