From: Mark Holm 
To: atm{at}shore.net
Reply-To: Mark Holm 


>
> Fortunately, the Foucault test assumes symmetry, so we don't have to use
> the 2D FFT which takes a LONG time to run, even on present day 2 GHz
> machines.  A 1D FFT will do the job and, like its name, it is FAST, so the
> cute idea of a simulated star test image with a real-time slider to go from
> inside to outside focus would be possible.
>
>


For the Foucault, and other tests that only work on one diameter, I suppose this
would work, though haven't tried it and am not mathematical enough to work
through the derivation. (I would have to try it as a computer program and
decide
if it gave reasonable results!)  Symmetry argues that it should work, and
usually symmetry wins in math.

However, whoever is doing the development might like to keep the 2-d case
in mind.  There is not all that much standing between ATM's and 2-D
testing. Didn't Jim Burrows say he is making progress on his computerized
2-d Hartmann test?


For 1-D surface profile output, I suggest a standard format where any
number of comment lines beginning with ; are allowed and the data are in r,
z pairs, in ascii, one pair to a line, with one or more spaces (not tabs
for simplicity) between each r and z and a cr or crlf after each pair. 
Extra spaces or tabs before or after each pair to be ignored, but
discouraged.

r and z always to be in millimeters, with z values carrying 4 places before
and 6 places after the decimal point as the usual.  r values may carry up
to 4 palces before and 2 after the decimal point as standard.  Probably the
smart programmer doesn't want to set those number format choices in stone,
but they should be sufficient for almost any atm application.  Maximum
clear radius would
be 9999.99 mm and maximum sagitta would be 9999.999999 mm.  the six places after
the decimal point for z would give 1 nanometer resolution, about 1/500
wavelength.  The 4 places before the decimal for r and z would let you
specify a
20 meter diameter, f/1 mirror.  That should be enough to keep amateurs satisfied
for a while.

The mirror vertex would be 0,0,0 and z would be positive away from the
mirror toward focus.  For the 1-d case, the direction in which r is
positive is fairly arbitrary.  For the 2-d case, I suggest positive x goes
to the right as one faces a mirror or lens from the focal point and
positive y goes up from that same vantage.

Perhaps there is already established a standard frame of reference for
optical systems, in that case, it might be better to go with an established
standard than specify a new one.

If you don't like ; as the comment specifier, I could easily be happy with
' or even /*  but NOT //*    (ooh, I begin to see visions of punched card
decks
every
time I type //*   ;)

Just don't require anything at the end of a comment.  I get more syntax
errors from that requirement than almost anything else.  Just make all
comment lines begin with the same character(s) and don't allow anything but
comments on a comment line.

Mark Holm
mdholm{at}telerama.com

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