Virginia TechChatterjee, M. R.Quinn, L. H.Banerjee, P. P.Poon, Ting-Chung2014-04-042014-04-041989-04-01Monish R. Chatterjee, Lauren H. Quinn, Partha P. Banerjee, and Ting-Chung Poon, "Rayleigh-Ritz optimization of the structure function for a Kolmogorov power density and an approximate analytical solution for the two-point electric field correlation function," Appl. Opt. 28, 1773-1777 (1989). doi: 10.1364/AO.28.0017730740-3224http://hdl.handle.net/10919/46956Beginning with the exact Kolmogorov power spectrum for an extended random medium (such as interstellar space), the structure function is first expressed as an inverse Fourier-Bessel transform. An approximate series representation involving fractional powers of the transverse coordinate is then optimized by an equivalent Gaussian expansion up to two terms using the Rayleigh-Ritz technique. The domains of validity as well as the coherence profile of the resulting analytical solution of the two-point electric field correlation function are examined. It is shown that the correlation in both the transverse and longitudinal directions persists over distances up to a few orders of magnitude greater than that for a medium described by a Gaussian structure function.application/pdfenIn CopyrightArticle - Refereedhttp://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-28-10-1773https://doi.org/10.1364/AO.28.001773