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Thread: Means to determine EXACT fl of a simple lens

  1. #1

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    Means to determine EXACT fl of a simple lens

    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

  2. #2

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    Means to determine EXACT fl of a simple lens

    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.

  3. #3

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    Means to determine EXACT fl of a simple lens

    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.

  4. #4

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    Means to determine EXACT fl of a simple lens

    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.

    Then

    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.

  5. #5

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    Means to determine EXACT fl of a simple lens

    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.

  6. #6

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    Means to determine EXACT fl of a simple lens

    Send it to Leonard or Emmanuel. : - )
    Brian Ellis
    Before you criticize someone, walk a mile in their shoes. That way when you do criticize them you'll be
    a mile away and you'll have their shoes.

  7. #7

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    Means to determine EXACT fl of a simple lens

    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. #8

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    Means to determine EXACT fl of a simple lens

    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.

  9. #9

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    Means to determine EXACT fl of a simple lens

    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.

  10. #10

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    Means to determine EXACT fl of a simple lens

    wg,

    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.

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