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Thread: Parallelism math

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    Question Parallelism math

    I'm trying to make some math to verify exactly how parallel front and rear standards need to be to still not give visible focusing errors for a certain aperture/coc.

    Ie I'd like to mathematically answer questions like "if there is an accidental swing/tilt of 0.05 degrees, will that be visible when focusing at infinity at f/11". As I evaluate different view cameras now and then it's a question I often have but I have no real good tool to answer it.

    I've tried to use the normal Scheimpflug formulas with very small angles, but that does not seem to work. Using them it actually seems to be better to have a little error than absolute parallelism :-)

    Someone that knows where I can find some math for this?

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    Subscriber and Workshop Member MGrayson's Avatar
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    Re: Parallelism math

    How did you get the slight error is better result? I can't imagine better formulas than the standard ones, although there are useful approximation for the field.

    Curious,

    Matt

    (Amateur photographer, but professional mathematician)

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    Senior Member Stefan Steib's Avatar
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    Re: Parallelism math

    Torger

    This will be dependent to the size of the pixels of the used back ! The size of the projected airydisks with a tilt will differ and from that relation you could calculate the allowed "swing". There was a nice article with some links here

    Do Sensors

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    Re: Parallelism math

    Quote Originally Posted by MGrayson View Post
    How did you get the slight error is better result? I can't imagine better formulas than the standard ones, although there are useful approximation for the field.

    Curious,

    Matt

    (Amateur photographer, but professional mathematician)
    I'm not sure, maybe they do work, shall look closer. Anyway with those you get with tiny angles a huuuuuge hinge distance, and large depth of field angles so it seems just too easy to fit the field of view inside the wedge.

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    Re: Parallelism math

    You would just need to calculate this based on the depth of focus--you don't what to use depth of field. It should simply come down to the f-number of the system and the CoC which should give you the tolerance at the image plane and you can calculate the angle that would be within that tolerance. The neat thing is this is not dependent on the focal length, but simply the f-number. This naturally assumes the lens projects a flat image plane. It also assumes the sensor plane intersects the center of the image plane. You could then take that and apply it to field calculations.
    Last edited by Shashin; 26th July 2013 at 09:51.

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    Re: Parallelism math

    I did not confirm the actual math, but you may need to tighten your definition of "infinity" to get the standard formulas to work for you across multiple formats with differing pixel pitches or CoC's. Suggest you try something simple on the order of unit focal/unit pixel pitch (or CoC) x 0.1m. As an example, for an 80mm lens on a 5.2U sensor, you'd get this:

    (80mm/.0052mm) x 0.1m = 1538.4m
    Jack
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    Re: Parallelism math

    Quote Originally Posted by Shashin View Post
    You would just need to calculate this based on the depth of focus--you don't what to use depth of field.
    Ahhhhh... you're right, that makes it easy. I just look at depth of focus, and make sure that for whatever definition of CoC I choose the depth of focus is within the sensor for some accidental tilt.

    So let's make an example; say we make a pixelpeep CoC of 2x pixel pitch and we have 6um pixels (Credo60, IQ260 etc) and shoot at f/11 => depth of focus = 2*11.31*12 um = 270 um. We probably don't want to be at the edge of depth of focus, so lets set tolerance to +/-50 um, and we have a 54mm wide sensor +50um on one side an -50um on the other we have a max allowed parallelism error of arctan(0.1/54) = 0.1 degrees.

    It sounds quite reasonable.
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