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Binocular Magnification vs Focusing Distance (1 Viewer)

Ed,

Yes, I'm sure about the singlet focusing lenses in binoculars. I've seen cutaways of Nikon, Zeiss, Leica and Swarovski that all show the same thing. I recall seeing a doublet focusing lens in a binocular only once and that was the Kern Focalpin Porro of about twenty years ago. I expect the patent is referring to correcting CA for more critical high magnification uses, like telescopes.

Henry

BTW, there is a very obvious increase in spherical aberration visible in a star test when an astronomical refractor corrected for infinity is tested at a short distance. I noticed this again recently when using an artificial star at about 10m compared to the same telescope at infinity. Of course, those scopes don't use focusing lenses and are only really well corrected for distances beyond about 50 times the focal length of the objective.
 
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A little birdie from the East Coast just told me that the 829 uses a single focusing lens that is convex towards the objective and concave towards the prisms. So that issue is resolved. Thanks, Henry.

Ed
 
Well, after going over the Nikon Patent several times, I was struck by two things. First, optical engineers assume a lot about my knowledge; and, second, my knowledge is embarrassingly limited. Still, being retired I've got time on my hands —if not on my side. ;)

Nowhere is it said that the objective changes its focal length. In fact, F is set to F=100 for all three "embodiments." I assume F=F(inf). They know it, no doubt; we can only vaguely assume it. Nowhere is it said that focusing on a near object .87 meters away will result in the same change in focal length for different embodiments. They know it, no doubt; we can only assume it.

So, this is my initial attempt to bring the thing down to my level. Do the numbers confirm that F(inf)=100 for the three cases? If so, what is F(.87) in each case?

Using the f1, f2, and d5 values in the tables, which are the focal lengths of the first and second groups and the separation between them, my initial calculations indicated that F(inf) was overestimated by 7-10% using the standard formula for the focal length of two components.

f(ab) = fa*fb/(fa+fb-d)

Then it occurred to me that these components are thick lenses, and distances are measured from the principal planes, not the lens surfaces. So d5 was corrected by assuming the principal planes are positioned about 1/4 back from the last surface in each group. Voila! All three estimates were now agreeably close to F(inf)=100. My confidence returned.

The second point, of course, is that F(.87) ≈ 79.2±.5., certainly not 100. Therefore, the focal length shortens by about 20% over the hypothetical focusing range, and is probably constant or near-constant.

After my neural network recovers, the next step will be to examine image size at the retina, for near and far distances — and that will determine whether magnification is invariant or not.

B :)
Ed
 

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Ed,

Thanks for the effort. I'm happy to leave the math to you and Ron. The thing I found most interesting in the Nikon patent was the notion of using an internal focusing group to maintain consistent aberration corrections at all distances, an idea new to me. I would think it's not that critical in binoculars, but a good idea in a birding telescope. In the future I"ll have to pay more attention to close focus star test results and resolution measurements of scopes with focusing lenses.

Henry
 
Hello Ed;

I was not going to post this soon but thought I would reply while I had a chance. I started to look at this but have not done much, except find the problems you mention. Looks like it will be awhile before I can devote any time, have to travel to Oak Ridge, TN for the next couple weeks, but may get time to play with this over the weekend.

So far, I have only tried the embodiment one figures. I used the published data for the elements. First, let me list a few of the assumptions I made in case we have a difference of opinion so we can discuss the same data. I am assuming the F=100 to be the EFL. I am also assuming the image plane in embodiment 1 to be 7.47 mm past the exit of G3 (prism) and that is the X point in the plots. It appears to me that the image plane (paraxial) is 78 mm from the front surface of the objective, Group 1. As you have already found and stated, there is something off and I am pretty sure it is in my assumptions or math somewhere. When I calculate the lens as shown, I get an Inf EFL of about 115mm and a .87m EFL of 89mm. The paraxial comes close to the same point (image plane) but about 7.552mm and 7.414mm behind the shown position. I have a problem, the Abbe Numbers and refractive index does not match anything in my glass library and with just the two values, I am somewhat limited to checking much. I tried the closest I could find, LAFN21 and FK52 but the results were just too far out of range to work with. Next problem I ran across but apparently handled differently than you but we found the same problem. When I calculated the focal length of group 1 I got about f-55.079 instead of the f-53.18 shown. When I scaled the surface data to get to the 53.18 mm figure the Inf plot came out to f-100.22 and at 0.87 m the f was about 79+mm (I forgot to write it down) the paraxial was within 0.2 mm of the x-value.

Apparently I have an assumption that is not correct (and you may have the same one, since I notice you show an adjustment in all 3 configurations). I was hoping to key in one of the embodiments that matched their figures as a check on my methods and procedures. Anyway, sounds as if we are coming up with the same numbers.

I have attached 3 cad pics showing the results from Nikon modified (the one with the scaled group 1) and Orig. Inf and Orig. close. I will get back with you when I have time to confuse myself even more with this exercise.

Best, have a good day.
Ron
 

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...As you have already found and stated, there is something off and I am pretty sure it is in my assumptions or math somewhere. When I calculate the lens as shown, I get an Inf EFL of about 115mm and a .87m EFL of 89mm. The paraxial comes close to the same point (image plane) but about 7.552mm and 7.414mm behind the shown position.

Ron,

I only gave your post a quick once over. Your are right, I'm talking about the EFL, which, as we know, is measured from the principal plane of the system (if it's a thick or composite lens) and not the lens surfaces. Computing principal point locations is beyond my skills, so I guesstimated that for G1 and G2 they would lie 25% inside their respective composite thickness. The thickness of G1 is Sum(d1...d4) and the thickness of G2 is Sum(d6,d7). Hence, d5 should be increased by 1.33 units to get the true separation between the two components. Assuming that fa and fb are correct (which you may still question), the value of F(inf) computed correctly, and so I'm also willing to accept that the computed value of F(.87)=78.83 is correct for embodiment #1.

