Is it important to know the manufacturers field stop when calculating True FOV? I notice that the indirect method of calculating (AFOV / Magnification) doesn't give the same True FOV that the manufacturer offers by using the actual field stop.

# Field Stop: Calculated vs Manufacturer?

### #1

Posted 21 October 2021 - 06:09 PM

### #2

Posted 21 October 2021 - 06:57 PM

My understanding is that distortion in the eyepiece optics can cause the simple relationship between field stop diameter (in mm), eyepiece focal length (mm), and eyepiece apparent field of view (AFOV) to break down.

If you are after the "True FOV" in degrees on the sky, then you are probably better off using the eyepiece field stop (in mm) and the scopes focal length (mm). That should avoid the distortion details inside the eyepiece.

### #3

Posted 21 October 2021 - 07:39 PM

That ratio does not account for ** angular distortion**... which is common... and especially-so as the Apparent Field of View increases.

* Rough estimate >>>* TFOV = AFOV / magnification

* Better estimate >>>* TFOV

^{o}= (180 x D

_{FS}) / πF --- where D

_{FS}is the diameter of the field stop, and F is the telescope's focal length

* Exact >>>* TFOV = 2 arctan (D

_{FS}/ 2F)

I'm not sure why people just don't use the exact one and be done with it. It's hardly any more complicated than the estimates. Maybe because the atan function is a wee bit perplexing, and intuiting that also involves realizing that the focal length is measured from the telescope's ~Image-Space Nodal Point~ to the Axial Focal Point... which waxes arcane. Tom

**Edited by TOMDEY, 21 October 2021 - 07:42 PM.**

### #4

Posted 21 October 2021 - 09:34 PM

I get the impression you can trust TV specs to be spot on. Others are hit and miss.

Scott

### #5

Posted 21 October 2021 - 09:40 PM

Be advised that often manufacturers advertised field stop is off a bit. Often it’s minor. I have two eyepieces with the exact same FOV. One is supposedly 19.3 and one 19.6. But then I have a Luminos where the advertised field stop is comically off. I don’t know what they were measuring, but it wasn’t the field stop.

I get the impression you can trust TV specs to be spot on. Others are hit and miss.

Scott

Also the field stop dimension provided is ~as the telescope sees it~ So if there is eyepiece glass between the physical stop and the telescope, it is that virtual image of the mechanical stop... as seen from the telescope side... that they are talking about. And it is *that *which is used in the exact equation. For TeleVue eyepieces, that should work just fine. Tom

### #6

Posted 21 October 2021 - 11:17 PM

Be advised that often manufacturers advertised field stop is off a bit. Often it’s minor. I have two eyepieces with the exact same FOV. One is supposedly 19.3 and one 19.6. But then I have a Luminos where the advertised field stop is comically off. I don’t know what they were measuring, but it wasn’t the field stop.

I get the impression you can trust TV specs to be spot on. Others are hit and miss.

Scott

Advertised and measured field stops are reported (when available) in Don Pensack’s Eyepiece Buyer’s Guide. Posted at the top of the Eyepiece forum.

### #7

Posted 21 October 2021 - 11:45 PM

Negative/positive eyepieces have such field stops but they cannot be used to calculate the true field. They have Effective field stop diameters that are different than the hard iris.

Unfortunately, many negative positive designs have their iris field stop diameters reported instead of their Effective field stops. It can lead to confusion. One popular eyepiece is listed with a field stop of 30.4mm though the eyepiece has an effective field stop diameter of 36.4mm, and it is the 36.4mm diameter that is used to calculate true field.

