## Abstract

We consider reconstruction of a wave field distribution in an input/object plane from
data in an output/diffraction (sensor) plane. We provide digital modeling both for
the forward and backward wave field propagation. A novel algebraic matrix form of the
discrete diffraction transform (DDT) originated in Katkovnik *et al.*
[Appl. Opt. **47**, 3481
(2008)] is proposed for the
forward modeling that is aliasing free and precise for pixelwise invariant object and
sensor plane distributions. This “matrix DDT” is a base for formalization of the
object wave field 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 field
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.

© 2009 Optical Society of America

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