Image Sharpness

How sharp can you get? As I noted earlier, Dawes based his resolution limit on his practical viewing experience. But why does a limit exist? Light consists of electromagnetic waves. Just like ripples on a pond when we toss in a few stones, light waves that interact can reinforce in some places and cancel in others. Circular telescope apertures diffract light so that it forms a series of bright and dark rings surrounding a star's image. These are most pronounced if we view the image with the eyepiece slightly inside or outside of focus.

In focus a star's image becomes a small dot with one or more faint diffraction rings around it. Imperfect telescopes and atmospheric turbulence make it difficult to see this pattern. In a perfect image the central dot, called the Airy disk, contains 84 percent of the light collected by the aperture. The first ring has about 7 percent, and the rest is distributed in successively fainter rings.

The 19th-century English physicist Lord Rayleigh established a slightly more lenient resolution limit than Dawes' for double stars. In his view, two stars are just resolvable if the center of one star's Airy disk lies in the first dark ring of the other's diffraction pattern. This Rayleigh limit equals 5.5 arcseconds divided by the telescope aperture in inches. Once you have enough magnification to see the diffraction pattern clearly, further magnification is "empty."

Experienced planetary observers use 20x to 30x per inch of aperture to see the most planetary detail. Double-star observers go higher, up to 50x per inch (which corresponds to a ½-mm exit pupil). Beyond this, telescope power and eye limitations degrade the view.

The atmosphere limits our sharpness. It is rare to find atmospheric conditions that allow any telescope to perform at more than two or three times the resolution capability of a good 4-inch. Sharpness is not exactly the same as resolution. Spherical aberration, defocusing, or adding a central obstruction subtracts light from the Airy disk and adds it to the diffraction rings. With a 50 percent central obstruction, the Airy disk is only 10 times as bright as the first ring, compared to 50 times as bright for an unobstructed telescope. The obstructed system may still split double stars at the Rayleigh limit, but just a touch of atmospheric defocusing will really mess things up.

The shift in light from the Airy disk to the diffraction rings also reduces contrast, rendering planetary details less sharp. Planetary observers using Newtonian reflectors want the smallest possible secondary mirrors for exactly this reason. Owners of large Dobsonians find that, for the finest resolution and contrast, an off-axis aperture mask (best placed near the mirror to minimize tube currents) gives the best of all possible worlds — unobstructed, color-free images. A 17-inch mirror can have a 6-inch unobstructed aperture.

Observational astronomy is an aesthetic pursuit for most amateurs. It seems presumptuous to try to quantify how high or low we can go, given the variety of instruments, subjects, atmospheric conditions, and eyesight that exists. I think, however, that two generalizations are valid: For the best low-power views, use the highest power that frames the subject. For the best high-power views, use the lowest power that reveals the detail you're looking for.