X-ray grating interferometer principle. (a) Setup with source grating , beam-splitter grating , and analyzer grating . The distances are , between and , , between and , and , between and the sample. (b) In the sample, the x-rays can be absorbed, deviated (angle ), or scattered (angular spread ) as illustrated. This induces local changes in the interference fringes. (c) The phase stepping curve is the intensity of a pixel as a function of the position of the interference pattern with respect to . It is characterized by its average intensity , its amplitude , and phase .
Cross sections obtained by scanning electron microscopy of (a) made by filling a silicon mold with gold, (b) made out of silicon, and (c) made by covering a silicon mold with a thin gold layer. The three gratings were produced in the clean rooms of CSEM in Neuchâtel.
(a) Transmission , (b) differential phase contrast , and (c) dark field images obtained by DPCi for a felt-tip pen imaged at 40 kV (no filter) with six phase steps over one period. Bottom images are enlarged images from the inset. probes the attenuation coefficient of the object while gives a measurement of the derivative in the direction perpendicular to the grating’s lines of the phase shift of the x-ray beam. reflects the local (ultra) SAS power of the sample that is, in this case, especially high in the highly structured ink tank.
The variance is plotted as a function of the mean output for a tube voltage of 50 kV. The error bars represent the standard deviation of due to the pixel-to-pixel inhomogeneities. In one case, 1.5 mm of silicon was used as filter (round markers) while on the other case, an additional 5 mm thick aluminum plate was added (square markers). In both cases, the data were fitted with a linear function (dashed and dotted-dashed lines). As they appear in the plot, the fitting coefficients depend on the energy spectrum of the incoming photons.
The relative uncertainties in (a) , (b) , and (c) were measured for a tube voltage of 50 kV as a function of the mean intensity , in the background case with (round markers), in the background case with (square markers), and within the 5 mm aluminum plate ( and ) with a visibility (cross markers). For each situation, the quantitative estimations of the model are indicated with solid lines (dotted line and dashed lines).
Expressions for the contributions to the uncertainties in , , and from the detector quantum noise and the phase stepping jitter.
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