EYEPIECE TRUE FIELD:
Calculations versus Drift Measurements

This is a comparative test of the CALCULATIONS of true field of an eyepiece, in a given scope, derived from the published ocular focal length and apparent field values (using two online Javascript scope calculators -- found here and here -- and the Waldee-Wood "Eyepiece" software) against actual tests done by an amateur astronomer, Paul Markov.

It should be noted that the Waldee-Wood Eyepiece program does not claim to calculate the actual true field; we explain that we are predicting the approximate visual field, because, logically, there is only ONE true field, and that's that! True is true; anything else, by definition, is NOT TRUE, or is an approximation or calculation. The other eyepiece calculators we've seen never make this distinction; and since the measured true field is almost always narrower than the calculated one, we wanted to make this issue very clear.

The eyepieces used are these, with "AF" designating the advertised  apparent fields:

Meade 40mm SWA 2-inch: 68° AF
University Optics 32mm König 1.25-inch: 52° AF
Meade 26mm Super Plössl 1.25-inch: 52° AF
Tele-Vue 15mm Plössl 1.25-inch: 50° AF

The telescope of Paul Markov is this one:

Meade 10" LX 200:
Optical Diameter: 10.0" (254 mm)
Focal Length: 98.4" (2500 mm)

"I did some rough measurements of the actual field of view of my eyepieces [in a Meade 10" LX-200] ...

"[Then] I did an accurate measurement of each eyepiece's field of view. I did this by aiming the telescope on a star close to the meridian at zero declination. With the telescope drive off, I timed how long it took a star to cross the field of view. The number of seconds divided by 240 gives the field of view in degrees. To convert to minutes, multiply degrees by 60."

Below is a chart made up of the values obtained in Paul's two methods of measuring the true field, shown in the last two columns on the right; the three columns on the left are calculated values from two online Javascript programs and "Eyepiece" software.

Paul's method of measuring the true field is not quite as precise as the one we recommend in "Eyepiece", which is explained in our Topic - Help file as follows:

                    MEASURING THE TRUE VISUAL FIELD

          If the field of view of the eyepiece/scope is very accurately
      measured, it is properly called the "true" or "real" field.  The
      procedure given by Luginbuhl and Skiff in "Observing Handbook and
      Catalog of Deep-Sky Objects" is as follows:

          Time the passage of a star as it drifts through the eyepiece field;
      multiply the (time in minutes) X (15) X (cosine of the declination of
      the star) to obtain the true field in minutes.  Thus, for a 4 minute 30
      second transit of a star at 10 degrees 30 minutes declination:

        (4.5)  X  (15)  x  (cos 10.5) = 66.37 minutes [or 66 min., 22 sec.]

          If you cannot conveniently obtain the cosine of the declination,
      an alternate method is to use a star very near the celestial equator,
      time the transit, and multiply the time by 15 to obtain the true field
      in minutes; the closer the star to the equator, the more accurate the
      result.

          The usual formula for mathematically calculating the true field from
      the eyepiece specifications, if there is absolutely no vignetting in the
      optical path, is:

         True Field = (Apparent Field Angle determined by the field stop
                       or barrel diameter) divided by (magnifying power)

          Not all eyepieces or telescopes comply with this absolute
      criterion of correct optical path design, so our program does not
      claim to calculate the "true field" of the eyepiece, but rather to
      predict the "estimated eyepiece visual field," which may be somewhat
      less if the eyepiece and telescope have not been perfectly defined.

So, Paul's resulting measurements may not be exactly the same as ones done by the Lughinbuhl/Skiff method we describe in "Eyepiece". And, this eyepiece review article by Otto Piechowski includes an addendum -- "Methods of Calculating the TFOV" -- that also covers two other methods: by measuring the field-stop, and by comparing against an accurate star chart, using a precise scale indicator.

On this forum, a question is asked to clarify the situation.

As I understand it - regardless of whatever size eyepiece you use, the theoretical TFOV as calculated from eyepiece size, focal length of the telescope, and AFOV is still restricted by the field stop diameter... Did I get that right? -- ColHut

An answer is given by a contributor with the moniker "Gargoyle_Steve, Space Explorer" (gee, don't you just love the cutesy names people come up with?):

Col what you've said is basically dead right - the actual theoretical limit of a 1.25" barrel ep (one in which the barrel diameter itself is the field stop) is approx 32mm I believe - anything over this is being vignetted by the barrel.

The precise calculation for True FOV using field stop diameter is :

TFOV = (180/Pi)*field stop / Scope focal length.

180/Pi converts the calculation from radians to degrees - approx 57.296

The problem can occur in actually measuring the field stop of a given ep, usually simple for standard plossls although it gets more difficult as the field stop gets smaller or harder to access to measure accurately. In some more advanced design ep's it can be very difficult to measure the field stop, especially for those designs where the field stop itself lies between lens elements inside the ep and is not externally visible as such.

