[henry link]

I decided to start a new thread on this subject, which has been under discussion in the thread "First Look at 7x42 EDG" in the Nikon subforum. I hope Surveyor will copy and paste his recent measurements from there.

The main question under discussion has been whether binoculars with internal focusing lenses are able to maintain constant magnification at any distance or show an increase in magnification at close distances like binoculars that adjust focus by varying the distance between the objective and eyepiece. Surveyor and Edz at Cloudy Nights Binocular Forum have measured increases in magnification at close distance for some binoculars using focusing lenses. I've measured other models with constant magnification. I'm hoping somebody will come forward with some knowledge about how these focusing lens systems are designed.

In the meantime here are the results of some magnification measurements I made yesterday comparing two binoculars with focusing lenses (the Zeiss FLs) to six Porros with moving eyepieces. I picked the six Porros for their close focusing ability. First measurement is closest focus for the right barrel of each binocular (combination of close focus setting and maximum positive diopter compensation) and second measurement is 80', the distance limit of my backyard test set-up.


Zeiss 8x42 FL: 7.91x at 77", 7.89x at 80'

Zeiss 8x56 FL: 8.07x at 94", 8.08x at 80'

Nikon 8x30 EII: 8.34x at 77", 8.03x at 80'

Nikon 10x35 EII: 10.49x at 112", 10.10x at 80'

Nikon 8x32 SE: 8.44x at 83", 8.08x at 80'

Zeiss 8x30B (Porro): 8.29x at 107", 8.14x at 80'

Swarovski 8x30 Habicht: 8.33x at 87", 8.06x at 80'

CZJ 8x50 Octarem: 8.37x at 146", 8.14 at 80'

Notice that most of the measurements (except the 8x42 FL) are above specified magnification. Magnification at infinity focus would be a little less than 80' in the Porros, but probably not much, maybe 0.02-0.04x. There are only about 2-3 diopters of focus change between 80' and infinity, but over 20 diopters between 80' and the closest focus. So, for reasons I don't understand I think all my figures are probably a little high, maybe about 0.5%. I don't really expect accuracy much better than 1%.

[Surveyor]

Henry;

I made some rough readings and I am now thinking that even the internal focusing lenses may exhibit some enlargement of magnification. The infinity measurements are iffy at best, done very quickly and hap-hazardly. The close up measurements should be pretty good

The two binos tested, Monarch 8x36 and Leica 8x32 BA, yielded the following approximate results. When time and conditions permit the procedures will be repeated to get a mean error range and check or verify the infinity readings.

------------------Monarch 8x36 (Lt/Rt)---------------8x32BA (Lt/Rt)

Infinity------------7.89x/7.91x-------------------------7.782x/7.791x
Close up-----------8.23x/8.17x—3.366m avg.----------8.176x/8.205x—3.391m avg.
------------------------/8.11x—2.763m----------------------/7.971x—3.364m???
----------------------------------------------------- 8.173x/-----------3.378m
Close up results-----.07x/.09x----------------------------.06x/failed (0.4x)
95% confidence < 0.1x

These rough observations seem to suggest that there may be as much as 0.2-0.25% per diopter change of at least some of these types of binocular.

Note: another factor found. The Monarch had to be refocused between barrel observations.

Have a good day.
Ron


Henry;
I agree fully with your statment "Notice that most of the measurements (except the 8x42 FL) are above specified magnification. Magnification at infinity focus would be a little less than 80' in the Porros, but probably not much, maybe 0.02-0.04x. There are only about 2-3 diopters of focus change between 80' and infinity, but over 20 diopters between 80' and the closest focus. So, for reasons I don't understand I think all my figures are probably a little high, maybe about 0.5%. I don't really expect accuracy much better than 1%.

I will do some checking, I have never checked at around 25m. It seems we are pretty much together at the close end and differ at the long end. I just used the photo method there and may it prove to be worthless.

BTW, for the sake of consistancy, which tube are you measuring. I will drop back to that for future reference.

Have a good day.
Ron

[Surveyor]

Henry;
I found these old photos of my collimator results before Monarchs went back to Nikon. There is too much camera movement and focus blur to be considered good enough to measure from, but they indicate I have a problem with my camera method, or at least a difference I need to account for.

The blue lines are a 6 arc minute grid (the grid is in 10th's of a degree). This grid is printed on paper and not an etched reticle. I still have a lot of work to do since I never used this for absolute power but just to compare one tube against the other.

