Cirkut "Gears" program discussion

OK, a long gap here but finally got all the parts together and had some time and a space to set it up, and I measured my rear nodal points using a very shade-tree-mechanic but effective rig shown here:



I used spare Horseman 4x5 monorail parts to hold everything and line it up. My "infinity light source" was a hack I read about on the internet: a junk camera with a piece of fully exposed then developed then scratched film held down in the film plane, and a light behind it, and a 50mm lens focused to infinity on the front. The standard with the lens-under-test was mounted to a section of rail that could move back and forth atop a bolt holding it to the lower rail, thus able to pivot at that bolt. So between that rail's mount and the standard riding on it, I could move the rail and standard back and forth relative to each other and relative to the far rear standard, which held a focusing screen. I could mess with the middle stuff to achieve the nodal point (where pivoting it does NOT move the image side to side on the focusing screen) and then move the rear standard with the screen to bring it into precise focus. The nodal focal length is then the distance between the SCREEN and the PIVOT POINT (not the distance between the screen and the lens, which is the nominal focal length that is usually discussed.)

So the answer to my long-ago confusion is now quite clear: the NODAL focal length (the only thing that matters when talking about Cirkut lenses) can be significantly different than the ACTUAL focal length (the one described by normal optical theory and marked on the lens.) It's not a matter of the lens being marked wrong, it's a matter of it being a different concept that is only very loosely tied to the actual focal length.

SO, some measurements...

On the T-R 6-1/2x8-1/2 6.8 triple convertible lens that came with my original camera, here are the marked focal lengths followed by the nodal focal lengths I measured:


Hey, those are within spitting distance of the numbers I came up with by back-calculating the focal lengths implied by my gear plates! (Probably even closer if I work the Lipari math for the 100' focus offset; these are all infinity measurements.)

I have a T-R 8x10 6.8 triple convertible lens that I picked up more recently and fitted to a Graflex lens board:



I have a Fujinon 150/5.6 that I want to play with for wide-angle Cirkut photos (not a very common thing!)

If someone is in desperate need of having a lens measured, rather than doing trial and error film tests with gears, I'd be happy to set this up again and measure your lens if it's already on a Graflex lens board...with the caveat that this is really hokey and not at all precise and is probably making any optical engineers in the audience throw up a little bit in their mouths... but it's going to get you a lot closer than reading the focal length markings on the lens, that's for sure!

Duncan

Duncan:

Had to laugh - I use an old Horseman for an optical bench, too, although I have mine mounted vertically.

Just one observation, though. You're using a 50mm lens to throw a 'grid'; I seem to recall a much longer focal length is better, but maybe infinity is infinity. Smarter folks than me can comment. Nice work.

Charley, whose last No 10 film stills sits in the camera, 'cause he doesn't think it rewound properly.

c.d.ewen said:

Duncan:

Had to laugh - I use an old Horseman for an optical bench, too, although I have mine mounted vertically.

Just one observation, though. You're using a 50mm lens to throw a 'grid'; I seem to recall a much longer focal length is better, but maybe infinity is infinity. Smarter folks than me can comment. Nice work.

Charley, whose last No 10 film stills sits in the camera, 'cause he doesn't think it rewound properly.

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Well it's a junk FTb, and I have pretty much every interesting FD lens that exists, so I can definitely throw something longer on there! Maybe I'll run the measurements again at 100 and 200mm. (I think the 300/2.8 will be too heavy for the duct tape holding the FTb on the old lens board ;-) )

Sounds like you need a big changing bag (or a darkroom) to open up that #10 and see what's going on...

Duncan

I think infinity is infinity. Though I changed from a crappy 50/1.8 lens to a 100/4 macro and WOW the image on the focusing screen sure was a lot sharper! So using a high quality lens on the sacrificial camera makes it a lot easier to tell when it's in razor sharp focus while doing these measurements.

