Memory efficient Fresnel diffraction from an interpolated wavefront to a limited ROI using matrix multiplication

The spatial frequency considered in the Fresnel diffraction is determined by the number of pixels in the wavefront. When we compute with more spatial frequency band, interpolation of the wavefront is required. Furthermore, though only a limited region of the propagated wavefront is required, the conventional methods must always compute the entire region. Their computational efficiency decreases to compute with higher spatial frequency for the limited region of interest. This study proposes a diffraction computation using compositon matrix multiplications. It can compute of only the region of interest with practically no errors, thereby reducing both computational load and memory usage. In particular, in cases with high interpolation ratios, we achieved a computational speedup of approximately 4.4 times compared to the conventional method.