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Thread: Math: Calculating distance scale based on focal length, FFD, helical travel

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  1. #1
    Corran's Avatar
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    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.
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    jim landecker JimL's Avatar
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    Re: Math: Calculating distance scale based on focal length, FFD, helical travel

    I've used the thin lens equation to calibrate helical mounts. Solve for image distance i. Then, i - focal length = incremental distance the helical needs to move from focus at infinity.

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    8x10, 5x7, 4x5, et al Leigh's Avatar
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    Re: Math: Calculating distance scale based on focal length, FFD, helical travel

    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
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    Re: Math: Calculating distance scale based on focal length, FFD, helical travel

    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.

  5. #5
    8x10, 5x7, 4x5, et al Leigh's Avatar
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    Re: Math: Calculating distance scale based on focal length, FFD, helical travel

    Quote Originally Posted by Dan Fromm View Post
    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
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    Corran's Avatar
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    Re: Math: Calculating distance scale based on focal length, FFD, helical travel

    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
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    jim landecker JimL's Avatar
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    Re: Math: Calculating distance scale based on focal length, FFD, helical travel

    Quote Originally Posted by Corran View Post
    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).

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    Corran's Avatar
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    Re: Math: Calculating distance scale based on focal length, FFD, helical travel

    Perfect, yes that's what I'm looking for. The example is very helpful. That makes it easy enough to calculate a rough estimate.
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    Re: Math: Calculating distance scale based on focal length, FFD, helical travel

    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.

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    Corran's Avatar
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    Re: Math: Calculating distance scale based on focal length, FFD, helical travel

    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.
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