[Author Prev][Author Next][Thread Prev][Thread Next][Author Index][Thread Index]
Re: [ATM] Doublets (was: Wide band refractor)
[Steve -- I hope you don't mind if I take this question back on-line.]
steve beccue wrote:
> I am just finishing a 8" f/14 achromat from Newport Glass.
> It is an old, and low performance design. Have you found
> better designs using their glass. Equivalently, have you
> found good designs using any comparable cost glass (e.g.
> about $350 for 8" aperature). I'd be very interested to
> know what one can do on a minimal budget.
BK7 and F4 are about as inexpensive as you can get.
The Newport web site provides an effective focal length of 112.74
inches for the 8 inch scope (f/14.0925) and a thickness of 1.28
inches; to match that thickness, I have arbitrarily selected
thicknesses of 0.72 and 0.56 inches for the two lenses. I also
assumed that the value of 112.74 given was not simultaneously the
BFL and EFL, but just the EFL, due to its match to the published
value of f/14.1.
However, to answer your question more completely, I did a little
more grubbing. In ATM 2, chapter A.6, the Wyld article provides
two prescriptions (from Dimitroff and Baker) using a crown glass
with index 1.517 and Abbe number 64.5 and a flint glass with index
1.617 and Abbe number 36.6.
Looking at Bob May's website, I found a Bausch and Lomb catalog
listing for a Borosilicate Crown 517645 and a Dense Flint 617366.
Using close Chance glasses as a starting point, I calculated the
following Cauchy dispersion formula coefficients:
BSC517645 DF617366
A0 2.27919628 2.54981183
A2 -0.0134311888 -0.0103099604
Am2 0.00650386047 0.0205224252
Am4 0.00136011224 0.00128401416
Am6 -1.59010773E-4 -7.34043284E-5
Am8 7.89080529E-6 6.66280515E-6
The above assumes, though, that the refractive index of the
Borosilicate Crown is actually 1.52690 for the g line (instead
of 1.52590). With that assumption, the fit for the crown glass
is worse than 1.0E-5 for only one wavelength. The fit for the
flint glass is a little worse with errors for about 5 wavelengths
being in the 1.0E-5 to 2.5E-5 range.
Using the above, scaling to 8 inch aperture, and extrapolating
to f/14.0925, the Dimitroff and Baker designs are:
1 2
R1 52.36773 65.54704
t1 0.7858 0.7813
R2 -48.63604 -40.41729
t2 0.0 0.35062
R3 -48.63604 -40.41729
t3 0.5615 0.5581
R4 -587.8264 -182.5148
t4 111.8849 111.2624
R5 -41.691 -40.402
Sc 0.590 0.587
Se 0.503 0.577
The photopic Strehl ratios are given for the center (Sc) and
edge (Se) of a 1.2 inch diameter field.
These achromats both have a minimum focus of about 551 nm. I
could find no real indication of the best correction wavelength,
so I arbitrarily left it at 555 nm for the GSUM calculation.
Using glass types of Schott BK7 (or N-BK7) and Schott F4 in the
GSUM program, the following prescriptions result:
A B C D
R1 51.695 65.282 68.487 62.964
t1 0.72 0.72 0.72 0.72
R2 -48.467 -39.938 -39.476 -40.278
t2 0.0 0.37076 0.01 0.65565
R3 -48.467 -39.938 -39.963 -39.867
t3 0.56 0.56 0.56 0.56
R4 -664.26 -183.06 -168.02 -196.63
t4 111.9136 111.2466 112.1284 110.5358
R5 -41.675 -40.274 -41.785 -39.140
Sc 0.553 0.550 0.554 0.547
Se 0.465 0.540 0.547 0.529
Prescription A is the cemented prescription that zeroes the longitudinal
error. Air-spaced prescription B retains the equality of the two
internal radii while also zeroing offense against the sine condition.
Prescription C minimizes lateral color while prescription D zeros the
longitudinal error for the 70 percent zone. Each of these prescriptions
pretty much still has the same wavelengths for the nulls -- about 513
and 605 nm that the Dimitroff and Baker prescriptions do.
I then let ZEMAX optimize the first three of these designs, using
photopic RMS wavefront error as the goal (with a LaGrange goal
being the EFL of 112.74), and allowing the minimum focus to migrate
as needed. The results were:
E F G
R1 55.237 65.04 69.18
t1 0.72 0.72 0.72
R2 -47.261 -41.397 -40.338
t2 0.0 0.272 0.01
R3 -47.261 -41.397 -40.748
t3 0.56 0.56 0.56
R4 -379.25 -188.07 -165.42
t4 111.9772 111.4867 1112.1319
R5 -41.729 -40.753 -41.818
Sc 0.526 0.528 0.534
Se 0.472 0.519 0.527
In nearly all cases, the photopic Strehl ratio is actually less
than that that results from the simple doublet algorithm! AND,
in turn, that result is worse than the original Dimitroff and
Baker design.
> Steve Beccue
> steve@beccue.com
--
Rick S.
http://users.rcn.com/rflrs
_______________________________________________
ATM mailing list http://www.atmlist.net/