Leica Reichert Jung Polyvar (models)

[wabutter]

I am trying to do the math and it doesn't work for me. IF you used a 1x objective with a 16mm FN , 15x eyepiece and put a stage micrometer in place, you would observe a 16mm FOV at 15x. If you put used the same objecive with a 10x/20mm FN, you would see a 20mm FOV at 10x. The object would appear to be large with the 15x eyepiece, but the FOV would still be smaller.

[apochronaut]

I made some images of a stage micrometer through the various 10X W.F. eyepieces used from the AO series 4 up to the common one used in the ATC 2000. I also included the recommended eyepiece used in the Stereostar 580. This provides an actual measure of the F.N. of each eyepiece, as measured. I would have also made one through a 30mm ocular tube Reichert WP10X, such as was used in the big Reichert Austria Poly scopes but it was difficult to mount effectively on my test stand and mount my camera to it. It however is the only eyepiece marked with it's F.N.
All images were made through an AO infinity corrected 10X .30 34mm parfocal planapo objective mounted in a standard AO stand with a reference focal length of 182.5mm. Cat. # 1321.
The images in order and the F.N. are .

1)cat. #146 W.F. 10X standard eyepiece for AO 2/4 and sometimes the later 15/35 series. F.N. as measured. 19.5mm
2) cat. #176 W.F. 10X standard eyepiece used in the 10/20 series.F.N. as measured 18.3mm.
3) cat. #176A W.F. 10X eyepiece made later in production of the AO 10/20 series indicated as preferable for use with the non-plan.achromats. F.N. as measured 18.3mm.
4) cat. #180 W.F. 10X standard eyepiece for the AO/Cambridge 100/110/120 series. F.N. as measured 20mm.
5) cat.#181 W.F. 10X standard eyepiece for the Reichert/Cambridge/Leica 410/420 series. F.N. as measured 20mm.
6) Cat. #191 W.F. 10X .standard eyepiece for the ATC 2000. F.N. as measured 20mm. Seems identical to the #181 except for a channel in the lower barrel to receive a locking screw.
7) Cat. #145 W.F. 10X standard eyepiece for the Stereostar 580. I do not know the reference length of the stereostars.F.N. as measured 20.25mm
8) Reichert WP10X/24 top. Clearly an F.N. 24mm eyepiece.

In performance , they are all fairly similar with each one having slightly different corrections for primarily field curvature, aligned with the requirements of the system each was made for. The 146 and 176A create considerable field curvature over about the peripheral 25% of the 10X planapo field. The 181 and 191 less but some, as do the 145 and WP 10X. The 176 and 180, designed for essentially the same system.with different F.N,s, are perfectly corrected for the 10X .30 planapo to their respective field stops. :

[apochronaut]

3 more.

[apochronaut]

I am trying to do the math and it doesn't work for me. IF you used a 1x objective with a 16mm FN , 15x eyepiece and put a stage micrometer in place, you would observe a 16mm FOV at 15x. If you put used the same objecive with a 10x/20mm FN, you would see a 20mm FOV at 10x. The object would appear to be large with the 15x eyepiece, but the FOV would still be smaller.

It is a system that is base 10, so it doesn't represent the real field vs. apparent field circmstance for a 15X or a 5X eyepiece intuitively.
An easier way to visualize it is if the 15X eyepieces had an F.N. of 20 as well , the same as the 10X eyepieces. That means that both visual fields would show exactly the same length on a micrometer but one would have to be 1 1/2X longer than the other in order to do so. With a 1X objective, each would show 20mm. In order for the 15X eyepieces to show 20mm at 1 1/2 times the magnification of the 10X eyepieces, the 15X image circle would have to be 1 1/2 X the diameter of the 10X eyepiece image circle. Such eyepieces do exist. The B & L U.W.F. 15X and some others I think too. Listed as having an F.N. of 20, they actually have an image circle 1 1/2X that of their companion 10X eyepieces, yet each have the same F.N.

A similar situation takes place with the AO/ Reichert # 182 and 184 15X W.F. eyepieces. Both have an F.N. of 16, so they have an image circle that is 20% larger than a 10X with an F.N. of 20. Their image circle is the equivalent that a 10X/24 eyepiece would have ( 16 X 1.5). In order for a 15X eyepiece to have the same diameter image circle as a 10X/20 eyepiece, it's F.N. would need to be 13.3333....

With a 5X eyepiece , the situation is reversed and an image circle that is 1/2 the diameter of a 10X , shows the same real field. This is the reason why a W.F. 5X eyepiece doesn't really exist. They will show a wide field but through a very narrow image circle, so the sense of the width of the field is distorted. Most systems that achieve some degree of W.F. with a low magnification eyepiece used a 6X. Reichert uses s 6.3X, which has a tolerably acceptable wide field feel to it.

