Our Eyesight

Eyesight is an engineering marvel. Think about it. Our eyes have an automatic iris, automatic focus, an aspheric lens, a curved image surface, a chemical image intensifier, a windshield washer-wiper, and a lens cover, all as standard equipment. And this is without mentioning the wonder of stereo vision!

While our eyes are not perfectly color corrected, our brain processes out the errors. Other defects vary from individual to individual. Fortunately, the common ones can all be compensated when one uses a telescope.

Among the most prevalent defects is astigmatism, which can be ameliorated with eyeglasses or by using only the small central area of our eye's pupil. To see an example of this, make a diamond-shaped aperture by pressing your thumbs and forefingers together. The harder you push them together, the smaller the aperture will become. Now place this opening close to your eye. You will probably see some improvement in resolution and depth of focus. (You may look silly to your companions at the dinner table, but it's great for reading the menu when you forget your glasses.)

Those who suffer near- or farsightedness can simply remove their eyeglasses to use a telescope, since the instrument can be focused to compensate for either defect. Floaters, those bits of debris in our eyes, are mainly a problem when we use magnifications that produce very small exit pupils that accentuate their visibility.

Our Telescopes

There are six important factors to consider with a telescope. The first is magnification, and by this I mean angular magnification. We see the universe in terms of angles. A 50-power telescope will make the ½° disk of the Moon appear 25° wide.

To achieve low magnification, use long-focal-length eyepieces. Telecompressor lenses can shorten the effective focal length of some telescopes, lowering the magnification of a given eyepiece used with that telescope. High magnifications can be obtained by using short-focal-length eyepieces.

Barlow lenses (which can even be "stacked") allow even a short-focal-length telescope to achieve absurdly high magnifications. But beware: these high magnifications may not be what we want! The 600-power, 2.4-inch "department store" telescope is a prime example of a malicious turn-off to budding amateur astronomers — the resulting field at that high magnification is too small, too dim, too fuzzy, and too shaky to be of much use. I'll discuss optimum magnification later.

F/number is of little importance visually. A "fast" telescope implies a short focal length and a large field. Fast, however, is a term borrowed from photography (an f/5 telescope can take a photograph with one-fourth the exposure time of an f/10 instrument). Visually, well-made fast and slow telescopes of the same aperture have no difference in image brightness or resolution.

Many binocular users know this already. While aperture, magnification, and exit pupil are the key specifications for binoculars, manufacturers never give the f/number of the objective as a specification. It means nothing as far as visual image brightness is concerned! I find that photographers have the most difficulty understanding this concept, because their experience that a faster f/number means brighter images on film and in the view-finder is so ingrained.

Field angle is another confusing subject. The true field of a telescope is the amount of actual sky we see in the eyepiece. It is determined by the field-stop diameter (the ring inside the front of the eyepiece that defines the edge of the field) and the focal length of the telescope.

Here's some information on typical telescope maximum fields for reference:

Focuser size (inches)	500-mm focal length	2,000-mm focal length
1¼	3.1°	0.8°
2	5.3°	1.3°

Eyepieces of very long focus may use the inside edge of the barrel as a field stop. This is why 2-inch eyepieces can have much larger true fields than 1¼-inch eyepieces. The in-side diameter of a typical 2-inch barrel is 1.7 times larger and has three times the area of the smaller barrels. Many eyepieces have field stops that are accessible for measurement by calipers. Others have field stops between the lens elements; such a stop's size cannot easily be used to determine the true field.

Regardless, you can find the true field of any eyepiece-telescope combination by the star-drift method. Point the telescope at a star near the celestial equator and, with the drive turned off, time the passage of the star centrally across the field. Since equatorial stars appear to move 15 arcminutes for each minute of time, you simply multiply the drift time in minutes of time by 15 to find the true field angle in arcminutes.

A rough approximation to the true field is obtained by dividing the apparent field of the eyepiece by the magnification. It's rough because eyepieces do not magnify linearly across the field, and a factor involving geometric "pincushion" distortion must be applied. Needless to say, this is usually known only to the designer. So use the star drift to determine true field accurately.

Apparent field is the angle perceived by your eye when the field stop is seen through the eyepiece. If you want to know which of two eyepieces is likely to have a larger apparent field, hold one up to each eye as if you were looking through binoculars. Position them so the field circles overlap, and it will be very clear which circle is larger.

Exit pupil is the image of the objective formed by the eyepiece. It's where you place your eye to view the entire field. Its diameter is equal to the objective diameter divided by the magnification. Binocular makers indirectly specify the exit pupil by always specifying the magnification and the aperture. The exit pupil may also be defined by the objective's f/number. For example, an eyepiece of 35-millimeter focal length, when used on an f/5 telescope, will give a 7-mm exit pupil. There is no single best exit pupil for low power or high power. As we shall see, it depends on many factors.

Resolution can be defined in many ways. By tradition, telescope manufacturers use the Dawes limit as a specification. During the 19th century in England, Rev. William R. Dawes observed with small refractors and found that he could just distinguish the components of faint double stars of equal magnitude when their separation was equal to 4.56 arcseconds divided by the aperture in inches. Of course it's just a guideline, since much larger or smaller scopes differ somewhat in performance. Furthermore, resolution is poorer when double stars have components of differing magnitudes.

The Dawes limit tells us nothing about the effects of contrast on resolving planetary details. It also ignores the fact that telescopes with apertures larger than about 9 inches can seldom achieve their theoretical ½-second or better resolution because of bad atmospheric seeing. Also, if the naked-eye resolution is 1 arcminute (for people with the best eyesight), you only need 120 power to see the resolution limit imposed by either Dawes' formula or the atmosphere. In practice, two or three times that magnification is more comfortable. Any magnification is possible, but I don't believe extraordinarily high powers reveal more than using 300x to 500x on any telescope.

Aperture gain will give you an idea of the faintest stars visible with a telescope. For example, the area gain of a 70-mm aperture over our eye's 7-mm aperture is 100 times. That's equal to a five-magnitude difference, so if 6th-magnitiude stars are visible with the naked eye, then 11th-magnitude stars should be seen in the 70-mm telescope. This reasoning ignores light loss in the optics.