# true field of view

### #1

Posted 26 March 2014 - 08:30 PM

### #2

Posted 26 March 2014 - 08:38 PM

Eric

### #3

Posted 26 March 2014 - 09:12 PM

### #4

Posted 26 March 2014 - 09:15 PM

If you prefer to use the field stop of the eyepiece (if you have that value), the

True FOV = Eyepiece Field Stop / Focal length of the scope * 57.3 (or 180/pi if you prefer).

### #5

Posted 26 March 2014 - 11:34 PM

Can someone tell me what the formula is that tells me the true field of view of a telescope and eyepiece? Does it matter the size of scope or the f/? If I knew the answer I forgot it I guess.

OK, here is the whole story...

. . . . . . . . .

**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 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, and Nu Aquilae. Generally, a stopwatch that is accurate to a tenth of a second or better should be used to do the timings and an average of several timings should be take to reduce the effects of timing measurement errors.

. . . . . . . . .

**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/FL**

where "EFSD" is the eyepiece field stop diameter and "FL" 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 57.3*EFSD/FL. 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 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.

### #6

Posted 27 March 2014 - 03:55 PM

True FOV = Apparent FOV of eyepiece

Apprant field of view = arcsin(Eyepiece aperture/FL).

So barrel size is not in the equation, however, Eyepiece aperture can not exceed barrel size.

### #7

Posted 27 March 2014 - 04:20 PM

All about field of view....

True FOV = Apparent FOV of eyepiece

Apprant field of view = arcsin(Eyepiece aperture/FL).

So barrel size is not in the equation, however, Eyepiece aperture can not exceed barrel size.

Well, the formula is not quite that... But barrel size does limit field of view indeed.

In the case where distortion is not present (barrel or pincushion etc.),

AFOV = 2*arctan(1/2*FS/EFL)

where FS is eyepiece field stop diameter and EFL is eyepiece focal length.

So a 1.25" 28 mm eyepiece with 27.5 mm field stop (practical maximum for 1.25" barrel) will have an AFOV of about 52 degrees. A 2" 28 mm eyepiece with 48 mm field stop (practical maximum for 2" barrel) will have an AFOV of about 81 degrees.

That's where the 52 degrees and 82 degrees values come from...

That's also why there are no real 82 degree AFOV eyepieces with focal length longer than 30 mm, no 100 degree AFOV longer than 20 mm, and why 1.25" eyepieces AFOV begin to decrease past 28 mm or so.

As for true field of view,

TFOV = 2*arctan(1/2*FS/OFL)

where again FS is eyepiece field stop diameter, but here OFL is objective focal length.

So in a 500 mm focal length telescope, the 1.25" eyepiece with 27.5 mm field stop will give a TFOV of about 3 degrees and the 2" eyepiece with a field stop of 48 mm will give a TFOV of about 5.5 degrees.

Hope that helps!

--Christian

### #8

Posted 27 March 2014 - 04:58 PM

### #9

Posted 27 March 2014 - 05:01 PM

So, I guess my question should have been... With a 12" DOB with a 2" Crayford focuser should I get the TFOV (or close) using the formula afov/mag?

Yes, it's always a pretty good approximation for telescopes.

--Christian

### #10

Posted 27 March 2014 - 06:01 PM

As for true field of view,

TFOV = 2*arctan(1/2*FS/OFL)

A few thoughts and comments:

- For any real world situation, there is no difference between the equation using the arc-tangent, HKang's equation using the arc-sine and David's which uses the angle itself. Even at 5 degrees TFoV, the three differ by about 0.2%. I use David's because it is the simplest and most intuitive.

- For those reading about the field stop for the first time, David touched on what the field stop is but I think it is worth explaining more fully.

When you look through an eyepiece, you see the edge of the image. What you are seeing as the edge of the image is the field stop, it is an actually ring placed at the focal plane of the eyepiece and it limits the field of view. For eyepieces like Plossls, orthos, Kellners and many widefield eyepieces, you can remove the eyepiece from the focuser and look down the barrel and see the field stop, it will be a blackened ring. Some manufacturers like TeleVue provide the field stop diameters for their eyepieces. You can also measure it.

As you might expect, the size of the true field of view is proportional to the size of that ring, the larger the ring, the greater the field of view. And as you might imagine, the longer the focal length of the telescope, the smaller the field of view. The three equations presented here are just formalization's of this. The equation

TFoV= AFoV/Mag is a simplification of these equations.