I have read that "calculating" true FOV by dividing magnification into apparent FOV gives an approximation only and may have up to 10% error, however it's still a fairly good guide and easily calculated in any ep where the apparent field of view is known.

IF you want a big field of view... get a good 2" ep in a longer focal length. Generally if you want a 30, 35, etc mm ep then it should be manufactured as a 2" barrel version for pretty much the reasons have related. You just can't get a really good "true" wide view in a 1.25" barrel.

I hope I've helped clarify things and not muddied the waters further.

Cheers! -- Gargoyle_Steve

It took me a while to find the apparent field measurements of the University Optics 1.25" König eyepiece; apparently it is 52 degrees, according to at least two websites, though another one claims 50. This would be roughly equal to the Orion "Sirius" Plössl 32 mm 1.25" eyepiece apparent field; one wonders why the König design was necessary. At any rate, the calculated true field, using either of the two online Javascript applets or the "Eyepiece" program, is MUCH larger than the results obtained by either of the two measurements by Markov, the more casual first measurement or the very careful drift-measurement. One perhaps might be tempted to conclude from this (assuming Markov made no mistake) that the claimed apparent field of this eyepiece is WRONG, and far too large.

The other oculars are within the range of deviation between the calculated value done by "Eyepiece" and the drift measurement that I have observed in my own testing: i. e., the true field derived from a drift test is ALWAYS smaller than the projected calculation. There are many explanations and caveats given in the Waldee-Wood software program to warn users to expect this ('garbage in=garbage out') since the advertised values are not always the actual dimensions of the oculars (due to the problem of manufacturers not always using identical methods of measuring and documenting their products, or even inflating some figures, or rounding them off favorably to make their numbers 'look good'.)

In the case of Paul's 2" barrel eyepiece, used on an LX 200 scope, there is also the possibility that vignetting has been caused by the optical system. Some experts have claimed that commercial f/10 Schmidt-Cassegrain scopes are not optimally designed for 2" low-power oculars.

The online Javascript calculators, and the Waldee-Wood "Eyepiece" program, appear to use similar calculation processes, though the rounding off is different. "Tim's" online calculator shows only the calculated true field in degrees (to many decimal points; it was necessary to round them off to fit into the table, and necessary also to do the conversion to arcminutes.)

Since, years ago, we had quite an exchange with David Nagler, the son of Al Nagler of Tele-Vue, about calculating the true field of eyepieces, with David taking some exception to our software, we made the effort to use the online Javascript calculator for Tele-Vue eyepieces on their official website, which calculates only for their currently available models. Interestingly, their OWN company figures for the Tele-Vue 15 mm Plössl, used in a scope with the same parameters as Paul's Meade 10", come out exactly the same as the values given in the Waldee-Wood "Eyepiece" program: same magnification (166.7x) , exit pupil (1.5mm), and field of view (0.3 d). How could you object to that?! But, note that Paul's two measurements -- the 'casual' one, and the more careful drift measurement -- are much narrower in field of view. Tele-Vue's own calculator yields 0.3d = 18 arcminutes. The "Eyepiece" program agrees with that. Paul has made two measurements, however, coming up with either 18 min (rough) or 15.25 arcmin (careful drift.) What does one make of this?

Well: there is the possibility that ALL of the calculations are skewed, for a given instrument, because the published Meade parameters are off with respect to any one telescope of that model line. Those figures are the average target values given for the entirety of the product; it is possible that individual scopes vary somewhat. There are other issues in play, too, involving arcane considerations about the use of star diagonals, and disparities in the methods of measuring eyepiece parameters. So, the difference of 16% is not entirely unexpected.

The moral, as we have said in our "Eyepiece" program help files, is to trust ONLY a true drift measurement. Expect the calculated field value to be over-generous by a factor of perhaps 5 to 20 percent. -- srw

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Update 3/31/07: I just found another version of Paul's report on his drift method calculations, which is one of his Deep Sky Observing articles, here. I assume it was written after the report he gave in his observing log, from which I obtained some data used in the table, above. BUT: Paul quotes different apparent fields for some of the eyepieces than the values given by the manufacturers. For instance: the Meade 40 mm SWA 2" eyepiece is specified by the maker as having an apparent field of 68 degrees; in Paul's article the value of 67 degrees is used. The discontinued (?) University 32 mm 1.25" König (no longer on the company website but advertised by some dealers) is specified as having an AF of 52 degrees, but Paul uses 50 degrees. This is illustrative of the problem that David Nagler complained to me about, more than ten years ago: the rather imprecise nature of the advertising of eyepiece apparent fields, which vary. I have discovered that a certain design of oculars, made in Japan, was advertised by two different American distributors with different AF's, one claiming 2 degrees more than the other: but they eyepieces were identical, except for the logo. Once again: when it comes to calculating the AF, garbage in=garbage out. The only accurate way of knowing true field is a drift calculation; but of course no two people will do THAT test exactly the same way, due to what is known as the "personal equation of astronomers", first noted more than a century ago by very careful professional visual astrometricians. The lesson learned is to be aware of the imprecision of many "truths" that we all tend to accept as being perfectly accurate and factual matters.

