On the difference between single- and double-sided bandpass filtering of spatial frequencies

It is well-known that bandpass filtering will lead to edge extraction in image processing. However, the difference between single- and double-sided bandpass filtering has never been compared and investigated in the literature. We investigate the difference between single- and double-sided bandpass spatial filtering in a 4-f coherent optical image processing system. We find that single-sided filtering can approximate the operation of a first-order derivative, while double-sided filtering gives a second-order derivative. Simulations and optical experiments confirm our findings.