These seem to indicate a left tube of 8.21x and right of 8.19x, much closer to the close up readings. Keep in mind that the actual bino to grid distance is only about 500mm though the focus and focusing elements are at infinity.

More study due, get back to you later.

Have a good day.
Ron

[henry link]

Ron,

Thanks for moving your post. I have a question about the following quote concerning your photographic technique back in the Nikon EDG thread.

"The infinity measurements are based on single observation of digital photos, one taken with the camera held above the bino with the sensor plane held approximately above the bino focal plane position. Another taken through the bino."

I have no experience with the equipment you use, but I was surprised to read that you align the focal planes rather than the fronts of the objective lenses. I confess I've been using the fronts of the objectives without thinking much about it. Aligning the focal planes doesn't make sense to me because binoculars with the same magnification can have widely different focal lengths, but even if using the focal plane is correct the position of a binocular focal plane would seem to be optically meaningless because the internal light path is not a straight line. Could that have influenced your infinity measurements?

Henry

[Surveyor]

Henry;
Interesting point. I did it out force of habit. When using survey collimators, the measurements are usually taken from the reticle position and in transits or total stations, the angle and distance measurments are taken at about the mid point of the instrument (as long as the rotation point is on the optical axis). It might be irrelevent since there is only about 50 mm difference between the objectives, less than .04% at 150m. I sent you an email with some results from last night, but I will try to repeat tonight and match the objectives and see what I get.

I did not use the camera on the close measurements because of the need to refocus from 3 meters to infinity through the bino.

Thanks for the tip. Have a good day.
Ron

Just had another thought. From the old camera days and photogrammetry, all the focal distance measurements were to the film plane mark on the camera. This does not mean this is right for this application though, so it bears investigation. Like you, it is something I did without thinking about it.

[Surveyor]

Henry;

I made some checks last evening in low light to get about the worse conditions I use to check and make sure I had my settings correct before and had not left the camera in one of the auto modes. The camera is used in the manual focus mode, set to infinity, and the aperture preferred mode to force the fastest shutter speed for wide-open lens.

The results were:
331-332 7.92605x 126 meters
329-330 7.92083x 126 m
327-328 7.90710x 126 m
325-326 7.90359x 133 m
322-321 7.89754x 133 m


with a quick, unsubstantiated short check of
314-315 8.14684x 3.65 meters

The above long focus results compare very well to two other occasions of measuring the same Monarch 8x36 by this method although one was before the binos were sent off and repaired and recollimated. The five results averaged 7.911022X with a standard deviation of .012x.

I did not use the camera method for the close focus tests because of the focus change required from 3 meter to the infinity setting when used through the bino. For that, I used the angle method.

Henry, to address your comments about the reference plane, I went back last night and did some shots on the same targets but not exactly the same circumstances. I used the camera at 2x to get a few more pixels and it was raining so the sharpness degraded a little.

The repeat result with the camera objective even with, or a little ahead of (I messed up from behind the camera, my camera has two lens extensions and I only saw one) the bino objective were:

333-334 7.95307x 133m
335-336 7.97360x 126m
337-338 7.91692x 133m
339-340 7.94808x 126m

These observations averaged 7.94792x with a standard deviation of .024. If we take the first results and add stdev we get 7.923 and take the second group and subtract stdev we get 7.924. Taking all nine observations as a group, the average is 7.92742, stdev .0256.

Even though the average is a little higher for the objective matched figures, I believe it to be a statistical anomaly because, thinking about the math, as you move the reference toward the target, the image gets larger so the divisor gets larger and makes the apparent power lower. I checked this by moving the camera about 3 meters closer to the target (about 2%) and left the binos on the tripod in the same position. The results were:

333-341 7.82644x 133-3m
335-342 7.84321x 126-3m

There are also some shots of a wall at 6.75 m, focal planes matched and 6.7 m, objectives matched. The first is the focal planes and the other two are the objectives. Don’t put much stock in them though, there was not enough sharp definition to match well enough to use.

I still believe matching the focal planes is right because when I use a booster on the exit pupil the image source is the focal plane of the bino and it is the way I have done it in the past (it irritates me when someone else says that). I cannot say that Henry is wrong though, I just don’t know. In the future, while things are set up, I will measure it both ways so I can compare them.

