Further aliasing-reduced shifted and scaled Fresnel diffraction

Aliasing-reduced shifted and scaled Fresnel diffraction has been proposed to calculate the diffraction between parallel planes with different sampling intervals and an off-axis offset. This method suppresses the aliasing caused by scaling, that is, setting different sampling intervals, but does not suppress the aliasing caused by the shift. We herein propose further aliasing-reduced shifted and scaled Fresnel diffraction, which suppresses the aliasing caused by both scaling and shift. The proposed method is devised on the basis of the sampling theorem and the Fourier shift theorem. Numerical verification and theoretical formulations, which demonstrate the validity of the proposed method, are presented. Numerical verification showed that the increase in computation time was limited to a maximum of 4.7% and the signal-to-noise ratio of the diffraction image was improved by up to 37.4 dB compared to the conventional method.