### #8

Posted 22 October 2021 - 12:02 AM

That ratio does not account for

... which is common... and especially-so as the Apparent Field of View increases.angular distortion

TFOV = AFOV / magnificationRough estimate >>>

TFOVBetter estimate >>>^{o}= (180 x D_{FS}) / πF --- where D_{FS}is the diameter of the field stop, and F is the telescope's focal length

TFOV = 2 arctan (DExact >>>_{FS}/ 2F)

I'm not sure why people just don't use the exact one and be done with it. It's hardly any more complicated than the estimates. Maybe because the atan function is a wee bit perplexing, and intuiting that also involves realizing that the focal length is measured from the telescope's ~Image-Space Nodal Point~ to the Axial Focal Point... which waxes arcane. Tom

The "exact" equation and the better estimate are equal for all practical purposes. These are small angles so the small angle approximation is sufficient

Consider the case of the NP-101 with the 31mm Nagler. This is about as wide as it gets in the telescope world.

Better Estimate = 180/Pi x 42/540 = 4.456 degrees

Exact Estimate = 2 atan (21/540) = 4.454 degrees

Now consider the significant digits. The field stop is specified as 42mm, the scope 540mm. TeleVue field stops are normally spec's to 0.1mm so if one assumes the 31mm Nagler's field stop is 42.0 mm, one can only justify 3 significant figures. That does not include the precision of the focal length of the scope.

With a longer focal length scope or smaller field stops, the difference is even smaller since the angle is smaller.

Consider a scope with a 1800mm focal length and a field stop of 22.3 mm:

Small angle approximation = 180/Pi x 22.3 mm / 1800 = 0.70983 degrees

Tangent calculation = 2 atan (22.3 /3600) = 0.70982 degrees

Even something as crazy as the 21mm Ethos in a scope with a 200mm focal length is well within reason..

Small angle = 10.34 degrees

Tangent = 10.37 degrees

Realistically, the small angle approximation is more exact than anyone has a practical use for and is more accurate than the number of significant digits supports.

Jon

- David Knisely, TOMDEY and CowTipton like this

### #9

Posted 22 October 2021 - 03:52 AM

I generally won't bother measuring the field stop physically unless it is a relatively simple eyepiece. Instead, I will calculate it by putting the eyepiece of interest in an equatorially-mounted telescope with a known focal length (not an SCT with moving mirrors) and, using the star drift timing method, measure the true field of view over multiple passes, taking the average as the final number. I then work backwards using the "simple" field stop formula TFOV = (180/Pi)*EFSD/Fl (EFSD is eyepiece field stop diameter and Fl is the telescope focal length) to get an "equivalent" field stop diameter for a given eyepiece which I can then use for a variety of different telescopes to determine what true field they may yield. I often use my old 10 inch f/5.55 Newtonian for getting useful field stop estimates, as I have actually measured its precise focal length (1410 mm) on my test bench I use for Foucault testing, although surprisingly, my Chinese 100mm f/6 refractor is pretty accurately at a 600mm focal length too. I have played with the various "Tangent" true field formulae over the years, but quite frankly, the older simpler Field Stop one is more than accurate enough (generally around one percent or less deviation from measured reality) to get me a useful true field "estimate" for a given eyepiece/telescope combination that I might want to use. If, for some particular reason, you *really* want to know the true field as accurately as possible, then it would be best to actually just measure it on the sky (it's not that hard). Then, you don't have to bother with field stops or focal lengths. Clear skies to you.

- Starman1 and Jon Isaacs like this

### #10

Posted 22 October 2021 - 04:49 AM

The "exact" equation and the better estimate are equal for all practical purposes. These are small angles so the small angle approximation is sufficient

Consider the case of the NP-101 with the 31mm Nagler. This is about as wide as it gets in the telescope world.

Better Estimate = 180/Pi x 42/540 = 4.456 degrees

Exact Estimate = 2 atan (21/540) = 4.454 degrees

Now consider the significant digits. The field stop is specified as 42mm, the scope 540mm. TeleVue field stops are normally spec's to 0.1mm so if one assumes the 31mm Nagler's field stop is 42.0 mm, one can only justify 3 significant figures. That does not include the precision of the focal length of the scope.

