Fourier-transform division filters are discussed. Using integrated squared error as a fidelity criterion with the magnitude of the filter transfer function subject to a constraint, the optimum spatial filter is developed. By consideration of the problem of image transformation, various methods for improving image reconstruction by altering image phase are discussed. The input-image phase and the desired output-image phase may be chosen to improve the performance of the filtering system. The problem is to shape the spectra of the input and the desired output. An algorithm, previously used for computing kinoforms, effectively determines an image phase that significantly improves the image reconstructed from the spatial filters.
B. Liu and N. C. Gallagher, "Optimum Fourier-transform division filters with magnitude constraint," J. Opt. Soc. Am. 64, 1227-1236 (1974)