The sagittal coma, Comas, is the diameter of the circle corresponding to ym, giving
As angular aberration, by the same conversion as for spherical aberration, we have
(Su'Jcoma* = -3 ^t-(206 265) = -3(Wi)gF (206 265) arcsec p 1 2 n'yi n'y1
(SuL)comas = -SlL (206 265) = -2(Wi/)gF (206 265) arcsec p s n'yi ' n'yi
if the parameter upr1, in the expression for Sii (Tables 3.4 and 3.5), defining the field, is measured in radians.
It should be noted that (Wii)gf, the full peak-to-peak wavefront aberration, is twice the wavefront aberration coefficient (Wji)gf of Eq. (3.191). This factor of 2 exists for all aberrations dependent on cosn ^>(= cos n^>), i.e. all aberrations except the axisymmetric ones with n = 0 in Table 3.1. For most technical purposes, the wavefront coefficient (Wji)gf is the more basic quantity, so it is used in the above relations.
The coma patch, as defined above, contains 100% of the geometrical energy. The 60° triangle enclosing the circles gives the characteristic asymmetric "flare" (Greek "coma" = hair) which makes coma the most damaging of the monochromatic aberrations. The best way to identify the direction (sign) is to remember that a Newton or Cassegrain telescope gives Sii negative from Table 3.3 and has "inward" coma, i.e. the point of the coma patch corresponding to the principal ray is pointing towards the field centre, the flare away from it.
Let us consider, as an example, the coma coefficients for a 1-mirror telescope or a classical 2-mirror telescope from Tables 3.4 and 3.5 respectively, for which the normalized coefficient with spr1 = 0 is simply -f . Then we have from (3.198)
(Su'p)Comat = 3 ^f7^ Upr1 arcsec = 16 ^N2) Upr1 arcsec , (3.199) where upr1 is expressed in arcsec and N is the f/no
3.3.3 Astigmatism (Shi) and field curvature (SIV)
The third term of (3.21) gives the combined effect of astigmatism and field curvature at the Gaussian focus:
The factor (y/ym)2 implies that astigmatism is essentially a defocus effect in the aperture, but the effect is dependent on the section in the pupil because of the cos2 ^ and sin2 ^ terms. As before, we can ignore the field dependent factor (n'/^m)2 since we are only concerned with aperture effects for a given field position. Eq. (3.200) transforms to
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