- As has been said, the maximum size of the field stop depends on the size of the eye piece barrel. There are a few 1.25 inch eyepieces which place the field stop behind the barrel and accept some vignetting (darkening of the edge of the field) but for the vast majority of the eyepieces available, it the maximum size is 28mm, the size of the filter threads. For 2 inch eyepieces, the practical limit is 46mm.

- The relationship between AFoV and TFoV is a complicated one because in the real world, eyepieces do distort the field of view. While there are loose relationships that approximate the relationship, in reality, if one wants exact numbers, then both the AFoV and the TFoV must be measured directly. David Knisely has some interesting techniques that one can use to measure the AFoV, it's an fun thing to do on a Cloudy Night.

When all is said and done, the simple relationship TFoV = AFoV/Mag is accurate to within 10% and is most often within %5 and sufficient for most purposes.

Jon Isaacs

### #11

Posted 27 March 2014 - 07:26 PM

I guess the manufacture of my eyepieces must have done a good job in saying what the AFoV was for my eyepieces. I say that because measureing the TFoV by the drift time method and computing the TFoV = AFoV/Mag gave me the same size field-of-view within seconds of arc. Who needs the field-of-view to the second anyway?When all is said and done, the simple relationship TFoV = AFoV/Mag is accurate to within 10% and is most often within %5 and sufficient for most purposes.

Having said that, I should also say that all manufactures are not as accurate with there published AFoV sizes so using the drift time method is the way to go for accurate field sizes.

### #12

Posted 27 March 2014 - 07:51 PM

When all is said and done, the simple relationship TFoV = AFoV/Mag is accurate to within 10% and is most often within %5 and sufficient for most purposes.

Geez, I think I said that a long time ago

Eric

### #13

Posted 27 March 2014 - 08:06 PM

I guess the manufacture of my eyepieces must have done a good job in saying what the AFoV was for my eyepieces. I say that because measureing the TFoV by the drift time method and computing the TFoV = AFoV/Mag gave me the same size field-of-view within seconds of arc.

What eyepieces would those be? I have measured both the AFoV and TFoV for a number of eyepieces and the differences were significant. In general the AFoV's I measured were consistent with the manufacturer's numbers. How are you determining the AFoV?

Jon

### #14

Posted 28 March 2014 - 01:26 AM

AFOV = 2*arctan(1/2*FS/EFL)

Ah, yes, the arctangent function once again raises its ugly head when it comes to field of view Unfortunately, this equation does

*not*yield an accurate value for the apparent field of view.

*rather than calculated (and measuring it requires only the simplest of optical setups). Formulae for AFOV just aren't at all necessary and, as the above formula demonstrates, are often inaccurate. For just one example, I have a University Optics 40mm Mk-70 Konig (2-inch barrel OD). I measured its apparent field of view at 68.8 degrees and its field stop diameter as 46.00 mm. Using the above formula would yield an apparent field of view of 59.8 degrees, which is 13.1 percent off of the actual measured value. Even just equating the two regular true field formulae and solving for the apparent field of view would yield the approximation:*

**The apparent field of view of an eyepiece is a measured quantity**AFOV ~ (180/Pi)*FS/EFE

which for my example or the 40mm Konig would give an apparent field of view of 65.9 degrees. That is still 4.2 percent below the actual measured apparent field of view, but would at least be somewhat more in the ballpark. Again, the only way to determine the apparent field of an eyepiece is to

*measure*it accurately.

As for true field of view,

TFOV = 2*arctan(1/2*FS/OFL)

Ah, well again, use of the arctan function here just isn't extremely necessary (and may be confusing to the beginner). If the amateur needs to know the true field of view an eyepiece gives in a given telescope, it is best to actually measure it using the star drift method, but if one can't do that, the simple field stop formula I noted in my first posting on the subject is more than adequate for the job. In my extended tests of the various formulae for true field of view, the field stop formula was consistently within 1.5% of reality, which is plenty accurate. For an example, in my 10 inch f/5.6 Newtonian (1410 mm measured focal length), my 30mm Orion Ultrascopic eyepiece (26.08mm measured field stop) gives a

*measured*true field of view of 63.78 arc minutes (1.063 degrees). The above formula (and using the correct number of significant digits (4)) yields a true field figure of 1.060 degrees, while the field stop equation gives basically an identical true field figure, both only 0.282% off of reality. Not much of a difference here. Even approximating the 180/Pi to 57.3 still will yield a true field of view estimate accurate enough for most amateur use.

