View Full Version : Means to determine EXACT fl of a simple lens

7-Mar-2006, 20:50
Since there is excellent optics readers on this forum, I am curious if someone can help me with this question. It is somewhat related to LF, as this same issue can be applied to photographic lenses.

I am having lenses made with a dual element design, for a stereo viewer. One singlet and one doublet in a barrel. The effective fl of the pair is 45mm. However, I need to determine the EXACT effective fl of each set up in a barrel, so I can pair them to match. I can alter the fl by changing the distance between the two elements.

I was trying to find a means to test to accurately test the fl, better then .1mm accuracy. I would assume this would involve using a secondary optical instrument, such as a microscope that looks through my lens to a focus target. Adjust microscope till it's in focus, then measure the focus travel the microscope made to acheive focus, use this distance on a look-up chart, which was prepared with test lenses of known fl's.

Or, maybe I am completely off and there is some other simplified method? Any help would be greatly appreciated. Oh, and I am trying to keep the aparatus under $5k, which would rule out expensive optics analyzers. TYIA

8-Mar-2006, 00:56
Focus the lens exactly on infinity. Then focus on an object to give 1:1 magnification. You can measure the object height and projected image height to confirm 1:1 magnification.
The lens extension necessary to move from infinity focus to 1:1 magnification is the exact focal length of the lens.

To focus exactly on infinity place a mirror over the front lens element. Then place a point source light just off center of the GG and focus the reflection on the GG.

Having determined the focal length you can determine the position of the rear principle point (if required) as one focal length distance from the GG forward when the lens is focused at infinity.

Whilst you should have no problem focussing accurately, measuring the distances accurately is likely to be more problematic.

Cost? zero if you have any LF camera available and the abilty to mount the lens onto it. I suspect that a very simple home made bench would work as just as well but a LF camera makes a good optical bench.

Emmanuel BIGLER
8-Mar-2006, 05:39
Rob's method is perfect and W.G. should try it first.

If the accuracy delivered by this method is not enough, then you are in need for some classical instruments of the optics lab and a classical method like Cornu's.

You'll need a collimator and a fixed-distance viewer, a kind of a small telescope that sees sharp at a given, fixed but asjustable finite distance. A small format camera fitted with a macro lens can be used for this. An object placed in the film gate of another small format camera can also be used to fabricate a collimator with a lens blocked to the "infinity" setting.

You'll also need and optical bench and means for moving the lens and the viewer;; plus means of reading distances with an accuracy in the range of 0.1 mm. This is not that easy to find in ordinary life.

The principles of Cornu's method are simple

1/ you set the collimator to infinity and illuminate the lens to be measured, through the lens the viewer allows you to see where the front and back foci are located i.e. where a sharp image of the collimator target is located ; reverse the lens to find where both sides focal points are located

2/ look for the position of finite distance objects and their images, e.g. something located close to the first and last lens vertex ; again reverse the lens to add some redundant measurements. Traditionnally a piece of paper was simply put just sticking on the first and last lens vertex (you probably don't want to stick anything on a precious piece of glass ;-)

3/ Newton's formulae will yield the focal length.

In detail :
1/If S is the source created at infinity by the collimator, S seen through the lens, both sides, will give you the positions of F2 back focal point and F1 front focal point (by reversing the lens).
So S-> F2 object (back) focal point, lens in standard position.
S-> F1 through the reversed lens yields the object (front) focal point.

2/ Let V1 be the first lens vertex and V2 the last lens vertex or simply V1 adn V2 are two objects located close to those vertices and easy to see.

Set the lens in standard position, see where V2 is located and see where W2 image of V1 through the lens is located. The positiopns of V2 and W2 are to be measured with respect to F2
Reverse the lens, see where V1 is located and see where W1 image of V2 through the reversed lens is located.
The positions of V1 and W1 are to be measured with respect to F1.

