Fig. 3.16. Third order coma as wavefront aberration to Table 3.26 reveals that the Rayleigh criterion for the wavefront aberration in the case of coma is only a crude approximation to the true physical effect, although the optimum tilt factor of 3 is exactly reproduced.

Since the tangential section of the optical imagery (the plane of the paper) has the aperture azimuth angles 0 and n, the full wavefront aberration as shown in Fig. 3.16 is, from (3.191)

It can be shown that

Fig. 3.17. Third order coma: lateral aberration form

The ray path for coma is shown in Fig. 3.17. The principal ray E'l, pr emerging from the centre of the exit pupil cuts the image plane at I . The marginal rays intersect at the point IM, either above or below I , depending on the sign of the coma. The upper ray has 0 = 0, the lower ray 0 = n. The Nijboer equations lead to the following ray coordinates in the image plane, referred to I , rf being in the tangential section, rfs in the sagittal section:

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