How is focal length measured?

[Chan Tran]

Correct in principle (I dd mention the front nodal point), but in practice this method does work to amateur accuracy. The reason is that the accuracy of this measurement is limited by how well you can measure:
1) the lens to subject distance, since you don't know the exact location of the front nodal point,
2) the extension, because this is a relatively small distance and I assume that the user is an amateur with say calipers or a micrometer, measuring the extension on a camera with a homemade fixture, not some kind of incredibly rigid and aligned optical bench.

If you set it up so the lens to subject distance is several times larger than the focal length, the error from not knowing the front nodal point is a small fraction of the subject distance, so it doesn't dominate the error budget.

I will give a worked out example, sorry for the tedium. Suppose you have a lens of focal length f=100mm (but you don't know this), and you focus it at a subject distance of d=1 meter measured. The extension from the lens equation is e=11.11 mm, measured. Most of us would probably only measure that to say the nearest 0.1 mm, an accuracy of 1% on e.

The lens equation 1/f = 1/d + 1/(f+e) can be rearranged into a quadratic: f^2 + e*f - e*d = 0. You can solve this with a calculator, or analytically:
f = (sqrt(e^2 +4*e*d) - e) / 2.

Suppose that the front nodal point is 10 mm different than where we thought it was. That means we would measure d=990mm or 1010mm, You can try plugging these numbers into the formula. You'll find that the inferred focal length would be 99.5mm or 100.5mm. A 1% error on subject distance leads to an 0.5% error on focal length (due to the prefactors in the formula and the square root).

It turns out that a 1% error on measuring the extension also leads to about an 0.5% error on the focal length. IMO, measuring the extension to 1% is difficult for an amateur without fabricating a jig.

It's possible to measure focal length much more accurately (I have a process lens that is marked with true focal length to 0.01 mm), but for that I think you'll need an optical bench and techniques that are beyond the scope of this discussion.

If you can indeed measure the focal length to 0.5 or 1% then it's worth it as the labelled focal length can be off by 4% or so.

 

[M. Axel Wikstrom]

Focus the lens at infinity and measure the distance between something on the lens such as the rear element, lens board, etc. to the film plane. Now focus on a small object until that object is the same size on the film as it is in real life and measure as above. The difference between the two measurements is the focal length.

 

[Bob S]

That is what got me thinking about it - you have to adjust for longer bellows, basically because you are changing your effective aperture, as far as I can tell.

You have to add exposure based on image ratio or magnification. At infinity no correction is needed. At ¼ lifesize you need an additional ½ stop exposure, at ½ lifesize 1 stop, at life size 2 stops, at twice lifesize 4 stops. You can adjust aperture or shutter speed or both to set the required compensation.

 

[wiltw]

If you focus on any object so that actual size = size on film plane while the lens internal focus mechanism is left at Infinity (that is, 1:1 magnification is achieved at the film plane) the subject to focal plane distance is 4 * FL

 

[Dan Fromm]

If you focus on any object so that actual size = size on film plane while the lens internal focus mechanism is left at Infinity (that is, 1:1 magnification is achieved at the film plane) the subject to focal plane distance is 4 * FL

You forgot the all-important inter-nodal distance.

 

[AgX]

That is why Axel's proposal (#27) is the better one.

 

[MattKing]

That is why Axel's proposal (#27) is the better one.

I agree, although it is a bit challenging if you are working with a 135 film camera.

 

[AgX]

If one got a grid screen one can be sure about image scale.

 

[Dan Fromm]

https://www.google.com/url?sa=t&rct...ideNotes.pdf&usg=AOvVaw0drsonYCCR_n6Vj0A3Zkp8

 

[Bob S]

I agree, although it is a bit challenging if you are working with a 135 film camera.

Why? Your focusing screen is 1 x 1 ½”. Makes it very easy to measure it against a ruler!

 

[AgX]

Well, not all finder screens yield full format sight. And they are not well accessible for metering such. A grid screen though typically can be taken out and the lines distances perfectly measured.

 

[Dali]

The aperture is measured as a ratio of the focal length, but the lens elements move forward and backward when focusing. How is the focal length determined? Is it based on the infinity focus, or the nearest focus, or something in between?

