Following Welford [3.6], it is sometimes useful to express (3.462) in terms of Cartesian coordinates in the form

i-(2n lofo [W2dxdy

where A is the area of the pupil over which the integrations are taken. This will have to take account of any vignetting in the system disturbing the circular (or annular) form of the pupil.

Bearing in mind the approximation of "small" aberrations involved, we must now consider what values the ratio I(Q)/In can assume. The Rayleigh criterion for resolution [3.131] discussed in ยง 3.10.3 above led to an intensity reduction between the images of a double star of about 20%. If we arbitrarily apply the same reduction to the intensity in the central maximum due to small aberrations, we have

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