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Chapter 10:
Propagation Through Complex Paraxial ABCD Optical Systems
Overview: The purpose of this chapter is to introduce the basic characteristics of a Gaussian-beam wave propagating through an optical system composed of one or more optical elements aligned on the optical axis between the input and output planes in the presence of atmospheric turbulence. This technique, which once again utilizes the paraxial approximation, is based on a scheme of representing optical elements by the 2 x— 2 ABCD ray matrices that were introduced in Chap. 4 for free-space propagation. We consider cases in which atmospheric effects exist along the entire propagation path, or are confined to only a portion of the path between input and output planes. Building off the development in Chap. 4 and its extension in Chap. 5 to include atmospheric effects, we specialize expressions for the second-order statistical moments E 2 (r 1 ,r 2 ) and E 3 (r 1 ,r 2 ) primarily for the case of a single optical element that we model as a "€œGaussian lens,"€ viz., a combination of a thinlens and finite aperture stop known also as a "€œsoft lens."€ Optical receiver systems which use a large collecting lens to focus the light onto a photodetector to reduce scintillation (i.e., to induce aperture averaging) represent one area of application where the ABCD technique has proven to be quite effective. In particular, we derive expressions for the irradiance flux variance in the plane of the photodetector for several cases of interest, including that of a Gaussian-beam wave. We take into account both inner scale and outer scale effects through use of the modified atmospheric spectrum and we use the method of Chap. 9 to extend results into the moderate-to-strong fluctuation regimes.
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