Expressions are derived for the dependence of the modulation transfer function (MTF) and the phase structure function (D sub phi) on the Kolmogorov turbulence parameters. In particular, it is demonstrated that certain measurements of the MTF and D sub phi can be interpreted in terms of an outer scale of turbulence being of the order 10-50 cm, values which typically can be expected under inversion conditions. (Author).

An analysis of experimentally observed far-field irradiance statistics, suggesting an approach to calculating the probability distribution for intensity fluctuations of an optical wave in a turbulent medium and expressions for measuring important wave characteristics. Two theoretical treatments of probability distribution are investigated. Because none of the proposed theories can account for irradiance statistics in a consistent manner, it is suggested that a modified geometric optics approach would lead to an improved quantitative understanding of the phenomena. Expressions are derived for measuring wave phase structure function and modulation transfer function. Results are useful in determining the limited resolution obtainable in forming an image through a turbulent medium, as well as in calculating the signal-to-noise ratio of an optical heterodyne detection system. (Author).

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This tutorial introduces the theory and applications of MTF, used to specify the image quality achieved by an imaging system. It covers basic linear systems theory and the relationship between impulse response, resolution, MTF, OTF, PTF, and CTF. Practical measurement and testing issues are discussed.

The pertinent theoretical background and the results of a group of experiments conducted over 0.4- and 1.17-km near-ground horizontal ranges are presented. (1) The log-amplitude variances for HeNe (0.633 μm) and CO2 (10.6 μm) laser beams were found to have a ratio of 26.8, which is in close agreement with the predictions of Rytov-based spherical-wave theory. (2) Published measurements of the saturation level of the log-amplitude variance are reviewed and several inconsistencies noted. (3) The spatial correlation function of irradiance field was measured and found to agree with theory. The degree of correlation between different frequency beams which had traversed the same optical path was also measured and compared to theory. The data exhibited an unacceptably large scatter and did not show the wavelength dependence. (4) The log-normal, Rayleigh, and Rice probability distributions are discussed in terms of their applicability to irradiance statistics. Relatively weak 10.6 μm irradiance fluctuations were found to be equally well described by the log-normal and Rice distributions; strong fluctuations obtained at 0.488 μm were clearly best described by the log-normal distribution.