Method to determine the EXACT focal lenght of a lens?

[Bill Glickman]

There is a lot of brilliant photo minds on this forum, someone hopefully will kn ow the answer to this. I have checked all my books and have not come up with a method to check this.

Most lenses that are labelled 150mm are not EXACTLY 150mm. Some may be 147 mm, some 152mm, etc. How can one determine what the EXACT focal length of a le ns is when the lens manufacturer will not release this information? There must be some type of target to shoot at X distance, then measure the results on film to determine the EXACT focal length the lens is. But I am not exactly sure how to do this accurately.

While in normal photography, this is not that significant. But when using a rotational Pan camera this is very significant. The focal lenght of the lens is entered into a formula to determine the exact amount of film that will get u sed during the rotational exposure. If the fl is off by only a 1mm, the image w ill be slightly distorted. Thank you in advance for your help....

[Bill C]

Hi Bill. I think this whole thing may come down to how EXACT you need to get when you say EXACT. (I don't have any appreciation for the situation in the panoramic camera so I don't know how far you need to go). Here is a general procedure where your own measurement procedures will be placing the limits on exactness; you will probably be hard pressed to get within 1%.

The basic formulas are: 1/focal_length = 1/object_distance + 1/image_distance, and magnification is the ratio of the two distances. They're explained a little more in the first section of photo.net's Optics Tutorial: http://photo.net/photo/optics/lensTutorial.html Your first problem will be that you need to accurately measure the object_distance to some point in the lens (front principal plane) that you can't accurately find. So your general method will be to use an object_distance SO LARGE that a slight error doesn't matter much.

Here's an example for a nominal 150mm fl lens: 1) Find a target of known size, say about 200 inches across (maybe draw two lines on the side of your house?). 2) Mount your camera on a tripod about 50 feet away, straight out from the target. Accurately measure the distance from target to the "front principal plane" of the lens (or just use the approximate center of the lens if principal plane is unknown). 3) Accurately focus the camera and take the picture. 4) Develop film and accurately measure the target size on film.

To calculate (but do your calcs more precisely than I'm showing here): 1) calculate magnification; it is the image_size divided by target size; in this case, say a 200 inch object divided by a 2 inch image = 200/2 = 0.01. 2) Calculate the image_distance; it is the object_distance times the magnification; in this case, 600 inches (same as 50 feet) times 0.01 = 6 inches. 3) Now, 1/focal_length will be equal to 1/object_distance + 1/image_distance = 1/600 inches + 1/6 inches = 0.1683 inches. Focal length = 1/0.1683 = 5.942 inches = 150.9 mm (there are exactly 25.4mm per inch).

Estimate your accuracy by calculating with the limits of what you think your measurement errors might be. Some things that will cause roughly a 1 percent error in this example: 1) a 6 inch error in the object_distance, or 2) A measurement error of 0.02 inch (1/50") on your film and 3) a focus error of 0.060 inch racking the lens out. Also, a larger target (and image) will improve your measuring accuracy; the downside is you'll be more affected by lens distortion and/or a focus error.

I was so excited about getting the first response up that I didn't check my numbers too carefully, so hopefully someone will catch me if I messed up! Hope this method will help!

[Pete Andrews]

What you're asking isn't easy without access to specialist equipment. It's true you can use all the calculations given above, once you have obtained some accurate measurements. It's obtaining those measurements that's the problem. In order to establish the conjugate focii of a lens (i.e. Image distance for any given subject distance) you need to know the position of the front and rear nodes of the lens, and the only way to establish this with sufficient accuracy is to use an optical bench with a nodal slide. Not the sort of kit you normally have lying around in the shed.

Establishing the true focal length of a lens is not an easy procedure, even with the right eqipment. That's why a calibrated process lens costs about half as much again as one off-the-shelf.

[Struan Gray]

I agree with Pete, but if you really want to do this the easiest way is to measure the distance between the front and rear standards at infinity focus and at 1:1. The difference is the focal length, whatever the positions of the front and rear nodes. Of course, this assumes you have enough bellows draw for 1:1.

Infinity can be found by focussing on a distant object, at least 20 focal lengths away. Alternately you can use a laser pointer, but the speckle patterns on the ground glass can be confusing and most of the cheap ones are not that well collimated anyway.

Infinity focus can also be found by autocollimation: mount a mirror on the front of the lens, place a small light on the ground glass and focus until the reflected image is as small as possible. This is the 'best' method but I've never found a satisfactory way to actually place a small light at the right position without drilling a hole in the middle of the ground glass.

