Diffraction and Interference of Partially Coherent Light Traversing Two Superposed Sound Fields

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Abstract
The diffraction and interference of a light wave passing through two superposed sound waves have been studied theoretically on the basis of Huygens' principle. As a result of frequency shifts in every deflected light ray caused by the sound waves, the instantaneous intensity resulting from linear superposition of the deflected light rays consists of the d.c. component as well as the a.c. component as a sum of beating signals among those rays, provided that the coherence time of the light is long enough compared with the period of a beating signal under consideration. A general formula for diffraction is derived and two-beam interference is considered as a special case. The resultant formula illustrates that the complex degree of coherence is modulated, after traversing the sound field, with a form of the Bessel function of zeroth-order which varies with Raman-Nath parameters as well as with the separation of two points on the wavefront of the light. This validity will hold so long as the inclination factors for the deflected light rays in Huygens' principle are regarded to be nearly equivalent. The results for progressive and standing sound waves are described as special cases.

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