The topic of using high powers to observe faint deep sky objects at the threshold of detection has been adequately covered elsewhere. Here I'm going to comment about similar applications of the same concept in photopic vision - the kind that is used when observing the planets and the moon.
Certain rules of thumb have grown up around magnification usage in telescopes. One rule says that anything in excess of 50x per inch of aperture is excessive. Another says that anything more than 30x per inch of aperture begins to degrade the image. All of these rules are promoted as general guidelines, but rarely as ironclad rules.
The usual justification for imposing limits to practical magnification are that the resolution of the naked eye is 1 arcminute (some people choose 0.5 arcminute for this value, others 0.75 arcminute, etc). Therefore it can be inferred that if you magnify the resolution limit of the telescope to one apparent arcminute in extent, you can see all of the detail the image has to offer. For example, a 10" telescope has a Dawes limit of almost exactly 0.5 arcseconds. To get a 0.5 arcsecond detail on a planet to be one apparent arc-minute in size, one must magnify the image by 120x. The person who chose a 0.5 arcminute resolution limit for the naked eye would say that 240x would allow the eye to resolve all of the detail present in the telescopic image.
This kind of analysis is flawed by several limitations. The first limitation is the arbitrary value for the resolution limit of the eye, which may be based on an average person's ability to split a double star (one arcminute is about right for this), or may be based on a less empirical or less rigorous criterion (the 0.5 arcminute value probably applies in this case). One is tempted to wonder, given these limitations, why almost every person is able to view electrical power lines from a distance that are only a few arcseconds across with no optical aid whatever.
The second, and far more fatal, flaw is that the rule assumes that the eye's resolution limit is constant, and does not vary with the contrast of the object to be discerned. This is the solution to the power line problem just mentioned. Thin black power lines seen against a blue sky exhibit very high contrast. If those black power lines were painted blue you'd have a real problem seeing them from the same distance - they would be camouflaged. You'd have to get a lot closer to tell that they were there. Similarly, a white sign with eggshell lettering wouldn't be very readable - you'd probably have to stand right in front of it and spend some time tracing out the letters. However a white sign with black lettering could be read from a much greater distance.
These are illustrations of the eye's dependence upon contrast in discerning extended surfaces. Contrast refers to the difference in brightness between two surfaces. It is found by taking the brightness of the first surface, B, subtracting the brightness of the second surface, b, and then dividing by the brightness of the first surface:
contrast = B - b / B
Under this formula, the contrast between perfect white and perfect black would be 1. The contrast between middle gray and white would be .5 - the same value as the contrast between middle gray and black. The contrast between a beige wall and a white wall would run about .13 or so.
A human eye is a great contrast detector. It can detect contrast of less than .0001, and if circumstances are optimum, it can detect contrasts of less than .00001. However, it can only reach these contrast thresholds if the object being viewed is large enough. If the contrast is close to 1, the object can be seen if it is very small; but if it is very low, the object must be bigger to be discerned.
Contrast on the planets and the moon can be extremely low. The contrast between the darkest belts of Jupiter and the brightest zones is only .1 or so. The contrast of the temperate belts varies, but is rarely above .001. Imagery of Jupiter with the Hubble Space Telescope and the Galileo orbiter suggest that real features with contrasts below .00001 exist in profusion - these are probably never likely to be seen from earth. On the moon, the contrast between some of the lava flow fronts is essentially .0001, and in some cases the contrast is 0 (the fronts can only be seen as topographic features). On the other hand contrast between the mare and the highlands is quite high - some .2 or thereabouts. So for each body there is a continuous sequence of contrasts, and the small, low contrast details are always going to be the toughest ones to see.
The problem with imposing an upper limit on telescope magnification is that many planetary details, which might otherwise be seen, could remain too small to reliably discern without what is popularly believed to be "excessive" magnification. In a study of 500 adults, a researcher came to the preliminary conclusion that two gray spots with a contrast over their backgrounds of .0001 had to be 5 arcminutes in diameter, and separated by the same amount, for the average person to see them.1
Under the traditional analysis, a 5" telescope has a resolution limit of one arcsecond, so it should be capable of seeing a one arcsecond dot with such a low contrast. To magnify it to the eye's supposed resolution limit of one arcminute takes only 60x, or 12x per inch of aperture. That's not big enough to see this dot according to the study, though, so let's invoke the 30x rule. To magnify it to 30x per inch of aperture requires 150x, but the dot will only be 2.5 arcminutes across - still not enough. To magnify it to 50x per inch, or 250x, it will be 4.1 arcminutes across. Now we are getting close, but we still aren't up to the magnification required to bring the spot to five apparent arcminutes in size. That will take 300x, which works out to 60x per inch of aperture.
The one arcsecond "limit" for a 5" telescope is arbitrary, though. The telescope can form an image in the focal plane of an object much smaller than that. The smaller the object, the fuzzier the boundaries and the less its contrast is preserved by the instrument, however - so there are limits to how small and subtle a planetary detail can be seen. On the other hand, the Cassini division is easily seen in a 5" scope, even though it is only about 0.7 arcseconds wide at most (it has very high contrast). Festoons on Jupiter can often run to .4 arcseconds wide but are also routinely seen with 5" telescopes (they have very low contrast). What this suggests is that a one arcsecond spot with a contrast of .0001 is not necessarily the limit. If you get a 0.9 arcsecond spot, you'll have to go above 60x per inch with that 5" scope, and even more for 0.8 arcseconds. At some point you run out of capability, and the telescope simply can't do the job, but where the boundary lies depends on both size and contrast.
Of course there are some pragmatic considerations to be made as well. Only very good optics can be pushed to magnifications in excess of 50x per inch without resulting in considerable image blurring and loss of resolution (poor optics may break down well before this). And of course seeing often limits the performance to the discernment of features one arcsecond or larger, no matter what their contrast. Pushing the magnification high can only be done on exceptional nights with optically excellent instruments.
In addition, the observer must be prepared to accept the consequences of some blurring in order to capture this resolution. A tack-sharp view at 30x per inch is not going to look sharp at double that. In a fine telescope, though, the resolution will be preserved. Resolution and sharpness, or acutance, are related quantities, but they are not in lockstep - quite a bit of blurring is necessary before resolution is affected at most spatial frequencies. The blurring at very high power is the result of correction problems in the telescope, light scattering from optical coatings, and of course the diffraction of light which occurs in all telescopes. The observer employing very high powers to discern small features with very low contrasts should be prepared to look for indistinct borders.
In the end, the only way to know whether this technique will work is to try it - crank the magnification up, and see what happens. If you don't like it, you can always go back down. If it helps, then you've added a weapon to your arsenal of planetary observing techniques.
This does not always provide the most aesthetically pleasing views, to be sure. But at times it is the only method that will do the job, and it was widely used by eminent observers of the visual era, such as the Bond brothers, E. E. Barnard, Nathanial Greene, E. M. Antoniadi, and other hawkeyed planetary masters. The technique is kept alive today by amateur planetary die-hards who tend not to talk about it much - so here you're finding the inside scoop.
1 The research is not yet published, but I'll try to remember to put a citation here when it is.
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