View Full Version : Math: Calculating distance scale based on focal length, FFD, helical travel

I am currently working on calibrating a number of lenses for the new Mercury camera, to assist with the creator and future possible users of this camera.

This is being done by eye - focusing on targets at certain distances, using a digital camera for critical focus. However, some ultrawide lenses do not really work this way due to short FFD. Ground glass focusing is pretty hard to be exact. And finally, human error can be a serious problem!

I was thinking today that it seems like there should be a formula for this. Knowing of course the focal length as well as the FFD, the amount of extension needed for each distance should be calculable right? And then by measuring the helical extension with a caliper and dividing that out by 360 degrees, a reasonably accurate focus scale could be made.

Am I correct in this? If so, what is the formula(s)? I imagine an Excel spreadsheet with the data and formulas could spit out numbers pretty quick, and then I could double-check them on the camera to be sure.

I've used the thin lens equation (http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/lenseq.html) to calibrate helical mounts. Solve for image distance i. Then, i - focal length = incremental distance the helical needs to move from focus at infinity.

1/focal length = 1/Dsubject + 1/Dfilm

all distances in mm.

Dsubject = front node to subject; Dfilm = rear node to film.

Check:

For 1:1 reproduction ratio, Dfilm = 2*FL and Dsubject = 2*FL, so

1/FL = 1/2FL + 1/2FL = 2/2FL = 1/FL

This is the thin lens formula, which requires that the front and rear nodes be coincident.

That's not normally the case with longer lenses, but it gets you pretty close.

Please note that ALL optical formulae use the ACTUAL focal length, not the number on the barrel.

And they use the ACTUAL front and rear nodal point positions.

If dealing with lenses significantly longer or shorter than "normal", the nodal points may be far from the center, even completely outside the physical lens. For example, the rear node of a short wide-angle lens may be between the rear lens element and the film. The front node of a telephoto may be way out in front of the front lens element.

- Leigh

Dan Fromm

7-Sep-2017, 19:31

What Leigh's words about nodal points mean is that the lens has to be collimated to the helical, cone and camera so that when the helical thinks the lens is focused at infinity it really is.

My list of links to useful info points to a post by Emmanuel Bigler, whom I greet in passing, on this forum that explains how to measure a lens' focal length.

What Leigh's words about nodal points mean is that the lens has to be collimated to the helical, cone and camera so that when the helical thinks the lens is focused at infinity it really is.

Yep.

The focal length of any lens is defined as the distance from its rear node to the film plane.

That definition does not know nor care anything about the physical lens assembly.

And the optical focal length is not in any way related to the Flange Focal Length (FFL).

The FFL is the distance from the front of the lensboard to the film when focused at infinity.

It's given on every datasheet for LF lenses.

Herr Dr. Bigler is certainly an acknowledged expert in this field.

- Leigh

In terms of collimation to the helical, I assume you mean that when the helical is at what is marked infinity, the lens is actually at infinity - correct? Since that is the "starting point," my procedure first is to focus the lens to infinity, and then mark the placement where this is on the scale, lining up with infinity on the start of the scale. This helical is blank, as opposed to one which is already marked for a certain lens online. One helical* is being used for all lenses, with each one getting a distance scale marked by hand - this is then transferred to a scanner, scanned, and made into an official scale template that can be attached to the lens/helical system permanently (if you want).

*Well, one helical for ultrawide lenses, a different one for wide/normal/etc. due to design differences

Lets talk about nodes. I did not know there was two nodes, or perhaps I am just not remembering. The rear nodal point is the flange focal distance, right? What is the front nodal point and how would one find/calculate it?

Let me reiterate that this exercise is not meant to arrive at absolutely perfect results, just a roundabout scale I can use to check my handwritten results for rough accuracy.

