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Telescopes and Resolution

Posted by Darren Drake   09/11/2006 07:00AM

Telescopes and Resolution
Telescopes and Resolution

I have been an amateur astronomer for about 30 years and have owned many telescopes. I also teach astronomy and work at the Cernan Space Center of Triton College as an astronomer/planetarium show operator. A while back in one of the forums here I stated that in an experiment I conducted that a telescope stopped down to 10mm could just resolve newspaper print at a distance of 47 feet. The aperture used was diffraction limited and seeing was no factor. This translates into a formula that for every inch of aperture a telescope can resolve print about 120 feet away. So given this, a 10-inch telescope should be able to just resolve newspaper print 1200 feet away. But it is assumed that the optics are diffraction limited as well as unobstructed. I wondered just what would happen if wavefront errors as well as percentage obstructions were considered and just what would these results reveal about how planetary performance would be affected.

To help determine how various telescopes would perform on such a test, I decided to use the star aberrator program to help simulate actual images based on various aberrations in the optical system. The results were quite fascinating.

To utilize the aberrator program, I photographed white on black print that was the equivalent of about 1.75 inches of newspaper print. This translates to about a 24 arc secsecond area as seen from 1200 feet. The aberrator program can then be used to simulate images as seen through various scopes with any and all types of aberrations. The simulation confirmed that a 10 inch aperture is only barely capable of resolving the lower case letters into individual characters. But since white on black print represents the highest contrast possible, it needs to be understood that these results translate only to high contrast lunar and planetary features such as the Cassini division, shadow transits on Jupiter, and various lunar features as shadow features near the terminator.

6" unobstructed perfect wavefront (top) 10" 20% obstruction 1/10 wavefront (bottom)

While experimenting with various hypothetical telescopes, I noticed that resolution of high contrast features, that is features with high spatial frequencies, could actually be improved by increasing the obstruction size. Furthermore, if the quality of the mirror is actually extremely poor, images can also be improved with huge obstructions that COVER UP some of the bad area in the optic. The reason is that the size of the airy disk actually decreases with poorer optical quality despite the fact that a great deal of light is thrown into the surrounding diffraction rings. These kinds of aberrations, poor wavefront error, and large secondary obstructions, only really affect lower contrast large features such as the cloud belts of Jupiter and Saturn but actually IMPROVE the ability to resolve high contrast features and split tight double stars. The tradeoff is that the features that are normally black are actually going to be gray and bright diffraction rings surround double stars.

14" 60% obstruction 2 waves (top) 14" 25% obstruction 1/5 wave (bottom)

In my simulations I compared images generated from telescopes of differing quality. Resolution of individual characters only started to become realized at about 10 inches of aperture as indicated earlier. No matter how perfect the optics were a 6 or 7-inch telescope proved incapable of resolving lower case letters. Interestingly, however, a really horrible 14-inch telescope with a wavefront error of 2 waves and an overwhelming 60 % obstruction (which actually helps) IS capable of resolving fine print. The edges of the letters actually prove to be fairly well defined but with the tradeoff of a gray rather than black background. While viewing this simulated image, it may help to view the screen from a greater distance to actually see the letters. While this may sound surprising that such a poor quality scope can in a sense out resolve a perfect 6 inch scope, it is important to keep in mind that this only pertains to high spatial frequency type features. The cloud belts of Jupiter and Saturn and other low contrast features will almost be completely washed out by the larger poor scope.

18" 20% obstruction 1/5 wave

So what does this information actually reveal about telescopes? First and foremost the resolution a telescope is capable of is dependent almost completely on aperture. To test a telescope's visual performance based on it's ability to resolve close double stars of equal brightness for example, does not really say a whole lot about the scope's optical quality as much as it's aperture which is already known. Also the ability to resolve the Cassini or even Enke divisions are similarly not a function of optical quality as much as they are good seeing, cool down, collimation, smooth optical surfaces, and eyepiece quality. Even a larger scope with a poor wavefront error can resolve divisions in Saturn's rings better than a perfect smaller telescope if seeing is no factor. Of course in the real world this is never the case and seeing would actually need to be extremely good, better than for the smaller scope, to accomplish this.

So the next time you're at a public observing event and someone asks, "how far can this scope see" or "how much does it magnify" you can tell them that it can resolve newspaper print at a distance of. (your scope's aperture in inches X 120 feet). This is an answer that makes sense to the layperson and will make them truly understand just what its capabilities are.