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Summary

This is a plot showing the fraction of light (normalized to the of the incident light) scattered by a (transparent) phase edge. The calculation is from the classical diffraction theory, and is given by s = 0.5 - 0.5 * cos(angle), where angle is the phase shift of the edge in radians. The calculation result is given as a percentage. Even for a gradual phase transition, as long as the illumination field extends much wider than the transition region, the result is still a very good estimate.

Derivation of result

The unscattered field amplitude (per unit area) is given in the classical diffraction theory by 0.5 + (0.5 exp[i*angle]). The 0.5 factor comes from the division of the scattering surface by the phase edge into one half that acts as a reference (first term), and a second half on the other side of the edge that represents the phase shift (second term in parenthesis). This is a complex number, whose magnitude squared corresponds to the unscattered light intensity. The result of this squaring of the magnitude is 0.5 + 0.5 * cos(angle). To obtain the scattered light intensity we subtract the unscattered intensity from the incident light intensity, which is normalized to unity. This leaves us with the result 0.5 - 0.5 * cos(angle).

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