If more accuracy is needed, then

*measuring*the true field of view using the star drift method would be more appropriate. However, since this is the beginner's forum, to get an idea of the true field of view an eyepiece may give, the following two formulae can both be "good enough":

**TFOV = AFOV/Magnification**(accurate to between five and ten percent typically)

**TFOV = 57.3*EFSD/Fl**, where EFSD is the eyepiece field stop diameter and Fl is the telescope's focal length (accurate to less than two percent error from reality). Clear skies to you.

### #15

Posted 28 March 2014 - 04:36 AM

I guess the manufacture of my eyepieces must have done a good job in saying what the AFoV was for my eyepieces. I say that because measureing the TFoV by the drift time method and computing the TFoV = AFoV/Mag gave me the same size field-of-view within seconds of arc. Who needs the field-of-view to the second anyway?When all is said and done, the simple relationship TFoV = AFoV/Mag is accurate to within 10% and is most often within %5 and sufficient for most purposes.

Having said that, I should also say that all manufactures are not as accurate with there published AFoV sizes so using the drift time method is the way to go for accurate field sizes.

Actually, the old TFOV = AFOV/Mag is an approximation only. Sometimes it hits the number pretty closely and other times, it does not. For one example, I have Orion's 15mm Ultrascopic eyepiece. It has a measured apparent field of view of 58.3 degrees and a 14.40mm field stop. In my 10 inch f/5.55 Newtonian (1410mm measured focal length), the eyepiece gives me a measured true field of view of 35.38 arc minutes at 94x. The AFOV/Mag formula predicts a true field of 37.2 arc minutes, which is 5.1 percent high. The Field stop formula comes closer in its prediction at 35.1 arc minutes. However, I have a William's Optics 30mm Widescan III eyepiece with a measured apparent field of 84.0 degrees and a 44mm field stop. In my 10 inch, it gives me 47x and a true field of 1.798 degrees, which is nearly the same as the AFOV/Mag formula gives me (1.79 degrees). Thus, sometimes the AFOV/Mag formula works well and sometimes it doesn't quite hit the nail on the head. That is why I like the Field Stop formula a bit better, as it provides a consistently good estimate for the true field of view (error is usually less than two percent). Clear skies to you.

### #16

Posted 28 March 2014 - 12:53 PM

I understand that AFOV is a measured quantity. This is why I wrote:

"In the case where distortion is not present (barrel or pincushion etc.),"

But I don't believe in magic--there must be a way to understand the discrepancies.

For instance, if an arrangment of lenses has an accurately known effective focal length, accurately known principal planes, an accurately known field stop diameter, and very well corrected distortion (in which I lump all the radial variations in magnification), I really am at a loss to explain why the apparent field of view as experienced by a human observer could not be computed using focal length and field stop diameter only.

I have no reason to doubt the validity of your measurements, but your measured AFOV always seem to be larger than that computed with the arctan method.

This would be perfectly understandable if pincushion distortion were present. Enough to account for the difference? I don't know. Are there other factors that could influence the discrepancy? I don't know just yet.

Anyway, the semester is almost over, very soon I will have time to put all my eyepieces on an optical bench and do some measurements. Regards,

--Christian

### #17

Posted 28 March 2014 - 07:08 PM

I used the AFoV listed for the eyepieces in the manufactures literature. Using David's formula for true field-of-view with drift times, TFOV = 15.04*T (*only* for near-equatorial stars), and the formula for calculating true field-of-view,I guess the manufacture of my eyepieces must have done a good job in saying what the AFoV was for my eyepieces. I say that because measureing the TFoV by the drift time method and computing the TFoV = AFoV/Mag gave me the same size field-of-view within seconds of arc.

What eyepieces would those be? I have measured both the AFoV and TFoV for a number of eyepieces and the differences were significant. In general the AFoV's I measured were consistent with the manufacturer's numbers. How are you determining the AFoV?

Jon

TFOV = AFOV/Mag, I got true field-of-view sizes that were the same. I did this with a stop watch using Mintaka, the north western star in the belt of Orion, a few years ago. Say what ever you wont, the results were the same for my eyepieces using both methods. The eyepieces used were:

TV Panoptic 24mm,19mm,15mm

TV Nagler 13mm Type 6

TV Radian 10mm, 5mm

TMB Planetary 7mm, 4mm

So say what ever you will, I am telling you that the TFoV came out to be the same using both methods for these eyepices. As David said,

Well for me and my eyepieces, it was very close, no difference at all.Actually, the old TFOV = AFOV/Mag is an approximation only. Sometimes it hits the number pretty closely and other times, it does not...

### #18

Posted 29 March 2014 - 01:15 AM

I understand that AFOV is a measured quantity. This is why I wrote:

"In the case where distortion is not present (barrel or pincushion etc.),"

But I don't believe in magic--there must be a way to understand the discrepancies.

