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


At 09:20 AM 3/10/2003 +1000, Frank Q wrote:
>
>Hi All
>
>A very interesting analysis.... Let me add my 2 cents' worth:
>
>For this, I'm looking at a diagonal that consists of a flat surface
>with a one-wavelength central flat depression - ie a combination
>of 2 flat surfaces.
>
>For light hitting the central section, this is the same as a diagonal
>which is wavelength/cos(45) further from the mirror compared with
>the edge portion.
>
>Now to get some realistic feel for this, assume that
>
>wavelength = 0.5 microns
>primary = 200 mm (8") (f/5)
>focal length = 1000 mm
>
>The airey disk size is d = 1.22 * f * wavelength / primary_diameter ie
>
>d = 3.06 microns
>
>And, the central portion of the diagonal creates an image which
>is (laterally) shifted by x = wavelength / cos(45) relative to the
>that formed by the outer portions of the diagonal. Plugging
>in the numbers gives
>
>x = 0.7 microns
>
>So, we're now looking at 2 superimposed airey disks, each
>with a diameter of 3 microns but sideways displaced by
>0.7 microns - ie about 1/4 of their diameter.
>
>For the 16" example:
>
>d = 3 microns
>x = 0.7 microns
>
>Some comments which have to be made are that (1) this is a VERY*
>simple and artificial situation and (2) the superposition of the airey
>disks needs to have the phase taken into account (after all, there is
>an optical path difference (opd) introduced by the depressed zone).
>
>opd = wavelength / cos(45) = 1.4 wavelengths (approx)
>
>which is roughly destructive interference over about 75% of the
>pattern!!!
>
>*VERY perhaps should be "ridiculuous"
>
>FWIW - My gut feeling is that you will end up with a pretty messy
>airey pattern.
>
>Apologies for metric measurements
>
>Cheers
>
>Frank Q
>


The above is an interesting model. It would be fun see exactly what kind of
pattern results.  But if the intention is to approximate a slightly curved
flat, it's a nice try that doesn't convince.

It's easy to see why not.  Suppose the diagonal is a concave hyperboloid,
correctly figured and collimated for the job.  With the principles of
geometric optics in charge, the image of an on-axis point star would be a
perfect point. Or if you prefer, wave theory would soften the point to a
perfect Airey disk.

The 2-plane approximation that intends to show the messed up image caused
by a slightly spherical diagonal then would do exactly the same messy job
on the perfect image.

Martial Thiebaux
Rawdon Hills, Nova Scotia

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