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I have quite a collection of home-made and oddball eyepieces which I don't know the focal length for. What is a good method to determine their focal length?

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One method would be to measure the eyepiece apparent field of view on an optical bench, then measure the true field of view on the sky that the eyepiece gives in the telescope. Then, one can determine the magnification with the old TFOV = AFOV/Mag formula and from the magnification, the eyepiece approximate focal length can be calculated (EPFL = FLT/Mag). It will be approximate only, but it should be a somewhat useful figure. The only other method would be to use an autocollimator on an optical bench, but for some shorter focal length eyepieces, it can be very difficult to impossible to do this. Clear skies to you.

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David W. Knisely
Hyde Memorial Observatory
http://www.hydeobservatory.info
Prairie Astronomy Club
http://www.prairieastronomyclub.org

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One method would be to measure the eyepiece apparent field of view on an optical bench.....

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How do you do that? What, if any, equipment is needed?

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Tom (Pegster)
DSH-8 (GSO Dob)
15x70 Oberwerks
SVP/ED80
WO 66 Petzval
Sears Discoverer EQ 60/900
8x42 Regals




History is Philosophy teaching by examples.
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One method would be to measure the eyepiece apparent field of view on an optical bench.....

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How do you do that? What, if any, equipment is needed?

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OK, here is how it is done...

MEASURING THE APPROXIMATE
APPARENT FIELD OF VIEW OF AN EYEPIECE

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 at a convenient height above the floor (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 will be. 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 and so that the barrel of the eyepiece is pointed at the center of the observing target. Look into the eyepiece with *both* eyes open and try to 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. 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 and looking in the eyepiece as you do this. 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 seem to 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 51.9 degrees. For best results, take the average of several of these measurements. Clear skies to you.

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David W. Knisely
Hyde Memorial Observatory
http://www.hydeobservatory.info
Prairie Astronomy Club
http://www.prairieastronomyclub.org

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Thanks for your help David, but I must be doing something wrong. In your example I get an AFOV of 30.86? Maybe I'm not using the ATAN function properly.

I'm entering '2', hitting ATAN, and getting result of 63.43, then multiplying by 18/37. What am I doing wrong?

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No, you always do the operation inside the parenthesis first before you employ the arc tangent function. First take 18.0 inches (the half-width of the target) and divide it by 37.0 inches (the distance from your eye to the center of the target). You should get 0.486. Then, take the arc Tangent of that (25.9) and multiply by two to get 51.8 degrees apparent field (a typo at the end gave the wrong last digit). Clear skies to you.

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David W. Knisely
Hyde Memorial Observatory
http://www.hydeobservatory.info
Prairie Astronomy Club
http://www.prairieastronomyclub.org

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I had always thought this was a (very) simple method:

1. In a (semi)darkened room, set up a light source (like a bright light bulb) at a distance at least 30X the approximate FL (if you don't know the FL, ten-twelve feet is a good start. Not many EPs are going to have a 4" or greater FL!)

2. Put the end of a ruler at about the same height as the light source against a white background (like a piece of paper) that is set face-on to the light source (the ruler is therefore perpendicular to the path of the light rays).

3. Place the EP along the ruler with the eye lens surface parallel to and toward the white surface, and move the EP toward the white surface until a focused image appears.

4. Read the distance from the surface of the eye lens to the white background - that is the EP FL.

Gurus - is this somehow incorrect?

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No, I'm afraid that this will give an incorrect result for the multi-element eyepieces we now have. It works only for a simple single lens with the "thin lens" approximation. Multi-lens systems do have what are known as "principle planes", positions where focal lengths can be measured from, but their precise location is difficult to determine without basically doing a detailed optical ray-trace analysis of the eyepiece (i.e., knowing what each element is and where it is placed). Measuring from the back eye lens may give a result which is in the rough ballpark of the actual eyepiece focal length for longer focal length units, but for shorter eyepieces, it will not yield terribly accurate results. One could use a very precise grid (like the Ronchi grating example done by Don Taylor) and image the grid with the eyepiece to give the size change of the image verses the actual object grid spacing. However, just imaging a point source would not be all that accurate. Clear skies to you.

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David W. Knisely
Hyde Memorial Observatory
http://www.hydeobservatory.info
Prairie Astronomy Club
http://www.prairieastronomyclub.org

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