I will do some reading on thin lens. It's been awhile. Just for reference, the data I have on each lens includes:

- "Real" focal length as provided by the manufacturer (yes I know each lens varies slightly, but we'll have to accept a slight bit of error there and use the official FL since this is a general scale for any lens of this type)

- Flange focal distance

- Extension of the helical to infinity, marked as such at the start of the scale

- Distance the helical travels outwards per degree of turn

In terms of collimation to the helical, I assume you mean that when the helical is at what is marked infinity, the lens is actually at infinity - correct? Since that is the "starting point," my procedure first is to focus the lens to infinity, and then mark the placement where this is on the scale, lining up with infinity on the start of the scale. This helical is blank, as opposed to one which is already marked for a certain lens online. One helical* is being used for all lenses, with each one getting a distance scale marked by hand - this is then transferred to a scanner, scanned, and made into an official scale template that can be attached to the lens/helical system permanently (if you want).

*Well, one helical for ultrawide lenses, a different one for wide/normal/etc. due to design differences

Lets talk about nodes. I did not know there was two nodes, or perhaps I am just not remembering. The rear nodal point is the flange focal distance, right? What is the front nodal point and how would one find/calculate it?

Let me reiterate that this exercise is not meant to arrive at absolutely perfect results, just a roundabout scale I can use to check my handwritten results for rough accuracy.

I will do some reading on thin lens. It's been awhile.

I don't think you need to worry about nodal points too much. You're calibrating infinity focus by eye on the GG, and then you want to mark various distances closer than infinity. Using the formula for a 75mm lens focused at 3m, for example: lens to film i = 1/(1/75-1/3000) = 76.9mm. So your helical will move the lens 76.9-75 = 1.9mm from the infinity focus position (away from the film).

Perfect, yes that's what I'm looking for. The example is very helpful. That makes it easy enough to calculate a rough estimate.

Jim Andrada

7-Sep-2017, 22:54

One of the reasons that (movie) film and video lenses are so damned expensive is that the distance scale is very accurate. You can focus by the numbers and in fact the way it's often done is that there are distance marks on the floor and as the camera dolly is pushed forward or back someone on the dolly has the full time job of focus pulling, ie setting the lens distance scale to match the tick marks on the floor - nobody is focusing by looking at a viewfinder. Even my lowly Canon C100 has a stud positioned to hold the end of a tape measure at the sensor plane so you can measure the distance to the subject and set your expensive video lens accordingly. Stills camera lens's focus scales are pretty sloppy by comparison.

Running the calculations for my 47mm and 58mm XL lenses my results are way off from reality. Perhaps the error accumulates as the focal length moves farther away from "normal" when using a simplified formula. Will test again with a normal lens soon.

Another possibility I just thought of is measuring the extension at infinity and at 3ft, and then extrapolating from there based on those values. I need to dig out my graphing calculator.

Jac@stafford.net

8-Sep-2017, 11:12

How interesting this is. I'm putting a 47mm S-A XL on my 4x5. The lens is replacing a lesser 47mm S-A f5.6 (pic) (http://www.digoliardi.net/super-wide-4x5-1.jpg).

My helical has distance markings but I'm almost certain they are arbitrary.

I plan on first getting the lens board just right so that when the helical is fully retracted it is on infinity. Initial infinity spacing will use brass shims and gaskets. Then I will focus using on the ground glass at my favorite distances, 3', 12', 24', mark them and be happy.

Running the calculations for my 47mm and 58mm XL lenses my results are way off from reality.

As I said before, the thin lens equation is only accurate for nodal points effectively coincident within the lens.

That is only true for lenses close to the "normal" focal length for a format.

You're trying to use it with lenses that are grossly shorter than "normal" for 4x5 (150mm normal).

Of course there are errors.

- Leigh

Jac - if you haven't seen, I posted an image of my Mercury w/ the 47XL on the "Show off your LF Camera" thread.

It's a nice setup, especially since I'm not inclined to build my own like you :). I can also swap lenses somewhat easily. Took it out last weekend and it worked great for 4x5 and 6x12.

I'm most likely to use just a few distances (or GG focus) but this is a "universal" calibration to assist other users of the camera...so trying to do the best I can.

Here's a rough image of the resulting focus points as seen on the GG as best I could, not checked against calculations:

169495

Leigh: yes, I know, hence why I'm going to check with a normal soon. I have only done the actual testing with extreme wides. Do you think using the values as seen at inf and at 3ft, solving for the rest in between, would work to check my accuracy?