Just curious.

Field of view for a given film format...?

 

[wiltw]

You forgot the all-important inter-nodal distance.

If you use a magnification calculator online, you will find a 100mm lens at 400mm focus distance reproduces 1:1
If you use a magnification calculator online, you will find a 200mm lens at 800mm focus distance reproduces 1:1

...like this one on the Cambridge Color web site https://www.cambridgeincolour.com/tutorials/macro-lenses.htm

Nothing in the calculator considers nodal position!

 

[Dan Fromm]

If you use a magnification calculator online, you will find a 100mm lens at 400mm focus distance reproduces 1:1
If you use a magnification calculator online, you will find a 200mm lens at 800mm focus distance reproduces 1:1

...like this one on the Cambridge Color web site https://www.cambridgeincolour.com/tutorials/macro-lenses.htm

Nothing in the calculator considers nodal position!

The calculators are wrong but the errors are small and have little practical significance.

 

[wiltw]

The calculators are wrong but the errors are small and have little practical significance.

Perhaps you might illustrate the error magnitude, assuming the mythical 100mm lens, and with two different assumptions about nodal location in the mythical lens, how much error is introduced for each case, for the derived FL, assuming 4 * FL captures 1:1

 

[Dan Fromm]

Perhaps you might illustrate the error magnitude, assuming the mythical 100mm lens, and with two different assumptions about nodal location in the mythical lens, how much error is introduced for each case, for the derived FL, assuming 4 * FL captures 1:1

Film-to-subject distance = film-to-rear node distance + internodal distance + front node-to-subject distance. This is true for all lenses at all distances.

From Schneider documentation, the 100/5.6 Symmar-S' internodal distance is -2.1 mm. The 150/9 G-Claron's is 3.3 mm. The 90/5.6 Super Angulon's is 35.2 mm. Non-zero, as the calculators you trust assume.

Do the calculations.

 

[wiltw]

Film-to-subject distance = film-to-rear node distance + internodal distance + front node-to-subject distance. This is true for all lenses at all distances.

From Schneider documentation, the 100/5.6 Symmar-S' internodal distance is -2.1 mm. The 150/9 G-Claron's is 3.3 mm. The 90/5.6 Super Angulon's is 35.2 mm. Non-zero, as the calculators you trust assume.

Do the calculations.

OK now trying to relate the engraved FL (assuming engraved FL = actual FL) to

film-to-rear node distance and
internodal distance and
front node-to-subject distance​

for a lens! If a 100mm lens is set up to create 1:1 image on film, the 4 * FL rule says subject-to-film is 400mm. But if you factor in your three different distances, your formula implies that the actual distance is NOT 400mm but something else.

I am just trying to understand this, as I am not an optical engineer who can readily interpret what you wrote into an example of what might really occur in real life, which is not 400mm subject-to-film distance... What might that error be...412mm actual distance subject-to-film, so the computed FL yields 103mm (412/4) rather than 100mm ?!

 

[Dan Fromm]

Hmm. Since you can't do the arithmetic, I'll do one example for you.

At 1:1, a lens' rear node-to-film distance is 2* focal length and equals its front node-to-film distance. That's 4*f plus the internodal distance. In the case of the 90/5.6 SA, 360 mm + 35.2 mm = 395.2 mm. Following your rule of thumb, you'd estimate the 90/5.6 SA's focal length as 395.2/4 = 99 mm. This is a 10% error.

For the other two lenses, the error is much smaller. This is why most of us usually neglect internodal distance when calculating, e.g., extension needed to get desired magnification. But for some lenses it matters. Your on-line calculators' authors did us all a disservice by not explaining this and by not giving their users the opportunity to input internodal distance.

Incidentally, I didn't present my formula. It isn't my opinion, as you seem to think, it is the way things are.

About FL as engraved. It is a number, that's all, and is rarely the lens' actual focal length. Not all lenses' design focal lengths -- this is the FL when the lens' prescription is realized perfectly in glass and metal -- are the same as the nominal FL engraved on the lens' barrel. For example, according to CEDIS-Boyer' s fiches techniques, the 800/10 Apo-Saphir's design FL is 817 mm. To add to the fun, not all lenses are perfect realizations of their prescriptions. So actual focal lengths are rarely equal to design focal length, which may not equal the nominal FL.