Have a good weekend.

Ed

PS. Note that I've used a universal correction, on the assumption that the principal plane is the same distance in from the outer lens surface in each embodiment. This is not strictly true, since it will vary based on the particular component lenses in the group. Given that F(inf) = 100, however, the problem could be worked in reverse to fine tune the locations in each case, and then see if the F(.87) numbers are in closer agreement. It's a toy exercise at best.
 
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Ed,

Thank you for finding and posting the patent application. It looks very interesting, unfortunately for a while I will not have enough time to read it as closely as would be needed.

Henry,

Where you have mostly looked at star-tests with traditional astronomical scopes, I have mostly used the star-test with scopes that employ internal focusing elements of either the Nikon variety or something resembling it at least on the face of it. With these scopes, there is usually remarkably little difference in aberrations between what one sees viewing an artificial star at 10.8 meters, a glitter point anywhere in the 30m-5km range or a real star light-years away in the night sky. What I see with the artificial star is pretty much what I see at infinity.

Kimmo
 
Kimmo,

Yes, I recall some discussion about this long ago. I think neither of us guessed that the focusing systems were causing our differing results at short distances. Presumably birding scopes that don't have focusing lenses will act like astronomical scopes and I wouldn't be surprised if some focusing lens systems are better than others at maintaining constant aberrations.

Henry
 
Ed;

I am, as you, assuming that fa and fb are the more correct values. My approach to the scaling of group 1 was somewhat different than yours since my preliminary calculations showed the principal point of group 1 at f(Inf.) to be 3.379 mm from the first surface and 2.7656 mm behind the last surface at f(.87), I tried a simpler approach of adjust group 1. I just took the spacing and radius values of each surface times approximately 96.55% (53.18/55.079) and came up with a 53.18 as the focal length. I did not change any of the other components in the chain and this led to a close enough fit that I quit at that point. I need to find more information on the glass specs. I really need the nf and nc values for my table, I probably could compute the unknown if I knew either nf or nc from the Abbe equation.

Since group 2 is between group 1 elements and the group 1 focal point (53.18) the entry cone is never collimated so I chose not to try to use any principal point calculations. My intermediate results indicate that, with collimated input, the principle point would be about the back surface but changes so drastically with focus distance (approximately 4.16 mm ahead to 9.11 mm behind from Inf. to 0.87m) that without iterative software it is beyond my scope of calculation.

Using the above conditions I arrived at EFL f(Inf.)=100.229, EFL f(.87)=79.105 and image plane errors of 0.146 mm (Inf.) and 0.158 mm. As a rough estimate, I generally assume tolerance to be about 1% of the EFL at the image plane for acceptable low power focus and aberration performance and this comes in well under that, about .2 mm for marginal aberration and .1 mm for the 70% zone aberration throughout the focus range. Until I get some refraction data for the red and blue I cannot see how this performs on coma, secondary spectrum, field curvature, lateral color or magnification without doing major changes to my spreadsheet cells and going to iterative functions instead of a simple lookup table, work I am not willing to do for this exercise.

FWIW, I found that I can change the group 1 glass to standard LAFN21 and PK1 glass and use all the published spacing and radii and come close to their results. Since all three embodiments use the same glass configuration for group 1, I have to assume custom glass or, at least, some I do not have data for.

Using the configuration with the standard glass, I come up with the EFL’s of 103.369 and 81.198. I miss the image plane by 1.634 and 1.623 mm. All the parameters I can check were within tolerance throughout the range except CA. CA calculated out by 1.25 mm+/- (0.26 mm tolerance) and since I am missing the image plane by 1.6 mm and the Abbe number is different by 15.6 this may be within range with the correct numbers.

Anyway, this exercise appears to come up with about the same numbers you have (0.4%), at least close enough for the focus knob to take care of it. I am really glad that you posted your findings. Since it appears that you found the same discrepancy that I did and we came to about the same conclusion, by apparently different methods, gives me some confidence that I have not totally screwed this up from the start.

If you, or anyone reading this, have any additional information that fits the published Abbe number and nd refraction, I would appreciate an email so I can add it to my library and continue this exercise.

You have a good weekend also Ed.



Henry;

Note the FWIW above. Even though the EFL is off 3.4% with the standard glass, the magnification at the image plane is only off 1.55%, smaller at close focus instead of larger.

Best to all.
Ron
 
Ron,

I don't know how relevant this is, but Nikon does in their advertisement literature rather often make mention of their own proprietary optical glasses, including ED glass. I have no further information on this, but perhaps it is conceivable that they indeed do have something that cannot be found in the Schott and Ohara catalogues.

Kimmo
 
Ron,

I don't know how relevant this is, but Nikon does in their advertisement literature rather often make mention of their own proprietary optical glasses, including ED glass. I have no further information on this, but perhaps it is conceivable that they indeed do have something that cannot be found in the Schott and Ohara catalogues.

Kimmo

Thanks Kimmo, I am sure you are right. I have been at a couple of Nikon sites and when I find something that mentions design or tech details and try to go to the page, I get blocked or asked for a password. Oh well, makes sense that they would not make it that easy to duplicate, same reason none of the others give you design details.

Good to hear from you, have a good day.

Ron
 
Ron,

Thanks. We have gone about things somewhat differently. But, I did the toy exercise and back-calculated the distances from the principal points using F(inf)=100 in each embodiment. The F(.87) values turned out to be 78.98, 78.95, and 79.99. That's a 1.3% spread in F(.87), the same as my original calculations. Oh, well, no more of that. ;)

Regards,
Ed
 
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