Analytic improvements to the atmospheric turbulence optical transfer function

David H. Tofsted

doi:10.1117/12.488594

5 September 2003 Analytic improvements to the atmospheric turbulence optical transfer function

David H. Tofsted

Proceedings Volume 5075, Targets and Backgrounds IX: Characterization and Representation; (2003) https://doi.org/10.1117/12.488594
Event: AeroSense 2003, 2003, Orlando, Florida, United States

Abstract

The standard method used for modeling optical turbulence effects on imaging uses an optical transfer function (OTF). To model this function the short- and long-exposure limiting cases exist. The short-exposure case is handled by modifying the long-exposure case to remove wavefront tilt assessed at the sensor entrance pupil. Then, depending on whether one is in the "near-field" or the "far-field," one of two subcases is used. These evaluations require a model of the refractive index spectrum. Typically this model is assumed to be the Kolmogorov spectrum where an inner scale is set to zero and outer scale is infinite. However, for real atmospheres the inner and outer scales affect turbulence predictions through a modified spectrum. The difficulty using non-limiting values for these parameters is that double integrals must then be assessed. However, in this paper analytic forms are developed to describe the spectrum, permitting analytic solutions to these integrals. The result is that we can express quantities such as the Fried coherence diameter in closed form accounting for both inner and outer scale effects. Also, expressions for the inner and outer scales of turbulence can be written as functions of the atmospheric surface layer stability. Lastly, it is shown that the near/far-field effect does not easily subdivide into two cases. In fact, the distance dependence of the tilt effect is shown to span a range of 107 in the governing dimensionless parameter. To model this continuum a unified treatment is considered.

Citation Download Citation

David H. Tofsted "Analytic improvements to the atmospheric turbulence optical transfer function", Proc. SPIE 5075, Targets and Backgrounds IX: Characterization and Representation, (5 September 2003); https://doi.org/10.1117/12.488594

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