Duncan

So to continue on with my investigations... Figuring out the nodal focal length at infinity is nice, and doable on a bench, but then how do you get the numbers you need for the 25/50/100 foot focal lengths to do the actual gear calculations? I've been using the first two pages of Jim Lipari's notes here:

http://cirkutcamera.com/docs/jim_lipari_notes_01.pdf

...but it bugs me to just accept equations on faith when I have no idea where they came from, nor can I find anything like them in google searches of optical theory. Not that I don't trust Jim! He was a genius! But still. Also, it bugs me that under 10" there's no "fudge factor" on the end of the equation, then at 11" it jumps up to 1.2, then slowly works its way towards 1 again as you get longer focal lengths. That's not how equations usually behave. If, when working from long focal lengths down to 11" that factor is going up and up a little bit at a time, it should keep going up at 10" and lower, right?

So I decided to take those equations out of the, er, equation. I took my measuring rig off the bench, and proceeded to measure the actual nodal focal point with lenses actually focused on objects an actual 25/50/100 feet away. I've only done 25 and 50 so far (it's hard to find 100 clear feet indoors, and it's too cold in the Chicago area right now to do all this outside...but I have a plan for doing it tomorrow morning.) And sure enough, the numbers I get are different by a statistically significant amount (1-2%). Enough to change what gear you'd use by a tooth or two, in many cases.

Using Jim's equations gets you close, and avoids the need to drag this crazy test rig all over the place, and the final choice of gears is determined by double-checking with film and a measurably square target anyway, but I am still curious where that equation comes from, and why my real world results don't line up with it. I'm keeping both sets of numbers in a spreadsheet, and once I am finally set up to use this camera to take actual negatives, we'll have our answer as to which method (or maybe neither!) produces the correct gear number to take proper-aspect-ratio pictures. Fascinating stuff. Once I get this all figured out I'll write it up and then people can just work the fairly straightforward math by hand, or do it in an Excel sheet that I'll set up. No need for the crazy GEARS program I don't think. But it still all comes down to knowing the nodal focal length of your lenses, which have no hard and fast relationship to the marked focal length, and there doesn't seem to be any shortcut around measuring that with a special rig.

Duncan

I did the real-world 100' tests today, and they still differ from the equation results, but by a lesser amount... which make sense, since the equation is specifying lens-extension from theoretical infinity distance, and that number goes down as the focus distance goes up, which would make the absolute value of the error smaller.

Some of this could certainly be chalked up to imprecision in my testing rig. A tiny measurement error on my part at the infinity setting can get blown up into a larger error via the equations, which would then compare unfavorably with the real-world measurements. Except you'd think those errors would be random, i.e. in both directions and by varying amounts. But they look fairly consistent across all focal lengths except the very longest one. Maybe the error is my infinity light source. I guess I could double check this by pointing the rig at a full moon one night once warmer weather comes? I think I'll actually do that. For now, my real-world measurements will guide my initial gear choices and we'll see what happens.

Duncan

I'm heading out to run errands so may not be up on your entire issue here, but have a couple thoughts.

Email me if you want to discuss the computer program. I believe we talked about the issues a while back. I run a modified version. Gordon Roth is an older source for gears and measurements that you might not have run into. He's still at it to an extent, but not doing email or internet. He has me run some calculations from time to time, and his impression is the same as mine that the computer calculations are nearly perfect. The simple formula cannot possibly be correct at different distances since the camera does not pivot on the nodal point. The computer program modeled the movements of all the relevant points and seems correct to me even at pretty close distances. I should be able to run some calculations for you if you like. But keep it simple or I'll get overwhelmed and not get anything done. Anyway, email me if interested.

I have never understood any point in establishing 25, 50, and 100 foot settings. Why not just mark the proper extension for each gear and let the distance fall where it is. Gears aren't continuous, so are almost certainly off at an artificially selected distance. This way you focus on the subject then pick the closest gear. It also avoids the jump Jim usually used.