3/ The distances F1V1, F1W1, F2V2, F2W2, can be computed by subtracting readings on the bench.
The trick is that you only have to measure differences in distances either in object space or in image space but you do not have to care from the thickness of the lens and you do not need to know where the principal planes are located.
Newton's formulae (do not care too much for the algebraic sign) yield the focal length without any reference to the principal planes or to the actual lens thickness:

F1V1 x F2W2 = -f^2

F2V2 x F1W1 = -f^2

Once the focal length is determined, if you wish, since you know where the foci are, you can compute where the principal planes H and H' are located, i.e. at one focal length ahead of the corresponding focus.

Leonard Evens
8-Mar-2006, 09:42
You can use the formula

v/f = 1 + M

where f is the focal length, v is the image distance and M is the magnification. The magnification can be determined by measuring the size of the image and dividing it by the size of the subject, presuming that subject plane, lens plane, and image plane are parallel. Unfortunately, you can't be sure of where to measure the image distance v from. But you can get around this by using two image distances, v1 and v2, corresponding to two magnifications M1 and M2.


v1/f = 1 + M1

v2/f = 1 + M2

Subtracting yields

(v1 - v2)/f = M1 - M2.

You can measure v1 - v2 by marking the image position for each and measuring the distance between the marks. Then

f = (v1 - v2)/(M1 - M2)

This is a variation of the case mentioned above where v1 = 2f, v2 = f, M1 = 1 and M2 = 0.

But the problem with this method is that you probably can't measure the distances all that accurately, and you then compound the problem by subtracting two relatively close numbers in the denominator. Also maintaining parallelism accurately enough may be difficult. So you should be careful to make sure the distances are not too close. To compensate for these inaccuracies, you should use a variety of different image distances and magnifications, the more the better, setting up the equipment indepdendently each time. If the measurment errors are random, then you would expect them to more or less cancel out in the average. The variation in the individual answers you get will give you some idea of how accurate the final average is.

Emmanuel BIGLER
8-Mar-2006, 10:04
There is another method but that requires something equivalent to a goniometer.
The focal length can be defined for small values of theta by the ratio between the linear size L of an image and the angular size theta of the object supposed at infinity : L=f . theta

Theta can be measured with a telecope mounted on a goniometric platform.
If the angle theta can be measured within a few percent and the image size within a few percent as well, the final precision will be in the percent range.

If you need a precision of 0.1 mm for a 100mm focal length this implies 0.1% which seems tough to achieve with amateur devices & setups.
A this level of precision the actual ambient temperature might become important.

Brian Ellis
8-Mar-2006, 11:07
Send it to Leonard or Emmanuel. : - )

Dan Fromm
8-Mar-2006, 11:27
Bill, your problem isn't matching lenses with fixed focal lengths, it is tweaking one lens to make its focal length match another lens'. So you don't have to measure. All you need is a fixture that will hold a target, a lens, and a ground glass. Let the lens be on a carrier. Move the carrier to focus. Then pop in another lens without moving the carrier and tweak it to focus. And then you'll have a pair that match.

8-Mar-2006, 11:46
Thank you all for the help....but I think there is confusion here over the type of lens being used and proposed solutions.

rob, your method I fully grasp for camera lens. But this lens, which is a dual elements in a barrel, consist of a singlet at the eye end, and a doublet on the subject end. Together, we have a 45mm fl magnifier. It is bascially a loupe, it will view film on a light box, with the doublet being 10 - 20 mm from the film, based on the eyes ability to focus. So this lens falls under the "magnifier" category, and I beleive the rules of engagement for fl detection are different vs. a camera lens. For example, when the lens is focussed at infinity, the subject is about 15mm from the doublet. I am not knowledgeable enough about optics details to understand how a magnifier differs from a camera lens. Or maybe robs suggestions do apply to this type of lens? I wanted to clear this up before I get into the actual methods.

Emmanuel BIGLER
8-Mar-2006, 12:03
to understand how a magnifier differs from a camera lens.

Your magnifying glass takes the objet located at about its object focal point and sends the image somewhere, not to infiniy but, say, to a few feet in front of you so that tou can see it comfortably.

