Derzhypolskyi A. Correlation transformations of optical fields and information processing in self-associative Fourier-holography scheme.

The thesis is dedicated to the study of correlation transformations of light fields in original Fourier-holography scheme. The named transformations yield a holographic data processing, holographic formation and stabilization of images, etc.. First, the basic principles of Fourier-holography are analyzed to build a generalized description of a holography scheme with arbitrary signal, reference and restoring beams as well as reconstruction in every possible order of diffraction. Based on such generalized model formulated is the original self-associative Fourier-holography scheme with identical signal and reference beams. A fundamental feature of the scheme is an associative reconstruction of recorded information. Detailed investigation of operation of the scheme gives an explanation and description of its key characteristics as associative memory system. These are: the dependance of the structure of associatively restored image on the parameters of fine adjustment of the scheme, and the dependance of quality of reconstructed image on the size of reconstructing part. In further study developed and investigated is the concept of optical encryption based on the self-associative scheme. As shown in the work, the concept has several important advantages as compared to known analogues. Namely: arbitrary choice of encryption/decryption key, redundancy of the key, tunable mode of highlighting of the key, possibility of flexible associative search in encrypted library. Transfer of the encryption scheme into virtual optics domain reveals a possibility to change the transformational kernel of encryption from Fourier transform to Walsh-Hadamard transform. Such a substitution significantly improves the operation of the scheme with digital data. Another appearance of correlation transformations in self-associative scheme may be effectively used for formation of required spatial intensity distribution of light on technological target and its stabilization against different aberrations in the system. The approach offered in the work minimizes the distortion of the structure of formed image caused by aberrations in forming laser beam. Revealed is that the key stabilizing role plays a random phase modulator used when creating (recording or synthesizing) a hologram. However, the use of random phase diffuser results in unwanted speckle noise in formed image. The solution to speckle problem is offered and tested in the work by means of incoherent averaging.