This weekend, I plan to take a table and some different equipment and check the same bino by two completely different methods if the other equipment comes in this week. I really hope the above method works out though; the other two are a pain to set up. But, so far, there are enough questions about this to still be verifying. I hope to get to a point where the repeatability and 95% confidence are less than .05x so the results should be good to 0.1x. But, as Henry says, 1% may be as good as we can get and that would be +/-0.1x.

Best to all.

[elkcub]

Maybe I'm missing something. However, if the ultimate question relates to the comparative size of retinal images, with and without binoculars, then why not use the the location of the retinal plane to determine distances? In a laboratory we would position the head using a chin or forehead mount, and then move the optics in front of the eyes.

Ed

[Surveyor]

First things first. As always, Henry Link is correct by using the objective plane. I have about finished my proof work and while thick objective cells do not show much difference at longer focal lengths, when the object distance gets short, especially under 1 meter, the math clearly supports Henry. My apologies Henry.

Ed;

While making some of these measurements that thought also occurred to me. But, in my opinion, we are trying to measure and compare hardware, specifically how the internal components affect the ratio of entrance pupil to exit pupil versus position. I think the retinal image would be subject to an individual’s eyesight. Hopefully, I understand your meaning correctly.

For me, the actual power has never been an issue, only the match between the left and right barrels.

Have a good day.
Ron

[henry link]

Ron,

Right or wrong, at least our results will be more comparable if we are measuring from the same plane. I'll try to borrow a few more examples of focusing lens binoculars to measure.

Henry

[edz]

Here's a few results from 5 different binoculars I've measured, 4 roofs and the Pentax Papilio

for these binoculars close varies from about 7-8feet to about 12feet.
These four roofs all have an internal movable lens
Pentax DCFHRII 10x42 Roof -- close 10.8x --- 100ft 10.3x
Celestron Regal 10x42 Roof -- close 10.5x --- 100 ft 10.2x
Celestron Regal 8x42 Roof -- close 8.5x --- 100 ft 8.1x
Bushnell Legend 8x42 Roof -- close 8.6x --- 100 ft 8.2x

Pentax Papilio -- close at 2 feet 8.0x --- 100ft 6.5x

I've also measured magnification in about another dozen porros between 8x40 and 12x50 and, like Henry, I've found most of them slightly above specifiec magnification. However, I've measured magnification in a 8 different large porros between 15x70 and 25x100 and only one was equal to specified. All the others were less or significantly less than specified. They really aren't useful for this question Henry asks.

edz

[edz]

Here's a few more, all porros, close focus at about 13-14 feet.

Pentax PCF WP II 8x40 -- close 8.2x --- 100ft 7.9x
Pentax PFC WP 8x40 -- close 8.0x --- 100 ft 7.5x
Leupold Yosemite 6x30 -- close 6.5x --- 100 ft 6.1x

edz

[henry link]

Ed,

Thanks for posting your measurements.

Binoculars with moving eyepieces appear to present a pretty straightforward case of increasing magnification as the eyepieces move away from the objectives, but the internal focusing lens systems are not so obvious. I haven't had an opportunity to measure any more of those, but I did jury-rig such a system to try to see how it works, using a Barlow lens as the negative focusing element between an objective lens and an eyepiece. This is what I found by moving these elements around a bit.

Moving the negative focusing element back away from the fixed objective has the effect of reducing the objective's effective focal length, so that the focal plane for infinity focus moves forward to a new position closer to the objective. If the eyepiece could be moved forward to meet this new focal plane position the result would be infinity focus in a shorter focal length system with reduced magnification. Since the eyepieces in these systems are fixed in a position behind the new focal plane the result is instead closer focus at the original infinity focal plane of the objective. Since there is no change in the distance between the objective and the eyepiece it seems to me that a system like this should naturally work to change focus without changing magnification. At least that's what my measurements have indicated so far (within about a 2% margin of error), so now I'm at a loss to explain the results that you and Ron have obtained showing increases in magnification at close focus. It would seem that this system could only work if focus changes instead of magnification.

Henry

[Surveyor]

Hi Henry;

Like you, I believe that with internal focus, the image size can be maintained throughout the focus range. I also have been pushing some lenses around, albeit on a spreadsheet, and have convinced myself of this. I have also come up with an explanation, at least subjectively, to explain measured differences to see if you concur or figure out a way to verify.