Why do you think that people who understand this advise posters who ask for help in designing fixed focus LF box cameras to design in some adjustability? Because trusting what's engraved on a lens isn't safe.

Further on this point, years ago I bought twenty (20) 38/4.5 Biogons mounted in fixed focus aerial cameras. Zeiss Oberkochen QC is pretty good, Even so, the cameras' manufacturer had measured each of my lenses' FL and marked it on the lens. The 38/4.5 Biogon's design FL is 38.5 mm. Mine's measured focal lengths ranged from 38.3 to 38.8 mm. Each had a shim in the form of a ring that sat between the back of the lens' shutter and the camera body to adjust focus to infinity. The shims had their thicknesses marked, to 0.01 mm.

 

[wiltw]

Thanks, I can do arithmetic. However, I do not adequately understand the terminology sufficient to know what to add vs. subtract. Your specific example was all I needed. Seeing quantification of 10% error as possible using your example lens allows even a layperson to comprehend the shortcomings of 4 * FL, as a 'close enough' estimate for field work fine, but for computing FL not good enough.

I do understand the reality of engraved vs. vs. actual FL. Over the years, multiple so-called 50mm lenses measured in Modern Photography reports to be 49.5 or 51.5mm based upon the vintage of design. We also see, particularly, this lie when we deal with macro lenses made for AF cameras, (e.g. the engraved 100mm lens closer to 75mm actual F -- 1:1 macro in spite of 0.3m focus distance would not be possible with true 100mm FL)

 

[Mr Bill]

I am just trying to understand this, as I am not an optical engineer who can readily interpret what you wrote into an example of what might really occur in real life,...

Having read a number of your astute posts on technical matters, I would say that if you wanted an optical engineering sort of text on your bookshelf, this is the one it should be: https://www.amazon.com/gp/aw/d/0070591741/ref=dbs_a_w_dp_0070591741

If money is no object I presume the current issue would be better, but with good used copies under $10, this is hard to beat. There are no reviews for this edition; see the newer edition for those.

I got this when I got a little deeper into optical work in my day job. Out of perhaps a dozen optical books it's the one that would be hardest to get away from me. Again, judging from what I've seen you post here, I think it might be the one for you.

 

[Sirius Glass]

I cannot guess where the nodal point is, so I mount the lens on the camera and focus with the ground glass.

 

[reddesert]

If you can indeed measure the focal length to 0.5 or 1% then it's worth it as the labelled focal length can be off by 4% or so.

There are a few cases, especially in the large format world, where lenses are unlabeled. Such as older lenses that may only have a plate size marked, or front/rear groups used as a convertible. In such cases it's useful and not a total curiosity to measure the focal length by measuring the extension required to focus at a known distance, although you may only get it to a few percent.

(Side note, single groups from a convertible, or unusual lenses such as telephoto/retrofocus are where you probably have to be most careful about the nodal point being in an unusual position.)

 

[John Koehrer]

As long as there's a tiny mention of makers fl. Leitz used to engrave the actual difference from marked focal length near the lens mount.

Yes, I know it's tiny format and the flange/standard is fixed but interesting to me how closely some makers tolerances are.

 

[Mr Bill]

I would say that if you wanted an optical engineering sort of text on your bookshelf, this is the one it should be: https://www.amazon.com/gp/aw/d/0070591741/ref=dbs_a_w_dp_0070591741

I think I'm gonna retract my recommendation. Going back into the book there's not much that is immediately pertinent - maybe three pages or so, and it's probably a pretty tough slog for anyone coming into it cold.

It's still a great book if you have the needs, but it's not really a photography book.

 

[M. Axel Wikstrom]

I agree, although it is a bit challenging if you are working with a 135 film camera.

I've never seen a lens for a 35mm camera without a focal length label. I have large format lenses that aren't labeled. (And isn't this thread is in the large format cameras sub-forum?) My instructions, post #27 should work fine.