Turbulence effects on short-exposure imaging through circular and annular apertures
Abstract
Short exposure imaging through optical turbulence is an important problem in terms of characterization of turbulence effects for system engineering purposes. The standard theory of short-exposure imaging through turbulence was developed by D.L. Fried in 1966. Fried developed a theory describing the mean short-exposure modulation transfer function (MTF) due to turbulence. But inconsistencies between Fried's results and experiments have been noted for many years. This dissertation corrects Fried's theory and expands the standard model to include annular (reflector telescope) aperture systems and the means to handle path varying turbulence. The standard theory is updated by retaining a tilt-phase correlation term. Inclusion of this term modifies the computed mid- and high-angular frequency responses of the turbulent MTF. At high frequencies the new theory predicts decay of response instead of the recovery to diffraction limited behavior. At mid-range frequencies, the new model predicts additional spectral energy. To model the new theory a database of 38,007 computed results was analyzed and a model based on three dimensionless parameters has been developed. One of these parameters characterizes turbulence strength; a second characterizes diffraction influences; the third is a dimensionless angular frequency. The new analytic model eliminates the near-field/far-field dichotomy of Fried's standard theory. The resulting model exhibits a 0.000175 RMS accuracy of the combined short-exposure MTF. Extension of the model to the annular aperture case involves an angle-ofarrival analysis for variable central obscuration size, extension of the tilt-phase computation to the annular case, and use of a stochastic least squares analysis technique to adapt the circular aperture model to evolution of the solution in the annular dimension, where the circular aperture case is equivalent to the limiting behavior as the central obscuration goes to zero. Results are obtained up to an obscuration width 95% of the full aperture diameter. The response for annular apertures exhibits an increased turbulence degradation with increasing obscuration size.
- Publication:
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Ph.D. Thesis
- Pub Date:
- 2013
- Bibcode:
- 2013PhDT.......120T
- Keywords:
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- Applied Mathematics;Engineering, Electronics and Electrical;Atmospheric Sciences