[wabutter]

Phil,
i need to do some of my own testing. i am not sure what you mean by Base 10. Our math system when using metric is base 10. I don't know the scale of the micrometer you are picturing, but it all of the images you took are with the 10x objective. The objective will see the same distance, that is apparent in you pictures. They appear to cover the same distance. . The actual field stop diameter. will regulate how much of the image will be viewed at the exit pupil of the eyepiece.

I'll get back when I have a chance work through some documentation. I'm out of town for the rest of the week.

regards,
Wayne

[apochronaut]

The pictures I posted are showing between 18.3 and 20.25 units, with 20 units across an eyepiece that is listed as having an F.N. of 20mm, so the scale must be in mm. So, I am showing the F.N.'s of the eyepieces but it doesn't matter to the current discussion about 15X eyepiece fields because there are no 15X eyepieces in the pictures.

The F.N. system is based on a 10X eyepiece and , 1 or, 10 or 100X objectives. It's all base 10. A 15X eyepiece is given an F.N. # as though it is a 10X eyepiece covering an equivalent field or partial field that a 10X does but because it is magnifying 1.5X that of a 10X eyepiece, if it has an F.N. greater than 13.33333... , it must have a larger image circle than a 10X eyepiece of 20 F.N. and once it has a 20 F.N. it's image circle will be 1 1/2 X the diameter of a 10X 20 F.N. eyepiece.
All you have to do is pick up an AO 10X W.F. eyepiece, any one, which are anywhere between 18.3 and 20+ F.N. by my actual measure of them above and then a # 147, 182 or 184 15X eyepiece , which are 16 F.N. and then hold them up to the light, one at each eye. You will see that the image circle to the field stop of the 15X eyepiece is considerably larger than that of the 10X eyepiece.

[hans]

Since the FN discussion started with what is considered "supported" I would point out that in this example:

It is a system that is base 10, so it doesn't represent the real field vs. apparent field circmstance for a 15X or a 5X eyepiece intuitively.
An easier way to visualize it is if the 15X eyepieces had an F.N. of 20 as well , the same as the 10X eyepieces. That means that both visual fields would show exactly the same length on a micrometer but one would have to be 1 1/2X longer than the other in order to do so. With a 1X objective, each would show 20mm. In order for the 15X eyepieces to show 20mm at 1 1/2 times the magnification of the 10X eyepieces, the 15X image circle would have to be 1 1/2 X the diameter of the 10X eyepiece image circle.

The F.N. system is based on a 10X eyepiece and , 1 or, 10 or 100X objectives. It's all base 10. A 15X eyepiece is given an F.N. # as though it is a 10X eyepiece covering an equivalent field or partial field that a 10X does but because it is magnifying 1.5X that of a 10X eyepiece, if it has an F.N. greater than 13.33333... , it must have a larger image circle than a 10X eyepiece of 20 F.N. and once it has a 20 F.N. it's image circle will be 1 1/2 X the diameter of a 10X 20 F.N. eyepiece.

The FN 20mm 10X and 15X are both using the same set of rays from the preceding optics meaning if one is supported then so is the other, as well as any other magnification of FN 20 mm eyepiece. What is changing is the apparent size of the field stop and image viewed through the eyepiece, as well as apparent brightness which must decrease as magnification goes up since all FN 20 mm eyepieces are working with the same light.

Since FN is measured in the intermediate image plane (and does not directly correspond to the apparent size of the field stop viewed through the eyepiece, as you already pointed out) I don't see how 10X is special or what it would mean for FN to be "based on a 10X eyepiece."

Going back to the original question:

However, it is a base 10 system. The F.N.s of 15X eyepieces can seem illogicsl because a 15X eyepiece with an F.N. of 16 can have s larger field of view than a 10X eyepiece with an F.N. of 20, yet a smaller field viewed. I.e. a larger diameter field stop but smaller diameter of field viewed through it.

If the system is considered to support FN 20 mm with acceptable quality then there is no theoretical problem with 15X at FN 16 mm. The field stop appears larger through the eyepiece than it does with 10X at FN 20 mm but it is still using only 16 mm (diameter) of the intermediate image.

[apochronaut]

I refrained ftom using telescope terminology. The term apparent seems to be a no no when it comes to microscopes but is widely used when it comes to telescopes. I have used it in the past. In terms of angular field of view then, a 15X eyepiece with an F.N. greater than 13.33333... will have an angular field of view greater than s 10X eyepiece with an F.N. of 20. I used the term image circle because I was trying to explain it in microscope terminology.. Most references to F.N. use base 10 arithmetic and explanations dumbed down to factors of 10. You seldom see references to F.N. theory using 15X eyepieces as a baseline, so when most people see a 15X eyepiece with an F.N. of 16, they assume that the field of view is only 80% that of a 10X eyepiece with an F.N. of 20.
F.N. is intuitively a completely dumb system. It should be replaced with terms more similar to what is used for telescopes.

