I was doing an exercise lately calculating an eyepiece AFOV directly from its geometry. It seems that this angle can be calculated as AFOV = 2 arctan(d / 2f), where d is the field stop diameter and f is the eyepiece focal length. Please refer to the attached picture.
Now, taking specs for, e.g., a 32 mm 1.25" Plossl from Televue website, d = 27 mm and f = 32 mm, we get AFOV = 45.7 degrees, good 8.6 % less than the claimed 50 degrees. Similarly, for their 40 mm Plossl, (d = 27 mm and f = 40 mm), the formula gives AFOV = 37.3 degrees, rather than the claimed 43 degrees.
What did I get wrong?
Well, I'm afraid that the thing that may have been wrong is attempting to calculate an accurate value for the apparent field of view of an eyepiece. The formulae used are often just approximations (particularly the old AFOV = Mag*TFOV which is often 10% or more off) or just plain wildly off of reality, so to expect them to be accurate may be a little unrealistic. The Apparent Field of View of an eyepiece is a measurable quantity only, and despite efforts to calculate it, it is what it is. Here is how you can measure it:
..........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:
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.
Edited by David Knisely, 26 May 2015 - 03:34 PM.