Dumb question about eyepieces

In calculating the field stop diameter of an eyepiece, I've always used the
formula:

Field stop = focal length * 2 * tan(apparent field /2)

which I *thought* was right. However, with Tele Vue eyepieces, I only get
the published figures if I use the sine function rather than the tangent
function. What's going on? Do all reasonably-wide-field eyepieces have
distortion?

Does an optics book discuss this somewhere?


--
Clear skies,

Michael Covington -- www.covingtoninnovations.com
Author, Astrophotography for the Amateur
and (new) How to Use a Computerized Telescope

Michael,
This could be a couple things. Naglers have their field stop internal to the
eyepiece, so there could be some magnification. This isn't true for Plossls,
so if the error is there across the product line, it's more likely, they use
whatever gives the larger number because that's what their competitors do.
Very common with 32mm 50* eyepieces.

But your Math is right from what I can tell. Optics frequently uses
approximations, since sin(angle) = tan (angle) = angle in radians for small
angles. That's one reason for second and third order aberrations off-axis.

Have fun,
Frank

"Michael A. Covington" wrote
in message ...
In calculating the field stop diameter of an eyepiece, I've always used
the
formula:

Field stop = focal length * 2 * tan(apparent field /2)

which I *thought* was right. However, with Tele Vue eyepieces, I only get
the published figures if I use the sine function rather than the tangent
function. What's going on? Do all reasonably-wide-field eyepieces have
distortion?

Does an optics book discuss this somewhere?


--
Clear skies,

Michael Covington -- www.covingtoninnovations.com
Author, Astrophotography for the Amateur
and (new) How to Use a Computerized Telescope

Michael,
This could be a couple things. Naglers have their field stop internal to the
eyepiece, so there could be some magnification. This isn't true for Plossls,
so if the error is there across the product line, it's more likely, they use
whatever gives the larger number because that's what their competitors do.
Very common with 32mm 50* eyepieces.

But your Math is right from what I can tell. Optics frequently uses
approximations, since sin(angle) = tan (angle) = angle in radians for small
angles. That's one reason for second and third order aberrations off-axis.

Have fun,
Frank

"Michael A. Covington" wrote
in message ...
In calculating the field stop diameter of an eyepiece, I've always used
the
formula:

Field stop = focal length * 2 * tan(apparent field /2)

which I *thought* was right. However, with Tele Vue eyepieces, I only get
the published figures if I use the sine function rather than the tangent
function. What's going on? Do all reasonably-wide-field eyepieces have
distortion?

Does an optics book discuss this somewhere?


--
Clear skies,

Michael Covington -- www.covingtoninnovations.com
Author, Astrophotography for the Amateur
and (new) How to Use a Computerized Telescope

function. What's going on? Do all reasonably-wide-field eyepieces have
distortion?

Does an optics book discuss this somewhere?


Michael:

This topic has been frequently discussed here and initially I presented a
formula similar to yours. However many learned folks such as David Knisely,
Brian Tung responded and pointed out that my formula did not agree with the
actual measured numbers.

I think that because of different eyepiece designs, there is no formula that is
exact but that the simple formula on the TeleVue page is the one that works the
best:

Field Size (°) = (eyepiece field stop diameter / telescope focal length) x
57.3 °.

The basic assumption seems to be that the field of view is a spherical surface
rather than a flat surface as I had assumed.

However when I think about AFOV, TFOV and how they are measured, it seems clear
to me that the spherical approach is the best one.

Apparent FOV is pretty nebulous concept because it cannot be measured directly.
It is normally measured by timing the drift of a star across the FOV and using
the magnification to compute the AFOV.

Now when I consider the path that the star takes as moves from the field stop
on one side of the focal plane to the other, its rate should be constant on a
spherical surface rather than a flat plane because the rotation of that star is
just a lever arm of the rotation of the earth.

The formulas used to compute magnification, field of view, apparent field of
view etc are all first order, and based on this simple curved surface.

The reality of course is the the actual equations are probably far more
complicated and dependent upon particulars for each eyepiece and even each
telescope-eyepiece combination.

But one needs to be consistent, trying to make a second order correction such
as you and I did means that all the relationships need to have second order
corrections. And those other relationships are still first order.

I am sure soon David, Brian and all the rest will respond, explain things more
clearly, point out my further logical mistakes, but for now, this ought to get
things started.

Happy Holidays to All...

jon

function. What's going on? Do all reasonably-wide-field eyepieces have
distortion?

Does an optics book discuss this somewhere?


Michael:

This topic has been frequently discussed here and initially I presented a
formula similar to yours. However many learned folks such as David Knisely,
Brian Tung responded and pointed out that my formula did not agree with the
actual measured numbers.

I think that because of different eyepiece designs, there is no formula that is
exact but that the simple formula on the TeleVue page is the one that works the
best:

Field Size (°) = (eyepiece field stop diameter / telescope focal length) x
57.3 °.

The basic assumption seems to be that the field of view is a spherical surface
rather than a flat surface as I had assumed.

However when I think about AFOV, TFOV and how they are measured, it seems clear
to me that the spherical approach is the best one.

Apparent FOV is pretty nebulous concept because it cannot be measured directly.
It is normally measured by timing the drift of a star across the FOV and using
the magnification to compute the AFOV.

Now when I consider the path that the star takes as moves from the field stop
on one side of the focal plane to the other, its rate should be constant on a
spherical surface rather than a flat plane because the rotation of that star is
just a lever arm of the rotation of the earth.

