[ATM] Spot Symmetry

["Richard F.L.R. Snashall" <rflrs@rcn.com>]

Here is Double Gauss variant that uses two pair of doublets (75 mm f^2/8):

    http://users.rcn.com/rflrs/dgauss02-40x.atm   ATMOS input file
    http://users.rcn.com/rflrs/dgauss02-40x.len   OSLO input file
    http://users.rcn.com/rflrs/dgauss02-40x.txt   TEXT prescription
    http://users.rcn.com/rflrs/dgauss02-40x.zmx   ZEMAX input file

For those who don't like my humor (many of you, I think), f^2/8 is
about f/2.8.  The field here is weird too, being 32/pi square
degrees; again, for those with humor restrictions, that's about
+/-5.7 degrees -- just over a +/-21 mm flat field, just about right
for 35 mm imaging.

For those with the free versions of these, note that these might
not be displayable with the number of surfaces needed.

In both ATMOS and OSLO, I stipulated the lens diameter by actually
specifying the clear aperture specification; in OSLO, I forced the
diameter to be checked (it is more or less automatic in ATMOS).  A
suggested diameter, as well as the clear aperture, are given in the
text prescription and ZEMAX input files.

Technically, this is an achromat (slightly over-corrected), in that
the secondary spectrum is, for the most part, parabolic.  However,
the correction is about 1 part in 1240, over the i-t band.

I use vignetting (about 5% at the edge of the field, but starting
just outside the 60% field point) to reduce the spot size.  That's
the reason for the mad specification of each clear aperture.  Both
the average and peak spot size, for a strongly UV weighted spectrum,
are largest at both the image center and edge (and roughly equal),
but smaller at the 70% field -- consistent with putting the flat
field at the mid-point of a curved field.  The actual Petzval radius,
though, is over 3 meters.

Here's what I'm asking about.  While there are other designs with
better RMS wavefront error and secondary color, this design seems
to have the best symmetry in the spot diagram over both field and
wavelength.  I do not have a concrete algorithm for achieving this,
nor even defining it, yet.  I saved off an OSLO spot diagram as
a compressed bit-map file:

    http://users.rcn.com/rflrs/dgauss02-40x.rle

Although it is just a sample spectrum weighting, this spot diagram
may give an idea of the symmetry to which I am referring.  What say
you?  How would you set define and set up as an optimization goal
such a concept?
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