1:1 is most easily done by pointing the camera at a well-lit ruler and using another to measure the projected size on the ground glass. Watch out for parallax between the measuring ruler on the outside of the glass and the image ruler on the inside. It doesn't matter if you change the position of the camera from that used to find infinity focus since it's the relative positions of the standards that matters.

If you have a monorail you can measure the distances easily with the depth gauge part of a vernier calliper. With a field camera it's a little harder, but if you don't move the back you can measure the distance from the front standard to any fixed part of the camera, so it shouldn't be too hard.

Alternately, use only Leica lenses: they have the actual focal length engraved on the barrel, accurate to 0.1 mm.

[Bill C]

I also agree with Pete, but on this part, "the only way to establish this with sufficient accuracy", there is still question on what is "sufficient" for you. If 1% is good enough, the first method ought to suffice.

I think Struan has a really clever idea with the homebrew autocollimation system. This might be improved by drawing a crosshair on the ground glass, illuminating it with a small spot of light and using that as a focus target. But I've never tried this and the spot of light might wash out the image too much.

Let me point out something with the change in standard position method: if you put your target 20 focal lengths away and focus, this will cause the standard to be about 5% farther out from the true infinity focus position. So if you settle on 20 focal lengths for the target distance (and repeat for a 1:1 conjugate) the change in standard position will be about 1/105% of focal length; you need to multiply the measured difference by about 1.05.

Also, with only 20 focal lengths to the object, you will again be faced with problems due to the uncertainty of the front principal plane position. However, you can estimate that position fairly closely like this: remove the lens, turn it backwards and form an image of the sun on a surface. The front principal plane is roughly the labeled focal length away from the image of the sun. If you make a reference mark on the side of the lens, you can use this as the base for measuring 20 focal lengths from the lens. If you were to use this method in conjunction with a pocket microscope for accurate focusing and a good caliper, I think you could expect to easily get within 1% accuracy without even processing film! Again, good luck!

[Bill Glickman]

Thank you Struan, Bill and Pete... If I do this distance test on a view camera, no need to expose film, right? I can simply measure the results on the gg, I assume this would give me the same measurement.

As for accuracy, well, I was hoping to get within +/- .5mm, but I am unsure from the answers above if this is feasable? 1% of 35mm is .35mm, that would be a very good starting point for sure. I would program this fl into the camera and run some test shots. Pete, if I focus on a target very far away, say 100ft. then isn't the exact nodal point insignificant when covering this much distance?

Bill C, I assume your sun experiment is a simple method to determine the front nodal point of the lens, right?

The lenses in question are from 35mm to 3000mm. I failed to mention, these are Mamiya MF lenses, not LF lenses. The rotational camera maker, Seitz does not make a mount for LF lenses, too bad though. Any additional input would be helpful. Thank you again...

[Michael S. Briggs]

The URL http://www.smu.edu/~rmonagha/mf/nodal.html has discussions of finding the nodal points of a lens. As previous answers have indicated, this is very useful information in answering your question, the exact focal length of a lens.

Data sheets for large format lenses usually indicate the locations of the nodal planes. As an example available on the web, Schneider's Apo-Symmar 180 mm f5.6: http://www.schneideroptics.com/large/Datasheets/aposym/aposym5,6-180/aposym5,6-1 80p1.htm The focal length is given as 180.8 mm, the separation between the nodal planes as -3.5 mm, the front focal length as 149.4 mm and the back focal length as 149.7 mm. What this means is that if you focus the lens on infinity, the distance from the image (ground glass) to the plane perpendicular to the optical axis which touches the center of the rear-most glass surface will be 149.7 mm. The rear nodal point will be 180.8 mm from the ground glass, or 180.8 - 149.7 = 31.1 mm in front of the plane touching the center of the rear-most glass surface. I think the minus-sign on the nodal-separation value means that the front nodal plane is actually 3.5 mm behind the rear nodal plane, rather than normal position of being in front.

The remaining question is what is the level of manufacturing variations. With make-shift equipement, it will probably be hard to do better than the values supplied by the manufacturer.

[Struan Gray]

Bill, I guessed you weren't making life difficult for yourself by using an aerial travelling-slit camera, but even so, 3000 mm panoramics on rollfilm? Do you print on ticker tape? Kudos in any case.

You don't need to expose film - ground glass will easily get you within a percent if your view camera is mechanically sound and you measure with an accurate enough tool (avoid wooden rulers :-). If you can fit a gg at the focal plane of your Mamiya you can use that and avoid worries about angular alignments. For best results do the measurement with a small aperture since at wide stops zonal aberrations can move the position of best focus away from the 'true' centre of the focal plane.

