Sunday, December 13, 2015

How to Choose an Eyepiece for a Desired Field of View (FOV)

Choosing an Eyepiece for a Desired Field of View (FOV)

With so many choices these days in wide-field eyepieces it can become confusing what with the interplay between magnification and field of view. (See Reviewing the Fundamentals below.)

For example, let's say you have your eye on one of the newer 82° or 100° apparent field of view eyepieces (or, you'd like to).  But, your question is, "What size eyepiece should I get (in one line of eyepieces) to achieve a particular field of view in another line?".  But, do you want to go through the trial-and-error process of picking an EP then calculating it's magnification then the resulting field-of-view?
Doing a little math, it works out that for a desired, or equivalent, field of view in another line of EP's, you simply multiply the targeted TFOV by the focal length of the chosen telescope and divide by the new EP's apparent FOV.
Now, as we know, the magnification achieved by a given eyepiece on a particular telescope is equal to the focal length of the telescope divided by that of the eyepiece ....

I.e.,    Mag (X) = FLt/FLep     (i)

And, from that, the true field-of-view (TFOV) is equal to the apparent field of view (AFOV) of an eyepiece divided by the system's magnification, from above ...

So,    TFOV = AFOV        (ii)

Substituting for MAG in (i) above ...
         TFOV = AFOV        (iii)  

Or, stated another way ...     
         TFOV = AFOV x FLep   (iv)

Therefore, the focal length of the eyepiece I would need, solving for FLep, is ...
         FLep = TFOV x FLt

I.e., to determine what EP focal length is needed for a desired True Field of View (TFOV), multiply by the focal length of the telescope and divide by the new EP's AFOV.

Example: Given an 8 inch f/10 SCT of focal length 2032.
You would like to have that 82°, 30mm EP, but it's expensive.

So, you're looking at a line of EPs with 72° (or, 68°).

Now, the TFOV of that would-be-nice-to-have 82°/30mm in the 8" SCT is 1.21°.

To achieve the equivalent FOV in the 72° line of EPs,
you would need .... 1.21 x 2032 / 72.   Or, a ~34mm ep. (You would probably opt for the 36mm  that is available.

In a 68° line of EP's, you would need a ~36mm eyepiece.


Reviewing the Fundamentals

AFOV is Apparent Field of View; TFOV is True Field of View.
AFOV is the field of view that you see when, without a telescope, you simply hold the eyepiece up to your eye and look through it, from the front, as you would if connected to a telescope.
It is limited by the field stop at the bottom of the barrel. If an EP is rated (sometimes stated on the barrel) to be 68° or 82°, or whatever, that is the angle you will see just looking through the EP.
TFOV (True Field of View) is what you see when you attach the EP to a telescope and is hence much narrower, since it is arrived at by dividing the native Apparent Field of View of the eyepiece by the combined system's magnification.
Both measurements are fairly precise since the manufacturer states the AFOV and the telescope has a pretty precise focal length.
Here is a real world example:
Telescope is an 8 inch f/10 SCT with a focal length (fl) 2032mm; the eyepiece is a 68°, 25mm focal length.
Magnification is equal to the focal length of the telescope divided by that of the eyepiece.
Or, in this example, 2032/25 = 81.28x.
True Field of View (TFOV) is equal to the Apparent Field of View (AFOV) of the eyepiece divided by the magnification.
Or, in this example, 68° / 81.28 = .8366°.

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