The attached picture is a made up lens configuration I used to test positions. All the data is made up since I have no actual design data to work with.

At the infinity focus position, with the focusing lens 50 mm from the previous surface the calculations were:
Focal length=229.724
F=4.52
Paraxial=106.7524
Magnification=4.0119
Image formed=167.825 (from front surface of the objective group)

With the image focused a 2 meters, the focusing lens 57.5 mm from the previous lens, the calculations were:
Focal length=194.953
F=3.84
Paraxial=99.6093
Magnification=4.0719
Image formed=167.825 (from front surface of the objective group)

As can be seen, if the eyepiece focal point is 167.825 mm from the front of the objective lens, then all from infinity to 2 meters should come to focus at that plane with the magnification between 4.01 and 4.07, or about 1.5%, with the larger image at short focus. Not bad results from guess work.

In this day of computer modeling, I imagine designers have software that they key in the dimensions and parameters they want to hold and the software calculates the Abbe number, refractive indices, spacing and surface radius to be used and selects the closest glass from a data base and then re-calculates for best fit. I would think that the later the version of the binoculars, the closer this scenario would fit, such as your FL’s, maybe my Monarchs, but older vintage bins like my Trinovids were designed by software a few generations older (we all know how much software has changed in the last 20 years) and may have been designed more closely to my trial and error approach.

Magnification is the ratio of image distance/object distance, so just coming up with a design that can take that huge ratio and bring it to a common plane by just moving a lens 7.5 mm is a tremendous balancing act. That is design; remember these have to be manufactured to a realistic tolerance, most of the time a 5% maximum is expected, so 2% would be a realistic expectation.

Anyway, that is my thoughts on the subject up to this point.

I am still waiting on some test components due to an error by an online vendor. I ordered two monoculars to modify ($30) and received two 8x42 Bushnell Legends roofs instead. Since the vendor never makes mistakes, it is taking forever to get it straightened out. I will get back to testing when I have my procedures refined and repeatable.

Have a good day.
Ron

[edz]

Henry /Ron

the power factor of any barlow lens ( negative lens) changes as the distance varies from the eyepiece focal point to palne of the negative lens.

If I place a barlow in a telescope and place an eyepiece in that barlow, I can increase the resultant power by sliding the eyepiece out, moving the ep focal point further from the negetive element. Likewise, pick up any 5 or 10 eyepieces and measure the distance from the shoulder to the focal point and most of them will be different. If I use an eyepiece with a focal point 10mm in front of the shoulder, the barlow might give a power factor of 2.0x. If I then use an eyepiece with a focal point 5mm behind the shoulder, the barlow might be giving a power factor of 2.2x. A hard lesson for astonomers to learn is that no barlow lens has a constant power factor with every eyepiece. It changes with every eyepiece because every eyepiece places its focal point at a different distance from the barlow element. We see astronomers all the time reporting critical measure magnifications, only to find out they were using a barlow and really have no idea at what magnification they were observing.

[Moving the negative focusing element back away from the fixed objective has the effect of reducing the objective's effective focal length, so that the focal plane for infinity focus moves forward to a new position closer to the objective. If the eyepiece could be moved forward to meet this new focal plane position the result would be infinity focus in a shorter focal length system with reduced magnification. Since the eyepieces in these systems are fixed in a position behind the new focal plane the result is instead closer focus at the original infinity focal plane of the objective. Since there is no change in the distance between the objective and the eyepiece it seems to me that a system like this should naturally work to change focus without changing magnification. ]

In an internal movable element binocular, the distance from the negetive element to the eyepiece focal point is always changing. Therefore, that has an effect on the power outcome of the system. In the above case, as the negative element is moved away from the objective, it is also moved closer to the eye piece focal point. Because it is now closer to the eyepiece, (the same as inserting an eyepiece with the focal point in front of the shoulder, therefore closer to the negetive element) it's effective power would be reduced.

Not sure if this will help, but here's an article that may be of some use.
http://www.brayebrookobservatory.org...BarlowLens.pdf

edz

[henry link]

Ed,

The tricky part of understanding these focusing systems is to shift your thinking away from the Barlow/eyepiece model in which infinity or some other fixed focusing distance is given and shifting the position of the negative lens changes magnification, but only after refocusing to the original focusing distance by changing the spacing between the eyepiece and the objective. In the case of a focusing lens system the elements are similar, but shifting the position of the negative lens between a fixed objective and eyepiece changes focusing distance rather than magnification exactly because the eyepiece/objective spacing cannot be adjusted to refocus to the original distance.

