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In this chapter we consider several problems for adaptive imaging in a turbulent atmosphere. It is well known that the angular resolution of diffraction-limited optical systems is determined by the ratio of the working wavelength λ to the diameter of the entrance pupil D [1]. When the image of an extraterrestrial object is formed, the resolution is determined by the ratio of the wavelength to the coherence length r0 [2, 3], whose value in turn is determined by the integral structure characteristic of atmospheric turbulence C 2 n . At the places where astronomical observatories are located, the typical value of r0 is roughly 10–20 cm for the visible spectral region. Up-to-date astronomical instruments include a primary mirror from 2 to 10 m in size. Their actual angular atmospheric resolution, which is on the order of 1 arcsec, proves to be D∕r 0 ~10–100 times worse than the diffraction limit and is mostly independent of the aperture diameter and the wavelength. The aim of an adaptive optics system is to suppress atmospheric blurring of an image and provide for the angular resolution close to the diffraction limit. The typical structure of an adaptive telescope is shown in the schematic below. A wavefront distorted by turbulent inhomogeneities is reflected from the primary and secondary mirrors and arrives at the wavefront corrector. Some of the energy of the corrected radiation is directed to the image recording system and the rest goes to the wavefront sensor, which measures residual aberrations and generates the corrector control signals.
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