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2 COHERENT SPECTRUM ANALYZER WITH MATRIX DETECTOR Object of study is the process of converting the light field in the coherent optical spectrum analyzers by performing spatial Fourier transform of the test signal. The subject of the study is the generalized characteristics of the coherent spectrum analyzers such as the working range of spatial frequencies, the spatial spectral resolution and the energy resolution, the space-bandwidth product. The purpose of the study is to develop the methods for calculating the generalized characteristics which define the maximum work efficiency of the coherent spectrum analyzers. Research objectives: 1. Consider physical bases of work of the coherent spectrum analyzer. 2. To investigate the physical and mathematical model of the coherent spectrum analyzer. 3. Consider the generalized characteristics of the coherent spectrum analyzers and methods for calculating them taking into account the aberrations of the optical system. 4. Analyze generalized and limiting characteristics of the coherent spectrum analyzers. It was considered the principle of operation of the coherent spectrum analyzers, defined its characteristics and generalized expressions for calculating them. The examples for finding them are given. The possibility of using the diffractive lens as a Fourier lens in the optical system of the coherent spectrum analyzer was discussed. Keywords: the optical information processing, the coherent optical spectrum analyzer, the spectrum analysis, the Fourier lens, the working range of spatial frequencies, the spatial spectral resolution, the energy resolution, the spacebandwidth product.