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[ATM] A Null Test
I thought I'd present some early findings...
I started tweaking a null test design using Melles Griot lenses, so designs
will be set up for those lenses: LPX309 300 mm f.l. planoconvex (D = 95
mm),
LPK065 -600 mm f.l. planoconcave (D = 94.2 mm) and LPX303 250 mm f.l.
planoconvex (D = 101.6 mm). I later found out that the MG site doesn't seem
to list LPX309 -- luckily, there may be several alternatives that include
(with some reoptimization):
Ross L-PCX357 R=155.0388 t=7.74 D=76.2
Newport KPX232 R=155.04 t=7.754 D=76.2
Ross L-PCX376 R=155.6178 t=10.4 D=95
JML CPX10458 R=155.6178 t=10.4 D=95
Melles Griot LPX309 R=155.62 t=10.4 D=95
Optosigma 011-4570 R=155.7 t=8.2 D=80
Optosigma 011-4770 R=155.7 t=11.2 D=100
Linos 312391 R=156.22 t=10.7 D=100
Spindler&Hoyer 312391 R=156.2256 t=10.7 D=100
The basic layout of the test is similar to a Ross Null Test in that the
light passes through the three lenses on both the forward and return
directions (See Peter Ceravolo's article.). For these setups, I
selected a 500 mm diameter mirror with conic constants of -0.8 to -1.2.
This range of conics constants cover most of several designs:
Ritchey-Chretien (both Cassegrain and Gregorian), Classical Cassegrain,
and Newtonian. The LPX309 planoconvex lens is nearest the source/knife
with the LPK065 planoconcave lens in the middle. An example prescription
is:
Surf Radius Thickness Glass Diameter Conic Note
OBJ 298.476 76.2331 4 0 source
1 Infinity 10.4 BK7 95 0 LPX309
2 -155.62 29.31369 95 0
3 Infinity 3 BK7 94.2 0 LPK065
4 311.2356 35.82609 94.2 0
5 Infinity 14.1 BK7 101.6 0 LPX303
6 -131.75 2035.169 101.6 0
STO Infinity 12.49376 500 0 stop at
mirror edge
8 -2500 -12.49376 MIRROR 500 -1.2 mirror
9 Infinity -2035.169 500 0
10 -131.75 -14.1 BK7 98.14704 0 LPX303
11 Infinity -35.82609 96.33898 0
12 311.2356 -3 BK7 75.90638 0 LPK065
13 Infinity -29.31369 74.31415 0
14 -155.62 -10.4 BK7 59.47545 0 LPX309
15 Infinity -76.2331 56.18785 0
IMA 298.476 4.009802 0 knife
Note: Leaving the diameters computed (by ZEMAX) on the return path
was for my benefit.
This combination is sufficient to test f/2.5 to f/3.3 mirrors:
f/2.5 f/2.5 f/2.5 f/3.3 f/3.3 f/3.3
K=-0.8 K=-1.0 K=-1.2 K=-0.8 K=-1.0 K=-1.2
t0 52.49215 66.03618 76.23310 74.68975 87.94469 99.42131
t2 51.76884 39.16714 29.31369 31.31073 18.07115 5.712305
t4 46.85110 40.98195 35.82609 35.26693 27.28308 19.10841
t6 2044.477 2039.650 2035.169 2847.064 2843.051 2841.557
d10 95.53217 96.89402 98.14704 76.80393 77.98929 78.76043
d12 66.53048 71.45829 75.90638 58.56477 63.47730 68.16789
d14 40.13300 50.74207 59.47545 45.78434 55.19209 63.94494
The field selected for this design was +/- 2 mm, allowing for some
misalignment of the forward and return paths. Even if a pellicle
is used to physically separate the source and knife and allow
tighter alignment, some tolerance will be needed.
On axis, the worst case error (f/2.5, K=-1.2) is better than lambda/46
P-V (green e-line) -- in all cases, the longitudinal error changes
direction twice across the semi-aperture.
Off axis, astigmatism seems to dominate. It seems to be fairly well
corrected here, as the worst case error (also f/2.5, K=-1.2) is better
than lambda/27 RMS at the field edge.
Faster than f/2.5, the restriction, seen at K=-1.2, is the available
aperture of the lens closest to the mirror. Slower than f/3.3, the
restriction, also seen at K=-1.2, is the separation between the
first lens and the planoconcave lens.
Now for the cute part;-) Interchange the two planoconvex lenses.
This combination is sufficient to test f/3.3 to f/5.0 mirrors:
f/3.3 f/3.3 f/3.3 f/5.0 f/5.0 f/5.0
K=-0.8 K=-1.0 K=-1.2 K=-0.8 K=-1.0 K=-1.2
t0 40.14796 55.92810 67.65114 76.38614 110.1226 104.7744
t2 81.40512 65.04342 52.67993 42.80672 5.426498 16.79347
t4 74.80451 68.78164 62.72810 55.39374 17.09104 28.63592
t6 2705.824 2702.497 2699.466 4418.633 4463.230 4397.879
d10 96.76945 97.86856 98.84198 69.25888 66.30842 73.15745
d12 60.15706 64.11848 68.02961 49.67239 59.81393 62.38797
d14 28.16121 38.27889 46.73764 38.11838 57.30619 56.95432
Again, the faster speed has aperture restrictions. In fact, the
full 2 mm field exceeds the 95 mm diameter lens at f/3.3; however,
the field center is still covered. Perhaps the full field is
covered with one of the 100 mm diameter alternative lenses.
Performance on-axis is good, better than lambda/250 P-V; two
longitudinal error direction changes are still present, except
at f/5.0,K=-1.2. Also with the exception of f/5.0,K=-1.2, off
axis correction is good, better than lambda/79 RMS at the field
edge.
What about f/5.0,K=-1.2? That's the bugaboo. From about f/4.3 to
f/5.0 at K=-1.2 and from K=-1.0 to K=-1.2 at f/5.0, there are two
solutions. The solution for the rest of the region does not meet
the interlens space requirement in that corner. For that corner
solution, the situation fortunately improves away from that corner.
At the "boundary" between the two solutions, two longitudinal error
direction changes are again present. Performance off-axis at the
corner is also not as good, lambda/19 RMS at the field edge.
At the "boundary" between the two solutions, the interlens spacing
gets small. I could not prove that there were any points that did
not have a valid solution. There also appears to be some overlap
in coverage; a lot seemed to depend on the (working from an existing
solution) desired amount of change in selected parameters (f number
or K value).
Of course, of one the problems with this test is the number of
lenses that must pass muster. They must also be kept in alignment
over the changes in spacing -- about 75 to 80 mm.
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