[Pete Andrews]

Hi, Bill G.

You're right in saying that the nodal point isn't an issue with distant subjects, but how do you measure 100ft to an accuracy of a millimetre or so? Also, the accuracy in measuring the image size needs to be scaled by the magnification factor. In fact the nodal point(s) don't really come into it if you use the image magnification as a basis for calculating EFL and measure the object to film-plane distance, but then you have to make the assumption that the lens is distortion-free. With wide-angle and telephoto lenses this almost certainly won't be the case.

I think Struan's autocollimation method is a good starting point. A laser makes a good point source for a reference, but the beam needs to be de-cohered by passing it through or off a diffusing surface before you can use it. You might be able to use the fact that the object to image distance is at an absolute minimum at 1:1 magnification, and that distance is 4 times the focal length. At any other ratio the distance is always more than 4 focal lengths.

I still think an optical bench, even a makeshift one, is the only practical way to get accurate results. A camera body will get in the way of taking meaningful measurements.

[Bill Glickman]

Wow, sorry guys, what a bad typo, that was suppose to read 35mm to 300mm lenses, not 3000mm. Sorry... No just basic landscape shots, no aerial.

[Bill C]

Hi Bill; yes, you are correct. I said principal plane, whose center could be called a principal point, which for your purposes is the same position as the nodal point.

I agree you could measure image size on the groundglass; however you need a fair amount of accuracy. Definitely use a magnifier and attach (clamp, tape, etc) your scale to the groundglass (don't attempt to hold by hand). When you read the scale, make sure your line of sight is perpendicular.

If you're going to use the groundglass directly, though, I think Struan's method of measuring change of lens position is superior. However, DO correct for a non-infinity target.

[Bill C]

Whoops! I meant to lead off with this:

>> Bill C, I assume your sun experiment is a simple method to determine the front nodal point of the lens, right? <<

[Doremus Scudder]

I love all the formulas,optics and mathematics involved in this discussion, so forgive me if I simply suggest that you contact the lens manufacturer with your question. Surely someone there knows the answer to your question as long as the manufacturing tolerances are close enough for your work, and they will more than likely be willing to help. Possibly you could even get them from the spec sheets you got with your lenses when you purchased them (if you kept them) or from their website. Regards, ;^D)

[Bill Glickman]

Doremus, I should have mentioned this in my post, your solution is the most obvious and simplest method of all. However, I did fully exhaust that avenue first. Mamiya, the makers of these lenses does not publish this information. I contacted the lens design dept. in Japan, and they claim they do not even have this information to offer? Seems odd to me also, but this is the case with most lens makers (non LF lenses). For example, Nikon, Sigma, Contax and Hassy will not disclose the image circle size of their lenses or their exact fl.... which are two important considerations for lens selection for this camera. (This represents the total choice of lens selection for this camera. The maker only makes mounts for these lenses)

As an update, the maker of this rotational camera, Seitz, claims the lens value for the lenses actual focal lenght must be known to within +/- .05mm for accurate calculation of film speed in the brain box. This value dictates the film travel speed... i.e. the speed the film must travel to get a perfect looking horizontal image image. Or course the vertical will always be perfect as it is not affected by film speed. Too fast, the image will appear stretched, too slow, the image will appear compressed. I spoke to other users of this camera, and most have just used a shotgun approach in the camera to get the fl accurate, i.e. just wing the values and look at the film, but considering the tight tolerance of +/- .05mm, this would be very cumbersome without having a reasobly accurate starting point.

My game plan is to use the methods above to get close to the exact fl, then put the lenses on the rotational camera and begin testing them in small increments from this starting point. I have not reported back yet, because the lenses got delayed in shipment. I appreciate everyone input, you have offered excellent insight.

One last tid bit of information... the maker of the camera sometimes will offer this information when known from their own testing, however they claim its not that valuable since identical lenses from the same maker have shown fl values of +/- 2% from each other. I am not sure if those lenses would have came from the same processing batch?

[Struan Gray]

The acceptable focal length error depends on the width of the camera's travelling slit. If the slit were infinitely thin a miscalculation would merely distort the image by making it too long or too short in the scan direction. This is easy to correct in the darkroom with a panoramic enlarger (or digitally). With a slit of finite width the projected image moves relative to the film during exposure so you get a mixture of distortion and blurring, and there's no way to get rid of the latter.

