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4.1 Introduction The problem of distortion-free imaging of distant objects in a turbulent medium has a long history. However, most of the schemes used for this purpose are based on adaptive methods of compensating for phase distortions that appear as radiation propagates from an object to a registration device. Recently, considerable interest has been drawn to the systems that remove phase distortions with the help of active aperture synthesis. They are based on illuminating the object by means of a transmitting aperture, which consists of transmitters with controlled positions that emit monochromatic or quasi-monochromatic radiation (Fig. 4.1). The transmitters are controlled in such a way that interference of radiation from various pairs of transmitters forms sinusoidal interference fringes with different periods and different orientations on the object surface. Furthermore, the receiving system registers contributions to the scattered radiation from the sinusoidal pattern formed by different fixed pairs of transmitters. In Ref. 56, these are assumed to be proportional to different spatial Fourier components of the object's optical image and different multipliers exp{iψ}, where ψ is the difference between the phase distortions due to the radiation propagation from both transmitters of each pair. After removing the factor exp{iψ} by means of an inverse Fourier transform, the object image is reconstructed. This method is called Fourier telescopy. In Ref. 56, an interesting algorithm is suggested for compensating for phase distortions. It is proposed to place the transmitters so that they form a square equidistant matrix in the transmitting aperture; different pairs of transmitters should be sorted successively in time. In addition, one takes the product of energies registered from neighboring transmitters. In Ref. 57, it is proposed that the number of transmitters is reduced considerably, placing them so that they form orthogonal arrays, their size being comparable with that of the square matrix suggested in Ref. 56. The number of different spatial Fourier components formed this way is the same as in the case of transmitters forming a square matrix. References 60–62 suggest using transmitters radiating at different frequencies and to illuminating an object simultaneously by all the transmitters. In this case, the received signal contains information about instantaneous Fourier components of the optical image and about instantaneous phase distortions.
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