Field number vs. field stop diameter in "negative" eyepieces

[hans]

Quick follow up question/clarification regarding:

... The FN is the field diaphragm of the eyepiece. ...

(I never understood where the positive/negative terminology for this classification of eyepieces comes from, but anyways...)

In a Huygens eyepiece, for example, where the field lens before the field stop modifies the size of the intermediate image, FN is still measured as if in the original, undisturbed intermediate image plane without the eyepiece present? In other words, the usual FOV = FN / magnification calculation is still valid but FN no longer matches the physical diameter of the field stop? Is that correct?

[Adam Long]

That's my understanding.

Measuring field width via a micrometer slide should determine whether it applies to your particular eyepiece?

[apochronaut]

So then, why not use angle as an indicator of f.o.v. ? Would it not be a better indicator of the field width?

[PeteM]

This may be QWERTY vs. Dvorak keyboards.

Having gotten used to field numbers, FN certainly eems simple enough. Use a 10x/22 eyepiece and I expect to see a 22mm wide field with a 1x stereo objective and a 2.2mm field with a 10x compound objective. Put a ruler or micrometer slide down and take a look. It's simple math and easy to measure. I do it frequently with stereo microscopes and sometimes with compound microscopes. And when (as has happened) a Chinese stereo eyepiece promises a 23mm field and only delivers 20mm at 1x (on a scope where other markings are true), I near instantly know not to trust that vendor again.

The main thing, at least for me, is to be able to compare the approximate field of view between different microscopes. While it's a matter of personal preference, I prefer the more immersive experience of microscopes that deliver at least 20mm FN - and sometimes 22-25mm. It's nice to know, in advance, what's promised.

Putting in a wider field eyepiece can also be useful to see what's happening at the edges of the field. If the OEM field number is, say, 20mm then a 22mm eyepiece might reveal chipped prisms, severe alignment problems, and how conservatively the maker spec'd things. Good makers seem to have a bit of a safety factor in their eyepieces. They might spec 20mm eyepieces, but the rest of the head and objectives are often decent out to 21 or 22mm.

Most of us could get used to microscopes (or wide-screen TV's for that matter) specifying their angle of view at some distance instead of field size or screen size, but there would be a bit of head-scratching, at least at the beginning, to figure if I wanted a microscope that promised something like a 50-degree view to my retina with glasses on and a 12.5x high eyepoint eyepiece.

[wabutter]

This may be QWERTY vs. Dvorak keyboards.

Having gotten used to field numbers, FN certainly eems simple enough. Use a 10x/22 eyepiece and I expect to see a 22mm wide field with a 1x stereo objective and a 2.2mm field with a 10x compound objective. Put a ruler or micrometer slide down and take a look. It's simple math and easy to measure. I do it frequently with stereo microscopes and sometimes with compound microscopes. And when (as has happened) a Chinese stereo eyepiece promises a 23mm field and only delivers 20mm at 1x (on a scope where other markings are true), I near instantly know not to trust that vendor

There are two side benefits of this calculation.
1. If the field of view does not calculate from the known properties, either the FN number is not correct, or the objective magnification is not as indicated. It is possible to actually calculate the objective magnification by knowing the FN and observing the measurable field of view. A 20mm FOV with a 20mm FN results in a 1x objective lens. A 2.0mm FOV with a 20mm FN results in a 10x objective..
As PeteM points out if the numbers don’t compute, there is good reason to question the information from the supplier..
One consideration to take into account is on a zoom based stereo, the indication of the zoom position could have some parallax error or just be off in the knob setting.
2. When you need to know the correct magnification in order to view the entire object size in one view, by knowing the field of view of a particular objective/eyepiece combination will allow you to select the right objective. The is true for both compound and stereo scopes. A pathologist will want to be able to see the entire tumor area on a tissue section. A PC board assembly worker needs to see the entire work area in a single view.
By knowing how big the sample area is, allows the simple selection of the correct objective magnification.

