Re: ATM "Diffraction Limited" a definition

["Alan Levin" <ailevin@ix.netcom.com>]

> From:          Andy Hochstetler <andyhoc@mindspring.com>
> To:            "'ATM List'" <atm@shore.net>
> Subject:       Re: ATM "Diffraction Limited" a definition
> Date:          Mon, 17 Feb 1997 17:58:09 -0000
> Reply-to:      Andy Hochstetler <andyhoc@mindspring.com>


> I wanted to better understand this topic, so...out of sheer curiosity, I 
> looked up the term diffraction limited in the McGraw-Hill Dictionary Of 
> Scientific and Technical Terms, 5th ed.
> 
> It gives the following definition:
> 
> "Capable of producing images whose separations are as small as the 
> theoretical limit imposed by diffraction effects."
> 
<analysis of size of Airy disk snipped>

Andy,

As your analysis showed, a clear round aperture with perfect
transmission characteristics gives a diffraction spot and a series of
rings whose size is related to the wavelength of light divided by the
diameter of the aperture.   Thus for a given wavelength, the diameter
of the spot and rings decreases with increasing aperture.  For any
size perfect round aperture, 84% of the light will be in that
central spot and the rest will be in the rings. 

If you have a real telescope, there will be roughness, errors of
figure, blockage, absorption of light etc that will cause less than
84% of the light to be contained in what was the diameter of the
central spot for the perfect aperture.  While different sorts of
imperfections will cause different kinds of problems, if you are
going to pick one number as a measure of optical performance, then
the Strehl ratio, that is the % of the actual telescope's light that
falls in the theoretical central spot divided by 84% seems like the
right single number.  If I have this definition wrong, I am sure
there is someone more knowledgeable here who can correct it.

This seems more in the spirit of diffraction limited.  The 
diffraction limit is getting 84% of the light in diffraction spot for 
that aperture.  The Strehl ratio is a measure of how close you are to 
that limit.  

As you know, being forced to describe something with a single number
limits what you can say, <g>.   To say more about a telescope system
you can use an transfer function that is a series of numbers to tell
you about how the system performs at various scales.  Fortunately
for both of us, that is a lecture that I am not prepared to give,
but I recommend Suiter's book on Star Testing Astronomical
Telescopes for an accessible discussion of transfer functions.  The
book, Astronomical Optics by Daniel Schroeder gives more formulas
and tables of results for various telescope designs.

The real point is that designing and building, or even buying a 
telescope happens in the real world were choices have to be made.  
These choices are based on what you want to do with a telescope, and 
how much time and money you are willing to spend on it.  There is no 
right answer, there are only more or less informed decisions.  I 
think that getting manufacturers to supply better information, and 
getting consumers to better understand it are the real challenges.  


Good Observing,
Alan