Schematic for the aliasing and frequency matching method. (a) Fourier transform of an ideal grid shadow [ in Eq. (2)]. : spatial frequency variable, : pitch of the grid line, : grid line frequency. (b) Sampling function denoted by a comb function in the frequency domain. [: pitch of the detector pixel, : detector sampling frequency] (c) The Fourier transform of a discretely sampled grid line shadow distribution is represented by a convolution of Fig. 1(a) with Fig. 1(b), which is denoted by in Eq. (4). The aliasing frequency can be observed when the grid line frequency is higher than the Nyquist frequency of the detector. The observable frequency range below the Nyquist frequency is marked as the shaded box. (d) Sampling at the grid line frequency makes the aliasing frequency appears around zero frequency.
Alignment tools used to align the grid and detector. Four micropositioners at each corner of the grid allowing the magnification adjustment of the grid shadow and microstepper driven stages on two axes for the horizontal translation and rotation of the grid.
Moiré pattern frequency as a function of the grid line shadow frequency. The detector sampling frequency is . The solid line indicates the theoretical prediction.
Line profiles of the simulated moiré patterns at different translation distances (sampling period: ; grid line pitch: ; septa width: ): (a) 0, (b) 20, (c) 70, (d) .
Moiré pattern acquired at different rotation angles: (a) , (b) , (c) , (d) .
The rotation angle of the moiré pattern as a function of the grid rotation angle. The solid line indicates the theoretical prediction.
Images obtained using a grid with a grid line frequency of at different gaps between the grid and detector: (a) , (b) , (c) , (d) . The corresponding projected grid line frequencies are specified within the parentheses (detector sampling frequency: ).
Nonuniformity of the images at different frequency differences between the grid line and the detector sampling (detector sampling frequency: ).
Comparison of the signal-to-noise ratios using an aluminium step wedge phantom with and without moiré pattern.
Specification of the carbon-interspaced grids used in the experiments.
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