[Scarodactyl]

Field number is based on a hypothetical 1x objective, not a 10x eyepiece. It's just a question what the diameter of the imaged field would be with a 1x objective, regardless of how large it looks to the eye.

[apochronaut]

Yes but the f.N. only matches the real or viewed ield with a 10X eyepiece.because they are the default and the system's logic is based entirely on 10X eyepieces. Other eyepiece magnifications can still have any F.N. as viewed through the theoretical 1X objective but their F.N. no longer equals the size of the field of view. If you measure a 20 F.N.field viewed through a 10X eyepiece at your eye : the actual diameter of the viewed field, with a transparent scale or ruler right as the image enters your eye, it will measure 20mm. When other magnification eyepieces are used that also have an F.N. of 20, the scale will not measure 20mm. A 20mm F.N. with a 15X eyepiece will measure 30mm and a 20 F.N. with a 5X eyepiece will measure 10mm.
Thus the difficulties of this thread.
In actual fact F.N. is an illusory and cumbersome system for many people to wrap their heads around because it only works accurately with 10X eyepieces. Although experience tells us that a 15X eyepiece with an F.N. of 16 will have quite a wide f.o.v., that number 16 held against the number 20 in someone's mind, indicates smaller. It makes the 15X eyepiece seem narrower in view, when in fact it is larger.
It is the angle of view or some sort of F.N. ratio that is missing on eyepiece specificitions. A composite measure such as magnification , angle of view and F.N. would give a more realistic picture of an eyepiece's performance. 10X/45-20 for instance, or 15X/50-16 as hypothetical examples. Another poseibility might be something like the magnification followed by a real field/ apparent field ratio 10X/20 : 1 and 15X/16 : 1.2 to use examples of actual AO eyepiece comparative fields. The higher last number would indicate a larger apparent field or viewing angle. A 5X " W.F." eyepiece would be 5X/20 : .5.

[Scarodactyl]

Yes but the f.N. only matches the real or viewed ield with a 10X eyepiece.because they are the default and the system's logic is based entirely on 10X eyepieces.

It seems to me that the confusion is arising from thinking of it this way, even if there's nothing technically wrong with it.
A 1x objective produces a 1x magnification with no eyepiece involved at all--you can put a sensor directly on it and get that image field on your sensor, with 1mm on subject equalling 1mm on sensor. From there the FN of an eyepiece is just telling you how much of that image the eyepiece can capture regardless of scale, and the magnification tells you how blown up it is. I think it's pretty intuitive and it makes comparing eyepieces really easy with simple multiplication--a 15x/14 is going to fill as much visual space as a 10x/21 while capturing a smaller portion of the field of view.

[apochronaut]

It's only intuitive if you already know it. I don't personally have a problem with it but for those unfamiliar with the system it id difficult. The way it is done in astronomy makes much more sense and the microscope world could learn a bit .

[hans]

I think the confusion is here:

If you measure a 20 F.N.field viewed through a 10X eyepiece at your eye : the actual diameter of the viewed field, with a transparent scale or ruler right as the image enters your eye, it will measure 20mm. ... A 20mm F.N. with a 15X eyepiece will measure 30mm and a 20 F.N. with a 5X eyepiece will measure 10mm.

It seems clear to everyone how 20 mm can be measured in the intermediate image plane per the usual definition of FN. But entering the eye? How should these 20 mm, 30 mm, and 10 mm measurements be made? All the light enters the eye via the exit pupil of the microscope roughly 1-2 mm in diameter and there is only a virtual image at a relatively large distance like 300 mm or more depending on how the eye is focused. An angular measure as already discussed does makes sense but I don't see how these "apparent size of the field stop measured in millimeters" numbers can make sense. Where exactly should they be measured?

[apochronaut]

How do you know it is clear to everyone? What is clear is that some people think that an F.N. of 16 has a smaller field than an F.N.of 20 because that is what is prnted on the eyepiece , not that the product of magnification and field gives the field size. How many times does the question of why is there no such thing as a 5X W.F. eyepiece come up? More than you think. It's because the F.N. system is cumbersome and the mechanism of use not clearly evident.
Here's a quick question : Which has a larger field of view. A 10X /19.5 eyepiece with a 30X objective or a 15X x/13 eyepiece with a 20X objective? While you are rolling the numbers around in your head or reaching for your calculator , I just looked at the eyepieces and the 10X eyepiece is marked 45° and the 15X eyepiece is marked 45° as well , or the 10X eyepiece is marked 10X /1 : .975 and the 15X marked 15X/ 1 : .975. Same visual field.


