Coherence Theory And Caustic Corrections

Mark J. Beran

doi:10.1117/12.934070

7 December 1982 Coherence Theory And Caustic Corrections

Mark J. Beran

Proceedings Volume 0358, Applications of Mathematics in Modern Optics; (1982) https://doi.org/10.1117/12.934070
Event: 26th Annual Technical Symposium, 1982, San Diego, United States

Abstract

Recent studies in underwater acoustics have shown how coherence theory may be used to determine the correct intensity distribution in the neighborhood of caustics. These studies may be of interest to the optics community and we review here the method developed. We begin with the basic equation governing the coherence function in the parabolic approximation. The radiation propagates in a medium with a variable mean index of refraction. A lowest order approximation to the basic equation yields the geometric optics solution. To next order we use a two-scale expansion to include the correction term to the geometric optics calculation. This gives the correct intensity distribution in the neighborhood of caustics and it is shown that in the limit of a point source the results reduce to those obtained previously. The results of a numerical example are given. Finally it is pointed out that if there is volume scattering, resulting from a stochastic variation in the index of refraction field, the method may be extended to determine the intensity corrections near a caustic due to this effect.

Citation Download Citation

Mark J. Beran "Coherence Theory And Caustic Corrections", Proc. SPIE 0358, Applications of Mathematics in Modern Optics, (7 December 1982); https://doi.org/10.1117/12.934070

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