From: Mark Holm 
To: atm{at}shore.net, scottythefiddler{at}cogeco.ca
Reply-To: Mark Holm 


Scott Donaldson wrote:

>>From what I have found so far, it appears that one could postulate a surface
> which merits a Strehl ratio of 1, (presumably perfect), but which also
> 'spills' some light outside the airy disk into the surrounding rings.    The
> strehl ratio has often been described as the ratio of light which reaches
> the airy disc compared with a perfect aperture.  However, it does appear
> that the Strehl ratio is somewhat different.
>
>


The way I read your statement, I think you imply that with a perfect optical

system, all the light in the image of a point source would go into the Airy disk

and none into the ring pattern.  This isn't so.  A perfect system puts 84%
(I think) of the light into the Airy disc and the rest distributes into the
rings.
  This is as perfect as one can get.

This rather surprising result is one of the reasons I argue that ray optics
is just plain wrong, and people should be very careful about how they use
it.  Ray optics just doesn't predict this diffraction pattern at all, but
every (well designed and figured) optical system produces one.*  (Of course
the diffraction pattern for a non imaging system such as a spectrograph may
be very different from the disc and rings pattern of an imaging system.)

The Strehl ratio is the peak intensity of the diffraction pattern of a real
system divided by the peak intensity of a perfect system of the same
aperture. The formula which gives Strehl ratio as a function of RMS error
is an approximation, though I understand it is a very good approximation. 
(Jim Burrows web site, already referenced in this thread, discusses this.)

If you go to my mirror cell design web page
http://telerama.com/~mdholm/atm/cells/index.html
then click the link "Diffraction Patterns", you will get to a
page on Geocities where I have calculated some diffraction patterns for
mirrors with specified imperfections.  (The imperfections are those caused
by support system induced deformation.)

The first diffraction pattern is for a perfect mirror (no deformation).  You can
see the first diffraction ring pretty easily in the graph, and if you look
carefully, the second and third are there too.

If you look at the entry for the three point cell, you will see that (for
this size mirror) the three point cell gives a Strehl ratio of 0.947.  If
you look at
the diffraction pattern for this cell, you will see that the peak height is
0.947.  The other graphs for the three point cell case show clearly that
the major effect of this particular mirror deformation is to remove some
light from the Airy disc and shift it into the diffraction ring pattern. 
Most of it goes in the vicinity of the first diffraction ring, both
brightening and widening the
first ring.



*(To be more accurate I should say that every optical system produces a
diffraction pattern, whether or not it is well designed or figured.  The
diffraction pattern may well be one that is not at all good for producing
faithful images, but it is still a diffraction pattern.)

Mark Holm
mdholm{at}telerama.com

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