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# Drift Testing to Determine Your Eyepiece's True Field of View

What if you want or need to know the angular diameter of an eyepiece's field of view in your telescope, that is, its "true field of view" (TFOV)? The simplest method is to divide the diameter of the eyepiece's "field stop" by the focal length of the telescope, both measured in millimeters, and to multiply the resulting fraction by a number which is usually expressed as 57.3 although it is actually the quotient of 180 divided by Pi. This will express the TFOV in degrees of arc, which you would multiply by 60 to convert it into arcminutes.

Unfortunately, however, the field stop diameters of most manufacturers' eyepieces are not conveniently available (TeleVue is an exception; it publishes the field stop diameters of its Nagler, Radian and Panoptic eyepieces). You can get some idea of the eyepiece's TFOV in degrees by dividing the eyepiece's readily available "apparent field of view" (AFOV) by its magnification power in your telescope, i.e. by the quotient of the telescope's focal length divided by the eyepiece's focal length, both usually expressed in millimeters. But, because of some optical issues that are too technical for a layman like me, this formula yields only a rough and exaggerated approximation of the TFOV.

You can measure the TFOV of an eyepiece with the drift test, noting how long it takes a star to drift from one edge of the eyepiece to the other while the telescope's tracking motor is turned off. This drift test can measure the TFOV fairly accurately, although it is obviously only possible for eyepieces that you already own or otherwise have access to, and not for others that you are thinking of acquiring. My suggested procedure for the drift test are as follows:

1. With your tracking motor still running, select a reasonably prominent star that is as close as possible to the celestial equator, and use your slow motion control to bring it to the center of your eyepiece. If you have an eyepiece with a cross reticle, you might use that eyepiece for this purpose before replacing it with the eyepiece whose TFOV you wish to test. By making sure that the star's drift path will take it across the very center of your field of view, you are trying so far as possible to make that path describe a full diameter of that field of view.

2. Use your slow motion azimuth or right ascension control to move the target star just out of view beyond the easternmost edge of the eyepiece and turn off the tracking motor. With a stopwatch, begin the timing when the star reappears at the edge of the field of view. If your target star is fairly bright you might see some glow from its light before the star is actually within the field of view, but the timing should not start until the star itself is in view.

3. The timing stops when the star, having drifted across the center, disappears on the opposite edge of the eyepiece's field of view.

4. I use the following formula to calculate the TFOV from the star's elapsed drift time, and a more detailed explanation of that formula follows below:

TFOV (in arcminutes) = S * (0.2506845 * COSDEC)

where S is the elapsed drift time across the eyepiece's field of view in seconds of time, and COSDEC is the cosine of the target star's declination in degrees (disregarding whether it is north or south of the celestial equator).

The formula was derived as follows: The star drifts across the field of view primarily because the earth, spinning about its polar axis, completes one rotation every day; but also because, as the earth revolves about the sun, it describes a complete orbit in a sidereal year. The earth's daily rotation causes any star on the celestial equator to drift through a complete 360º during any period of exactly 24 hours; this amounts to 15º per hour, or 1º per 4 minutes, or 15 arcminutes per minute of time. The earth's orbital revolution adds a complete 360º around the celestial equator per sidereal year. Using 365.2425 days as the length of a sidereal year, I concluded that there are 525,949.2 minutes of time in a sidereal year (365.2425 * 24 * 60), and because a complete 360º circle contains 21,600 arcminutes (360 * 60) the earth's orbit adds 0.0410686 arcminutes (21,600 ÷ 525,949.2) per minute of time to the apparent drift of a star at the equator (this figure is an average, since the rate of the earth's orbital motion is not constant under Kepler's second law, but I would not try any further refinement on this account and I doubt that any is necessary). Thus, a star located at the celestial equator will drift through 15.0410686 arcminutes every minute of time, which amounts to 0.2506845 arcminutes of drift per second of time.

But your target star is not likely to be precisely on the equator. The further from the equator it is, the longer it will take the star to drift across the angular width of your eyepiece's field of view and the smaller will be the angular measurement of its drift per unit of time. I accommodate this by multiplying the drift of a point on the equator by the fraction which is the cosine of the declination (in degrees) of the target star (at the equator, declination 0º, the cosine is precisely 1). If you then express the drift you have timed in minutes of time (with a fraction of a minute as a decimal, not in seconds), the TFOV in arcminutes would be M * (15.0410686 * COSDEC), where M is the measured time of the drift in minutes and COSDEC is the cosine of the drift star's declination. I choose to express the drift I have timed in seconds of time by dividing 60 into the 15.0410686 arcminute drift per time minute at the equator to arrive at the formula I have expressed above in paragraph 4 of my suggested procedures. I find it quicker to use seconds of time in this fashion than to restate the seconds that follow completed minutes as shown on my stopwatch as a decimal fraction of a minute.

Once you have determined its TFOV in this telescope, you can also calculate the diameter of the eyepiece's field stop that is so difficult to obtain from most manufacturers. Although this specification is useful only for the calculation of a TFOV and you have already measured this eyepiece's TFOV in the telescope at hand, you might need it if and when the eyepiece is to be used in other telescopes. The field stop in millimeters is the product of the eyepiece's TFOV in the telescope you used in the drift test, but expressed in degrees (using decimal degrees instead of arcminutes and arcseconds), multiplied by the quotient of that telescope's focal length in millimeters divided by 57.3 (i.e. by 180 divided by Pi).

