Resolution and Seeing

By Mike Luciuk

There is much emphasis, when discussing telescope optics, on the resolution capabilities of the instrument. The quantification of telescopic resolution is somewhat a subjective process. Examples are the Rayleigh, Dawes, and Sparrow criteria. For more detail on this topic, please refer to “Telescope Optics” by Rutten and van Venrooij. The well-known theoretical Rayleigh resolution limit, similar to Dawes but more restrictive, is based on diffraction

where  is the resolution in radians,  is the wavelength and D is the objective size. We typically select a  of 550 nanometers (5500 Angstroms), which is the wavelength the eye is most sensitive to. With this wavelength, and D in meters, the formula for  in arcseconds simplifies to

Therefore, AAI’s diffraction resolution for its 10-inch (0.25 m) and 24-inch (0.61 m) telescopes would be 0.54 and 0.23 arcseconds, respectively. We know, of course, that our telescope’s resolution is nowhere near as good as the Rayleigh diffraction formula implies. The reason is atmospheric seeing.

Earth-based telescopes, including our naked eyes, must contend with image distortion and scintillation caused by atmospheric disturbances as light reaches us from outer space. That’s why stars twinkle and images blur and dance when viewed with telescopes or binoculars. This effect worsens as the zenith angle increases. Recall that the zenith angle is the angular distance from the zenith, and equals 90 degrees at the horizon. Temperature changes and winds create variations in atmospheric refractive indices resulting in these image distortions. This condition is called “seeing”, and is a prime consideration in selecting the location of an observatory.

Atmospheric seeing varies considerably based on location, weather conditions and time of day. The average seeing in Muana Kea, a prime location, is about 0.5 arcseconds, while the Mount Wilson observatory has seeing in the 1 arcsecond range. These are mountain locations, which have better seeing than our local New Jersey sites. Our conditions typically result in 1 to 4+ arcsecond seeing. So if our seeing is in the 1 to 4 arcsecond range, what does this imply about effective telescope resolution apertures?

For 1 arcsecond seeing, the effective aperture is 0.138 meters or 5.45 inches and for 4 arcsecond seeing, it’s 0.0346 meters or 1.36 inches. In other words, the effective resolution capability of AAI’s large telescopes is that of a 5 1/2-inch instrument, or likely, even smaller. This is especially the case in solar viewing, where the Sun’s energy creates significant atmospheric turbulence and seeing in daytime degrades to the 2 to 4+ arcsecond range. Since AAI’s telescopes are larger than our seeing limitation, their greatest benefit over smaller telescopes is their light gathering capability, an important nighttime advantage. It should also be pointed out that when viewing with larger apertures, there might be brief moments of near diffraction limited resolution. However, when used photographically, seeing will usually be the limiting resolution.

How can the effects of seeing be minimized? Ideal locations are remote mountain peaks with prevailing winds coming from the ocean. Hawaii, the Chilean ranges and the Canary Islands are prime examples. In our area, avoiding weather fronts and locating instruments on grass will help. In my personal solar photography experience, stopping down a telescope’s aperture to 4 – 6 cm consistently yields the best results.

A good amateur Internet site on estimating seeing effects is by the Portland, Oregon based Rose City Astronomers

Of course, professional observatories have begun to deal with seeing using active and adaptive optics, where mirrors are tilted or deliberately distorted to compensate for atmospheric effects. These adjustments can take place in the millisecond range, yielding resolutions rivaling that of the Hubble Space Telescope. As an aside, one should recognize that radio telescopes are not bothered by seeing (or light pollution) because they deal with much larger wavelengths, in the decimeter or meter range.