# Eyepiece Aparent Field of View?

### #1

Posted 11 February 2013 - 08:27 AM

### #2

Posted 11 February 2013 - 10:09 AM

Hope this helps,

Greg

### #3

Posted 11 February 2013 - 12:32 PM

As to measuring AFoV if not known, there are different ways to do this.

You can hold a flashlight against the skyward end of an eyepiece and project an image of the field stop onto a wall. If the flashlight cannot fill the full circular field with light, you can swing the flashlight so as to alternately see opposite sides, while the eyepiece is held immobile. Try to maximize the projection distance, as this improves accuracy in your calculation.

Measure the diameter of the projected image of the field stop. Measure the distance between the wall (at the center of the image) and a distance behind the eye lens equal to the eye relief (more on this below.)

The apparent field if view equals

ARCTAN([ diameter / 2] / projection distance)

If unknown, the eye point, or eye relief distance is where a sharp image of the telescope's objective is formed some distance behind the eye lens. Fir most eyepieces, this varies between about 8-20mm. If your projection distance is large, you could simply assume an eye point of about 1/2 to 2/3 the eyepiece focal length. For example, if the projection distance is 600mm, an error of 10mm on the eyepoint distance introduces a 1.6% error in your calculation. (You can see how a large projection distance improves accuracy.)

### #4

Posted 12 February 2013 - 04:31 AM

You can hold a flashlight against the skyward end of an eyepiece and project an image of the field stop onto a wall. If the flashlight cannot fill the full circular field with light, you can swing the flashlight so as to alternately see opposite sides, while the eyepiece is held immobile. Try to maximize the projection distance, as this improves accuracy in your calculation.

Glenn:

David Knisely has a nice post with a drawing that describes this technique.

Determining the AFoV

I have used David's technique but held the eyepiece in a scope and projected a beam of collimated light (from another scope) into it's objective. Then I found I could just use one scope with the light source on a tripod. A scope is a good way to mount large eyepieces securely.

It's definitely an interesting experiment, the size of the circle projected on the wall is quite impressive and the difference in the projected beam between a 15 degree difference in AFoV is impressive.

Jon

### #5

Posted 05 May 2013 - 08:45 AM

With all that said, I cannot see how this EP can be claimed to be 68 degrees. Or is this method so crude to be basically unreliable? For one thing the light was not truely collimated. I did the measurement 42 inches from the wall and held the light 18 inches behind the eyepiece. I did experiment with greater eyepiece-to-light distances but did not see the circle size change. 18 inches gave me an easily viewable circle.

I find it hard to belive that Baader could fudge this number knowing that it is "easily" measured. I did notice that the position of the circle moves around on the wall as the angle of the incoming light is changed. Could they be measuring the limits defined by the extreme positions of the circle?

### #6

Posted 05 May 2013 - 09:11 AM

I find it hard to belive that Baader could fudge this number knowing that it is "easily" measured.

You did not mention how much effort you made in measuring the distance from the eyepiece to the position of the exit pupil. This is a small but significant correction and the measurement needs to be carefully done. If you didn't measure the location of the exit pupil, then using the eye relief specification for the eyepiece would provide a first cut, something like 20mm, making the distance from the wall closer to 41 inches.

42 inches seems like a long distance to the wall, the circle would be about 57 inches in diameter. I believe I was closer. When I did it, I mounted the eyepiece in a refractor and mounted the light on a tripod pointed at the objective lens.

Jon

### #7

Posted 05 May 2013 - 11:20 AM

### #8

Posted 05 May 2013 - 04:28 PM

Again I'm just amazed that Baader could get a free pass on fudging the number. Thats a huge selling feature. I'd be willing to bet they have some way to defend it.

Oh BTW, I put in the 14mm "Fine Tuning Ring" and got the same results.

### #9

Posted 05 May 2013 - 05:13 PM

### #10

Posted 05 May 2013 - 05:58 PM

Since TF= (FSEP/TFL)*57.296,

and we know FSEP (Field Stop of Eyepiece) for the 21 Hyperion is 22.5mm, then we can figure out the True Field as = (22.5/TFL)*57.3

Compare that to the timed True Field.

The difference is likely to be distortion, or error in the figure for the focal length of your telescope (TFL).

If I assume a minimal distortion at the edge, I get an apparent field of 64 degrees, so it is likely the distortion percentage is higher than a minimal figure at the edge.

But, how well have you measured the focal length of your scope?

You will get highly inaccurate results if you use TF = AF/M

not the least reason of which is the likely inaccuracy in knowing the true focal length of the eyepiece (which could be +/- a couple tenths) and the last of knowledge of the exact focal length of your scope, so M is questionable.

Then there is experimental error: even if you take 4 timings of a star on the celestial equator, you could be off a bit. And arithmetic rounding errors creep in: since a sidereal day is 1436 minutes long, not 1440, the passage of 1 degree of field takes 3.989 minutes, not 4.

So let's assume you DON'T know the focal length of your telescope.

Since you can measure true field directly, what is the Telescope Focal length that yields that true field with a 22.5mm field stop?

