The use of spatial filtering for optical interpolation between sample values of a function is studied. Onedimensional interpolation between channels of density or area modulated spatial signals is analyzed and the effect of nonzero sample width presented. A new bound is given for the error due to the number of samples being finite. It is shown how exact optical interpolation of periodic functions may be obtained from the samples of only one period by the use of a diffraction grating in the frequency plane. An experiment demonstrates the application of interpolation to processing signals from a simulated sensor array.