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Chapter 2:
Modeling an Adaptive Optics System
In Chapter 1, we discussed methods for numerically simulating the propagation of an optical wave through the atmosphere. The approaches considered allow adequate modeling of turbulent distortion and thermal blooming of coherent optical radiation. However, the development of a numerical model for atmospheric distortions of optical waves is not our objective; it is only a tool for studying the efficiency of adaptive correction of distortions introduced by a propagation medium in the operation of optical systems. In the schemes and algorithms of adaptive correction discussed in this book, it was presumed that the optical feedback loop necessarily included three principal elements: a reference wave containing information on inhomogeneities of the refractive index of the medium, a wavefront sensor extracting this information, and a wavefront corrector. In a system operating by the phase conjugation algorithm, the corrector introduces predistortions into the emitted wave, and in the compensation system it corrects aberrations of the radiation received. To study the efficiency of adaptive correction of atmospheric distortions, one should keep in mind the finite spatial and temporal resolution of an adaptive system, i.e., its ability to control the wavefront (or wave phase) to be corrected with a certain speed and in some finite range of spatial scales. The temporal resolution of an adaptive system is determined on the one hand by the correction algorithm and on the other hand by the operating band of the frequencies of the electronic, mechanical, and optical elements of the system. The spatial resolution, in turn, is mostly determined by the geometry of such key elements of the system as the wavefront sensor and the corrector. In this chapter we consider just this aspect of the problem, i.e., development of an efficient numerical model of the sensor and corrector from the viewpoint of making allowance for their geometry, in particular the arrangement and number of elements.
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