B2 The Fraunhofer and Fresnel Approximations

We can simplify Eq. B.l by noticing some symmetries and by casting the problem in another coordinate system. First, we place the source at a distant on-axis location so that s is a very large constant. Then we can pull the eiks /s wave function constant out of the integral and bury it in the normalization constant. Because we are using a focusing lens or mirror, we pretend the receiver point is also very distant by "unbending" the wave-front (Born and Wolf 1980, pp. 382386). In the Fraunhofer approximation (which is what this unbending is called), the important quantities are no longer the distances but the off-axis angles from the center of the aperture to the distant sensor.

This approximation is written as (Hecht 1987, p. 494)

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