Jac@stafford.net

8-Sep-2017, 11:52

Jac - if you haven't seen, I posted an image of my Mercury w/ the 47XL on the "Show off your LF Camera" thread.

Leigh: yes, I know, hence why I'm going to check with a normal soon. I have only done the actual testing with extreme wides. Do you think using the values as seen at inf and at 3ft, solving for the rest in between, would work to check my accuracy?

I'll look for your Mercury camera. Leigh may be able to help you. I don't have the math skills to extrapolate.

I can offer a tip regarding measuring distance for testing using the ground glass. I use a laser range finder

in evening light to set the actual distance, then focus and mark the helical.

I've been looking all over my house for an old laser measuring tool this past week. Wish I could find it, and don't want to buy a new one, but yes that would help for sure!

Since I'll be "focusing" via a digital image for calibration on normal lenses, it's easier. The ultrawides are especially hard because the focus targets are tiny specks on the GG. My 38mm XL calibration could be totally wrong because the huge DOF at any focus point farther than a few feet and because it's not really that sharp to begin with at f/5.6.

Dan Fromm

8-Sep-2017, 12:08

Running the calculations for my 47mm and 58mm XL lenses my results are way off from reality. Perhaps the error accumulates as the focal length moves farther away from "normal" when using a simplified formula. Will test again with a normal lens soon.

Bryan, interpolating is incorrect.

There's no magic to it. If you can establish the infinity position and focal length, you're set. From there, magnification given extension from the infinity position is ((focal length + extension)/focal length) - 1. Film plane to subject distance will be rear node to film plane distance (= focal length * (magnification +1) + front node to subject distance (= focal length * (magnification + 1)/magnification) + internodal distance (get it from the lens' data sheet). Just do a little algebra to get extension given film plane to subject distance.

Thanks Dan! I will give the numbers another run when I have a chance. For now I've gotta get back to filling some erosion and replacing my downspouts in prep for this hurricane.

I used Dan's formula to make an excel spreadsheet and redo the helical calibration for my home-made 6x9 camera with 58mm SA XL. The focus mount is a Fotoman, marked for 65mm. I had previously used the thin lens formula which worked pretty well down to about 7 ft. The formula taking internodal distance into account is much more accurate at close distances though. The data for Schneider's lenses are still on their website, for example, here (https://www.schneideroptics.com/pdfs/photo/datasheets/super-angulon/super-angulon_xl_56_58_3.pdf) for the 58mm. There's an explanation of the optical terms here (https://www.schneideroptics.com/nomenclature.htm).

Does anyone know if similar data is available anywhere for Rodenstock or Nikon lenses? The Fujinon brochures give all the data necessary for their lenses.

If you're interested, my spreadsheet can be downloaded here (https://www.dropbox.com/s/azrj3vtuc158zde/Focus%20Calibration.xlsx?dl=0).

169536

Dan Fromm

9-Sep-2017, 17:41

Nikon, yes, Rodenstock apparently no. You can find data on LF Nikkors by following the link in my list, see the Lens section's stickies.

Thanks Jim, for the past hour I've been looking around trying to figure out what those variables meant on the optical data sheet, and just came back to see you've answered my question!

So if I am reading this correctly, HH' is the "internodal point," yes?

I plan on making an Excel spreadsheet with all of this data for as many lenses as I can find and will share it here.

So if I am reading this correctly, HH' is the "internodal point," yes?

H is the front nodal point. H' is the rear nodal point.

So HH' is the distance between the two, the internodal distance.

Please note that H and H' define their functions in the lens design.

Their physical location can be anywhere, and in any order.

H' is the point from which all light headed toward the film emanates, the apex of the cone.

Front nodal point H has a similar function for inbound light, though not as intuitively obvious.

- Leigh

Right, I said that wrong, I did mean the distance inbetween. So that makes sense.

I found this interesting site when searching more info on internodal distance:

https://people.rit.edu/andpph/text-graphical-method-focal-length.html

Does anyone know if similar data is available anywhere for Rodenstock or Nikon lenses?

The Fujinon brochures give all the data necessary for their lenses.

Full datasheets are available for all modern lenses of all major lens brands.

