Introduction
"The men of experiment are like the ant, they only collect and use; the reasoners resemble spiders, who make cobwebs out of their own substance. But the bee takes the middle course: it gathers its material from the flowers of the garden and field, but transforms and digests it by a power of its own. Not unlike this is the true business of philosophy (science); for it neither relies solely or chiefly on the powers of the mind, nor does it take the matter which it gathers from natural history and mechanical experiments and lay up in the memory whole, as it finds it, but lays it up in the understanding altered and disgested. Therefore, from a closer and purer league between these two faculties, the experimental and the rational (such as has never been made), much may be hoped."
Bacon, Francis [Francis Bacon, Novum Organum, Liberal Arts Press, Inc., New York, p 93.]
Using Filters
Firstly, there is no one filter that is a universal panacea. A broadband (also called and LPR or Light Pollution Rejection) filter is probably the best to start with, in that it is relatively mild and helps to delete the worst effects of artificial light. Planets and stars look weird, everything takes on a green cast and the image is considerably fainter. However, certain objects respond well, the benefit being vastly increased contrast. Of course, going to a dark site would be even better. Often called UHC (Ultra-High Contrast), narrow-band "nebula" filters let through even less wavelengths, and the cut-off is much steeper. So they basically have much more of the same effect. They therefore work even better, but on fewer objects (and are of course much worse for all other possible targets). Both of these are severe notch filters, aggressively blocking specific wavelengths and letting other key wavelengths through. If the object you wish to view does not emit in the passbands, you will see nothing. If it is a good match, then you will see more because of improved contrast. Planetary nebulae are generally good subjects for these, but it is useless to try them on galaxies, because galaxies transmit in an essentially continuous spectrum.
Another interesting filter, which is extremely good for a handful of objects only, is an OIII (oxygen three) filter, which lets through the light emitted by ionised oxygen to the exclusion of virtually everything else. So the Eta Carina nebula (for example) is stunningly rendered, but the number of suitable subjects is severely limited. Similar comments apply to the other specialised filters (e.g. Sulphur SII, hydrogen-alpha, hydrogen-beta, etc.) Apart from limiting the spectrum available, all of the filters mentioned cut out light at all wavelengths, so the image gets quite faint. You really need a large telescope (more than 8-inch diameter, preferably bigger than 10) for them to be viable.
One thing not generally realised is that these filters are not absorbtion filters (like a polarising or plain coloured filter) but work by destructive interference. As such, they have many coatings, each extremely thin and tightly controlled. So they difficult to make, hence expensive and delicate. More interestingly, they are highly reflective - this means that light coming in the eyepiece end gets reflected back to your eye and the image is consequently much poorer. You need to wear a hood and use the rubber eyecup to get the most from them.
My advice on the above is to go to a star party and try other people's filters before making a purchase. Few people have seen the Horsehead Nebula, which is notoriously difficult object, and the right filter can reveal it in even modest instruments. That's exciting. But do you want to pay a couple of grand for the priviledge, when you can get professional images off the net? Or put the money towards some other accessory.
A few more comments, just to round off the discussion...
For comets, a Swann filter is often promoted, to assist in discerning the ion tail. By comparison to the others mentioned above, this is a mild filter, but again dedicated to a particular subject.
The Moon can benefit from a neutral-density (or crossed polariser) filter, to cut the glare, but this is more for comfort than anything else. The planets can benefit by using plain coloured filters, bringing out features like the cloud belts of Jupiter, or dust storms and the polar cap of Mars. For these, my advice is to go to camera shop and get some second-hand photographic filters. Kokin make a good range of optically good plastic filters that are quite inexpensive and capable of being cut to fit your needs. Similarly, if you have a refractor that exhibits colour fringes on bright objects due to chromatic aberration, you can improve the image by intrioducing a "minus violet" or (less efective) "skylight" filter, again cheaply obtainable from camera outlets. These look a pale yellow in colour.
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