Backward discrete waveeld propagation modeling as an inverse problem: toward perfect reconstruction of waveeld distributions

1 We consider reconstruction of a wave…eld distribution in an input/object plane from data in an output/di¤raction (sensor) plane. A contribution of this paper concerns both a digital modelling for the forward and backward wave…eld propagation. A novel algebraic matrix form of the discrete di¤raction transform (DDT) originated in [1] is proposed for the forward modelling which is aliasing free and precise for pixel-wise invariant object and sensor plane distributions. This "matrix DDT " is a base for formalization of the object wave…eld reconstruction (backward propagation) as an inverse problem. The transfer matrices of the matrix DDT are used for calculations as well as for the analysis of conditions when the perfect reconstruction of the object wave…eld distribution is possible. We show by simulation that the developed inverse propagation algorithm demonstrates an improved accuracy as compared with the standard convolutional and discrete Fresnel transform algorithms.