Field stop size and AFOV

I thought the field-stop diameter in a distortion-free eyepiece should be focal-length x 2 x tan(AFOV/2).

However, for a 31 Nagler T5, with AFOV = 82 degrees, this gives a field stop diameter of 31 x 2 x tan(41 degrees) = 31 x 2 x 0.869 = 53.9 mm, but the TeleVue spec says 42 mm.

For a TV 32 Plossl, FS = 32 x 2 x tan(25) = 29.8mm which is still 10% bigger than the spec'd 27mm.

Why don't these numbers match? One guess is that the focal "plane" is spherical, then 'tan' would be replaced by 'sin'. Now, for the Nagler, we get 40.6 mm and for the Plossl we get 27 mm, much closer to the actual.

The actual focal surface cannot be spherical, because the edges of the field would be far out of focus (7.6 mm for the Nagler, and 3.0 mm for the Plossl), but the numbers don't work for flat focal planes.

What am I missing? Distortion? Vignetting? Marketing vs. Engineering?

Allen

Allen:

First: I think it is important to remember that concepts like AFOV are first order simplifications functions that are actually quite complicated.

So in that sense, the approximations used are much simpler than trig functions. They are angular sections of circles/spheres rather than triangles.

From that perspective then, the nominal AFOV:

Eq. 1: nAFOV = 57.3 deg/radian x(Field Stop)/(Focal Length eyepiece)

I think somewhere on the TV site this is mentioned but I could be wrong.

I use the term: "nominal Apparent Field of View" to mean the Apparent Field of View that results from using the above equation. Secondarily, it should also be the AFOV that results from actual measurements of the TFOV along with first order analysis that says:

Eq. 2: nAFOV = Magnification of Scope x TFOV, where Mag Scope = Focal length Scope/ Focal length eyepiece.

The Apparent Field of View has various other factors included, advertising, field distortion, inaccuracies in the focal length of the eyepiece...

Again, Magnification, focal length, field of view are all first order approximations of higher order systems so the accuracy is in accordance with the approximations.

This is my current take on the subject. When I first became interested in this subject I began by using the tangent functions but extended discussions on S.A.A. with the David Knisely and others convinced me of the above.

Since then, I have measured the TFOV of various eyepieces using my TV Pronto against a tape measure at a distance and found that Eq. 1 and Eq. 2 agree reasonably well.

Best wishes, clear skies

jon isaacs

You're computation is for zero rectilinear distortion. For zero angular magnification distortion,

field_stop = focal_length * AFoV * pi / 180.

Wide angle astronomical eyepieces usually come within several percentage points of having zero angular magnification distortion, but rectilinear distortion is often less well-controlled (as you have discovered!).
--
Mike