Your last two sentences have it right. The magnification (at infinity) would be reduced when a focusing element moves back toward the eyepiece, but only if the eyepiece can also move forward to reach the new focal plane for infinity focus. If the eyepiece can't move in response to the changed position of the infinity focal plane, as in a binocular with internal focusing, then the focusing distance is reduced while magnification remains the same (or close to it).

Henry

[elkcub]

Originally Posted by henry link

...

Moving the negative focusing element back away from the fixed objective has the effect of reducing the objective's effective focal length, so that the focal plane for infinity focus moves forward to a new position closer to the objective. If the eyepiece could be moved forward to meet this new focal plane position the result would be infinity focus in a shorter focal length system with reduced magnification. Since the eyepieces in these systems are fixed in a position behind the new focal plane the result is instead closer focus at the original infinity focal plane of the objective. Since there is no change in the distance between the objective and the eyepiece it seems to me that a system like this should naturally work to change focus without changing magnification. At least that's what my measurements have indicated so far (within about a 2% margin of error), so now I'm at a loss to explain the results that you and Ron have obtained showing increases in magnification at close focus. It would seem that this system could only work if focus changes instead of magnification.

Henry

Henry,

Basically I agree with your analysis, which is essentially what I was trying to say in post #28 of the other thread, except that I should have said "...moves the image toward the zero point of the system" rather than away from the field lens of the eyepiece, although it does that too.

With regard to actual internal focusing mechanisms, I located Nikon's 1997 Patent 5615049 dealing with an "Internal Focus Objective Lens." (see attached.) This is extremely interesting for several reasons, even beyond your original question, but would have been somewhat abstract were it not for the fact that the same basic 5-lens optical design is used in the Swift Warbler Model 829. I have a cut-away version of this binocular that Nicolas Crista recently sent to me that allows examination of each lens component individually, as well as the transport mechanism. All the surface curvatures are the same as shown in the patent diagrams, and if I had an optical bench I could measure the focal lengths of each element or group.

This Nikon invention, therefore, is probably licensed to many other Japanese manufacturers, like Hiyoshi who makes the Swift 829 and many others. It's not too much of a leap to assume that it's the basis for what's used in the LX L, and perhaps the basis for the new EDG. How similar it might be to Zeiss and Swaro designs, of course, is not clear.

More important than a small change in magnification, IMO, are potential changes in the aberrations as a function of focusing distance. Unfortunately, CA is not [shown], but it is evident that the instrument's image quality does vary with focusing distance.

Elk (EdH)

[henry link]

Excellent research, Ed! Unfortunately I don't have time to really read this now, guests arriving for dinner, but I think this specific system is probably for the Fieldscopes. They use a doublet for the focusing group. The LX L binoculars use a singlet, but I imagine the principles are the same. A singlet is probably considered good enough for low magnification.

Henry

[Surveyor]

Ed;

Thanks much Ed, a very informative piece of research. It will take quiet some time to digest all in there. Could take months.

I did notice that CA and secondary spectrum was discussed towards the end of the document and controlled by conditions 5, 6 and 7 and labeled Condition 5 at the bottom right side of page 11.

Thanks again and have a good day.

Ron

[elkcub]

Henry/Ron,

Thanks. I'll have to disassemble my 829 cut-away a bit further to see if it uses a singlet or doublet focusing lens. In any case, I know by inspection that it's a negative group as formulated in the patent.

To tell you the truth, my eyes glazed over with all the details, but I'll look further for references to CA control.

Regards,
Ed

[elkcub]

Oh, yes, there is an excellent discussion of how the boundary conditions affect CA, so I simply should have said that graphs aren't shown for CA as they are for SA, astigmatism, and coma. (I've corrected my post.)

Based on Condition (4), lines 26-31, I'm rather surprised that an expensive implementation of this design would use a singlet rather than a doublet for G2, because it might be "...difficult to correct and balance the CA in the infinite and close focus conditions."

Are you really sure about the LX L, Henry?

Ed

[henry link]

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.

[elkcub]

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

[elkcub]

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.


Ed

[henry link]

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

[Surveyor]

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