With a longer focal length scope or smaller field stops, the difference is even smaller since the angle is smaller.

Consider a scope with a 1800mm focal length and a field stop of 22.3 mm:

Small angle approximation = 180/Pi x 22.3 mm / 1800 = 0.70983 degrees

Tangent calculation = 2 atan (22.3 /3600) = 0.70982 degrees

Even something as crazy as the 21mm Ethos in a scope with a 200mm focal length is well within reason..

Small angle = 10.34 degrees

Tangent = 10.37 degrees

Realistically, the small angle approximation is more exact than anyone has a practical use for and is more accurate than the number of significant digits supports.

Jon

* Yep; that's good!* The reason I always derive

*exact*equations is so that the degrees of approximations become overt. I fondly recall a paper we were composing for some JOSA or SPIE journal regarding space-borne segmented systems. The primary co-author used a quadratic approximation, and I derived the exact form and handed it to him. He seemed a wee bit miffed, and said it didn't matter; I yawned and sipped my coffee. And years earlier in Optics 442 class, I interrupted the teacher, pointing out that he used the sin of an angle, whereas it should be the tan. He was downright irate, and said it didn't matter --- which in his context... it most certainly did matter! I yawned, and took a puff on my cigarette. Tom

### #11

Posted 22 October 2021 - 05:42 AM

Is it important to know the manufacturers field stop when calculating True FOV? I notice that the indirect method of calculating (AFOV / Magnification) doesn't give the same True FOV that the manufacturer offers by using the actual field stop.

There are possible sources of the difference:

(1) angular distortion

AFOV = TFOV*MAG works only in a very first approximation. More correct expression looks like this: AFOV = (1 + D_{ep})*(1 + D_{lens})*TFOV*MAG where D_{ep} - common angular eyepiece distortion, D_{lens} - common angular distortion of scope lens (mirror) or approximately AFOV = TFOV*MAG + ( D%_{ep} + D%_{lens})*TFOV*MAG/100% - with distortion in percentage form.

My measurements show that for typical eyepiece angular distortion value is in range -5%...+5%. Distortion of scope main mirror/lens is usually less.

(2) difference between physical and effective FS diameter

Eyepieces with Balow-like component before FS have natural difference diameter of FS between their elements and virtual FS limiting FOV.

(3) error in the eyepiece datasheet (e.g. bad copy)

- Starman1 and j.gardavsky like this

### #12

Posted 22 October 2021 - 11:19 AM

I long ago abandoned the old TFOV = AFOV/Mag formula, as my tests indicated that for my 'suite' of eyepieces (even with their accurately measured AFOV values), it can be as much as 5.1% off of what I actually measured (the simple Field Stop formula had a maximum deviation of 1.4%). Still, it can be useful for sort of quick "off the cuff" estimates if you don't yet know the field stop. However, I recall the AFOV/Mag formula being seriously "abused" by certain eyepiece retailers and manufacturers to get apparent fields that are way off of what they really are. The Antares 5-8mm Speers Waler adjustable focal length eyepiece was one in particular. Now the eyepiece itself was pretty good (one of my favorites even now), but the early ads for it used the AFOV = TFOV*Mag formula to create some silly apparent field of view claims for that particular eyepiece (81 to 89 degrees depending on the focal length selected). I measured the apparent field of view using my "both-eyes open" method, and got 78.5 degrees, a figure that didn't appear to change as I moved the eyepiece's focal length selector (movable "Smyth" field flattening lens) so I guess for those early production advertisements, it was all about selling the darn thing instead of the truth. I did calculate a couple of "effective" field stop diameters for the maximum and minimum focal lengths of the 5-8 Speers-Waler, but usually I don't bother with others, as I would rather just sit back and enjoy the view in that eyepiece with the ability to tailor the power to suit my needs at the moment. Clear skies to you.

**Edited by David Knisely, 23 October 2021 - 01:54 AM.**

- Jon Isaacs likes this