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From: jwl@ernie.Berkeley.EDU (James Wilbur Lewis)
Newsgroups: sci.space,sci.crypt
Subject: Beating the diffraction limit (was Re: satellites)
Message-ID: <22572@ucbvax.BERKELEY.EDU>
Date: 14 Jan 88 01:30:37 GMT
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Reply-To: jwl@ernie.Berkeley.EDU.UUCP (James Wilbur Lewis)
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In article <531@srs.UUCP> lee@srs.UUCP (Lee Hasiuk) writes:
>>    From Jenkins & White, Fundamentals of Optics p331
>>    Minimum angle of resolution in seconds = 1.220 * ( lambda / D )
>>    Where D is the diameter of the aperture and lambda is the wavelength
>> of the light. It is physically impossible, using 1 image, to get below 
>> this limit. 
>
>In a complex analysis class, we were told that the diffractive 'limits' of
>lenses and mirrors could be bypassed to a certain degree through the use
>of analytic continuation.  Anyone care to comment?

The diffraction component of the point spread function for a given wavelength 
and aperture is known; it should be possible to beat the diffraction limit
by deconvolving this function with the image.  I've seen this done for 
out-of-focus images, and the results are remarkable.

The real problem, it seems to me, is noise introduced by the atmosphere
(and other factors, I suppose...).  Since you can't remove the noise
analytically, information is truly lost.  It is not clear (to me) how this
effect varies with aperture; amateur astronomers often prefer a small
aperture/high f-ratio instument  to larger (and theoretically better
resolution) "light bucket" type 'scopes for planetary observations where
light grasp isn't the limiting factor.  Are larger apertures really more
sensitive to "seeing", or is this an artifact of the difference in focal
ratios/optical quality?  Would this effect be irrelevant for a telescope 
above the atmosphere, where one doesn't have to worry about air boiling 
around inside the tube?

-- Jim Lewis
   U.C. Berkeley