AFOV (Apparent Field of View)

How do I calculate this for my eyepieces, or is it a matter of gauging
the FOV by eye -- perhaps by looking at starfields with known apparent
distances between the stars?

Actually, I'm a little confused between FOV and AFOV.

Many thanks,

Sean

Sean O'Dwyer wrote:

How do I calculate this for my eyepieces, or is it a matter of gauging
the FOV by eye -- perhaps by looking at starfields with known apparent
distances between the stars?

Actually, I'm a little confused between FOV and AFOV.

Well, Sean, there are two types of field of view: Apparent Field of View
(AFOV), and True Field of View (TFOV). The TFOV is the field of view that a
telescope covers on the *sky* with a given eyepiece. It is usually measured
in degrees for wider fields or in "minutes of arc" for smaller ones (there are
60 arc minutes in a degree). For example, many low power telescope fields are
on the order of one degree or smaller (one degree *on the sky* is nearly twice
the angular size of the full moon. Thus, if your telescope and eyepiece
combination yields a true field of one half degree, you would see most if not
all of the entire full moon in when looking into the eyepiece.
Apparent Field of View (AFOV) is the angular size of the field that your
own *eye* sees when just looking into the eyepiece (whether its in a telescope
or not). Take an eyepiece out of the scope and hold it up to a bright
background and look into the eye-lens end (the one you normally look through
when its in the telescope). You should see a large bright disk of light
(maybe a little fuzzy at the edges). The angular diameter of that disk as
seen by your eye is the AFOV. To get an idea of what this all means, take an
old toilet paper tube (4.375 inches long and 1.75 inches wide) and put it up
against your eye. The area you can see in front of you of the rest of the
room out of that tube will appear to be about 23 degrees wide to your eye.
The AFOV of eyepieces range from as little as 30 degrees for some simple
designs like Ramsdens or HM eyepieces to as much as 85 degrees for the
expensive "wide-field" eyepieces like the Naglers. However, most eyepiece in
the moderate cost range have Apparent fields of view ranging from a little
above 40 degrees to nearly 60 degrees.

CALCULATING TRUE FIELD OF VIEW

The true field of view of an eyepiece/telescope combination 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. The true
field of view 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 field will be in minutes of
arc, and if the time is in seconds, the field will be in seconds of arc. For
example, if a star has a declination of 27.0 degrees, and a measured drift
time of 2.50 minutes (2 minutes 30 seconds of time), the true field of view is
then 33.5 arc minutes. 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. 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 a Zeta Aquarii, Delta Ceti, 10 Tauri, Delta Orionis,
Alpha Sextantis, Zeta Virginis, Nu Aquilae, ect.
However, 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.
The Apparent Field of View method calculates the true angular field on
the sky a telescope will show using a given eyepiece by taking the Apparent
Field of View of that eyepiece (the angular span your eye sees when looking
into the eyepiece) and dividing it by the magnification that eyepiece gives
when used in the telescope: TFOV = AFOV/Mag, where Mag is the focal length of
the telescope divided by the focal length of the eyepiece. 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.
The 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 (about 57.296).
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.
The field stop method is a little more accurate than the AFOV/Mag method,
but the field stop can sometimes be a bit hard to measure yourself (and field
stop figures are not often provided by the manufacturer). The apparent field
figures given by most eyepiece makers tend to be only very approximate
figures, although with a little trigonometry and a simple jig, the AFOV can
also be measured if you have the eyepiece in hand. Clear skies to you.

--
David W. Knisely
Prairie Astronomy Club: http://www.prairieastronomyclub.org
Hyde Memorial Observatory: http://www.hydeobservatory.info/

**********************************************
* Attend the 11th Annual NEBRASKA STAR PARTY *
* July 18-23, 2004, Merritt Reservoir *
* http://www.NebraskaStarParty.org *
**********************************************

Wow, thanks so much for such a clear and useful post.

Sean

Wow, thanks so much for such a clear and useful post.

Sean

Sean O'Dwyer wrote:

How do I calculate this for my eyepieces, or is it a matter of gauging
the FOV by eye -- perhaps by looking at starfields with known apparent
distances between the stars?

Actually, I'm a little confused between FOV and AFOV.

Well, Sean, there are two types of field of view: Apparent Field of View
(AFOV), and True Field of View (TFOV). The TFOV is the field of view that a
telescope covers on the *sky* with a given eyepiece. It is usually measured
in degrees for wider fields or in "minutes of arc" for smaller ones (there are
60 arc minutes in a degree). For example, many low power telescope fields are
on the order of one degree or smaller (one degree *on the sky* is nearly twice
the angular size of the full moon. Thus, if your telescope and eyepiece
combination yields a true field of one half degree, you would see most if not
all of the entire full moon in when looking into the eyepiece.
Apparent Field of View (AFOV) is the angular size of the field that your
own *eye* sees when just looking into the eyepiece (whether its in a telescope
or not). Take an eyepiece out of the scope and hold it up to a bright
background and look into the eye-lens end (the one you normally look through
when its in the telescope). You should see a large bright disk of light
(maybe a little fuzzy at the edges). The angular diameter of that disk as
seen by your eye is the AFOV. To get an idea of what this all means, take an
old toilet paper tube (4.375 inches long and 1.75 inches wide) and put it up
against your eye. The area you can see in front of you of the rest of the
room out of that tube will appear to be about 23 degrees wide to your eye.
The AFOV of eyepieces range from as little as 30 degrees for some simple
designs like Ramsdens or HM eyepieces to as much as 85 degrees for the
expensive "wide-field" eyepieces like the Naglers. However, most eyepiece in
the moderate cost range have Apparent fields of view ranging from a little
above 40 degrees to nearly 60 degrees.

CALCULATING TRUE FIELD OF VIEW

The true field of view of an eyepiece/telescope combination 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. The true
field of view 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 field will be in minutes of
arc, and if the time is in seconds, the field will be in seconds of arc. For
example, if a star has a declination of 27.0 degrees, and a measured drift
time of 2.50 minutes (2 minutes 30 seconds of time), the true field of view is
then 33.5 arc minutes. 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. 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 a Zeta Aquarii, Delta Ceti, 10 Tauri, Delta Orionis,
Alpha Sextantis, Zeta Virginis, Nu Aquilae, ect.
However, 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.
The Apparent Field of View method calculates the true angular field on
the sky a telescope will show using a given eyepiece by taking the Apparent
Field of View of that eyepiece (the angular span your eye sees when looking
into the eyepiece) and dividing it by the magnification that eyepiece gives
when used in the telescope: TFOV = AFOV/Mag, where Mag is the focal length of
the telescope divided by the focal length of the eyepiece. 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.
The 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 (about 57.296).
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.
The field stop method is a little more accurate than the AFOV/Mag method,
but the field stop can sometimes be a bit hard to measure yourself (and field
stop figures are not often provided by the manufacturer). The apparent field
figures given by most eyepiece makers tend to be only very approximate
figures, although with a little trigonometry and a simple jig, the AFOV can
also be measured if you have the eyepiece in hand. Clear skies to you.

--
David W. Knisely
Prairie Astronomy Club: http://www.prairieastronomyclub.org
Hyde Memorial Observatory: http://www.hydeobservatory.info/

**********************************************
* Attend the 11th Annual NEBRASKA STAR PARTY *
* July 18-23, 2004, Merritt Reservoir *
* http://www.NebraskaStarParty.org *
**********************************************