The image moves at a speed proportional to the camera's angular velocity divided by the focal length. This means you need to know your focal lengths to within a constant percentage error, not an absolute amount. The percentage is formally equal to whatever amount of on-negative blurring you find acceptable (usually some fraction of the circle of confusion) divided by the slit width.

If you don't know the slit width you can always take take Seitz's figure on trust. If we assume that the 0.05 mm figure is for the angular field of view of a normal lens, the percentage is about 0.1%. So for 300 mm you only need to measure the focal length accurate to 0.3 mm, but for a wide angle you need to do better than 0.05 mm.

You can't trust the manufacturer's design specification if you need this sort of accuracy. It is very, very expensive to produce an imaging lens with an exact focal length. Even in lenses like the Zeiss 300 f2.8 for Hasselblad, where the grinding and mounting of the lens elements is adjusted for slight variations in the glass's optical properties, the focal length is allowed to vary. The ISO standard is 5%, but most high-end and large-format lenses do better than that.

Pictorially the change in the angle of view caused by a few percent's deviation is insignificant. Even for things like photogrammetry and repro work where the exact focal length is important, the usual practice is to measure the lens after it has been built, and adjust the camera to suit. Of course, the change in the position of the focal plane is important, which is why accurate rangefinders have to be calibrated to an individual lens. So you may find that manufacturers like Leica who have to match lenses to rangefinder cams keep a list of serial numbers and exact focal lengths, but I seriously doubt if many medium format lens makers bother.

[Struan Gray]

Oops. Make that: "the image moves at a speed proportional to the camera's angular velocity *multiplied* by the focal length"

[Pete Andrews]

Hmmm. Needing the focal length to 0.05mm puts a different complexion on things. FWIW I've thought up two more methods that don't need an optical bench, but they do need some precision equipment.

(OK, OK, I recant on the optical bench thing, it's all too cumbersome to bother with, unless you got access to a proper optical lab.)

The first method is to calculate the EFL from the angle of view of the lens, (again, prone to error from lens distortion, I'm afraid). You need to mark the centre of a GG screen with a fine vertical line, and another fine vertical line an exact known distance (say 20mm) to the left or right of the centre. The camera is mounted on a turntable with accurate degree divisions marked off on it. You focus the camera on a small bright object at infinity (a bright star or venus perhaps) with one of the lines bisecting the star. The angular position of the camera is noted. Then you rotate the camera to bisect the star with the second line, and note the new angle. The angular difference and the known distance between the lines are used to calculate the EFL.

F= distance between lines/tan(angle)

Unfortunately, some quick calculations show that you need to measure the angle to better than 0.05 degrees to get anywhere near 0.05mm accuracy.

The second method is an attempt to utilise a true focussing method while minimising the error from not knowing the front nodal plane.

Set up the camera with a distant, preferably infinite, object in view, and an object at an accurately known distance of 6 metres from the front of the lens. I figure 6 metres is sufficient to minimise the nodal error, but still small enough to be accurately measurable. You need an engineers dial gauge (clock) which you use to measure the extension of the lens from its position at infinty to the 6 metre focus position. (The extension with a 50mm lens, for instance, is only 0.42mm, so an accurate means of measuring small distances is essential). I suggest you fit a UV filter on the front of the lens and run the dial gauge against the glass surface of the filter.

Having got your extension, which we'll call X, use the following formula to calculate F (focal length), u is the object distance, in this case 6000mm:

F=(square root of(u times X))- X/2

You really need to solve a quadratic equation to get the Nth degree of accuracy, but the above formula is close enough at this sort of distance, and given that there is still an error from not knowing the front nodal plane position.

[Struan Gray]

While all our suggestions represent various good ways to measure the focal length, I think Bill G's idea of on-film testing for the final stage will be less hassle and more relevant. Not because I believe film-based testing is instrinsically better in photography (don't get me started on *that* one), but because in this case the error is a) controllable and b) well behaved either side of the optimum. Testing on film will also automatically correct for any slight errors in the programming or gearing of his particular camera.

Once you have a reasonably accurate figure, take short panoramas of a point source (a laser pointer will work here) with the camera deliberately set at equal intervals above and below the nominal value for the focal length, out to about +/- 10 %. With a microscope (or a ruler on a print) the asymmetric blurring will be obvious. Plot the longitudinal size of the blurred feature against the nominal focal length on a bit of graph paper and the mimimum of the curve tells you the 'correct' focal length immediately. It doesn't even matter exactly how you measure the size of the blur, provided you're consistent.

If you're prepared to burn film and do this in two or more stages you don't even need to find the focal length first. An initial run will probably get you within 1% and a second one nail it from there.