Abstract

When light is reflected or refracted at a moving Gaussian surface, the observer sees a number of moving images of the source, which appear or disappear generally in pairs; such an event is called a “twinkle.” In the present paper the number of twinkles per unit time is evaluated in terms of the frequency spectrum of the surface and the distance of the source O and observer Q, on the assumption that the surface is Gaussian and that OQ is perpendicular to the mean surface level.

A solution is found first for a single system of long-crested (or two-dimensional) waves, and then extended to the case of two such systems intersecting at right angles.

The rate of twinkling is found to depend, apart from a scale factor, on two parameters of the surface, one of which, α, increases steadily with the distance of O or Q from the surface; the other, d, discriminates between waves of standing type and waves of progressive type. Over a considerable range of α, the rate of twinkling is almost independent of d, but for large values of α the rate is much greater for standing waves than for progressive waves; waves of intermediate type are included in the analysis.

© 1960 Optical Society of America

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