Regarding my comment that one can measure the field stop in mm at the eye ; well you can. There is an image of the field stop in your eye and a metric scale can be superimposed across it, right at your eye relief point. Thus, the 10X eyepiece with it's attendant F.N. # is measured 1 : 1 but other magnification eyepieces must be ratioed. Am I suggesting , that, as a measuring stick for eyepieces ? No but it is clear that the F.N. system was evolved utilizing the 10X eyepiece as s default benchmark. This is of course because microscopes are largely an objective mediated system, whereas telescopes are largely an eyepiece mediated system, so there has been more attention given to the rational description of telescope eyepiece performance. Microsvope objective data bases are fed with all kinds of specifications. If objectives had mouths they would be force fed and at 5 star restaurants. The poor eyepieces have to line up at a soup kitchen for scraps and not only that, they all find out they wear the same shoe size and are related. Give the eyepieces some specifications that bring them some dignity.

[wabutter]

I am now beginning to see how ts has been confusing. Scarodacyl’s is a fair description of what happens in a microscope system. If one were to take the eyepiece out of the system, with an infinity objective, with a bright enough light source the image would be projected to the ceiling. The magnification would be dependent on how far away it was from the back aperture of the objective. This is the real image.
However, with an eyepiece in the optical path, the image being viewed is virtual. A representation of the object about 250mm away from the viewer. The eyepiece magnification is only relevant to the apparent image size in ratio to the actual size.

In order to close the loop on this it is important to understand the conjugate planes in the microscope system. There are two.
Conjugate image plane consisting of the field diaphragm, object, field stop of the eyepiece(where the FN is measured), retina of the eye.
Conjugate illumination plane: lamp filament, back aperture of the objective, eyepiece exit pupil, lens of the eye.

A 10x objective with An eyepiece FN 18 will see 1.8mm of the sample
A 20x objective with an eyepiece FN 18 will see 0.9mm of the sample
A 10x objective with an eyepiece FN 20 will see 2.0mm of the sample
A 20x objective with an eyepiece FN 20 will see 1.0mm of the sample
A 10x objective with an eyepiece FN 22 will see 2.2m of the sample
A20x objective with an eyepiece FN 22 will see 1.1mm of the sample
A 10x objective with an eyepiece FN 16 will see 1.6mm of the sample

The magnification of the eyepiece plays no role in how much of the sample the will be seen, regardless of the ca or spherical corrections are employed. The real image is presented to the tube lens that presents it to the conjugated image plane in the eyepiece and is limited by the field stop at the conjugate plane.

One other combination that might be of interest; in the Polyvar, the tube lens was in the mag changer, so there 3 tube lens on the biological stand and 4 in the industrial. The bio stand offered a 0.8x mag changer, when combined with a 10x objective, effectively became a 8x. The standard eyepiece for the Polyvar had FN 24mm, resulting in a 30mm FOV. Correspondingly, if the 1.25x mag changer was used the FOV was reduced to 19.2mm

[apochronaut]

The hangup is the difference between f.o.v. and image circle. All of the stuff you posted is obvious but the system as it exists does not adequately or easily explain or predict to a naive user that a 15X eyepiece with a smaller F.N. will have a larger viewing field ( not field of view) than a 10X eyepiece with a larger F.N.. I have a question, Wayne. When was the the last time you looked through a pair of 15X eyepieces in a microscope?

[hans]

First question:

...and the 4/5/7 reflect the height index 4 in the first position supports a 25mm FN eyepiece, the 5 is 22mm FN the 7 supports a 20mm FN. All intermediate image components, those that mount between the objective ba and the tube lens. had a corresponding height index number and and supported FN in their description as well
A Dueal view bridge has a height indes of 3/25 so it will support a 25mm FN. The ergo spacer is 2/25, drawing attachment 3/20. Each height index number is equal to 15mm. So if you were to stack a dual view bridge with and ergo spacer you would have a height index of 5, so the max FN eyepiece you could use with that combination would be 22mm.

I am curious about the term " supported "? Do you mean the F.N. at the field stop in the eyepiece or the image circle of the objective or the maximum f.n. of the optical tube?

I would say Wayne answered that pretty thoroughly. This is now a different question:

The hangup is the difference between f.o.v. and image circle. All of the stuff you posted is obvious but the system as it exists does not adequately or easily explain or predict to a naive user that a 15X eyepiece with a smaller F.N. will have a larger viewing field ( not field of view) than a 10X eyepiece with a larger F.N..

I don't think anyone suggested FN as a good or intuitive way to specify apparent field of view to a naive user. The hangup was over the idea that FN is somehow "based on" a 10X eyepiece and that 10X is a special case because "the actual diameter of the viewed field, with a transparent scale or ruler right as the image enters your eye" is equal to FN only for a 10X eyepiece.

The use of FN earlier in the thread was about specifying the size of usable image you get from some combination of objectives/accessories/tube lens and had nothing to do with apparent field of view in a visual eyepiece. How should a manufacturer specify that if not using FN?

