Re: Incorrect Seidel aberration calculations in lens design codes

Helpful person wrote:
On Feb 22, 2:21 pm, Al Greynolds <awgreyno...@xxxxxxxxxxxxx> wrote:

Yes, the Seidels are a 4th order approximation to the wavefront
aberrations but should include ALL effects up to that order. The
contribution from the 2nd order term can be substantial when it nearly
cancels the curvature coefficent leading to a surface that is flat on
axis but with higher-order wiggle. In fact corrector plates in
Schmidt (or Wright or ...) telescopes can be modelled very accurately
by a conic surface with just an additional 2nd order term instead of
the usual much higher order expansion. For a discussion of this see:

http://www.breault.com/resources/kbasePDF/wp_osa_001_superconic_and.pdf

Al

We must agree to differ. Using Seidels for higher order correction
seems to me to be a strange method. For series expansion of
aberration coefficients I would expect better results using Buchdal's
methods.

www.richardfisher.com


One of the nice things about Seidels is that (unlike Zernikes[*]) they're pretty well independent of things like vignetting. No real lens designer is going to lens design analytically at this point--the necessary approximations too sloppy to make all that algebra worthwhile--but that isn't true of us optical instrument folks.

We use off-the-shelf lenses, leaving the high-aperture, high-NA stuff to the real lens designers, but then we do all kinds of unnatural things such as image through flow-cell windows or put acousto-optic cells in converging beams. At low NA, aberrations up to fourth order aren't terribly hard to calculate approximately, and they make it pretty easy to figure out what to change to fix the problem.

Cheers,

Phil Hobbs

[*] Zernike polynomials are orthogonal only on perfectly circular pupils, and the expansion isn't that well conditioned, so a small amount of vignetting will cause largish changes in all the Zernike coefficients down to the lowest orders. Zernikes also ignore amplitude and polarization, which are (*ahem*) sort of important in real life, and high-order Zernikes include high spatial frequency components that suffer from obliquity rolloff and eventually become evanescent. So the apparent rigour of using a complete orthonormal expansion is mostly illusory.
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Relevant Pages

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