Vol. 5, issue 03, article # 7

Abstract:

Algorithms for reconstructing the wave front and for compensating the phase distortions of the radiation field by means of a phase conjugate adaptive optical system which account for the measurement noise and errors in control with a phase corrector are developed in the framework of the statistical approach on the basis of the methods of calculus of variations and matrices. The phase distributions being reconstructed and compensated are calculated using the a priory information about the statistical characteristics of the wave front being measured, measurement noise, and errors of control. Equations have been obtained and studied for the Karhunen-Loeve orthogonal modes which guarantee the least error in compensating the phase distortions of the radiation field for the fixed number of modes realized by the phase corrector with the prescribed response functions without errors in their approximation. Results of calculations of the errors of reconstruction and compensation for the number of the measuring channels of a Hartmann sensor and of the actuators being equal to 3, 7, and 19 are given and discussed depending on the intensity of measurement noise and errors of control.