From: Mark Holm 
To: Jim Burrows , ulhas{at}nagpur.dot.net.in, atm{at}shore.net
Reply-To: Mark Holm 




Jim Burrows wrote:

>
> Mark,
>
> Are you using the Mahajan (best) approximation to the Strehl, 1/exp((4
> pR/550)ý), R = surface RMS, nm, Suiter, Eq. (13.2), p. 238 (using good
> ol' symbol font in Eudora )?  I get the following:
>         RMS     Strehl
>         14.2    .900
>         16.7    .865
>         12.9    .917
>         18.2    .841    18.2 = 12.9*sqrt(2)
>         15.2    .887    15.2 = sqrt( 8ý + 12.9ý)
>
> Regards,
>
> Jim Burrows



I actually used both of the equations on your web site (and present the
results of both).  The numbers quoted are from the second, which gave
slightly higher values.

Straight out of the Javascript from the live version of the page, the code is:

1 / Math.exp(Math.pow(4 * Math.PI * totalrms / wavelength, 2))

Let me try it again.

OK, I see the problem. As is my habit, I had my reference wavelength set at
500 instead of 550.
I'll have to write Ulhas and explain.

Thanks for double checking me Jim.

Ulhas, If your eyes are extra sensitive to blue light, you might want to
use my numbers rather than
 Jim's.

Actually, the choice of reference wavelength is a little problematic,
especially for visual use.
 Dark adapted vision has it's peak sensitivity at 500 nM, color vision has it's
peak at 550.
So, don't we use dark adapted vision in our telescopes?  Yes and no.  To
see fine detail, the kind
of thing that pushes the telescope's resolution limit, the image has to be
bright enough for us to
use at least some color vision.  Why, because the color vision cells are
also the ones that give us
 acuity for fine detail.  If the image is too dark for color vision altogether,
we can't see fine
 detail.  The opthamology boys call color, or daytime vision photopic, dark
adapted vision scotopic,
 and the sort needed for seeing detail in telescope images (except for the moon
and sun) mesoptic
 (or maybe it is spelled mesopic).  In mesoptic vision, both the color cells
(cones) and the dark
 vision cells (rods) are active.  Anyhow, one can still argue, because the
color vision cells are
 sensitive to shorter wavelengths than 550 nM.  550 is just the peak
sensitivity.

I still think 14.2 nM RMS is a bit too much for the primary of a visual
Cass. The secondary isn't
 likely to be better.  (Cass secondaries are reputed to be hard to figure).  If
you do the numbers,
 as my calculator page allows, you can see that, in a two mirror system, a
real, though not huge,
 improvement can be made by improving one of two mirrors a moderate degree.
You do run into
 diminishing returns by improving only one mirror of a set, so it doesn't pay
to get carried away
 with it, but putting the effort into the easier of the two mirrors to figure
pays off reasonably
 well, to a point.

Mark Holm
mdholm{at}telerama.com

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