jwl@ernie.Berkeley.EDU (James Wilbur Lewis) (01/14/88)
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
brucec@orca.UUCP (01/17/88)
In article <22572@ucbvax.BERKELEY.EDU> jwl@ernie.Berkeley.EDU.UUCP (James Wilbur Lewis) writes: >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. > Similar computations can also be done to remove motion-blurring. If the distortion characteristics of the intervening medium are known (or can be approximated to some reasonable degree), they can be also be removed. This makes it easy to look through wavey glass, but leaves something to be desired when looking through the atmosphere, because of the imperfect knowledge about the medium. Still some enhancement is possible. >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? Yes, larger apertures are more sensitive. As I recall (I may very well be wrong, this information comes from many years back in my memory), there is a critical size of roughly 10 cm., established by the size of the average convection cell in the air. Distortion is least when all of your image goes through a single cell (on average). There are some things which can be done to remove atmospheric distortion even though it varies with time in an unpredictable fashion. First, recognize that there are several sources of distortion: 1) Unpredictable translations of the image caused by changes in the refractive index of the air you look through as a function of time. This is mostly of concern when taking moving pictures, or trying to compare one picture to another (although taking pictures of the janitor next to the general you want to know about can be embarrassing). Where this is a problem in single images is when the motion takes place in a time of the same order as the exposure length (or the integration time of the CCD). This can be handled as motion-deblurring. 2) Arbitrary affine geometric distortions caused by what you might call the "funhouse mirror" effect: Changes in the path of the light rays over the field of the image. Since this affects only the large-scale geometry of the image, it can removed by applying an inverse transform, which can be determined interactively if need be (twiddle the knobs 'til it looks right). This gets harder if the distortion changes on the same time-scale as the exposure time. I haven't read of any research on this problem (guess who's most interested in it), but I would guess that applying motion-deblurring with different parameters in each of several regions of the image would be useful. This might also help when the image is viewed through several convection cells, since the distortion transformations will change abruptly at the edges of a cell. 3) Haze. This is equivalent to a loss of image contrast. Since most of the human image recognition capability is based on boundaries (high-spatial-frequency components of an image), edge-enhancement helps here. This is a useful preprocessing step for the first two effects. Theoretically, taking a number of images of the same area and correcting for angular changes due to the flight path of the observer could allow some averaging out of distortion. I suspect this technique isn't all that useful, since the improvement should go as the square root of the number of images used in the average, and you just don't have that long a time during which a low-orbit bird is over any one place. By the bye, the newspaper article I read stated that these incredible feats of imaging could be done through cloud cover, which I very much doubt. Even infrared doesn't see perfectly through clouds, and since IR wavelengths are longer than light, the diffraction limit on angular resolution is larger for a given aperture optic. --------------------------------------------------------------------------- "The galaxy-spanning luminous arcs reported by M. Mitchell Waldrop in Research News on 6 February have a very simple explanation. They are part of the scaffolding that was not removed when the contractor went bankrupt owing to cost overruns." "Arthur C. Clarke, Sri Lanka" My opinions are my own; no-one else seems to want them. Bruce Cohen UUCP: {the real world}...!tektronix!ruby!brucec ARPA/CS-NET: brucec@ruby.TEK.COM overland: Tektronix Inc., M/S 61-028, P.O. Box 1000, Wilsonville, OR 97070
howard@COS.COM (Howard C. Berkowitz) (01/22/88)
In article <8801192122.AA06886@ames-pioneer.arpa>, eugene@PIONEER.ARC.NASA.GOV (Eugene Miya N.) writes: > Bruce, you made some excellent comments about this problem! > However, I would like to add one comment about what you said about > removing motion blurr. Rather than do it computationally or > optically, it's just much simpler to move the recording instrument or > media. (If I had a quarter for every roll of film I've hunched over, > I'd be rich.) A number of photorecon satellites do exactly that, according to Dino Brignoli, a retired senior CIA recon expert who has a rather interesting "road show" on photoreconnaissance and history. I heard him a few years ago at the Washington chapter of the Society for Photographic Scientists and Engineers. He said that one of the major breakthroughs in imaging satellites, which was classified for some time, was using moving backs both to cancel motion and allow much longer exposure times. -- -- howard(Howard C. Berkowitz) @cos.com {uunet, decuac, sun!sundc, hadron, hqda-ai}!cos!howard (703) 883-2812 [ofc] (703) 998-5017 [home] DISCLAIMER: I explicitly identify COS official positions.