[apochronaut]

F.N. is an arbitrary system. It is a code system stamped on some eyepieces, only some. There seems to be a begrudging compliance on the part of manufactuers. Maybe there is a reason? In existence, and you can look them up on ebay right now and find at least some of these, so they sre pretty common are the following. An unbranded W.F. 10X-15.5 eyepiece, a Bausch & Lomb 10X/23 eyepiece and another physically almost identical Bausch & Lomb 10X/22 eyepiece.
The W.F. 10X-15.5 -eyepiece has an F.N. of 18. The 15.5 is the eye relief. Swift in one incarnation.
The 10X/23 also has an F.N. of 18. The 23 is the ocular tube diameter.
The 10X 22 has an F.N. of 20. I think the 22 is the eye relief.

With objectives, I admit that occasionally a special purpose, usually lower magnification objective does not have an N.A. on it but in general there is compliance with putting an N.A. on an objective, something lacking when it comes to eyepieces. Objectives until approx. 1900 , used to be described by an angle of acceptance or an angle of view , which by mathematical formula has been turned into and universally adopted as the N.A., short for numerical aperture. Admittedly, N.A. is not intuitive but it is almost universal and has real and fairly understandable properties where factors are used, such as the relationship between N.A. and empty magnification resulting in a limitation on how many times the objective can be magnified without a loss in resolution. This is quite definitive. N.A. X 1000 and that's the limit, irregardless of the N.A. or magnification of the objective. The N.A. can be used to determine the theoretical resolution if that information is of value.

In astronomy, eyepiece technology has flourished for obvious reasons. Eyepieces are the telescope's objective changer, so a rational system of field of view has evolved. Telescope eyepieces have a specification for an apparent field of view as an angle and that in combination with the optical properties of the telescope determines the true field, determined by the field stop. It seems a more rational system.

I guess I would hope that with microscope eyepieces the system would use an apparent field or field of view plus a true field or "field viewed" type of system and terminology. I suspect it would be easier to follow for some microscopists, not to mention the discontinuity associated with eyepieces carrying disparate specifications. One can deduct something from 15.5mm to the exit pupil but it should be more intuitive. This is all outside of the hornet's nest of corrections that are built into eyepieces. Eyepiece specifications need to be universalized in a more rational way.
and yes, the F.N. system is a base 10 system. The entire theory revolves around the 10X eyepiece. The descriptions of how the F.N. system works are carried out using a hypothetical 1X objective and 10X eyepiece. Measure the exit pupil of a 10X/20 eyepiece and see what you get. Only with the 10X eyepiece can you easily and quickly determine the diameter of the field. Quick : what is the diameter of the field using a 10/20 eyepiece with a 50X objective? Quick : what is the diameter of the field using a 12.5X/17.5 eyepiece with a 50X objective? Are you still there? How about describing the F.N. system using an 8X/17 eyepiece with a 63X objective?

I'm still waiting. Oh, I see. Your batteries needed charging. Ever wonder why the 12.5X eyepiece is going the way of the Dodo, when it is the most practical eyepiece to use with the most common 100X objective around ; a 1.25 N.A. ? F. N. and reticles in tenths. Both become inconvenient to work with.
I realize that the 1/10/20mm sequence used as a tool to describe the F.N. mechanism is to make things simpler for explanation purposes but when I pick up that huge WP10X/24 eyepiece pictured above ( the one with the F.N. 24 from a system that supports a 30mm field at the field stop, just to be clear) and I hold it and a tiny AO cat.#182 W.F. 15X ( F.N.16 !) up to the light and see that they both have the same field stop diameter, I have to question the system. I guess I would prefer that each were marked with an angle, that would indicate the size of the apparent field or field of view immediately. Both eyepieces would be quickly known to have the same field stop diameter and the magnification clearly marked on them indicates that one would show 2/3 of the real or true field or viewed field of the other
Maybe it is just a personal preferance.
Eyepiece specs. in general need an overhaul.

[hans]

Ok, so to clarify:

The entire theory revolves around the 10X eyepiece. The descriptions of how the F.N. system works are carried out using a hypothetical 1X objective and 10X eyepiece. Measure the exit pupil of a 10X/20 eyepiece and see what you get. Only with the 10X eyepiece can you easily and quickly determine the diameter of the field.

Regarding my comment that one can measure the field stop in mm at the eye ; well you can. There is an image of the field stop in your eye and a metric scale can be superimposed across it, right at your eye relief point. Thus, the 10X eyepiece with it's attendant F.N. # is measured 1 : 1 but other magnification eyepieces must be ratioed.

Yes but the f.N. only matches the real or viewed ield with a 10X eyepiece.because they are the default and the system's logic is based entirely on 10X eyepieces. Other eyepiece magnifications can still have any F.N. as viewed through the theoretical 1X objective but their F.N. no longer equals the size of the field of view. If you measure a 20 F.N.field viewed through a 10X eyepiece at your eye : the actual diameter of the viewed field, with a transparent scale or ruler right as the image enters your eye, it will measure 20mm. When other magnification eyepieces are used that also have an F.N. of 20, the scale will not measure 20mm. A 20mm F.N. with a 15X eyepiece will measure 30mm and a 20 F.N. with a 5X eyepiece will measure 10mm.