The formulas used to compute magnification, field of view, apparent field of
view etc are all first order, and based on this simple curved surface.

The reality of course is the the actual equations are probably far more
complicated and dependent upon particulars for each eyepiece and even each
telescope-eyepiece combination.

But one needs to be consistent, trying to make a second order correction such
as you and I did means that all the relationships need to have second order
corrections. And those other relationships are still first order.

I am sure soon David, Brian and all the rest will respond, explain things more
clearly, point out my further logical mistakes, but for now, this ought to get
things started.

Happy Holidays to All...

jon

On Sat, 20 Dec 2003 17:24:15 GMT, Frank Bov
wrote:

In calculating the field stop diameter of an eyepiece, I've always used
the formula:

Field stop = focal length * 2 * tan(apparent field /2)

which I *thought* was right. However, with Tele Vue eyepieces, I only
get
the published figures if I use the sine function rather than the tangent
function. What's going on? Do all reasonably-wide-field eyepieces have
distortion?

Does an optics book discuss this somewhere?


Try this simple formula to calculate the theoretical field stop of an
eyepiece:

FS = (AFOV * FL)/57.3

Lawrence Sayre

On Sat, 20 Dec 2003 17:24:15 GMT, Frank Bov
wrote:

In calculating the field stop diameter of an eyepiece, I've always used
the formula:

Field stop = focal length * 2 * tan(apparent field /2)

which I *thought* was right. However, with Tele Vue eyepieces, I only
get
the published figures if I use the sine function rather than the tangent
function. What's going on? Do all reasonably-wide-field eyepieces have
distortion?

Does an optics book discuss this somewhere?


Try this simple formula to calculate the theoretical field stop of an
eyepiece:

FS = (AFOV * FL)/57.3

Lawrence Sayre

Michael A. Covington wrote:

In calculating the field stop diameter of an eyepiece, I've always used the
formula:

Field stop = focal length * 2 * tan(apparent field /2)

which I *thought* was right. However, with Tele Vue eyepieces, I only get
the published figures if I use the sine function rather than the tangent
function. What's going on? Do all reasonably-wide-field eyepieces have
distortion?

Well, to be honest, the only way to determine the true size of an eyepiece's
field stop is to physically measure it. However, for those with internal
field stops (Naglers, Ultrawides, ect.), the field stop isn't exactly
accessable (although I did take apart my Meade 14mm Ultrawide: 20.3mm field
stop). I can come up with an "equivalent" field stop via the exact true field
measurement in the scope and working backwards with the field stop formula for
true field of view: TFOV = (180/Pi)*EFSD/Fl, where EFSD is the eyepiece field
stop diameter and Fl is the telescope focal length. For the field stops in my
eyepieces I can actually measure, the field stop formula yeilds true fields
which are within one or two percent of the actual measured fields, so it works
pretty well. I have used this to "approximate" the equivalent field stop for
one bizarre eyepiece I have; the 4.9-7.9mm Speers-Waler. At its longest focal
length, the equivalent field stop is about 11.3mm, and at its shortest focal
length, its about 7.7mm. 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 *
**********************************************

Michael A. Covington wrote:

In calculating the field stop diameter of an eyepiece, I've always used the
formula:

Field stop = focal length * 2 * tan(apparent field /2)

which I *thought* was right. However, with Tele Vue eyepieces, I only get
the published figures if I use the sine function rather than the tangent
function. What's going on? Do all reasonably-wide-field eyepieces have
distortion?

Well, to be honest, the only way to determine the true size of an eyepiece's
field stop is to physically measure it. However, for those with internal
field stops (Naglers, Ultrawides, ect.), the field stop isn't exactly
accessable (although I did take apart my Meade 14mm Ultrawide: 20.3mm field
stop). I can come up with an "equivalent" field stop via the exact true field
measurement in the scope and working backwards with the field stop formula for
true field of view: TFOV = (180/Pi)*EFSD/Fl, where EFSD is the eyepiece field
stop diameter and Fl is the telescope focal length. For the field stops in my
eyepieces I can actually measure, the field stop formula yeilds true fields
which are within one or two percent of the actual measured fields, so it works
pretty well. I have used this to "approximate" the equivalent field stop for
one bizarre eyepiece I have; the 4.9-7.9mm Speers-Waler. At its longest focal
length, the equivalent field stop is about 11.3mm, and at its shortest focal
length, its about 7.7mm. 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 *
**********************************************

"David Knisely" wrote

Well, to be honest, the only way to determine the true size of an
eyepiece's
field stop is to physically measure it.

Along this same line, how does one know if the eyepiece's stated focal
length is accurate? You, David, extensively answered this question once
before, but I am still surprised that a TeleVue, with their fancy charts and
graphs, would state a focal length so inaccurately (see below).

The only aspect of the eyepiece/telescope combination I *can* measure is the
true field of view. If the stated field stop/apparent field of view of a
TeleVue eyepiece is accurate, then I can work backwards to find the true
focal length...which so far is somewhat inaccurately stated by TeleVue. For
example, if my 4.8mm Nagler is really 4.8mm, then the apparent field of view
is 71.55 degrees, not 82. (I made several 'drift' timings of a star at the
equator.) Since the afov sure *looks* a lot wider than 71.55, I interpret
the focal length as being shorter than 4.8mm.

Howard Lester




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