[ATM] Re: Focal plane curvature

[Vladimir Sacek <vladis.2@juno.com>]

Bob,

>Generally tho, the focus error needs to be corrected and this will
send off the color error which means that you need to do some other
changes
to get that error out of the design.<

That's right, chromatism correction comes first, and field curvature is
more or less accepted as it comes after that (photographic objectives can
and do attempt to optimize it by introducing negative astigmatism). I
went through the aberration coefficients given in Mahajan's book
(Aberration theory made easy), and it nicely reduces for a contact
doublet to the sagittal curvature 1/Rs=[(n1+1)/n1f1]+[(n2+1)/n2f2], and
tangential curvature 1/Rt=[(2n1+1)/n1f1]+[(2n2+1)/n2f2] with the best
astigmatic surface (median) curvature being 1/Rm=1/2Rs+1/2Rt, and the
relation to the Petzval curvature 
3/Rs-1/Rt=2/Rp (n1 and n2 are the refractive indici, and f1 and f2 focal
lengths of the front and rear lens, respectively).

For some reason, results (compared for the median curvature) don't
necessarily agree with ray tracing. It seems to be pretty close for
strongly curved objectives, while giving somewhat lower than actual
curvature for those with relatively mild curves. It is no good for
cemented objectives, which have stronger field curvature. Surprisingly,
the 1/3 f.l. approximation seems to be nearly as good, on average.

Vlad

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