My main lens kit has all of the Rodenstock APO-Sironar-S lenses.

I had no trouble finding their engineering data online.

The same is true for Nikon and Fujinon lenses. I have and use lenses from both makers.

- Leigh

Full datasheets are available for all modern lenses of all major lens brands.

My main lens kit has all of the Rodenstock APO-Sironar-S lenses.

I had no trouble finding their engineering data online.

The same is true for Nikon and Fujinon lenses. I have and use lenses from both makers.

- Leigh

Leigh, if you could share any links to Rodenstock info it would be greatly appreciated! None of the brochures I've found have anything on principal points, etc.

Leigh, if you could share any links to Rodenstock info it would be greatly appreciated!

None of the brochures I've found have anything on principal points, etc.

Hi Jim,

I'm sorry but I no longer have that info

My research on these was many years ago.

The results have not survived multiple computer updates.

- Leigh

Using the data from Schneider's website, I made an Excel spreadsheet to calculate common focus distances, up to 3.75mm which is one full revolution of the Mercury UWA focus mount.

Anyone else can adapt this data to their lenses and focus mounts. If you know the focus mount's extension amount in a 360 degree turn, you can calculate where to place your markings by dividing the extension amount given for a focus distance by the extension at 360 degrees, and multiply that by 360 to get the degrees to turn the helical to where your marking will be placed.

http://www.garrisaudiovisual.com/photosharing/Schneider SAXL Focus Extensions.jpg

If anyone sees an issue with these calculations, let me know!! I can send this sheet to anyone who wants it and you can input your own data.

Dan Fromm

17-Sep-2017, 06:45

Bryan, I'm sure your calculations are fine, but what if the lens in hand's focal length doesn't match the number engraved on it?

Bryan, I'm sure your calculations are fine, but what if the lens in hand's focal length doesn't match the number engraved on it?

Indeed, if you don't know the EFL of your lens and you don't know how accurate the infinity position of your lens is (down to 0.01mm both values) it is entirely futile to produce spreadsheets with values down to 0.01mm precision.

On the other hand Corran, photographers must be in awe to see you indicate them the distance to the subject right down to 1 micron! Um, just don't smoke that stuff every day, for your own good.

I put in enough significant digits to get me close to the distance I wanted. I also didn't want to compound rounding errors, though I imagine Excel keeps all of the decimal places. On my chart there is one more column with the degrees of turn so I can mark the focus scale on the Mercury and I wanted that as accurate as possible.

Regarding the 'true' focal length, yes I am aware that is dependent on the lens. Since I can't know the exact focal length of others' lenses, I used the default value from Schneider. If one wants to be exact they can measure their lens and edit the values accordingly. Or instead, I guess I can just not publish the rough values at all here? Sheesh.

EdWorkman

17-Sep-2017, 09:42

I wonder what the subject to be photographed is?

How is the distance from the lens focal point to the subject useful without knowing the depth of "satisfactory" [YMMV] sharpness, unless of course one is making maps/engravings/printed circuits?

With 3D subjects, that counts. And near-far varies with f stop. So why would .01 mm matter for practical , 3D photography??

Good Lord, take 'em or leave 'em. The extension for the helical to reach 360 degrees was 3.75mm, not 3.7 or 3.8 so I kept it that precise, plus one more digit in some cases to get more accurate on the distance. Next time I'll just keep the data to myself.

Indeed, if you don't know the EFL of your lens and you don't know how accurate the infinity position of your lens is (down to 0.01mm both values) it is entirely futile to produce spreadsheets with values down to 0.01mm precision.

Calibration of the infinity position of the lens can be done using a groundglass on the film rails and a distant subject or diy collimation setup, and the EFL is known fairly accurately from the manufacturer's data. The point of this exercise is to get accurate enough extension values of the helical relative to the infinity position. Given that these generally wide angle lenses and focusing will be done by scale with a cushion of depth of field, it's true that sub-millimeter (or even millimeter) accuracy for film-to-subject is not necessary, but those are just numbers on a spreadsheet - who cares how many decimal places there are? Personally, though, I would start off with nice round numbers for the film-to-subject distances.

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