The problem is that, for whatever reason, your formula is just not all that correct. Let's take a very real-world example: the Tele Vue 17mm Ethos (29.6mm field stop diameter). I have verified that it has a field that has nearly zero distortion all across its whopping 100 degree apparent field, and its field stop figure is quite accurate. Your formula would calculate an apparent field of view of 82.1 degrees, but since the Ethos has a 100 degree apparent field, this is even farther off from reality (almost 18% low). I have a 14mm Explore Scientific "100 degree" eyepiece which, unlike the Ethos, does have a mild amount of pin-cushion distortion. Its actual measured apparent field is 101 degrees and its field stop is 24.47mm. Your formula would yield an apparent field of 71.5 degrees, which is even farther off from the actual number (29% low). These results with extreme field values point to a definite flaw in the analysis that lead to the derivation of the formula for apparent field which you gave. With some sort of detailed ray-tracing of the eyepiece, an accurate apparent field might be calculated, but not with some simple formula. The closest that a simple formula might come would be equating the two true field equations and solving for the apparent field. For the 17mm Ethos, the calculation would give an apparent field figure of 99.8 degrees, which is pretty close (probably because the field stop is an "effective" one designed to yield fully accurate true field figures using the field stop formula). Even for my 14mm ES100 with its visible pin-cushion distortion, this approximation yields 100.2 degrees, which again is a fairly decent figure even with that distortion. However, for my 24mm Panoptic, the formula would calculate an apparent field of 64.5 degrees, which is about 5.1 percent low. While that approximation (AFOV = 57.3*EFSD/EFL) may be somewhat useful in the rough sense, like the old AFOV/Mag formula for true field, it is an approximation at best. Again, apparent field of view is what it is (there is no overriding reason to calculate it when you can easily measure it). Clear skies to you.

### #19

Posted 29 March 2014 - 04:01 AM

**MEASURING THE APPROXIMATE**............

....

**APPARENT FIELD OF VIEW OF AN EYEPIECE**....

"Both-eyes Open" Technique:

MATERIALS: 1. A Meterstick, Yardstick, or other linear device whose length is accurately known, which can be hung vertically on a wall, and whose exact middle or center is accurately marked. This could also be a narrow strip of paper of known length with its exact middle and ends marked clearly. This object will be known as the observing "target".

2. A method of holding and properly supporting an eyepiece rigidly in a horzontal position (like a bracket attached to a camera tripod), but which can be manually moved towards or away from a measuring target.

3. A tape measure.

STEP #1: Mount the vertical "target" (ie: the Yardstick or its substitute) on the wall so that its exact middle is will be about same height above the floor as the center of the eyepiece. For a meter stick, the midpoint will be the 50cm mark, and for a yardstick, it will be the 18 inch mark. Mark this midpoint with a visible marking like a small piece of tape or a black felt tip marker, so the middle can be easily seen from a distance.

STEP #2: Mount the eyepiece at a height above the floor which is exactly the same as the mid-point of the target, so that the observer can look into the eye lens with the eyepiece optic axis or barrel horizontal and parallel to the floor. Make certain the eyepiece is as horizontal as possible, and that it can be easily moved towards or away from a nearby wall from as little as two feet from the wall to as much as six feet away.

STEP #3: place the eyepiece straight out from the wall from where the observing "target" is located. Look into the eyepiece with *both* eyes open and merge the images of the eyepiece field of view and the target. Make the center of the superimposed eyepiece field centered on the mid-point mark of the observing target as closely as possible, and keep your head level with the floor (ie: keep your eyes at the same height above the floor).

STEP #4: Look at the top and bottom of the target, again with both eyes open. With both eyes open, try to make the top and bottom edges of the eyepiece field match the top and bottom edges of the target on the wall by carefully moving the eyepiece towards or away from the wall. Make certain when moving the eyepiece that it remains pointed exactly towards the center of the observing target, and that its height above the floor does not change. Once the edges of the eyepiece field match the top and bottom of the target, take the tape measure and measure the distance from the back of the eyepiece just beyond the eye lens (ie: where your eye was sitting when you were looking through the eyepiece) to the middle of the target on the wall. If the target has a length of "2Y" and the distance to the wall you measured is "D", then the apparent field of view of the eyepiece is then AFOV = 2*ATAN (Y/D), where Y is *half* the total length of the target and ATAN the arc-tangent (or inverse tangent) function. For example, if you were using a yardstick (36 inches in length, or Y = 18.0 inches) and your eyepiece field matched its length at a distance of 37.0 inches from the center of the target, the apparent field of view of the eyepiece would be about 51.8 degrees. You may have to look around a bit and be careful about eye placement to see the edges of the field stop and get the edges to line up properly with the outer target marks, so this method is not quite as accurate as the next one:

"Projection" technique:

MATERIALS: 1. Small flashlight with adustable front lens (Maglight is ideal).