How does this impact careful amateur viewing? Well, very slightly. In my case, without a micrometer eyepiece whose true field is known with precision, I will have difficulty in estimating the diameter of galaxies and very well-defined planetary nebulae. I can look at the field width, and guess how large the object is; my guess is often quite inaccurate compared to a carefully measured photo. But, of course, photos and CCD images reveal more of faint objects than the dark-adapted eye. Is a nebula 10 minutes in diameter, or 12... or larger or smaller? Recently this quandary occurred to me when comparing my estimate of the size of the bright region of IC-429 with the value derived by the careful observer Steve Gottlieb (part of this report on my observation of the nebula.) There will be inevitable variations in the comprehension of one's eyepiece true field, the "personal equation" of the observer, and the efficiency of a given telescope (and sky darkness background) when comparing reports. Who is "right"? At least, one may make some effort to establish a control of the known factors of one's optics, by proper calculation AND measurement.

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Update 4/19/08: While trying to determine the validity of an eyepiece sketch I'd made, using a rather obscure, discontinued ocular -- the old Orion "Lanthanum" 7.5 mm 1.25" barrel model -- in my 4.7 inch aperture f/5 refractor, I decided that it was absolutely essential to know PRECISELY what my actual true field had been: because I had made the alleged 'discovery' that the nebula IC-466 in Monoceros, was in fact wider in diameter, to my eye, than the measured value of 1x1 arcminutes given in the Uranometria 2000.0 Deep Sky Field Guide, and most other resources I'd checked. But, I did find a particular deep rendering of the POSS-II plate images that suggested that my wider value might be right. I had used the specs for the eyepiece apparent field that were provided to me by an Orion employee; I don't think that this information was generally advertised, but the oculars have been unavailable for such a long time that I've discarded all my old catalogues to verify that the apparent field was said to be 50 degrees, very similar to a Plössl type. I had used this value when calculating the performance of the ocular, employing my old computer program "Eyepiece": and, for a 50d apparent field, in my 4.7 inch scope the "estimated visual field" (as I call the calculated prediction of true field) would have been 37.5 degrees. I had actually decided, after making many observations, that the field width was not that wide, and had changed my chart to indicate 35 degrees, which I thought might be closer to the real true field.

But, to check and see if my drawing of nebula IC-466 was even remotely correctly sized, I badly needed the absolute, objective fact: the "true" field. The only way to determine that is with a complex instrumental test -- which I can't do -- or a careful drift test. So, this very morning at midnight, I selected a star that was close to the celestial equator (in fact, at +03 degrees declination, a bright star that I figured was 'close enough') and twice timed the drift of the star from one side of the field to the other, after having carefully set up my scope on an equatorial mount in my driveway.

The average value was 119 seconds, which by the procedure given by Paul, above ('the number of seconds divided by 240 gives the field of view in degrees. To convert to minutes, multiply degrees by 60) results in a true field of about 30 arcminutes, NOT the 37.5 derived by means of the advertised apparent field! (though what I glean from obscure literature about eyepiece calculations suggests that for narrow field oculars, this derivation might be in error by as much as several percent.) If true this is, in fact, one of the worst cases of deviation I've found, for it means that, working backwards, the apparent field of this ocular is not "50 degrees" as claimed, but 40 degrees. This is confirmed, colloquially, by posts I've read by a few persons who have commented on that series of eyepieces: I remember well reading the statement that 'the field of view is much closer to that of an ortho than a Plössl.'

During the day -- sans telescope -- I held my 7.5 mm Lanthanum up to my right eye, and my 11 mm Knight-Owl widefield ocular (80° apparent field as advertised, but 76° as drift-tested by one amateur), and pointed them at the empty bright sky. Indeed, the narrow circle of light of the Lanthanum's field seems to have about half the diameter of the gigantic bright circle seen through the Knight-Owl, a very rough comparison but one that tends to confirm my calculation.

Well: at least now I know; but -- drat! -- it means that I'll have to set up the scope again and do a drift test with my 12.5 and 9.5 Lanthanum oculars, too; and re-check the 7.5 mm unit as well. The moral: don't blindly trust advertising claims for eyepiece specifications; and it won't hurt to measure the actual focal length of your scope. -- srw