If you reverse the loupe, the image of a distant object will focus where you put your slide or negative.
From there Rob's method works perfectly. Start from this suggestion and check whether the precision is sufficient for your needs.
Methods like Cornu's work for any kind of lens even a negative or afocal lens. For sure it is overkill but didn't you mean : EXACT ? ;-) For a converging lens like yours, simpler methods exist as pointed by Rob and Leonard.
I know that the eyes have a certain capability to merge stereoscopic pairs even if the magnification is slightly different. So the question is in what means "slightly".
Good luck. It is easier than you think.

8-Mar-2006, 16:10

I'm no expert on lenses but I just happen to know the method I gave as the simplest without requiring expensive equipment. I think you can gather from what has been written that its either a full optical bench or a cheap mock up. Since a large format camera acts as a cheap mock up all you need is the ability to be able to mount your lens on a LF camera. Any old LF will do but if you go for one which has a large lens mount board size then it should make it easier to fabricate a board which can accept your lenses and the cost should be nowhere near 5K. Having said that, since you are thinking in terms of 5K just for doing this then I guess you are expecting some return on the exercise otherwise as a one off exercise it would make far more sense to send the lenses out to a pro to do it for you.

Also, if you are designing this thing then why not design in an adjuster in the same way a pair of binoculars have a focus adjuster on one side. That way the viewer can adjust to the point of visual accuracy without the need of complex and time consuming testing procedures. That way the required manufacturing tolerances become less stringent.

8-Mar-2006, 17:17
rob, good issues, I should have explained further. The ultimate goal is to have a matched pair of lenses, less than .1 mm total variance in fl. The lens design is such that, varying the distance of the eye element (singlet) from the film element (doublet), you alter the effective fl of the optical train. The amount of change in fl vs. the seperation is ... .2% fl change per 0.5mm change in separation. The barrel will be designed with fine threads to allow for small changes in seperation. So, as Dan picked up on, the goal is getting matched pairs of effective fl lenses, not neccessarily determining the exact fl of each optical train, but I could not think of a better way to accomplish this goal, then matching effective fl's and tweaking them for pairing.... this further explanation may open up some possibilities. I think there is a nugget floating in the concept of setting up a dual test system, whereas each lens projects on the same gg, side by side. A 2" high straight line is projected on the gg, then tweak one of the trains till the lines are the exact same height...but not sure of the ability to measure lines on the gg. It may be easier to simply read the distance between two standards.

Also, this procuedure is not being used for a one time run. I plan to pair about 400 optical trains, for each run, ending up with 200 matched pairs, with effective fl's within the tolerances mentioned above. So the system will be used for each production run, hence why I am willing to spend some money to get it right, as sending all the elements to a lab would be very costly, not to mention, I want to be assured the work is done right, and if that is possible with a home brew system, I am willing to do what it takes.

BTW, the inter eye magnification tolerances were learned from a study performed 20 years ago regarding magnfication deviation in each eye when viewing the same object. It showed the % of test subjectst that were bothered (headaches, strain, etc.) at different magnification variances. So I am confident I am chasing the right number, I just need a simplified method to get there, and it seems it is possible without ultra expensive equipment.

So before I get too burried in the math to accomplish this, I am curious now that I have explained it in more detail, if the proposed techniques are still considered optimum.


8-Mar-2006, 18:08
But like binoculars, if you have one adjuster which adjusts both barrels focal length simultaneously and one fine adjuster which adjusts only one barrels focal length to match them, then providing the adjustments cover the lens and barrel manufacturers tolerances then there should be no problem and little testing required. i.e. you should only need to test a sample of the lens/barrels supplied for manufacturers tolerances. If you don't want to incorporate a fine adjuster then you have a lot more tesing and precision assembly to do.

I think a LF camera would be OK for a small amount of testing but not for large quantities. One issue would be rigidity of the standards and parallelism of the standards. That might be fine for one off tests but for bulk tests it could be time consuming to be constantly checking the checking equipment.