I agree that the best way to mark the camera would be the precise distances for relevant gear/lens combinations. For instance, maybe one lens would have markings at 17.5 feet, 48 feet, and 80 feet, which would be the *exact* distances to match up with gear tooth counts...rather then shooting at 25/50/100 and just accepting the slight error in the pictures. I'm quite sure they did it that way originally to make it easier on the random photographers that they suckered...er talked into buying this camera rig to make huge sums of money. If Jim's formulas are borne out as sound somehow, then I could certainly back-calculate the distances for specific gear/lens combos. Doing real-world measurements would require a bit of repetitive testing to find the camera-subject distance at which the lens had the nodal focal length that goes with a certain gear.

I'd be curious to see behind the curtain of the complicated program. Because according to the patent (see my post #8 in this thread) they very cleverly work around the fact that they are utterly ignoring the nodal point as a pivot point for the camera. The trick is to pull film past the slit AS IF the camera were pivoting on that point, and the narrow slit means that the very slight error introduced never builds up very far before being reset in the next moment by the slit moving to a new area of film. So it's important to know the true nodal focal length of the lens focused at that distance, and the circumference of the drum and the number of teeth on the ring gear, and then you know how fast to pull the film past the slit (by way of the pinion gear selection) like you would if the camera were rotating on the proper pivot point. But it's not pivoting on that point and that's OK. And no other gear selection is going to make the picture look better, i.e. there is no way to fix that accepted error by using a different gear. The only way to improve it would be to get the camera to pivot at the correct point. But that improvement is probably imperceptible.

Duncan

Yes, it works fine, and you can ignore the error at longer distances, but the motion is complex and difficult to calculate at close distances. I'm not aware of anybody successfully doing that before the computer program, and it works remarkably well.

I doubt there was anything particularly clever in the Cirkut patent, just making a well known principle into a practical product. There was at least one earlier camera working in this way.

Jim's notes just look like the simple gear calculation complicated by the unnecessary step of calculating the 25/50/100 ft extensions and best approximate gears. If you run the simple gear calculation you describe, then mark each gear on a scale with the proper extension from infinity, then you can easily calculate and add the marks for the 25/50/100 foot distances as separate marks without throwing away the information about where the gear really falls.

Jim and I talked about this, but he seemed to feel it was necessary to offer the traditional gear scale setup for people used to that. I think I did get him to start making a mark for the exact extension for the gear, at least some of the time.

Still, none of this fixes the error that accumulates at closer distances. Does Jim show something he did other than calculate the extension for 25 feet, then jump a gear for the long cell?

Mark Crabtree said:

Still, none of this fixes the error that accumulates at closer distances. Does Jim show something he did other than calculate the extension for 25 feet, then jump a gear for the long cell?

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All I have from Jim is in that one PDF (which is notes collected by Len, and blessed by Jim's kids for me to post online.)

I'll have to ponder the "error at closer distances" concept. There's no question that as you extend the bellows for closer and closer distances, the nodal focal point changes by a larger and larger amount. So maybe you're saying Jim's equations don't truly compensate for that? But it seems like my real world tests would. I could trivially measure the actual nodal focal length of these lenses at whatever distance (until my extra-long bellows runs out, for the longer lenses!) Maybe that's the thing to do. It's not hard to find a space big enough to use my rig to measure that for an object 10 feet away! It was finding 100 clear feet of indoor space that was a problem.

Duncan

(Edited to add: come to think of it, if the bellows runs out who cares I'll just remove it from the rig, since I'm not taking pictures or worrying about light leaks. I just need the image to show up well enough on the ground glass to focus and see when it stops moving as I pivot the nodal slide...and I can probably do that by just making sure the room isn't overly bright.)

Why isn't the actual nodal point just the focal length you calculated, plus the extension? Everyone I knew did it that way. The error is significant at distances closer than 25 feet, and about 1 gear tooth at that distance with the long cell. As far as I know, Jim's figures are just based on the simple formula as used for any camera, which can be simplified down to a single number. I still have a number in my head but would want to check it before posting. I got that from Jim, and the explanation, almost 40 years ago now. Jim's calculations look complicated because of figuring the distances. Oh, BTW, I meant to say that you should be able to find those formulae in any basic optics book. Kingslake is always a good start. The should be easy to find online if you know what to search for, but I don't have a suggestion. I have them jotted down from calculating various things manually over the years.