[wabutter]

This may be QWERTY vs. Dvorak keyboards.

Having gotten used to field numbers, FN certainly eems simple enough. Use a 10x/22 eyepiece and I expect to see a 22mm wide field with a 1x stereo objective and a 2.2mm field with a 10x compound objective. Put a ruler or micrometer slide down and take a look. It's simple math and easy to measure. I do it frequently with stereo microscopes and sometimes with compound microscopes. And when (as has happened) a Chinese stereo eyepiece promises a 23mm field and only delivers 20mm at 1x (on a scope where other markings are true), I near instantly know not to trust that vendor

There are two side benefits of this calculation.
1. If the field of view does not calculate from the known properties, either the FN number is not correct, or the objective magnification is not as indicated. It is possible to actually calculate the objective magnification by knowing the FN and observing the measurable field of view. A 20mm FOV with a 20mm FN results in a 1x objective lens. A 2.0mm FOV with a 20mm FN results in a 10x objective..
As PeteM points out if the numbers don’t compute, there is good reason to question the information from the supplier..
One consideration to take into account is on a zoom based stereo, the indication of the zoom position could have some parallax error or just be off in the knob setting.
2. When you need to know the correct magnification in order to view the entire object size in one view, by knowing the field of view of a particular objective/eyepiece combination will allow you to select the right objective. The is true for both compound and stereo scopes. A pathologist will want to be able to see the entire tumor area on a tissue section. A PC board assembly worker needs to see the entire work area in a single view.
By knowing how big the sample area is, allows the simple selection of the correct objective magnification.

[hans]

Thanks for confirming. Most of the introductory guides on the internet say something about measuring in the intermediate image plane without saying explicitly what should be done if the size of the intermediate image is modified in the eyepiece. I have always assumed FN = FOV * magnification should be taken as the definition even if the size of the intermediate image is altered because things would be confusing otherwise, but that sort of assumption is not always safe.

[apochronaut]

One of the problems with the F.N. calculation is that it is simple and easy to determine only as long as a 10X eyepiece is being used. As was amply illustrated in the other thread that probably stimulated this one, once you have field stops that are rationalized based on maximizing optical possibilities and different and fractional eyepiece magnifications the system usually then requires a calculator or physical measure in order to determine the FN. ; hardly user friendly and even more so when there is no F.N. marked on the eyepiece barrel, the F.N. is only theoretical and derived from nonsensical theoretical calculations, or the numbers stamped on the barrel are incorrect or intended to designate something else altogether.
Most people respond positively to the field of view ( apparent) in combination with the real or true field view and I would wager that for an average user, the apparent field of view would weigh more heavily. If this were not the case, then there would be more widespread use of 5X eyepieces, where you can achieve a very wide true field of view but a paltry apparent field of view.
If the angle of the eyepiece was always understood, then the viewing possibilities of the apparent field would be and could easily be combined with the magnification to provide a good sense of the view, even without even looking in the microscope.

[hans]

I started a separate thread because the very specific question in the title has noting to do with eyepiece magnification, apparent or angular field or view, exit pupil, or anything else like that. I also didn't want to further clutter up that other thread where Wayne was sharing info on the Poly* microscopes.

Personally, I feel satisfied that my understanding of those concepts is reasonably complete and internally consistent and I know how to calculate any one of the things based on others. If you want to further discuss confusion and relationships among conjugate planes, stops, angles, etc. I suggest another new thread.

I know from previous discussion that you have a low opinion of the Nikon MicroscopyU site Wayne pointed you to and it is not my favorite site either. Instead I recommend the videos by that guy with a modified Zeiss microscope who puts on demonstrations showing conjugate planes (and even more abstract stuff like diffraction orders) all with real, in-the-flesh, physical demonstrations/experiments.

I don't remember his name but I believe MichaelG has posted links before, maybe MichaelG or someone else remembers.