That is all talking about measuring exit pupil like this:

measure-exit-pupil.jpg (124.32 KiB) Viewed 1590 times

[apochronaut]

Of course. You are viewing the exit pupil from what, 10 inches away with a camera lens. I don't know where uou have your screen. My point was that the apparent field your eye sees right st the cornea is 20mm. Put the scale at your eye.

[wabutter]

F.N. is an arbitrary system. It is a code system stamped on some eyepieces, only some. There seems to be a begrudging compliance on the part of manufactuers. Maybe there is a reason? In existence, and you can look them up on ebay right now and find at least some of these, so they sre pretty common are the following. An unbranded W.F. 10X-15.5 eyepiece, a Bausch & Lomb 10X/23 eyepiece and another physically almost identical Bausch & Lomb 10X/22 eyepiece.
The W.F. 10X-15.5 -eyepiece has an F.N. of 18. The 15.5 is the eye relief. Swift in one incarnation.
The 10X/23 also has an F.N. of 18. The 23 is the ocular tube diameter.
The 10X 22 has an F.N. of 20. I think the 22 is the eye relief.

With objectives, I admit that occasionally a special purpose, usually lower magnification objective does not have an N.A. on it but in general there is compliance with putting an N.A. on an objective, something lacking when it comes to eyepieces. Objectives until approx. 1900 , used to be described by an angle of acceptance or an angle of view , which by mathematical formula has been turned into and universally adopted as the N.A., short for numerical aperture. Admittedly, N.A. is not intuitive but it is almost universal and has real and fairly understandable properties where factors are used, such as the relationship between N.A. and empty magnification resulting in a limitation on how many times the objective can be magnified without a loss in resolution. This is quite definitive. N.A. X 1000 and that's the limit, irregardless of the N.A. or magnification of the objective. The N.A. can be used to determine the theoretical resolution if that information is of value.

In astronomy, eyepiece technology has flourished for obvious reasons. Eyepieces are the telescope's objective changer, so a rational system of field of view has evolved. Telescope eyepieces have a specification for an apparent field of view as an angle and that in combination with the optical properties of the telescope determines the true field, determined by the field stop. It seems a more rational system.

I guess I would hope that with microscope eyepieces the system would use an apparent field or field of view plus a true field or "field viewed" type of system and terminology. I suspect it would be easier to follow for some microscopists, not to mention the discontinuity associated with eyepieces carrying disparate specifications. One can deduct something from 15.5mm to the exit pupil but it should be more intuitive. This is all outside of the hornet's nest of corrections that are built into eyepieces. Eyepiece specifications need to be universalized in a more rational way.
and yes, the F.N. system is a base 10 system. The entire theory revolves around the 10X eyepiece. The descriptions of how the F.N. system works are carried out using a hypothetical 1X objective and 10X eyepiece. Measure the exit pupil of a 10X/20 eyepiece and see what you get. Only with the 10X eyepiece can you easily and quickly determine the diameter of the field. Quick : what is the diameter of the field using a 10/20 eyepiece with a 50X objective? Quick : what is the diameter of the field using a 12.5X/17.5 eyepiece with a 50X objective? Are you still there? How about describing the F.N. system using an 8X/17 eyepiece with a 63X objective?

I'm still waiting. Oh, I see. Your batteries needed charging. Ever wonder why the 12.5X eyepiece is going the way of the Dodo, when it is the most practical eyepiece to use with the most common 100X objective around ; a 1.25 N.A. ? F. N. and reticles in tenths. Both become inconvenient to work with.
I realize that the 1/10/20mm sequence used as a tool to describe the F.N. mechanism is to make things simpler for explanation purposes but when I pick up that huge WP10X/24 eyepiece pictured above ( the one with the F.N. 24 from a system that supports a 30mm field at the field stop, just to be clear) and I hold it and a tiny AO cat.#182 W.F. 15X ( F.N.16 !) up to the light and see that they both have the same field stop diameter, I have to question the system. I guess I would prefer that each were marked with an angle, that would indicate the size of the apparent field or field of view immediately. Both eyepieces would be quickly known to have the same field stop diameter and the magnification clearly marked on them indicates that one would show 2/3 of the real or true field or viewed field of the other
Maybe it is just a personal preferance.
Eyepiece specs. in general need an overhaul.

Let’s not conflate nomenclature differences with actual physical optical properties. The FN and corresponding FOV, are not arbitrary at all, this is not theory, but the laws of physics at work.
The FN is the field diaphragm of the eyepiece. Please don’t confuse real image, Field of View and apparent image. These are all different and separate from each other. Not to be used interchangeably.