The computer program fixes all that. Why not deal with get that info up to date. I assume it would be simple for any computer geek to set up an ap today to do this. I'll work on posting my modified version later if you are interested. Do you not have a copy? There should be an OSX application to run BASIC, but I mostly use it on an older computer in the basement. My friend Doug has shot at least one car interior with a #10. I assume we figured the gear that way. It will take a lot of tests to get that close otherwise, and the same again with a different lens or distance.

I just looked at the notes again and see that there does appear to be a fudge factor in there for the distance error. I'm sorry if I missed discussion of that earlier. That may have been something he kept to himself, or came up with later. I assume it is based on a close distance test of a particular situation, then interpolation to others. It would probably work okay at moderate distances. My recollection is that he Jim switched to using the computer program shortly after it came out, but still using the 25/50/100 foot scale, which may be how the original program was set up. I'd have to look at it to see. You do have a copy of the original?

Mark Crabtree said:

Why isn't the actual nodal point just the focal length you calculated, plus the extension? Everyone I knew did it that way.

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I do not have the program. I'd really like the source to the program! I could recode it in something modern.

The actual nodal point should indeed be the infinity nodal point plus the extension. When i use my rig to find the infinity nodal point, and use Jim's equations to find the extension...it does NOT match the modal point I get when actually setting up the lenses at each of the distances. Is Jim's equation wrong? (Probably not.) Am I using it wrong? (Possibly.) Is my "infinity light source" on the bench not really infinity? (My current leading theory.)

In the end what really matters is the negative. Are square objects square? Only one gear will get you the closest, and the gears are a pretty coarse adjustment, so once you find it you'll know. All these calculations just save you test film (and getting gears cut needlessly.) But I'd like to take advantage of these tools if I can get them, and my tests, and my camera, and the test negatives I'll run, to all match eventually.

Thanks,
Duncan

I think relying on shooting squares is problematic; it should work, but has not worked well in practice worked for me. I calculate the gears, then shoot a test shot before doing a job. If it looks good I'm satisfied.

I've found that everybody seems to get a different result with their nodal point rigs, but always insist their result is accurate. None seem to agree with the number the manufacturer writes on process lenses. Again, I have no solid explanation for that, but suspect you are correct in thinking that is the problem. I tend to believe the manufacturers measurement when available. I would at least start with one of those as a way to eliminate a variable. The Turner Reich is funky when converted and probably the hardest to nail down; in practice it works pretty well.

I plan to head downstairs now and figure out how to copy my program. I could run a test calculation for you easily if you give me your focal length. Do you have a marked process lens? Also diameter of take up drum with 3' or so of film on it. What model/vintage #10? The drums tend to vary over time, but my impression is they are similar for quite a while in a production time. The variation is relatively minor anyway.

I forgot to mention the "double the focal length" test to confirm or measure focal length. Very clumsy, but I've done that when nothing else agreed. You should get a life size image (1:1) at double the focal length. Very fiddly, but perhaps you could think of a rig for setting that up. That is the number I have the most confidence in since you have two clearly defined points to measure between - object, and image on the ground glass. Obviously needs more than a Cirkut Camera extension, but doesn't really need to be completely light tight.

I do not have any process lenses, marked or otherwise. I measured my drum circumference with all the leader and two wraps of "film" (printer paper) to be 11.625" on I believe an early 20's #10 (I'd have to double-check which one I was measuring.)

There is clearly some subjectivity when determining the nodal point by the "the image doesn't move when the lens is pivoted" method but I treat it like determining if something is in focus - move it clearly to each side of the optimum, then walk it in until you're at the point where moving it in either direction makes it worse.

So to be clear on the "double the focal length" thing. If I have a 12" lens and put something 24" away and then focus on it, it should appear life size on my ground glass? But that has nothing to do with nodal focal length (or does it?)

