Computational inverse coherent wave field imaging

We consider reconstruction of a wave field distribution in an input/object plane from data in an output/diffraction (sensor) plane. For the forward propagation of the wave field the matrix form of the discrete diffraction transform (DDT) originated in and is used. This ¿matrix DDT¿ is aliasing free and precise for pixel-wise invariant object and sensor plane distributions. A contribution of this paper concerns a study of the backward wave field propagation as an inverse problem for the diffraction kernel. The analysis of the conditioning of the transfer DDT matrices is presented in order to find when the perfect reconstruction of the object wavefield distribution is possible. This condition number can be used as an indicator of the accuracy of the wave field reconstruction. Simulation experiments show that the developed inverse propagation algorithm demonstrates an improved accuracy as compared with the standard convolutional and discrete Fresnel transform algorithms.