Re: [ATM] OSLO ASPHERIC FORMULA

["vladimir sacek" <vla@toast.net>]

Keep in mind that the raytrace optimum (0.866 neutral zone) 
is not the best focus location. A camera doesn't image the 
raytracing blur - it images intensity distribution, and it has the 
tightest concentration at the location of the best focus (0.707 
neutral zone). Doesn't hurt that the 0.707 neutral zone 
corrector is shallower by a factor of 2.25 too.

Spherochromatism of the Schmidt corrector is actually 
simple to express. The neutral zone is a zone of zero 
refraction for all wavelengths. Thus, they all meet at the 
mirror focal point for that zone. The difference is that only 
one wavelength can be optimized for zero spherical 
aberration. For other, aberrated wavelengths, what determines 
best focus location is the peak diffraction intensity, not the blur 
size. For the longitudinal spherical aberration "z" normalized 
to 2 (z=0 for the paraxial focus location and z=2 for the 
marginal, regardless of the sign of aberration), the RMS 
wavefront error varies with the factor 
s=sq.rt.[1+0.9375z(z-2)]. It gives the minimum error for 
z=1 (which is the 0.707 zone focus), smaller by a factor of 
two+ from the error at the circle of least confusion 
(0.866 zone focus), and four times smaller than error at 
either paraxial or marginal focus.

There is no reason whatsoever to favor 0.866 neutral zone 
location - or any other - over the 0.707 zone position. The 
best possible outcome is to have best diffraction foci of 
aberrated wavelengths coinciding with the optimized 
wavelength focus. The wavefront error difference for 
non-optimized wavelengths between 0.707 and 0.866 
neutral zone corrector may and may not be significant, 
but why choose a harder to make corrector version, 
that is also optically inferior?

Btw, the wavefront error of non-optimized wavelengths for 
the standard Schmidt corrector (spherical primary) is given 
as a p-v error of spherical aberration in units of the wavelength 
(Lambda) by W=dsD/512(n-1)LambdaF^3, with "d" being the 
index differential vs. optimized wavelength, "s" the above 
error factor for the spherical aberration defocus with z=2N^2, 
"N" being the neutral zone position (0 to 1), D the aperture 
diameter and F=f.l./D. For the Wright version, it will be greater 
by a factor (1+K), "K" being the mirror conic.

Vlad
_______________________________________________
ATM mailing list http://www.atmlist.net/