Duncan

frobozz said:

I do not have any process lenses, marked or otherwise. I measured my drum circumference with all the leader and two wraps of "film" (printer paper) to be 11.625" on I believe an early 20's #10 (I'd have to double-check which one I was measuring.)

There is clearly some subjectivity when determining the nodal point by the "the image doesn't move when the lens is pivoted" method but I treat it like determining if something is in focus - move it clearly to each side of the optimum, then walk it in until you're at the point where moving it in either direction makes it worse.

So to be clear on the "double the focal length" thing. If I have a 12" lens and put something 24" away and then focus on it, it should appear life size on my ground glass? But that has nothing to do with nodal focal length (or does it?)

Duncan

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Yes, approximately. And the nodal point should be exactly in the middle.

You set up an object to focus on; I think I used a ruler of some sort. A moveable easel would make it a lot easier. Then you setup a camera and fuss around to you get the image on the ground glass to be exactly the same size as the object. I had to butt two cameras together to do it, and that was probably not a really long lens.

Mark Crabtree said:

Yes, approximately. And the nodal point should be exactly in the middle, but all you need to do is divide by two.

You set up an object to focus on; I think I used a ruler of some sort. A moveable easel would make it a lot easier. Then you setup a camera and fuss around to you get the image on the ground glass to be exactly the same size as the object. I had to butt two cameras together to do it, and that was probably not a really long lens. Once you get that setup, measure the subject to ground glass and divide by two.

Click to expand...

Well now you're blowing my mind. I'm definitely going to have to set that up and try it!

But this may relate to another question I had about Jim's equations - again, not questioning Jim, questioning whether my understanding of how to use them is correct. His notes say to plug the NODAL length into the extension equations. I get why those equations precisely specify the extension when plugging in the normal optical focal length of the lens. But plugging in the nodal point? Does the nodal distance also obey the exact same optical equations? Seems like it couldn't. (Or maybe that's where the fudge factor comes from.)

SO just to throw some made up numbers into your scenario above. I have a 12" lens. So I put a 4" tall object 24" away from the lens (from the physical center of the lens?) and then move my ground glass back and back and back until the object is in focus, it will, by optical definition appear 4" tall on the ground glass? So far I can wrap my head around this. But you're also saying if that distance from the lens to the ground glass is, say, 60", then the nodal point will be 42" in front of the ground glass? ((24+60)/2)? That's the part that's freaking me out. If that's true, it almost seems like with slightly more complex equations, we could start all of these calculations by knowing the precise true OPTICAL focal length of any lens, which is much easier to measure than the nodal point.

Time for more experiments with my franken-rig!

And thanks for all the programs. Off to study those now.

Duncan

I probably misspoke, or just glossed over something, or both. I don't enjoy sounding like an idiot, but that seems to be what happens here. I want to contribute information to make sure it is preserved, but simply don't have the time to do it properly. I spent quite a number of hours on this yesterday and just can't do that regularly.

I believe I should have said that you divide by 4. The bellows extension will be double the focal length, but you can't measure that without knowing the nodal point, so you take the full distance from gg to subject.

The nodal point distance is the focal length. There are two things you want to know, and the should amount to the same thing. I think what you really want to know is magnification, just as I assume you would on a process camera.

Charley and Jamie should know all this stuff and can probably explain it more clearly.

I've edited out the confusing line in my original posts. Hopefully you can sort out my mess.

On the issue of what Kodak was doing to figure out gears. I don't think we'll ever know much for certain, but most people I've talk to assume that Kodak had targets at the 25, 50, and 100 foot distances. They would have had a very good idea of the correct gears based on bellows extension alone. They may or may not have checked focal length beyond that; if they had, I would have expected it to be penciled or inked on somewhere like other companies did. They would shoot tests with the gears the expected and matched up a scale that agreed with that. The original scales were somewhat crude, but adequate at the distances Cirkuts were used. Gordon Roth has the most direct experience with this of anyone I know, or have known. He worked in the Kodak studio in the 50's and also for Gundlach (who made the Turner Reich lenses). Gordon met the last workers remaining from the old Cirkut operation. I think they still had a small presence when he was there; probably just repairs by then, but they did sell old stock for a long time. He thinks this probably how the gear calculation worked there.

