TELESCOPE PERFORMANCE II - RESOLUTION Last updated: 10 February 2001

From: sherrodc@ipa.net (Clay Sherrod)

TELESCOPE PERFORMANCE II - Splitting Hairs - The Resolving Power of Your Telescope -------------

We have explored in past reports how your telescope is limited in "light gathering" simply by the size of the total surface area of the glass or mirror used as the objective (or primary optical element) of the scope.

Indeed - and somewhat unfortunate - "big IS usually better" in astronomical telescopes, but this does not mean that smaller instruments cannot reveal striking images, resolved minute double stars, peer at galaxies millions of light years distant, see tiny craterlets within larger craters and, yes, even discern the SHAPE of a rapidly orbiting satellite as it streaks by.

To me, the "satisfaction" that you feel with your telescope, and hence the enjoyment of astronomy is three-fold:

1) Being able to "see" enough variety of bewildering objects in the cosmos to keep your appetite whetted for yet another night. Even with the SMALLEST telescope there are MORE objects visible than you can possibly see throughout the sky in your entire lifetime (yes, even with GO TO computer capability!);

2) Knowing the LIMITS of your optical instrument, from the eye...to binoculars....to your telescope; you cannot be satisfied if you THINK you should be seeing more than your telescope is capable of revealing! In large part, many of the advertisements for popular telescope and the packaging that we see emblazoned in full color suggests that we can see a whole lot more than we actually can to the eye. Many times, the result of this is disappointment.

3) Now that you know you can see many, many objects, and you have acclimated yourself to the fact that those objects will likely appear different in your 3-inch telescope than they do in Hubble Space Telescope photos, the third - and in my opinion the GREATEST - satisfaction is being able to SHARE your enthusiasm. If YOU are not excited about that great view of Saturn through your telescope, how in the heck are you going to get Ma and Pa outside on a cold night to "share" in your luke-warm grandeur?

Aside from talking about telescope limitations, let's talk for just a brief minute about YOUR LIMITATIONS. No, I am not talking about social, economic, appearance nor educational limitations....I am talking about your ability to actually FIND the stuff in your telescope you should be seeing!

Those who get a nice scope and give up early on the hobby quickly are those who can find the moon, maybe Saturn and Jupiter....Venus is easy....perhaps accidentally stumble across the Orion Nebula. Maybe they got that telescope just because they read in the paper that the "comet of the decade," Comet Whatshisname, is about to appear in the evening sky.

Once the comet's gone.....what are they going to look at? Indeed, if you want a bargain in a telescope, trying looking through the classifieds right after a popular comet has disappeared from view!

RESOLVING POWER AS A FUNCTION OF WHAT YOU CAN SEE

If you haven't already, check out my discussion on limiting magnitude elsewhere on this web site. "Limiting magnitude" is how FAINT you can see with any optical instrument: your eye, binoculars, telescope. The larger the telescope typically, the fainter object you can see. Telescopes are like rain buckets; you're simply going to get more water in one that has a bigger opening than the smaller one next to it.

The light-gathering power is also a determining factor in the RESOLUTION of the telescope; all things equal, such as optical quality and telescope design, a larger telescope will "resolve" finer detail. What does this mean?

Good resolution means that you can clearly see Cassini's division in the rings of Saturn, while a smaller telescope cannot make out the black thin gap. It means that you might glimpse the gossamer "festoons" in the equatorial belt of Jupiter and be able to "split" a double star to see BOTH stars as individual points of light instead of an elongated oval of two connected images. If there are hundreds of very tiny craters inside of Plato on the moon, a larger scope usually has a chance of seeing more of them than the smaller telescope if the craters drop BELOW THE RESOLVING LIMIT of the smaller scope.

FACTORS THAT DETERMINE TELESCOPE RESOLUTION

The size (diameter of the objective) of a telescope is not the only factor in resolution; others play into the equation as well:

1) Aperture - the larger the telescope the smaller an object can be seen and the closer the spaces between objects (I.e., double stars) that can be distinguished;
2) Optical quality - like in any item, a quality optical system will resolve finer detail than one of mediocre or poor quality;
3) The Atmosphere - read carefully my article concerning "seeing and transparency" so that you can determine the quality of the air around you. The largest telescope at a star party cannot resolve to its limit (discussed below) if the air is unsteady;
4) The Observer - YOU. A keen eye is necessary to reach your resolving limit; things that affect your eyesight are: 1) normal eyesight; 2) eye fatigue or disease; 3) extraneous light such as streetlights; 4) actually "knowing" what to look for; 4) use of alcohol and/or tobacco; 5) knowing how to use "averted vision." (discussed following); and, 6) AGE, with younger eyes being much more keen than older ones!

