Binoculars are specified by a series of numbers and letters, for example, 15x70 BIF.GA.WA. The numbers tell you the size of the binocular and the letters give additional information. The first number is the angular magnification, the second is the aperture of the objective lens in millimeters. The example therefore has a magnification ("power") of 15, an aperture of 70 mm, a body of Bausch & Lomb (a.k.a. "American") construction (B), individually focusing eyepieces (IF), rubber armour (GA), and wide-angle eyepieces (WA). There is a complete list of designation letters in Appendix F.

The numbers in the binocular specifications give rise to a variety of binocular ratings that are sometimes quoted by manufacturers and vendors. The most common are:

• Relative Brightness. This is the square of the diameter of the exit pupil. The exit pupil diameter is calculated by dividing the aperture by the magnification (power). For example, for 10x50, the exit pupil is 5 mm and the relative brightness is (50/10)2 = 52 = 25. However the calculation for a 20x100 binocular, through which a great deal more can be seen, gives exactly the same relative brightness:

(100/20)2 = 52 = 25, so this is an inadequate rating to use for astronomical binoculars. Incidentally, this is also the relative brightness that is calculated for the Mark-I eyeball (1x5) of a human being approximately 60 years old! Whereas it does give information about the surface brightness of extended objects, it says little about the overall performance. I have no doubt that I see far more in my 10x50 binoculars than I do with the naked eye, and that I see significantly more in my 20x100 binocular.

• Twilight Index or Twilight Performance Factor. This was used by Carl Zeiss International as an indication of the distances at which comparable detail would be seen in different binoculars. It is calculated by finding the square root of the product of the magnification and aperture. For the two binoculars above the calculations are:

In this instance, the larger instrument has an index that is double that of the smaller instrument. In other words, if the smaller binocular is used to observe a target object at a given distance from the observer, the same amount of detail will be visible at double the distance in the larger instrument. This is not really applicable to visual observational astronomy where we are usually not concerned with the relative distances of objects and consider them to be effectively at the same distance.

• Visibility Factor. Roy Bishop devised the method to evaluate the visibility factor simply by multiplying the magnification by the aperture in millimeters. For our two binoculars above we obtain:

The larger instrument has a visibility factor four times greater than the smaller one. Bishop justifies this by stating: "in the larger instrument stars will be four times brighter and extended images will have four times the area from which the eyes can glean information, with luminances being the same."1 While this is objectively correct, I am not convinced that it reflects the subjective experience of observing through both instruments.

• Astro Index. Alan Adler's2 astro index evaluates the product of the magnification and the square root of the aperture in millimeters. For our two binoculars above, we obtain:

This gives the larger instrument an astro Index of 2.8 times the smaller one; this is certainly closer to the experience of observing through them.

Others have tried to expand on these by including the effects of coatings, baffles, and other aspects of individual quality, but, although these may be more precise, they incorporate a certain amount of empirical experimental data and are not as valuable for a quick evaluation, prior to purchase, of likely performance.3

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