Solving for TFL (telescope focal length),

TFL = (EPFS*57.296)/TF in degrees.

EPFS =22.5mm for the 21 Hyperion, so:

TFL = (1289.16)/TF in degrees.

So, my advice to you is to not use the manufacturer's claims for apparent field to calculate true field if you have the field stop figure. And if the telescope focal length is known EXACTLY, then the difference between the calculated true field using the field stop figure and the actual true field will be distortion, and having some degree of distortion isn't abnormal.

The real question is where the manufacturer comes up with the apparent field figure. It's calculated in the design phase of the eyepiece. It's not experimentally determined. And here is something to keep in mind: the apparent field will vary slightly by the focal length of the scope in which it's used. So, though we could determine exactly what the apparent field is in our scope by deriving it, it's not an accurate enough figure for our true field determination. Field stop is the better figure to use.

But, alas, even the field stop can be derived from other characteristics of the eyepiece and can be an "Effective Field Stop" rather than an "Actual field stop". Either way, using the field stop to calculate true field is even easier if you know the image scale of your telescope (degrees per millimeter of focal plane.

Example:

My dob has a focal length of 62.50" = 1587.5mm.

If I arbitrarily pick 50mm as my focal plane width, I get a True field on the focal plane of 1.8047 degrees. Divide by 50 and I get 0.0361 degrees per millimeter on the focal plane of the scope.

Multiply that by the field stop and I can tell you the true field for any eyepiece with a simple multiplication (e.g. 31mm Nagler, 42mm Field Stop, 1.516 degrees true field)

It's that easy IF you know the focal length of the scope and IF you know the field stop of the eyepiece. Magnification doesn't even enter the picture, and neither does apparent field (so why not just trust the MFR's apparent field figure?).

If you have the 2013 Buyer's Guide to Eyepieces (posted at the top of the Eyepieces Forum), there is a field called "Calculated Field Stop" which presumes the mfr isn't lying about the apparent field and will calculate a field stop instantly if you insert the focal length of your scope in the formula for the cell where 1400 is placed. If you know Excel, you can copy the formula down to the bottom of the spreadsheet (it won't work for zooms).

If the manufacturer's field stop figure is listed, the discrepancy in the calculated figure and the true figure is distortion (or the manufacturer is lying about the Apparent Field).

Boy, that really muddies the waters, doesn't it? I see the apparent field test described as having a lot of experimental measurement errors, though, and thought I would point out that the apparent field is not the best way to calculate true field.

### #11

Posted 05 May 2013 - 07:38 PM

OK, you can work backwards from the formula to find the apparent field, but it will be an Effective Field of View.

Don:

I believe Rick is using David Knisely's projection method of measuring the AFoV of an eyepiece. Basically you project the light backwards through the eyepiece, measure the distance from the exit pupil to the wall, do a bit of trig and arrive at an AFoV.

Rick seems to be surprised that the numbers are not in exact agreement with the published values. Given the possible sources of error in this technique, particularly in the execution and the various assumptions, I would be happy to be within 3 degrees.

Jon

### #12

Posted 05 May 2013 - 07:59 PM

My interest in the AFOV is not as a ladder to further parameters but is for its own sake. I like a wide view. (Who doesn't ) The wider the better. So when I see an eyepiece billed as 68 degrees I expect it to show my eyeball 68 degrees of view. 61 is good for sure. And if I see 64 then that's really good. But I paid for 68. And of course I don't have an angular readout on my eyeball so Glenn's little tutorial on physically measuring the AFOV seemed like a nice way to truth check the manufacturer.

### #13

Posted 06 May 2013 - 12:24 AM

I did take into account the eye relief distance. The largest measurement for circle was 52.5 and I think that was the straightest shot which gave the 64 degree result.To get 68 degrees with a 52.5 inch circle my distance would have to be off by 3 inches.

Again I'm just amazed that Baader could get a free pass on fudging the number. Thats a huge selling feature. I'd be willing to bet they have some way to defend it.

Oh BTW, I put in the 14mm "Fine Tuning Ring" and got the same results.

If you are having problems with the projection technique, try the "both eyes open" technique:

...........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. It also tends to yield a slightly larger apparent field figure than the projection technique sometimes. Clear skies to you.

### #14

Posted 06 May 2013 - 11:02 AM

### #15

Posted 06 May 2013 - 11:39 AM

Just turn off the clock drive if there is one, then aim the scope at a star very near the celestial equator. Record when the star first enters the field, and when it exits the field. The star needs to travel across the center of the field to assure it is going across a field diameter rather than an off-center chordal line. Measure several FOV transits and average the results.

As David Knisely correctly points out below, you can use any star as long as you know its declination.

Earth turns very close to 15 angular arc seconds in one time second. Stars appear to move faster nearest the celestial equator and slowest at either pole. The angular speed follows cosine(declination). Therefore, multiply the averaged FOV transit time in seconds by 15, then by cosine(declination). This gives the true field in angular arc seconds. Divide by 60 to give the true FOV in arc minutes, and again by 60 to give the true FOV in degrees. This method accounts for everything (eyepiece distortion, atmospheric refraction and dispersion, etc.). Should be more than enough accuracy for you.

