From: "Richard Schwartz" 
To: 
Reply-To: "Richard Schwartz" 


I seek a definition of the maximum diffraction limited resolution the
equivalent aperture.  If an aperture is uniformly attenuated, it still has
the same resolution, so this leads to...

EA=(2/sqrt(pi))*Int(A(x,y)*dx*dy)/max(A),

where A(x,y) is the real-valued apodizing function (never greater than 1,
and is 0 outside the aperture) and surface integral is over the entire
light collecting area.   So for a refractor, A is 1 everywhere, max(A) is
also 1,
and you end up with the diameter of the aperture.   The nice thing about
this is that it allows comparison of interferometers, scopes with
black-painted edge chips, square apertures, and other weird stuff whose
images may or may not have diffraction rings, vane spikes, etc.

But does this make sense for all systems?  You would have an 8" newt
with a big fat diagonal working as well as a 4" refractor or
shiefspiegler...   Are
there any great diffraction thinkers out there?




----- Original Message -----
From: "Frank Q" 
To: "Vladimir Galogaza" ;
"ATM shore"

Sent: Thursday, March 06, 2003 2:42 PM Subject: Re: ATM Diffraction due to
secondary sizing.


>
>
> ----- Original Message -----
> From: "Vladimir Galogaza" 
> To: "ATM shore" 
> Sent: Thursday, March 06, 2003 4:03 PM
> Subject: Re: ATM Diffraction due to secondary sizing.
>
>
> >
> >
> > >One way I know of for eliminating rings is through apodization, but
> > >then this just increases the size of the central disk - you have just
> > >as much resolution as before - no more, no less.
> >
> > I seriously doubt this " no more no less" statement.
> >
> > Resolution problem due to diffraction on aperture boils down
> > to the Airy disk size. Increasing the central disk size equals loss of
> > resolution, fringes or not. This is so because of how resolution is
> defined.
>
> But you still have the rings that interfere with the detail in the image
in
> the
> vicinity of the the Airy disk. --- Apodization increases the diameter of
the
> central maximum, and if you choose a suitable profile (eg gaussian), the
> central
> disk would be insignificant (not detectable with your eyes) just about
> where the first ring started. Try experimenting with Fourier transforms
> of circular apertures with and without a modulation factor applied
> across the surface.
>
> After having written the above paragraph, it is obvious that a more
> accurate (versatile ??) definition of "resolution" is required !!!
>
> BUT - the bottom line is -- If your magnification is high enough that
> you have to mentally interpret what the image would look like in the
> absence of diffraction, then is that image really worth looking at ?
>
> I would rather lower the magnification, get a better and wider field of
view
> and enjoy looking through the telescope rather than worry about the
> idiosyncracies of different diffraction patterns.
>
> >
> > Loss or increase of contrast is just another consequence of diffraction.
> > But keeping resolution and decreasing aperture is contradictio in
adjecto.
> > In usual noncoherent case. Interferometric Aperture synthesis for
> resolution
> > increase is not what we are talking about on this thread.
> >
> > Redefining definition of resolution is possible but then we are not
> talking
> > about the same thing.
> >
> >
> >
>
>
>

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