Generalized Laplace's Operators Realized By Computed-Generated Spatial Filters.
Andrzej Kalestynski · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1988
Generalized Laplace operator is defined as Δr'r" = ∂r'/∂xr' + ∂r"/∂yr", where r', r" are numbers. The operation is realized in coherent optical system by means of spatial filters. The transmittance of the filter T r'r" (u,v) has been computed by the Lohmann method.Plotted drawing after suitable deminishing is inserted in the back focal plane in the imaging system. In the image plane of the system we obtain searched derivative of the input function g. Generally the derivatives could be various in different directions with any order. The images of Δr'R" for r',r" = 1/2, 3/4; 1, 3/2; 4/3, 7/4 are realized.