The Relationship of Eye Relief to Eye Lens Diameter and FOV (1 Viewer)

I wear glasses so adequate eye relief is critical for me, particularly as the converging lenses for my far-sightedness effectively reduce the eye relief, whereas diverging lenses for the near-sighted would effectively lengthen it.

I was looking at 8x32s recently at my dealer's and he insisted on showing me a Leica Ultravid but, before looking through it, a look at it was sufficient to tell me that the eye relief would be impossibly short. The eye lenses of the oculars were very small. Large eye lenses will allow a large AFOV and/or long eye relief.

AFOV is 2 arctan 0,5(eye lens dia. - exit pupil dia)/eye relief.
Exit pupil is objective dia./magnification and as AFOV is defined by FOV (in m @ 1000 m or yds @ 1000 yds) and magnification, it ends up with a simple calculation:-

Eye relief = 1000(eye lens dia. - exit pupil dia)/FOV. magnification

This value for eye relief, of course, applies to the plane of the eye lens.

Here are some values calculated for bins to which I had access:-

Swarovski SLC 7x42, 16,3 mm

Meopta B1 7x42, 18,2 mm

Swarovski EL 10x42 SV, 19,8 mm

Kowa Genesis 10x33, 15,7 mm

These values tie up rather well with my subjective impressions.

John

Is this affected by the magnification of binoculars often varying across the field both with spherical and aspherical elements in the eyepieces?
Sometimes the magnification varies in a wavy form across the field.
Often the magnification reduces at the edge, sometimes only in one direction causing round objects such as the Moon becoming oval shaped.
And the magnification top, bottom, left and right at the edge is sometimes different.

Is the magnification of a binocular quoted usually the central magnification? I presume it is.

In addition if each eye has different dioptre correction then I think the magnification in each eyepiece may be effectively different.

Binastro said:

Is this affected by the magnification of binoculars often varying across the field both with spherical and aspherical elements in the eyepieces?
Sometimes the magnification varies in a wavy form across the field.
Often the magnification reduces at the edge, sometimes only in one direction causing round objects such as the Moon becoming oval shaped.
And the magnification top, bottom, left and right at the edge is sometimes different.

Is the magnification of a binocular quoted usually the central magnification? I presume it is.

In addition if each eye has different dioptre correction then I think the magnification in each eyepiece may be effectively different.

Click to expand...

A rectilinear image (neither barrel nor pincussion) would result in some ovality of round objects at the edge of the FOV.

Surely you don't mean differences between top/bottom and left/right? Any half-decent bin will be rotationally symmetrical.

Magnification is the quotient of effective objective aperture and exit pupil.

The effect of diopter correction on magnification would be negligible. Even the increase in magnification at the usual minimum close focus would be very small.

John

John,
This is interesting, thanks for the idea and calculations. I had the same idea not long ago. I mentioned it over on the Cloudy Nights Binoculars forum, and one of the optics professionals there, Glenn LeDrew, took issue with me.

He said that what defines the field of view, strictly speaking, is not the edge of the eye lens, but the edge of field stop. The field stop appears inside the optic, so there is no way to measure it. But, the eye lens must be at least large enough so that the field stop can be seen through it. In principle, the eye lens could be bigger than necessary.

His explanation made sense to me, and I assumed that "our" idea must be wrong by a large amount. But your calculations show that it is quite accurate in a practical sense. Apparently, manufacturers don't waste glass by making the eye lens bigger than necessary.
Ron

Hi Ron;

Without going back and reviewing the whole thing, I mostly agree with John.

The focal length of the objective and field stop and the field stop and focal length of the eyepiece determine the FOV and the AFOV (power).

The eye lens diameter for a given AFOV determines eye relief as per (approx.) John’s math.

It has been a long time since I have been through the whole sequence but you can check it out, in case I am not remembering all the details, at:
http://www.telescope-optics.net/eyepiece1.htm


Edit: Ron, I just noticed that you said that Glenn was referring only to FOV and I agree with that in regards to the field stop.

For information only:

Technical Data supplied by Swarovski for my SLC 7 x 42 B ("B = eyeglass wearers eyepiece") gives an exit pupil distance of 19mm; FOV of 140 m @1000 m. FOV in degrees: 8* And Subjective FOV in degrees: 55*

I measured the diameter of the exposed portion of the oculars at 23mm.

I can see the entire FOV while wearing large aviator type sunglasses.

Bob

Hello Bob;

Hope you made it through the storm OK. Your data for the SLC seems to fit fine.

tan(27.5°)•19 mm=9.9 mm • 2=19.8 mm which is less than the 23mm lens available. Thanks for the data.

If this bino only had a 15mm eye lens, then the eye relief would be in the 14 mm range.

Thanks for your help.
Indeed there are obvious differences in edge images top, bottom, left and right, but it seems to depend what prisms are used.
And it may be that there are further differences with mid or all orientations, but I have mainly looked for the 4 mentioned.
With wide angle porroprism binoculars such as 10 x 50 Zeiss Jenoptems these differences are easy to see.
Of course they are different, maybe mirror images between the left and right barrels so with two eyes it is more difficult to see these differences as the two eyes compensate.
With roof prisms I don't know how different types are affected, and of course there are different types of porroprisms, and some odd part mirror prism designs.

With just glasses as my eyes differ by about 1.5 dioptres I can see a large change in magnification with each eye, although this is not noticed when using both eyes to view say the T.V.
That is why I wondered if the same effect is seen with binoculars.

Televue literature deals with field stop sizes.

Bob,

I measured the eye lens of my SLC 7x42 at 22 mm. It's not a "Neu" but I don't think they changed the optical design.

I used the ISO definition of AFOV to arrive at the above formula. For the SLC it works out at only 52,2°, which seems very narrow but we probably all think in terms of the old TFOV x magnification or manufacturers' figures. Nikon seems to be the only one to adhere to ISO, which is more accurate but nevertheless relies on the magnification being an integer. An absolute measurement was described here: http://www.birdforum.net/showthread.php?t=146768&highlight=AFOV+green+laser.

John

PS: I just mounted my SLCs on a tripod and did a rough measurement of the AFOV looking through the objective at the edge of a distant building. I arrived at 54°.

John Russell said:

Bob,

I measured the eye lens of my SLC 7x42 at 22 mm. It's not a "Neu" but I don't think they changed the optical design.

I used the ISO definition of AFOV to arrive at the above formula. For the SLC it works out at only 52,2°, which seems very narrow but we probably all think in terms of the old TFOV x magnification or manufacturers' figures. Nikon seems to be the only one to adhere to ISO, which is more accurate but nevertheless relies on the magnification being an integer. An absolute measurement was described here: http://www.birdforum.net/showthread.php?t=146768&highlight=AFOV+green+laser.

John

PS: I just mounted my SLCs on a tripod and did a rough measurement of the AFOV looking through the objective at the edge of a distant building. I arrived at 54°.

Click to expand...

John,

I measured mine again a few more times with the metal ruler I have and I can't argue with 22mm. It's not easy to locate the exact starting and ending points.

Bob