Date sent:        Mon, 1 Dec 1997 17:39:17 -0800
From:             Mike McJimsey <mikem@hpoclrd.sj.hp.com>
To:               dwhysong@physics.ucsb.edu
Subject:          Airy disk calculations
Copies to:        Paul@laughton.com

Hello David,

I thought you might be interested in another way of looking at the
same data that you generated for the Airy disks of the different
telescopes.  I'm including data for the optical transfer functions
(OTFs, also called MTFs) of the same telescopes that you analyzed.
You can easily plot the data using a spreadsheet or plotting
program to compare the different OTFs.  You can see that the 8"
will always transfer contrast better than a 4" will.  The 5" is
nearly identical with a 8" up to a relative spatial frequency of
about 0.3, but falls well below the 8" above that frequency.  As
a result, I would expect the 8" (perfect except for the 34%
obstruction) to outperform the 5" (perfect unobstructed aperture)
in all cases, which was not as clear from your calculations of the
point spread functions.

By the way, I used software that can be purchased with Suiter's
book on star testing astronomical telescopes.  It allows you to
easily calculate point spread functions, OTFs, resulting images
both in and out of focus, etc.  It is very useful in getting
a more intuitive understanding how diffraction works in a
telescope.  It also allows you to specify transmissions
coefficients for generating obstructions and apodizations, as
well as the amount of low and high order spherical aberrations.
It easily generated the same graphs that you did, as well as the
OTFs.  Maybe Paul Laughton would be kind enough to allow the OTF
graphs to be appended to your calculations to allow people a
different way of looking at the performance differences between
the telescopes.

If you have any questions, please feel free to let me know.
 

Sincerely,

Mike McJimsey
mike_mcjimsey@hp.com



Optical Transfer Function - Contrast

Spatial Freq      4"/0%       5"/0%      8"/34%   9.25"/37%
           0           1           1           1           1
        0.01       0.969       0.976       0.977       0.978
        0.02       0.946       0.957       0.959       0.962
        0.03       0.916       0.934       0.936       0.941
        0.04       0.885        0.91       0.912       0.919
        0.05       0.857       0.887        0.89       0.899
        0.06       0.829       0.865       0.869        0.88
        0.07       0.801       0.843       0.848        0.86
        0.08       0.773       0.821       0.826        0.84
        0.09       0.744       0.798       0.804        0.82
         0.1       0.716       0.776       0.782         0.8
        0.11       0.689       0.754       0.761        0.78
        0.12       0.661       0.732        0.74        0.76
        0.13       0.634        0.71       0.718       0.741
        0.14       0.606       0.688       0.697       0.721
        0.15       0.579       0.666       0.676       0.701
        0.16       0.552       0.645       0.655       0.682
        0.17       0.526       0.623       0.634       0.662
        0.18       0.499       0.602       0.614       0.643
        0.19       0.473        0.58       0.593       0.624
         0.2       0.448       0.559       0.573       0.605
        0.21       0.422       0.538       0.553       0.586
        0.22       0.397       0.517       0.533       0.567
        0.23       0.373       0.497       0.513       0.548
        0.24       0.348       0.476       0.494        0.53
        0.25       0.324       0.456       0.475       0.511
        0.26       0.301       0.436       0.456       0.493
        0.27       0.278       0.416       0.438       0.475
        0.28       0.255       0.396       0.419       0.458
        0.29       0.233       0.376       0.403        0.44
         0.3       0.212       0.357       0.389       0.422
        0.31       0.191       0.338       0.379       0.405
        0.32       0.171        0.32       0.371        0.39
        0.33       0.151       0.301       0.364       0.377
        0.34       0.133       0.283       0.358       0.367
        0.35       0.115       0.265       0.353       0.358
        0.36       0.097       0.248       0.348       0.351
        0.37       0.081       0.231       0.344       0.345
        0.38       0.065       0.214        0.34        0.34
        0.39       0.051       0.197       0.336       0.336
         0.4       0.038       0.181       0.332       0.333
        0.41       0.026       0.165       0.329       0.329
        0.42       0.016        0.15       0.326       0.326
        0.43       0.007       0.135       0.323       0.323
        0.44       0.002       0.121        0.32       0.321
        0.45           0       0.107       0.317       0.319
        0.46           0       0.093       0.314       0.316
        0.47           0       0.081        0.31       0.314
        0.48           0       0.068       0.307       0.312
        0.49           0       0.057       0.304        0.31
         0.5           0       0.046         0.3       0.308
        0.51           0       0.036       0.296       0.306
        0.52           0       0.027       0.292       0.304
        0.53           0       0.018       0.287       0.301
        0.54           0       0.011       0.282       0.299
        0.55           0       0.005       0.277       0.297
        0.56           0       0.001       0.271       0.294
        0.57           0           0       0.265       0.291
        0.58           0           0       0.257       0.288
        0.59           0           0       0.248       0.285
         0.6           0           0       0.237       0.282
        0.61           0           0       0.225       0.278
        0.62           0           0       0.213       0.274
        0.63           0           0       0.201        0.27
        0.64           0           0        0.19       0.265
        0.65           0           0       0.179       0.259
        0.66           0           0       0.168       0.253
        0.67           0           0       0.157       0.247
        0.68           0           0       0.147       0.238
        0.69           0           0       0.136       0.228
         0.7           0           0       0.126       0.218
        0.71           0           0       0.116       0.207
        0.72           0           0       0.107       0.197
        0.73           0           0       0.097       0.187
        0.74           0           0       0.088       0.177
        0.75           0           0       0.079       0.167
        0.76           0           0       0.071       0.157
        0.77           0           0       0.063       0.148
        0.78           0           0       0.055       0.138
        0.79           0           0       0.047       0.129
         0.8           0           0        0.04        0.12
        0.81           0           0       0.033       0.112
        0.82           0           0       0.027       0.103
        0.83           0           0       0.021       0.095
        0.84           0           0       0.016       0.087
        0.85           0           0       0.011       0.079
        0.86           0           0       0.006       0.071
        0.87           0           0       0.003       0.064
        0.88           0           0       0.001       0.056
        0.89           0           0           0        0.05
         0.9           0           0           0       0.043
        0.91           0           0           0       0.037
        0.92           0           0           0       0.031
        0.93           0           0           0       0.025
        0.94           0           0           0        0.02
        0.95           0           0           0       0.015
        0.96           0           0           0       0.011
        0.97           0           0           0       0.007
        0.98           0           0           0       0.004
        0.99           0           0           0       0.001