Schematic measurement setup and sample arrangement. is the source grating, the beam splitter grating used for the phase stepping, and the analyzer grating. The samples are a square PMMA bar aligned along the diagonal and a square Al bar.
Plot of a Rician distributed amplitude for constant and four different values of . As the distribution broadens with increasing noise level, it becomes skew and its mean shifts toward higher values.
Experimental results for the sample arrangement shown in Fig. 1. in (a)-(d) transmission and (e)-(h) dark field contrast for four different exposure times. In (a), the Al and reference regions-of-interest are indicated by a solid and a dashed rectangle, respectively. As the SNR decreases, the dark-field signal rises above unity in areas in which attenuation is present, as visible in images (g) and (h).
(a) Measured mean visibility for the reference region-of-interest (asterisks) and the Al bar (circles) and (b) its standard deviation as a function of the noise level . The solid and dashed lines describe the analytically expected values in the limit of high and low SNR, respectively. The rise of the visibility with increasing noise level indicates a breakdown of information transfer.
Measured mean (asterisks) and median (circles) dark-field signal as a function of the noise level for (a) the reference region and (b) the Al bar. The solid and dashed lines describe the analytically expected values in the limit of high and low SNR, respectively. In the limit of low SNR, the dark-field signal approaches a value related to the transmission of the sample, while it remains constant in the absence of a sample. The median is a better suited estimator for the expectation value than the mean, due to the skewness of the underlying distribution.
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