8-Mar-2006, 19:32
rob, sorry, I forgot to address the diopter adjustment issue. I can NOT use a diopter adjustment on one lens similar to binos. The reason is, it would create a source of mis matched magnfication by people who do not suffer the problem. This can occur when the diopter is set off of zero, yet the user can still focus the system as the DOF is great enough to allow this to happen. So it can introduce a problem that otherwise would not have existed. instead, I keep both lenses at near equal magnification, and if a person has astigmatism, they wear their spectacles to correct this problem when using the viewer. I have built enough eye releif into the lens system so spectacles users will have no problems getting their eyes positioned at the optimum 30mm distance from the singlet.

Agreed on the flexibility of the standards for measuring...but its the concept I am after, as a custom made jig can be built to correct the shortcomings of using a view camera.

> To focus exactly on infinity place a mirror over the front lens element. Then place a point source light just off center of the GG and focus the reflection on the GG.

As for this description..... front lens element = the eye element (singlet) right? The source point light would be what type of light? I assume it can be positioned behind the gg, (not between the gg and doublet) projecting through a drilled hole in the gg, near the lens center. Then move the gg up and back till the light on the gg becomes sharp around the edges. Do I have this right? My thinking is, drill the hole in the gg just off center axis, then the focused light on the gg will be VERY near the light source, both being as close to center axis.

IF this is right, I am thinking this system is ideal, as with a solid optical bench, this system can be easily measured, i.e. I am now spreading the range of measurement out, which will reduce the margin of error vs. measuring the focus distance of each lens on the gg.

> Then focus on an object to give 1:1 magnification. You can measure the object height and projected image height to confirm 1:1 magnification.

I grasp the concept here, but want to nail down the details. Is this process treated identical to using a view camera trying to focus an object at 1:1 ? So I would move the lens to and from the subject, till the object is 1:1 on the gg. To keep it in focus on the gg, I adjust the spacing between the gg and the singlet lens. Do I have this right? The measurement is from the subject plane to the frosty side of the gg. Right?


8-Mar-2006, 20:35
"front lens element = the eye element (singlet) right?"

yes, so that the light passes right through all elements of lens and then back again. The mirror should be as closeto lens element as possible and a first surface mirror would be optimum.
The singlet will be on the subject side of the test setup.

"My thinking is, drill the hole in the gg just off center axis, then the focused light on the gg will be VERY near the light source, both being as close to center axis."

yes. Any light source which is small enough and probably needs to be shielded to cut out extraneous light. An led would probably do it or one of those laser pointers or possibly a micro torch. There are some GG's available which are clear in the center but it would probably be better to drill a hole to stop any chance of refraction of light from GG.

"So I would move the lens to and from the subject, till the object is 1:1 on the gg."

at 1:1 magnification the subject is exactly twice the focal length from the lens and the lens is exactly twice the focal length from the GG. (this is why the lens extension from infinity gives you the fl but it only works at exactly 1:1 magnification) This means you have to be able to adjust both the subject distance and lens to GG distance. A change in one is likely to require a change in the other until equilibrium at twice the focal length is achieved. Since you will know the approx fl to start with it should just be case of tweaking the positions to get it spot on. The larger the subject height then the less measurement error there should be (I think). You will have to determine the max subject height you can use for the focal length of the lens. Depends on image circle size.

Once you have determined the max subject height you can use, and providing you always use that subject then you can place height marks on the GG so that you can adjust the focus and subject distance until it fits the marks thereby negating the need to actually measure the height of each test. i.e. you use the GG itself as the ruler. The marks should obviously be the height of the subject apart. This will require that the subject position remains vertically and horizontally static in relation to the GG for all tests but should simplify the process.

Donald Qualls
8-Mar-2006, 21:51
Wheee! Lots of text up there. All of it depends on knowing when an image is "in focus" and when it's not.

There's a simple way to find that out that doesn't depend on how tired you eyes are.

Make a mask to go in front of the lens, with 3 or more holes -- the simplest is three holes radially distributed, but the holes can even be randomly located. Now, instead of a "scene", focus a point light source. You'll *very* easily be able to see when the three-or-more spots of light cast by the holes in the mask coalesce into a single point; that's when you're in focus.