Although some manufacturers may not list the field number on the eyepiece, does not negate the fact that it is exists and is measurable. The standard nomenclature by the major manufacturers is and has been 10x/22 and some reference to compensation if present. Where 10x is the magnification and 22 is the field number. Please refer back to my earlier post describing the conjugated image plane. My discussion only has relevance to the Field of View through the eyepiece. Once again, the eyepiece magnification does not come in to play. The exit pupil of the eyepiece is not conjugate to the image and measuring its diameter does not represent the FOV for the objective. In order to observe the size of the FOV, either look through the eyepiece with a metric stage micrometer mounted instead of a sample, to record it, place the camera sensor at the conjugate image plane, ie where the retina of your eye would be and capture the Image.
We have not been talking apple and apples. Your example of a 15x/20 eyepiece returning a30mm isn’t possible.

To address your question of how big is the field with a 50x or 63x the math is quite simple
20/50 = .400 FOV
22/50 = .440 FOV
17/50 = .340 FOV
17/63 = .269 FOV
And so on. The eyepiece mag is not a factor in the equation. That is the sample diameter you will see through the eyepiece.

On to NA. Older objectives were notate by their focal length. It is no accident that DIN, Royal Microscopy Society, NIST have brought about standards that have been adopted by the major manufacturers. NA is used today because it represents the cone of light that is collected by the condenser and presented to the objective. Better yet is the fact that it can be expressed mathematically. NA = n sin(angular aperture)
Better yet, it is used in the formulas to calculate the maximum useful magnification, resolution, depth of field, and working distance.
Yes, the 12.5x eyepiece would optimize the magnification for a 100x/1.25 however, the 12.5x eyepiece I have are 16mm FN
So you would have an objective field of 0.160 mm at 1250x total mag, while the 10/22 eyepiece would offer a 0.220mm FOV at 1000x. The removing power would be the same for both combination, Most users have opted for the ease of use the larger field of view provides, not to mention the benefits to parcentration in the operation of the scope as well. Most modern scope offer a 1.25 mag changer so if the additional mag is required, it it flipped in with out any compromise.

[hans]

Of course. You are viewing the exit pupil from what, 10 inches away with a camera lens. I don't know where uou have your screen. My point was that the apparent field your eye sees right st the cornea is 20mm. Put the scale at your eye.

The strip of lens paper being projected onto is at the exit pupil pretty close to where the cornea/iris of a viewer's eye would be. Camera distance is not relevant because the lens paper and transparent scale are held pressed together both the same distance from the camera. If you have been talking about measuring exit pupil this whole time, that's where the confusion is. As Wayne already pointed a couple times out by mentioning conjugate planes, the circle of light in my photo is an image of the objective aperture (I made sure the condenser diaphragm was open well beyond the objective NA) and the size of it is related to neither the eyepiece FN nor the apparent size of the field stop. And even if that was an image of the field stop, the size is not at all close to the FN. Can you take a similar photo showing how you are placing the scale to measure 20 mm?

[apochronaut]

Only if the camera was in my eye. The image circle at the enrance to the eye is 20mm. If you hold a quarter out at arms length it will obscure the moon but if you bring it right close to your eye it will obscure a third of the sky.

[apochronaut]

Your example of a 15x/20 eyepiece returning a30mm isn’t possible.

No , we aren't talking apples and apples. You seem entiely stuck on the actuality of the true measurements you have provided and that is all true mathematically but you had to get out a calculator to determine at least some of them didn't you? I said, quick question. You have proven my point. The system isn't exactly user friendly for magnifications and dimensions that are off the beaten path but is when the numbers and dimensions are normalized inside an easy to mentally picture round base 10 reference. The F.N. system is arbitrary because there are no laws of physics or math to prove that it be the only system of value for it's purpose. It has been chosen.

Going back to the quote I retained above. I don't think I ever implied that an F.N. 20 field would return a 30mm field. It is pretty obvious that is not possible. I will rephrase that because either I jumbled the words or you misunderstood them.
A 15X/20 eyepiece produces an image circle that is the same size that a 10X/30 eyepiece would produce.There, that should be clear and if it isn't , it just proves my point even more, that the F.N. system is cumbersome and inadequate to describe the experience of viewing.