Let's say that all of the above factors are "good" and you are at a star party in which there are many telescopes - all of the SAME quality but in many different sizes. For this example, and for you to better understand how "resolving power" comes into play for all things astronomical, we will only use the example of DOUBLE STARS.

[NOTE: There are many excellent books which list challenging double stars for tests with any telescope size, from 2.4" to 24" aperture. My favorite is Robert Burnham's CELESTIAL HANDBOOK, a three-part alphabetical reference to every constellation and interesting objects within them.]

The acid test for a telescope is the resolving power, but no one should be slighted who owns a small telescope....again, just know and understand your limitations are reserve your efforts within YOUR telescope's capabilities!

With all the telescopes at the star party, here is the list of apertures and here are the double stars (hypothetical under excellent steadiness) that they are looking at, clearly resolved, or "separated with a dark space between each star." The separation is given in SECONDS OF ARC.

As a reference, the MOON is one-half degree, or 30 MINUTES of arc; just like on the clock, there are 60" (the symbol ["] means arc seconds, and the symbol ['] means arc minutes) in ONE ARC MINUTE, meaning that the expanse of the moon as we see it is 30 (minutes arc) x 60 (seconds arc in each arc minute) or: 1800 arc seconds across. Sounds big, huh? It IS when you consider what even the smallest telescope is capable of resolving.

Your EYE by itself is capable of resolving something as small (or as close as) TWO MINUTES ( 2' ) ARC in the sky. That in itself, knowing that the Moon is only 30 arc minutes across is a pretty small space!

So here is a report on HOW CLOSE a double each of our participants can just separate into two stars:

Ramon's 2.4" refractor - 1.9" arc (wow....that's close if the moon is 1800" arc!)
Susan's 3.5" Maksutov - 1.3" arc (we're really closing in!)
Dilbert's 4" refractor - 1.14 " arc (see how much closer the stars are getting?)
Bruce's 4.5" Newtonian - 0.10" (now we're cookin' below one second arc!) Clay's 5" Maksutov - 0.91" (this is getting exciting!)
Laura's 6" Newtonian - 0.76" (getting into some serious doubles here)
Michael's 8" Schmidt - 0.57" (these stars must be getting faint!)
Bocephus' 10" Schmidt - 0.45" (does it even matter after they're so close?)
Halley's 12" Newtonian - 0.38" (she beat everybody, but her scope is a mess)

In actuality, there are few nights when those limits can be reached. The closest resolution (or finest detail) that your telescope can make out is limited by an astronomically-accepted "law" known as "DAWE'S RULE."

If there were no atmosphere to look through and we lived in a perfect world, Dawes' limit tell us to simply DIVIDE the number "4.56" by the aperture of your telescope IN INCHES to get the values for the star party above. Likely, they were having their party on the moon with no air, since the steadiness of the air is the greatest limiting factor to reach "Dawes' Limit."

I know you are wondering, because it seems to be so important: "What MAGNIFICATION is necessary to reach the maximum resolution of my scope?" Actually, in this case, magnification DOES help to a degree and ONLY up to a certain limit. Magnification, of course magnifies unsteady air just like it does your object, but it does help in a couple of ways:

1) Use about 30x per inch aperture to reach the maximum resolving power on a good night; on a "perfectly steady" night you can use up to 50x per inch aperture; this allows the "image scale" to be large enough for the human eye to actually discern ITS OWN limiting resolution;
2) Up to 30x per inch aperture (about 105x on a 3.5" scope) will darken the background sky, thereby increasing contrast of your brighter object against the less bright sky or increase the contrast between a bright planet and a dark faint detail.

Every telescope is different; there are some telescope that I have used that have "knocked the socks" off of Mr. Dawes, splitting doubles far beyond this empirical value; on the other hand, I have seen telescopes that have fallen way short of even CLOSE to the limit they should achieve.

Get you a good reference book and go out and find your limit for yourself....that is what amateur astronomy is about: self-discovery! If you have a computerized telescope, most directories have the best double stars; find ones that fit your Dawes' limit as determined above....and see if you can see some sky between them.

Let us know what you find. I would be most interested to see how good YOUR scope performs on the "acid test" of all telescope functions!

P. Clay Sherrod
Arkansas Sky Observatory
Conway / Petit Jean Mountain
Arkansas

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