Re: Nijboer-Zernike theory

A few comments

"The theory diffraction theory of aberrations" is the name of Nijboer's
thesis and was published in 1942. Frits Zernike was Nijboer's professor. At
that time the Nijboer-Zernike theory could describe the optical point-pread
function of an aberrated lens in a number of specail cases: in best focus,
low numerical aperture and for small aberrations only. The extended
Nijboer-Zernike theory is published in 2002, and in a paper written by
Janssen and a second paper by Braat. These papers, and especially the newer
ones, discuss "the diffraction theory of aberrations" in its most general
sence: full vectorial (for high numerical aperture lenses), through-focus
and for large aberrations. The real nice and new part is that the new theory
allows not only the "forward" calculation , i.e. calculating the
point-spread function given the aberrations, but also the inverse
calculation, i.e. retrieving the aberration coefficients (the so-called
Zernike coefficients) given the through focus points-spread function .

The extended Nijboer-Zernike method was developed to qualify high-end
optical lenses (or mirrors), for example lithographic lenses. It is
therefore an alternative for interferometery and even offers various
advantages over traditionally used phase interferometers.

Finally, lens optimization based on minimizing the wavefront aberration, or
balancing Zernike terms for specific applications is common practice among
various manufactures of lithographic lenses.

regards, Peter

All ENZ-papers can be downloaded from the website:

http://www.nijboerzernike.nl/



"Gransdpa" <j.rayces@xxxxxxxx> schreef in bericht
news:1131072730.722194.100500@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
>
> "Extended Nijboer-Zernike (ENZ) Analysis & Aberration
> Retrieval" is an exceedingly interesting paper by Braat, Dirksen and
> Janssen dealing with the application of Zernike's orthogonal
> polynomials to fields other than interferometry.
>
> In the introduction the authors state the following:"A very
> elegant result provided by the circle polynomials is the automatic
> balancing of aberrations of various orders. This balancing problem, for
> a long time a Holy Grail in optical design and the subject of
> mysterious rules of thumb among the optical designers, was solved in
> one single stroke by the values of the coefficients of various powers
> of the radial coordinate in the polynomials"
>
> This is not new, it is as old as the circle polynomials: yes, 71
> years. Even in 1951 Zernike himself pointed out in the article "The
> Diffraction Theory of Aberrations" (Symposium on Optical Image
> Evaluation, National Bureau of Standards Circular 526) "Or expressed
> in the old way: Each circle polynomial contains next to the highest
> power of r a number of lower powers which balance it in the best way.
> It is worth while to dwell somewhat longer on the question of balancing
> and on the tolerances that result from these calculations"
>
> If these statements are true, can anybody please tell me why lens
> designers are so reluctant to accept a lens design code that optimizes
> strictly on the basis of manipulating the coefficients of Zernike's
> expansion of the wave aberration function?
>


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