Mark Crabtree said:

I probably misspoke, or just glossed over something, or both. I don't enjoy sounding like an idiot, but that seems to be what happens here. I want to contribute information to make sure it is preserved, but simply don't have the time to do it properly. I spent quite a number of hours on this yesterday and just can't do that regularly.

I believe I should have said that you divide by 4. The bellows extension will be double the focal length, but you can't measure that without knowing the nodal point, so you take the full distance from gg to subject.

The nodal point distance is the focal length. There are two things you want to know, and the should amount to the same thing. I think what you really want to know is magnification, just as I assume you would on a process camera.

Charley and Jamie should know all this stuff and can probably explain it more clearly.

I've edited out the confusing line in my original posts. Hopefully you can sort out my mess.

Click to expand...

Yes, you were up later than me sending me all that stuff, and you're a time zone later than I am! I appreciate the effort, don't apologize for errors.

I'll run some tests and figure out how all that works, with the object at twice the focal length.

I'm currently of the opinion that nodal point is only roughly related to true optical focal length, in that it going to be somewhere near the physical lens, so a long lens will have a long nodal point distance. But I've not seen anything so far to convince me that it is algorithmically related to optical focal length. It's a separate thing that needs to be measured for each and every lens. I understand that this is the "focal length" that needs to be entered into the programs though.

Thanks,
Duncan

Mark Crabtree said:

On the issue of what Kodak was doing to figure out gears. I don't think we'll ever know much for certain, but most people I've talk to assume that Kodak had targets at the 25, 50, and 100 foot distances. They would have had a very good idea of the correct gears based on bellows extension alone. They may or may not have checked focal length beyond that; if they had, I would have expected it to be penciled or inked on somewhere like other companies did. They would shoot tests with the gears the expected and matched up a scale that agreed with that. The original scales were somewhat crude, but adequate at the distances Cirkuts were used. Gordon Roth has the most direct experience with this of anyone I know, or have known. He worked in the Kodak studio in the 50's and also for Gundlach (who made the Turner Reich lenses). Gordon met the last workers remaining from the old Cirkut operation. I think they still had a small presence when he was there; probably just repairs by then, but they did sell old stock for a long time. He thinks this probably how the gear calculation worked there.

Click to expand...

Remember that one of my original camera's scales was manufactured with the gear number "31" embossed in it in the normal fashion, but then a "0" had been stamped over that to make that gear a "30" - exactly what you'd expect if they made up a bunch of scales based on their experience with the cameras but then tested each and every camera and lens combination before shipping it, correcting for any deviations they found.





I still think that for any combination of focal length and subject distance, there's going to be one gear that makes the pictures look right. So they totally could have figured out the gears originally through a whole bunch of trial and error, instead of with any sort of calculations. Then it would just be a matter of testing each camera before shipping, to make sure it had more or less the same specs as previous combinations like that, and adjusting for any errors they found by restamping the plates.

Oh, and to a point in your previous post: yes, it is really all about the magnification factor. Everything else here is just a way to get to that, the heart of the issue. For a certain sweep of distance in reality, you need a magnification-factor-adjusted sweep of film on the other side of the lens.

Duncan

OK I did some tests.

The part where putting an object at twice the focal length from the lens makes it appear 1:1 life size on the ground glass is pretty straightforward to prove even with my shade-tree rig. The 10.5 setup of my T-R is pretty much dead-on for that setup. The 18" cell alone, however, does not quite bear it out. But that just means it's not actually 18", right? I've had other clues that this wasn't the case. It appears lifesize on the ground glass once the object is about 32" in front of the lens, meaning it's really more like a 16" lens. I believe this, rather than doubting the formula.