Should greatly simplify all the other bits...

8-Mar-2006, 22:03
the more I think about this the less I think it will work for the level of accuracy you require. I think the problem will be measuring the height of the image on the GG. The lens extension should be no problem with some kind of micrometer but the projected image height change will be negligible with plus or minus 0.1mm lens extension so getting exact 1:1 magnification is unlikely.

8-Mar-2006, 22:04
> at 1:1 magnification the subject is exactly twice the focal length from the lens and the lens is exactly twice the focal length from the GG. (this is why the lens extension from infinity gives you the fl but it only works at exactly 1:1 magnification)

rob, here is where I think my simple compound lens doesn't fit this scenario.... I fully understand what you describe above for camera lenses, I have tested this many times. However, for this lens, the distance from the eye releif point (which is 30 mm from the Singlet) to the subject is 94.5 mm, yet the effective fl of the combined lenses is 45mm. Now, if this lens was a single element such as one doublet, then thethe subject to lens distance, focussed at infinity would be equal to the lens fl. But that is NOT the case here, and is why I question how this lens would fit the same mold as lenses, where the lens fl matches the focus distance at infinity. Make sense?

Now, the next issue is the gg to singlet distance. I appreciate your concept here, it's what we use in a view camera. Change the gg to lens distance, and the focus on the gg changes drastically.

However, that does NOT occur with these type lenses. If you look through a loupe, and move your eye (gg) to and from the loupe, the focus will not change, only the field of view changes. I need to get my head around these issues first, as there seems to be too many differences between the way my lens performs vs. a normal camera lens? make sense? Any thoughts?

Donald....your method would work with a lens that acts more like a camera lens. But I think robs methods provides an easier means of measurement.....

8-Mar-2006, 22:38
There is a simpler way but you will still have the problem of measuring image height accurately.
As has already been stated, you don't actually need to know the focal length. Therefore you can forget infinity focus steps.

All you need to do is to place lens barrel in camera at a fixed and repeatable distance from a subject with the singlet towards the subject. An image will be projected onto the GG and the height can be measured. Place next lens into camera without moving anything and with singlet same distance from subject. Image height should be the same if focal length is the same. If not adjust lens and retest second lens making sure singlet to subject distance remains the same as first test and that distance between camera standards does not change beween tests.

I think this should work without knowing focal length and is much simpler to test but you will still have the problem of being able to detect image size difference for a 0.1mm change in fl.

8-Mar-2006, 23:07
methinks that if you have the means to capture image from gg and enlarge by projection then you will be able to measure a very small change in image size. A digital back for the camera would be ideal but I guess thats out of the question.

8-Mar-2006, 23:56
> A digital back for the camera would be ideal but I guess thats out of the question.

rob, not sure why you lost confidence in this suggestion, I think its the breakthrough I was looking for! Brilliant! Use a digital camera with about 150 pixels per mm. This should measure projected image to .01mm. A variance of .01 mm in subject height for a 20mm tall subject represents .05% difference in magnfication represents a difference in fl of .02mm.... this assumes a lens of about 45mm effective fl. So, therefore, I can nail each lens to within .02mm fl, even though the fl value itself is insignficant. Now, I need to massage these numbers a bit to develop a fast way to covert the difference in image height to to % of variance in effective fl. Make sense? Thanks for your continued persistence....unless I forgot something, I think this is a winner!

9-Mar-2006, 00:34
now don't get too excited because since GG is frosted it will not give a truly sharp image. i.e. it will be quite fuzzy when photographed with a digital camera and hence will be difficult to judge down to the levels you just calculated. Let us know how it works out.

9-Mar-2006, 00:59
rob, the digital camera records the target directly from the lens, no gg used now l!!!! That is the beauty of this!!

9-Mar-2006, 01:44
if you have a camera that can do that then yes it is by far the best but how are you going to measure focal length now you have a camera where the gg was going to be.