Mike

PS: Thanks Dave for catching my hasty omission. Mike

### #16

Posted 06 May 2013 - 08:01 PM

Does it matter that much? 68 or 64 degrees?

False advertising matters. (

*If*it is 64 or less and they know it.) It should matter to their competitors. Unless they're also lying.

### #17

Posted 07 May 2013 - 01:26 AM

+1 for the star drift method. The OP wanted to know true field. This is just like timing occultations and transits.

Just turn off the clock drive if there is one, then record when a star first enters the field, and when it exits the field. The star needs to travel across the center of the field to assure it is going across a field diameter rather than an off-center chordal line. Measure several FOV transits and average the results.

Earth turns very close to 15 angular arc seconds in one time second. Therefore, multiply the averaged FOV transit time in seconds by 15. This gives the true field in angular arc seconds. Divide by 60 to give the true FOV in arc minutes, and again by 60 to give the true FOV in degrees. This method accounts for everything (eyepiece distortion, atmospheric refraction and dispersion, etc.). Should be more than enough accuracy for you.

Mike

Well, not quite. One needs to know the star's declination in order to do the star drift method accurately if the star is notably farther than a few degrees from the celestial equator. 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 almost any convenient star (other than those quite near the celestial poles), 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 (to around 0.14% accuracy), 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.

Clear skies to you.

### #18

Posted 07 May 2013 - 05:09 AM

Does it matter that much? 68 or 64 degrees?

False advertising matters. (Ifit is 64 or less and they know it.) It should matter to their competitors. Unless they're also lying.

When you can positively measure the AFoV to within a fraction of a degree and analytically demonstrate the validity of the techniques you are using, that might be the time to consider making claims of false advertising.

At this time though, I think there are enough questions about the validity of the measurements, the assumptions made, the possibility of systematic errors, I consider an interesting exercise but not one I am fully confident in.

What did you find using David's second technique?

Jon

### #19

Posted 07 May 2013 - 05:56 AM

M.

### #20

Posted 07 May 2013 - 07:19 AM

Mike

### #21

Posted 07 May 2013 - 11:54 AM

Similarly, the star is allowed to drift not quite centrally across the field. To 1% accuracy, the star can pass 0.13 of the field radius from the center, and to 2% accuracy, 0.2 of the field radius.

If one has a rough idea of the equator's location in some part of the sky (e.g., that it passes very near delta Orionis), a suitable star can be chosen and treated as having zero declination. And a trial pass or two with even a non-equatorially mounted scope to ascertain by eye alone a sufficiently close to central drift.

### #22

Posted 07 May 2013 - 03:39 PM

Does it matter that much? 68 or 64 degrees?

False advertising matters. (Ifit is 64 or less and they know it.) It should matter to their competitors. Unless they're also lying.

Generally, I can measure the apparent fields to an accuracy of around half a degree or so with a little work. Much beyond that, it probably isn't really worth worrying about. What I have found is that most of the published eyepiece apparent fields of view are within a degree or two of what I get on the bench. There have been a few exceptions however. In the case of the variable Speers-Waler eyepieces (the 5-8mm and 8.5-12mm focal length models), the manufacturer/retailer apparent field claims for the 5-8mm model went from 82 to 89 degrees when the actual eyepiece had a *fixed* measured apparent field of view of 78 degrees. It was pretty clear in that case that all the manufacturer/retailer had done was work backwards from the old TFOV = AFOV/Magnification formula, so the claimed apparent field figures were useless. Also, some eyepiece "families" (the Orion Ultrascopics for example) have apparent fields of view that vary from eyepiece to eyepiece, yet some retailers just give one figure for the lot that can be more than two or three degrees off the figures for each different eyepiece. I would prefer that the retailers just give a single field stop figure for each of their eyepieces (or equivalent field stop figure based on a star-drift calculation) rather than playing games with apparent field of view (the Field Stop formula for true field is more accurate than the old AFOV/Mag formula anyway). However, with the exception of Tele Vue, this isn't generally being done, which is a little sad. Still, it doesn't take much work on the part of amateurs to discover the real truth behind the figures for their own eyepieces. Clear skies to you.

### #23

Posted 10 May 2013 - 04:44 AM

Does it matter that much? 68 or 64 degrees?

False advertising matters. (Ifit is 64 or less and they know it.) It should matter to their competitors. Unless they're also lying.

When you can positively measure the AFoV to within a fraction of a degree and analytically demonstrate the validity of the techniques you are using, that might be the time to consider making claims of false advertising.

Jon

I did not make a claim of false advertising. I was asked if it mattered that much to me if the FOV was 64 instead of 68. I answered that question with specific caveats. Notice the word "if" in italaics. Don't read more into my post than is there. Admitingly I could have worded that better. How about: A few degrees of missing FOV wouldn't matter that much but receiving what was advertised does. I also said in another post that I'm sure the manufacturer has some way to defend their number.

I appreicate the help given here explaining various methods of measureing the AFOV. I have not had the time to attempt other methods. Maybe that says something about how much it matters to me. When I get the time I may give them a try.