Re: spherical aberration as a function of conjugate


<david_a119@xxxxxxxxx> wrote in message
news:1145415258.672439.265560@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


Suppose I have a really good camera lens or microscope objective that
gives diffraction-limited performance if I use it at the conjugate
ratio that it's designed for. If I know the prescription for the lens,
I can use Zemax or Oslo to calculate the amount of spherical aberration
that I'll get if I use the lens at some other conjugate ratio. But
there's no way I can get the prescription from Nikon or Zeiss. If one
doesn't know the prescription, to calculate spherical aberration as a
function of conjugate ratio one needs to know whether the lens
satisfies Abbe's sine condition, Herschel's sine condition, Helmholtz's
tangent condition, or some other condition. (I personally can't
calculate spherical aberration even if I do know the equations of the
principal surfaces, but I know that some people can.)

snip

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Under certain assumptions you can get a pretty good idea about
what's going on if you know the third order aberrations for a set
of conjugates.

Example:

An ideal perfectly corrected microscope objective
(for a set of conjugates) will exhibit aberrations
if you depart from the optimal situation.

In this particular instance spherical aberration and
coma will appear.

spherical aberration coeff:

DELTA sph = -(((NA)^4)/(8*M^2))*dx'

where

DELTA sph is the max. wavefront aberration
NA is the numerical aberration
M is the magnification
dx' is the image plane displacement

For the coma the corresponding formula is:

DELTA coma = (((NA)^3)/(2*M^3))*(theta)*dx'

where theta is the field angle in image space.

Depending upon what you can tolerate in terms
of image degradation you can determine the
departure from the prescribed conditions etc.

The derivation of the above formulas is not
too difficult but this entails a good knowledge
of aberration theory, something that no lens
design program *by itself* will impart you.

Again the above formulas are limited to the third
order






.

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