It sounds like you have it in mind to build your own special rig for this and I guess you will swap a GG screen for the digi back as necessary.

p.s. invoice is in the post...

9-Mar-2006, 01:57
yes, digital back replaces gg.

The only purpose of this exercise is pair lenses whose image heights (recorded and measured in graphics software) are within a certain % of each other... the details to be determined, but the tolerances are there.... image magnification is what is being measured, and that can be back tracked to fl...but I will forgo that, in lieu of just matching magnification.

I look forward to your invoice... :-)

9-Mar-2006, 19:48
rob, hold the invoice!

This gig tricked me... my lens is a magnfier, so it will not focus an image on a gg or a digital sensor, dah....arggggggg.... However, I can use a camera lens, if the nodal point of the lens can be put 30mm from the end of the viewing lens, then the camera will focus it on the digital sensor.

9-Mar-2006, 20:19
but I thought from what Emanuel Bigler wrote, that by reversing the "loupe" so that the doublet is at the camera/gg end it would project an image. To test that it will project an image hold the lens under a desk lamp facing down onto the desk and move it up and down to see if the bulb image is projected onto the desk. Works for my nikon lupe regardless of which round it is. Same for my horseman loupe.

9-Mar-2006, 22:31
rob, I am no lens expert, hence this post :-) But the optics designer that designed this lens claims, you can not turn the lens around for these tasks. yes, it will project an image, but you can't discover the properties you need to know in this regard. The light path is a one way street as for lens performance. This is specially true due to the very short fl.... I wish I could explain more.

10-Mar-2006, 00:34
If the lens will project an image, which I think it will, then changing the focal length will change the magnification in which case you can detect it. You don't need to measure anything about the actual properties of the lens. You only need to make comparative tests so maybe its true you can't measure focal length but you can still see comparative changes in magnification. Put that to your lens designer and see what he says.

Doug Kerr
19-Dec-2006, 12:05
. . . and I beleive the rules of engagement for fl detection are different vs. a camera lens.

(What follows is not in any way in conflict with what has been said about focal length determination - I just wanted to comment on your observation.)

Note that any lens-like optical system (regardless of construction or intended use) has a focal length (actually, the precise optical engineering term is "effective focal length", for a reason I won't bore you with right now), and it is always defined in the same way. The truly valid, generalized techiques for determination of focal length apply in any case.

Of course, when we consider the use of a lens for different purposes (such as a camera lens vs. a loupe), the use we make of the focal length parameter may be different.

In addition, in making calculations involving the operation of a lens, we in general need to take into account the locations of the two principal/nodal points of the lens (the principal and nodal points are in the same location for a lens immersed in the same medium - such as air - fore and aft, but have different definitions, so we keep diferent names for them). In the fanciful "thin lens", we assume that the two nodal/prinipal points are in the same place (namely, hafway through the lens, although since a true thin lens has no thickness, that definition really has no meaning!) When we deal with the lens in a simple (non-compound) loupe, the "thin lens" conceit serves us pretty well.

Best regards,


Jim Jones
19-Dec-2006, 20:11
If I were trying to get 200 pairs of matched focal length magnifiers, I might not bother measuring the absolute focal length of any of them. Rather, I would transilluminate an appropriate test target and project it with the doublet closest to the target. A screen can be placed quite some distance from the lens. Move the screen until the image is in focus, and measure the distance between two points on the test target. You can use a yard stick for this instead of precise equipment. Note this measurement on the lens. Do this for all 400 lenses. Now match them up in pairs.

Michael Gudzinowicz
20-Dec-2006, 08:32
You could use an enlarger with lenses mounted on a board. The focal length of a "thin" lens would be fl=(2 + 1/M +M) * dist where "M" is the magnification and "dist" is the carrier to easel distance. Do not change "dist", but adjust spacing and refocus until the magnifications match. With "dist" = approx 900mm (any 4x5 enlarger), M would be around 17.9 for a 45 mm lens. It isn't the perfect approach, but it will permit matching to the tolerances you require.