Setting up the nodal point to measure it is a little annoying with my rig, because moving the nodal point moves the lens, which means I need to keep moving the tripod with the ruler I'm focusing on, to compensate. But I did all that. And in both cases it's off from the theory that says it's midway between the object and the GG. With the 10.5 lens the GG is 46" away from the object when focused, but the nodal point does not seem to be at 23" but rather 22.5" With the 18 (really 16) lens the GG is 67" away from the object, but the nodal point does not seem to be at 33.5" but rather 32.5" A lot of this could be chalked up the crudeness and inaccuracy of my rig but that's pretty far off and always in the same direction. So I don't know.

I think it's a great way to determine the true optical focal length of a lens, but maybe not so useful for Cirkut needs, since I need the nodal focal length at much further object distances than that anyway.

In mulling over the simple-ish Lipari gear calculations vs the gears program I realized the real-world way that the program is better by far: it gives you precise distances at gear tooth counts. I had pondered a method for back-calculating those distances using Jim's math but hadn't quite worked it out, and the gears program has worked it out, ergo it's a better approach, period.

Still working on the port to C. My stretch goal would be to port it to Excel - are my mad Excell skillz up to that? We'll see. The equations inside are mostly identical to Jim's but with different "fudge factors" for distance, and of course with the back-calculations of distances for gears. I still don't have an opinion yet on the necessity of the measurements for gear and film plane offsets for each camera.

Duncan

Mark Crabtree said:

I believe I should have said that you divide by 4. The bellows extension will be double the focal length, but you can't measure that without knowing the nodal point, so you take the full distance from gg to subject.

The nodal point distance is the focal length. There are two things you want to know, and the should amount to the same thing. I think what you really want to know is magnification, just as I assume you would on a process camera.

Click to expand...

OK, reading up on optical theory a bit, put together with what you have been telling me here, here is what I now believe to be true (anyone can feel free to jump in and point out any continuing errors in my thinking!)

As you say: nodal point = actual focal length. The markings on pretty much all lenses are wrong (not just rounded up to the nearest whole number, but often off quite a bit) in terms of the precision needed for these calculations, though they're fine for general camera use.

SO, one way to find the actual focal length is with a nodal slide and focused at infinity. With a good infinity light source (yet to be determined if mine is good!) that makes for a reasonably compact setup on a bench. It still has the slightly squishy, subjective determination of where exactly the nodal point is that means the object doesn't move on the GG.

Another way is with your 2*focal length, 1:1 image size setup mentioned above. Because all lenses are marked wrong the only reasonable way to do this is to move the parts around on the bench UNTIL the object is 1:1 on the GG, and then make the measurements. That's a little less subjective a determination, if you have a reasonably well marked GG, but still open to slight error. But notice no nodal slide required! SO at that point the object is by definition 2 focal lengths away from the focal point. And the GG is also 2 focal lengths away from the focal point. The whole thing is completely symmetrical. Thus, as you realized above, the way to get the actual focal length once that is set up, is to measure the complete object to GG distance, and divide by 4. The only problem with that is the sheer distance the setup covers once the lenses get to any sort of length more than about 12". But no nodal slide required, less subjectivity in the setup.

I'm going to keep refining my setup with both of these methods and see if I can get more precise measurements on my lenses, and perhaps even get these methods to agree. I may have to buy a few more lengths of Horseman rail, and some more bellows though! I was amazed at how even the tiniest amount of light, like the little light illuminating my ruler, could bounce around the room and wash out the image on the GG if I had no bellows in between.

Duncan

Last night it was finally clear and there was a nearly full moon. So despite the 18 degree F temperature, I hauled my rig outside to do some tests.

First off, it's really hard to focus on the moon on a 4x5 ground glass - it's so small! Similarly hard to tell if it's moving back and forth when I swivel the nodal slide. And hard to do any of this with impending frostbite. But within the crude precision of my setup, I was happy with how the results compared to my infinity light source. Most within .1mm to .2mm or so. So I'd say the infinity light source concept works, and is easier to use (and warmer!). But I'm also going to look at making a long enough rig to do it the other way, because that would be even easier still in some ways.

Duncan