The resolution of images formed from turbulence-degraded lensless Fourier-transform holograms is analyzed for gaussian and exponential refractive-index structure function models, first by a geometrical-optics method and then by Schmeltzer’s series-expansion method, under the assumption that the random logamplitude and phase perturbations across the entrance pupil of the recording apparatus are locally stationary processes with gaussian statistics. Both long and short exposures are treated.
The resolution of turbulence-degraded holographic images is governed primarily by a function m2(r1), for which analytical expressions are derived and results of experimental measurements are given. The analytical results obtained for m2(r1) by the geometrical-optics method are identical with those obtained by Schmeltzer’s series-expansion method. The measurements were made by an interferometric technique for horizontal atmospheric propagation paths of 86 and 542 m. In addition, holographic images of an extended object were obtained for the 86-m path.
JACK D. GASKILL, "Atmospheric Degradation of Holographic Images," J. Opt. Soc. Am. 59, 308-318 (1969)