Re: [ATM] Fun With Airspace

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

I mentioned that the BaK1/SF2 combination was one of the
better Photopic combinations.  In an earlier note, I
exhibited some solutions where a cemented achromat had
simultaneously zero spherical aberration and coma, albeit
at a non-user-selected wavelength.

Here are two cemented achromats (100 mm f/10), optimized
for Photopic performance:

	http://users.rcn.com/rflrs/d06-14x.len
	http://users.rcn.com/rflrs/d06-15x.len

The first is the N-BaK1/SF2 combination.  The Strehl ratio
runs from 0.661 in the center to 0.558 at the edge of
a 24 mm diameter field.  In that same region, the RMS
spot radius runs from 7.8 to 8.2 microns -- the worst
case spot radius (over the 450 nm to 670 nm band) runs
from 42.9 to 46.1 microns.

The second is the N-BK7/SF2 combination.  The Strehl ratio
runs from 0.654 in the center to 0.554 at the edge.  The
RMS spot radius runs from 8.0 to 8.4 microns -- the worst
case spot radius runs from 42.5 to 45.5.

Thus, except for the worst case spot size (hardly a great
performance measure) the N-BaK1/SF2 combination beats the
N-BK7/SF2.

Is there a simple reason for this?  Looking at the Seidel
aberrations, the N-BaK1/SF2 pair has a zero Spherical
aberration coefficient at about 635 nm and a zero Coma
aberration coefficient at about 620 nm.  The end-to-end
(i.e. from 450 to 670 nm) range of each is 0.00253 and
0.00009, respectively.  The Astigmatism coefficient is
0.00036.

The N-BK7/SF2 pair has a zero Spherical aberration coefficient
at about 560 nm and a zero Coma aberration coefficient at
about 500 nm.  The end-to-end range of each is 0.00210 and
0.00009, respectively.  The Astigmatism coefficient is
0.00036.

Thus, in third order Seidel coefficients, the N-BK7/SF2
combination beats the N-BaK1/SF2 combination by 15 percent
or so in Spherical aberration, but the two are roughly equal
in Coma and Astigmatism.  The perfomance difference does not
appear to be the result of a third order difference.

The minimum focus of the N-BaK1/SF2 combination is at 525.0
nm, while the minimum focus of the N-BK7/SF2 combination is
at 528.4 nm.  Not too much difference... but looking at
the N-FK5/F2 combination:

	http://users.rcn.com/rflrs/d06-16x.len

that has a minimum focus at 529.0 nm and beats even the
N-BaK1/SF2 combination, so it cannot be the location of
the minimum focus that matters.

There is a difference, however, in the secondary spectrum.
The maximal focal difference over the 450 to 670 nm range
for the N-BaK1/SF2 combination is 1087.3 microns, while
that for the N-BK7/SF2 combination is 1152.3 microns.  The
corresponding values for the F-C band are 937.1 and 950.5
microns, respectively.  Also, the performance difference
is consistent with the N-FK5/F2 combination which has
values of 1060.9 and 899.9 microns.

It might appear, then, that the primary performance
difference in these glass combinations is the residual
secondary spectrum...


(The N-FK5/F2 combination has a Strehl ratio that runs
from 0.696 to 0.589.  The RMS spot radius runs from 7.2 to
7.7 microns and the worst case spot radius runs from 38.3 to
41.3 microns [just in case you're still reading to this
point].)

-- 

Rick S.

http://users.rcn.com/rflrs


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