Re: [ATM] Cassegrain vs. Gregorian (secondary testing)

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

Richard F.L.R. Snashall wrote:

    >
    > Assuming I made this at all comprehendable, is it reasonable?
    >

I simulated a test of this, using lateral error rather than longitudinal
error.  In the calibration, the five zones (20%,40%,60%,80% and 100%)
had lateral errors in column 2 (cal) below (results are in microns).
To check the model of two pass vs one pass, I checked a test of a
spherical secondary.  The five zonal values are given in column 3
(sph) below.  Not precisely double the calibration results, but, to
me, the model looks somewhat reasonable.

I then simulated the secondary test itself.  The zonal values are given
in column 4 (sec) below.  Using the separation of the focal plane
(338.24 mm), the model values ( -t*(1-k)*(y/R)^3 ) are given in
column 5 (model) below.

zone       cal        sph        sec        model      full

0.2       0.6189     1.0515     3.1874     2.1145     1.9496
0.4       4.7106     8.0490    25.1343    16.9158    15.7131
0.6      14.5176    25.0831    82.7355    57.0908    53.7003
0.8      29.6817    52.3331   188.9622   135.3264   129.5988
1.0      45.5767    83.5845   350.3906   264.3094   259.2372

These do not concur well with the secondary test results.  However,
the secondary test results do not reflect the calibration.  Twice
the calibration results would have to be subtracted (two pass vs
one pass).  The full calibration compensated values of the test
measurements are given in column 6 (full).

The model of the reflected angle ( (1-k)*(y/R)^3 ) only
accounts for the 4th power terms.  A quick check of the
full differences of the two conicoids differs by only a
fraction of a micron, but might have to be taken into
account for an extremely fast secondary.

I checked the validity of using the distance between the lenses
and the source/knife as the multiplier (when the focal length
of the lens nearest the mirror is reasonably close to the RoC
of the mirror), rather than using the full-blown matrix terms.
In this case, the transformation matrix is:

             [  0.94653844   341.02074570  ]
             [ -0.00496576    -0.73258987  ]

whose inverse is:

             [ -0.73258987  -341.02074570  ]
             [  0.00496576     0.94653844  ]


The discrepancy between 338.24 and 341.02 would actually make
the error somewhat larger (about 2.3 microns at the edge??).

-- 

Rick S.

http://users.rcn.com/rflrs





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