Telescope Reviews: AFOV vs TFOV

MEASURING AND CALCULATING THE TRUE FIELD OF VIEW

Although the True Field of View of an eyepiece/telescope combination can be calculated with at least two common formulae, its actual size can only be accurately determined by using a star field of known size, or by using the star-drift method (a better choice). To use the star-drift method, take a star of known declination and, with any drive systems turned off, time exactly how long it takes for the star to go from one field edge directly through the center of the field and over to the opposite field edge. For equatorially-mounted telescopes, this can be done for any convenient star, but for altazimuthly-mounted "Dobsonians", it is a bit easier to use a star near the meridian (ie: pretty much straight south but fairly high above the southern horizon). The True Field Of View (TFOV) is then:

TFOV = 15.04*T*Cos(delta)

where "delta" is the star's declination, "Cos" is the Cosine function, and "T" is the measured drift time interval. If the time is measured in minutes, the true field will be in minutes of arc, and if the time is in seconds, the true field will be in seconds of arc. For example, if a star has a declination of 25.5 degrees (ie: 25 degrees 30 minutes), and a measured drift time of 2.75 minutes (ie: 2 minutes 45 seconds), the true field of view is then 37.3 arc minutes in diameter. For comparison, the moon's angular diameter is around 30 arc minutes (half a degree), so this eyepiece/telescope combination would just barely allow the full moon to fit in the field of the eyepiece. For stars within 3 degrees of the celestial equator, the Cosine function can be approximated to 1, and the formula becomes:

TFOV = 15.04*T (*only* for near-equatorial stars)

Alternatively, a near-equatorial timing in minutes can also be divided by 3.989 to get the true field in degrees. Some useful stars for this kind of measurement are: Zeta Aquarii, Delta Ceti, 10 Tauri, Delta Orionis, Alpha Sextantis, Zeta Virginis, Nu Aquilae, ect.

CALCULATING APPROXIMATE TRUE FIELD OF VIEW

It can also be nice to have a simple formula which can give the amateur a rough idea of what true field of view an eyepiece will give in a telescope without the amateur having to buy the eyepiece and go out to measure things. Two such formula do indeed exist: the Apparent Field of View method, and the Eyepiece Field Stop method.

1. APPARENT FIELD OF VIEW METHOD: this calculates the true angular field on the sky a telescope will show using a given eyepiece by dividing the Apparent Field of View of that eyepiece (the angular span your eye sees when looking into the eyepiece) and divides it by the magnification that eyepiece gives when used in the telescope:

TFOV = AFOV/Mag

where "AFOV" is the eyepiece apparent field of view and "Mag" is the magnification or "power" that eyepiece yields when in the telescope. For example, if an eyepiece has an apparent field of 50 degrees and yields 45x in the telescope, the true field will be approximately 1.1 degrees. Generally, with accurate Apparent Field figures, the Apparent Field of View method can often get within 10 percent of the actual true field of view on the sky. However, some eyepiece retailers or manufacturers don't always provide extremely accurate figures for their eyepieces, although many amateurs are able to measure the apparent field with simple "optical bench" setups.

2. EYEPIECE FIELD STOP METHOD: involves measuring the physical diameter of the Field Stop at the front of the eyepiece. The field stop is usually a ring or narrow baffle located just in front of the front "field" lens of the eyepiece. In some more complex wide-field designs, the field stop may be inside the front field lens between the elements, and in some less-expensive eyepieces, the field stop is the eyepiece barrel itself. The field for a given eyepiece is given by:

TFOV = (180/Pi)*EFSD/TFL

where "EFSD" is the eyepiece field stop diameter and "TFL" is the telescope's focal length. The "180/Pi" out front is just the number of degrees in a radian, so the formula can be approximated as

TFOV = 57.3*EFSD/TFL. For example, if the eyepiece has a field stop diameter of 25.40mm (1 inch), and the telescope focal length is 1410mm, the true field of view with that eyepiece will be about 1.032 degrees. Most eyepieces with 1.25 inch OD barrels will have field stop diameters of less than 28mm, while 2 inch OD barrel eyepieces will have field stops of less than 47mm. The Eyepiece Field Stop method tends to be somewhat more accurate than the Apparent Field of View method (often within two percent of the actual field on the sky) as long as an accurate value for the field stop diameter can be obtained.

Clear skies to you.

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David W. Knisely
Hyde Memorial Observatory
http://www.hydeobservatory.info