Correlation restoration of images by nonlinear superimposed Fourier holograms

The responses of sub-holograms self-formed as part of a multiplex hologram when recording superimposed holograms forming it in a 4$f$ Fourier holography scheme with angular multiplexing of plane reference waves on a recording medium with quadratic nonlinearity of the exposure characteristic are considered. The sub-holograms implement a model of correlation restoration of the images described by the complex-valued amplitudes – hetero-associative memory. The model can be related to the concept of Ghost Imaging: the response of each sub-hologram is described by convolution of the reference image used to record a superimposed hologram with the function of correlation of the input field with the reference image of another superimposed hologram. The inversion by the sub-holograms of the specific weights of the reference images in the responses relative to their ratio when recording the superimposed holograms is shown. An analysis of the correlation mechanism of amplification in the response of the amplitude of the restored reference image under its size decreasing in relative to the constant size of another reference image is given. The theoretical conclusions are confirmed by numerical simulation.