There are microscopes and heads out there that provide immense real fields of view. 35% wider than than the average modern norm. You have to stretch your orbs or turn your head yo view the entire field. A lot of people aspire to having such a field. When I was considering buying a new biological microscope , I considered paying the extra for a wide field head, a bargain for I think it was only 550.00 extra and for a trinocular too. The current field that I use is about 70% of that U.W.F. head and I wonder. What is the purpose of that ultra wide field? Is it to see more information on the slide or is it the wide field experience?
A pathologist needs a wide field, so to a metallurgist or anthropologist, where breadth of the sample and relationships between the elements of the sample are a big component of the reason for viewing in the first place. With average hobby microscopy, or even a lot of professional work, the field diameter doesn't matter that much as long as it extends into the periphery of the visual field. Ultimately, the slide is going to be moved for a more criitcal examination if there are details in the periphery, of interest. The wide field does give a sense of awe though. When a 15X eyepiece with it's wider apparent field is used, there is a portion of that awe revealed. An average W.F. 15X eyepiece will provide a 125% greater apparent field compared to it's companion 10X eyepiece , even if the real field is only 80%. The perception of having a larger field seems to override, at least partially, the inadequacy of it's real field coverage. Were it to have the same size image circle as the 10X and thus only a 67% field coverage, I suspect things would be quite a lot different.

[hans]

Only if the camera was in my eye. The image circle at the enrance to the eye is 20mm. If you hold a quarter out at arms length it will obscure the moon but if you bring it right close to your eye it will obscure a third of the sky.

I thought this 20 mm was some physical measurement you personally had made and were asking me to replicate. Or is it some kind of hypothetical thought experiment? Regardless, exit pupil from a typical 10X microscope eyepiece is a pretty basic, well-defined thing and if some circle of light measures 20 mm it cannot be the exit pupil, that's too big. It must be some other circle of light you are mistaking for the exit pupil. A photo showing what you are measuring, if this is a measurement you personally have made, or a quick sketched diagram if it is some kind of hypothetical thought experiment, should help clear up what measurement you are actually talking about.

[hans]

No , we aren't talking apples and apples. ... I will rephrase that because either I jumbled the words or you misunderstood them.
A 15X/20 eyepiece produces an image circle that is the same size that a 10X/30 eyepiece would produce.

I don't think it can ever be apples to apples unless you specify more carefully which "image circle" you are talking about measuring. You were just talking about exit pupil, now this sounds like you are talking about the apparent size of the field stop but that would have to be an angular measure, not measured in millimeters like you were saying before.

[wabutter]

In my forty years of working in microscopy, I have never heard of or had defined what an “image circle” is relative to the image size. And frankly the description in this thread makes it even less certain.

Apochromat, I can’t continue with this thread, you are conflating and confusing recognized microscopy terminology and laws of physics, to the point that it impossible to reconcile.
Microscopy is hard is not intuitive to understand. There is math used frequently and the numbers don’t always line up for easy in your head calculations. Referring to the hypothetical 1x objective is minimizing the calculation, when in fact it is not hypothetical, but readily exist. Almost every stereo microscope has a 1x objective either fixed or in the zoom. Macroscopes routinely use 1x as do forensic comparison scopes.
I would suggest that you have not tested what I have described. Just to make it clear, the FOV is how much of the sample you can see, it is not the projected image presented to the eye. (Image circle?) I will once again point to the conjugate image plane as compared to the conjugate illumination plane.
Please check out this web, it has a nice interactive tutorial

https://www.microscopyu.com/microscopy- ... ld-of-view

The above website should provide a conclusive solution, I’m done

[apochronaut]

It is apochronaut, not apochromat. That is a type of lens. It is not always easy to rely on one's perception of things around you when you are bound in a system and can't get out.
I used the term image circle to describe what is being seen because you were relying entirely on theory out of a book, which at the very start I suggested was not readily available to some. When you say the 34mm parfocal system "supports" a 20mm F.N. and I measure it at 18.3, then what is that 18.3 ? Then you dispute that, because there was no scale of measure. Weii, it doesn't matter because the 18.3 is presented relative to other eyepiece fields that measure at 20, clearly measured with the same scale because it is in the pictures. When I suggested that a 15X/20 eyepiece produces an image circle that is the same size as a 10X/30 eyepiece would produce you nitpick about terminology. Image circle is a terminology that is used in optics, maybe not in this context in your experience but it is pretty understandable. Does field stop diameter work better?
Let me put it another way. A 10X/30 F.N. would produce a field that was out to your ears. So would a 15X/20 F.N. eyepiece. So would a 10X /60° eyepiece or a 15X/60° eyepiece, to use perception through the eyepiece as a measure.
Since I don't use the passwords always to be a member of the club, I'll just have to put up with not being a member of the club. I don't know the secret handshake anyway.

[apochronaut]

No , we aren't talking apples and apples. ... I will rephrase that because either I jumbled the words or you misunderstood them.
A 15X/20 eyepiece produces an image circle that is the same size that a 10X/30 eyepiece would produce.

I don't think it can ever be apples to apples unless you specify more carefully which "image circle" you are talking about measuring. You were just talking about exit pupil, now this sounds like you are talking about the apparent size of the field stop but that would have to be an angular measure, not measured in millimeters like you were saying before.

Correct. At the eye relief plane, where the exit pupil is viewed most efficiently or comfortably , measure the diameter of the image.