2. A method of holding and properly supporting an eyepiece rigidly in a horizontal position (like a bracket attached to a camera tripod), but whichcan be manually moved towards or away from a measuring target. Also needed is a way to hold a flashlight horizontally so its beam goes directly into the field lens of the eyepiece.

3. A tape measure.

4. A wall with a large sheet of paper on it (butcher paper or newsprint is fine).

STEP #1: Mount the eyepiece so that the eye lens is facing the wall with the long axis perpedicular to the wall. Place the flashlight several feet away from the eyepiece and oriented so that its collimated beam can enter the field lens of the eyepiece.

STEP #2: Turn on the flashlight and turn out the room lights. Adjust the lens of the flashlight to produce a concentrated and roughly collimated parallel beam as it heads into the eyepiece.

STEP #3: Look at the wall and move the flashlight laterally until a large white disk appears on it (with wide-field eyepieces, only a portion of this disk may be visible at any one orientation of the flashlight). Measure the diameter of this disk.

STEP #4: Find the point behind the eye lens where the light from the flashlight appears to be coming to the most point-like focus. This is the "focal point" of the eyepiece. Then, measure the distance from that point to the middle of the projected light disk on the wall. If the projected disk has a diameter of "2Y" and the distance to the wall from the focal point is "D", then the apparent field of view of the eyepiece is then AFOV = 2*ATAN (Y/D), where Y is *radius* of the disk and ATAN the arc-tangent (or inverse tangent) function. Also, if you measure the distance from the focal point to the surface of the eye lens, that is the eye relief of the eyepiece. This method seems to give more consistent values for the apparent field, but also in some cases will produce an apparent field of view that is slightly smaller than that obtained by the "both-eyes open" technique.

Clear skies to you.

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### #20

Posted 29 March 2014 - 04:20 AM

I have measured AFoVs using David's project technique. It is most interesting to see the differences between eyepieces, the diameter of the projected circle between a 50 degree eyepiece, a 68 degree eyepieces and an 82 degree eyepiece is surprisingly large.

But.. when all is said and done.. for most purposes the simple equation TFoV= AFoV/Mag is all one needs..

Jon

### #21

Posted 29 March 2014 - 07:13 AM

In the case where distortion is not present (barrel or pincushion etc.),

AFOV = 2*arctan(1/2*FS/EFL)

where FS is eyepiece field stop diameter and EFL is eyepiece focal length.

David K wrote:

The problem is that, for whatever reason, your formula is just not all that correct. Let's take a very real-world example: the Tele Vue 17mm Ethos (29.6mm field stop diameter). I have verified that it has a field that has nearly zero distortion all across its whopping 100 degree apparent field, and its field stop figure is quite accurate.

Obviously they mean something very different with "distortion". And no wonder - the phoograpy term "distortion" is for mapping a plane (object) to a plane (film), and simply not applicable to EPs that map a flat (almost) image at the focal plane to a (larger or smaller) virtual celestial sphere. This problem is the opposite of mapping a spherical Earth to a flat map.

In either case, you may preserve some aspect, while others are distorted (The Mercator projection preserves angles, but not distances or areas!).

With real EPs, in particular modern well corrected types with negative field lens like the Naglers or the Ethos in David's example, conform closely to AFOV=FS/EFL (multiply by 180/pi = 57.3 to take the angle from radians to degrees.)

Here, the radial magnification is constant over the field - a circular object like Mars at opposition will be the same radial size even though compressed to an ellipse toward the field edge. And (terrestrial) straight lines will distort by bending.

I partly disagree with Buddy - I have measured the 24 Panoptic, and (like the Plössls I measured) it has a noticeable increase in manification toward the field edge - conspicuous when watching the Moon. And accordingly, it would have an AFOV of 64.5 deg if not (instead of 68). An old Nagler 1 conformed accurately to the calculations.

With a hypothetic EP that would keep the circular shape, the apparent size will shrink near the edge, and one that does not bend lines will instead flatten a circle tangentially.

Is this important? well, at least it teaches us to forget the idea of "distortion-free" - there is no distortion-free eyepiece (maybe a Ramsden 40 mm in a 0.965 barrel would come close ).

Nils Olof