Unfortunately, however, the field stop diameters of most manufacturers' eyepieces are not conveniently available (TeleVue is an exception; it publishes the field stop diameters of its Nagler, Radian and Panoptic eyepieces). You can get some idea of the eyepiece's TFOV in degrees by dividing the eyepiece's readily available "apparent field of view" (AFOV) by its magnification power in your telescope, i.e. by the quotient of the telescope's focal length divided by the eyepiece's focal length, both usually expressed in millimeters. But, because of some optical issues that are too technical for a layman like me, this formula yields only a rough and exaggerated approximation of the TFOV.

You can measure the TFOV of an eyepiece with the drift test, noting how long it takes a star to drift from one edge of the eyepiece to the other while the telescope's tracking motor is turned off. This drift test can measure the TFOV fairly accurately, although it is obviously only possible for eyepieces that you already own or otherwise have access to, and not for others that you are thinking of acquiring. My suggested procedure for the drift test are as follows:

1. With your tracking motor still running, select a reasonably prominent star that is as close as possible to the celestial equator, and use your slow motion control to bring it to the center of your eyepiece. If you have an eyepiece with a cross reticle, you might use that eyepiece for this purpose before replacing it with the eyepiece whose TFOV you wish to test. By making sure that the star's drift path will take it across the very center of your field of view, you are trying so far as possible to make that path describe a full diameter of that field of view.

2. Use your slow motion azimuth or right ascension control to move the target star just out of view beyond the easternmost edge of the eyepiece and turn off the tracking motor. With a stopwatch, begin the timing when the star reappears at the edge of the field of view. If your target star is fairly bright you might see some glow from its light before the star is actually within the field of view, but the timing should not start until the star itself is in view.

3. The timing stops when the star, having drifted across the center, disappears on the opposite edge of the eyepiece's field of view.

4. I use the following formula to calculate the TFOV from the star's elapsed drift time, and a more detailed explanation of that formula follows below:

TFOV (in arcminutes) = S * (0.2506845 * COSDEC)

where S is the elapsed drift time across the eyepiece's field of view in seconds of time, and COSDEC is the cosine of the target star's declination in degrees (disregarding whether it is north or south of the celestial equator).

The formula was derived as follows: The star drifts across the field of view primarily because the earth, spinning about its polar axis, completes one rotation every day; but also because, as the earth revolves about the sun, it describes a complete orbit in a sidereal year. The earth's daily rotation causes any star on the celestial equator to drift through a complete 360º during any period of exactly 24 hours; this amounts to 15º per hour, or 1º per 4 minutes, or 15 arcminutes per minute of time. The earth's orbital revolution adds a complete 360º around the celestial equator per sidereal year. Using 365.2425 days as the length of a sidereal year, I concluded that there are 525,949.2 minutes of time in a sidereal year (365.2425 * 24 * 60), and because a complete 360º circle contains 21,600 arcminutes (360 * 60) the earth's orbit adds 0.0410686 arcminutes (21,600 ÷ 525,949.2) per minute of time to the apparent drift of a star at the equator (this figure is an average, since the rate of the earth's orbital motion is not constant under Kepler's second law, but I would not try any further refinement on this account and I doubt that any is necessary). Thus, a star located at the celestial equator will drift through 15.0410686 arcminutes every minute of time, which amounts to 0.2506845 arcminutes of drift per second of time.

But your target star is not likely to be precisely on the equator. The further from the equator it is, the longer it will take the star to drift across the angular width of your eyepiece's field of view and the smaller will be the angular measurement of its drift per unit of time. I accommodate this by multiplying the drift of a point on the equator by the fraction which is the cosine of the declination (in degrees) of the target star (at the equator, declination 0º, the cosine is precisely 1). If you then express the drift you have timed in minutes of time (with a fraction of a minute as a decimal, not in seconds), the TFOV in arcminutes would be M * (15.0410686 * COSDEC), where M is the measured time of the drift in minutes and COSDEC is the cosine of the drift star's declination. I choose to express the drift I have timed in seconds of time by dividing 60 into the 15.0410686 arcminute drift per time minute at the equator to arrive at the formula I have expressed above in paragraph 4 of my suggested procedures. I find it quicker to use seconds of time in this fashion than to restate the seconds that follow completed minutes as shown on my stopwatch as a decimal fraction of a minute.

Once you have determined its TFOV in this telescope, you can also calculate the diameter of the eyepiece's field stop that is so difficult to obtain from most manufacturers. Although this specification is useful only for the calculation of a TFOV and you have already measured this eyepiece's TFOV in the telescope at hand, you might need it if and when the eyepiece is to be used in other telescopes. The field stop in millimeters is the product of the eyepiece's TFOV in the telescope you used in the drift test, but expressed in degrees (using decimal degrees instead of arcminutes and arcseconds), multiplied by the quotient of that telescope's focal length in millimeters divided by 57.3 (i.e. by 180 divided by Pi).

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