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  1. #1

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    Depth of focus (NOT field) calculation query

    Hoping the LF subforum to be the most appropriate for this question ...

    Do please note this is NOT a question about depth of field!

    I am a very inadequate mathematician indeed, and thus I am struggling to determine the depth of focus for a given focal length, aperture and format. (I am trying to establish the room for error I might have if I wanted to construct a fixed-focus LF "box" camera.)

    The parameters are:

    Lens focal length: 150mm
    Aperture: f/45
    Format: 10"x8"
    Assumed Circle of Confusion: 0.2mm
    Object distance: 1000m (i.e. for all intents and purposes, ∞)

    The Blessed Wikipedia offers the following equations:
    t=2Nc(v/f)
    where t=depth of focus, N=f/stop, c=circle of confusion, v=image distance and f=lens focal length.

    as well as t≈2Nc for all but large magnifications

    My Focal/Ilford Manual also offers t=2Nc(v/f), but also

    t=(2f^2)/h, where h=hyperfocal distance (presumably for a given focal length and f/stop?)

    I had assumed that the depth of focus would be in the order of a perhaps only 2 or 3 millimetres at most, but however I plug numbers into the equations I get a range of answers from 17mm up to the quite absurd 120m!

    I presume I am misunderstanding something rather basic, to say the least.

    SO ... how should one use these equations to correctly calculate depth of focus? (or is there a simpler way?)

  2. #2
    wildbill's Avatar
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    I can't help with the math, at all.
    There isn't much room for error though and that's why it's the most important measurement when building a camera. Why do you want to know and what are you going to do with these numbers when you come up with them?
    www.vinnywalsh.com

    I know what I want but I just don't know how to go about gettin' it.-Hendrix

  3. #3

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    Use a software DoF tool. I use Barnack . You'll have to define the 8x10 format in the database which is easy. The putting in your numbers for focal length and aperture and CoC gives me a depth of focus of 18.3 mm. I used a 35mm CoC of 0.027 mm in Barnack which equates to 0.203 mm on 8x10 inch.

  4. #4

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    18mm is right unless you are doing macrophoto with your LF(!!). BUT, that is total range of allowable error. Margin of error either side of the "perfect" position is half that.

    Plus, if you plan on a fixed-focus camera, you need as much margin as you can get for depth of field. If you start eating into that margin with errors of positioning the lens, so much lost in quality or flexibility...

    Finally, I find it strange to scale the acceptable CoC proportional to the size of the negative. It means you have no better expectations for sharpness (relative to image size) in LF compared to miniature format.

  5. #5

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    wildbill: I explained my reasons for wanting the numbers in the 4th sentence of my OP.

    spijker: thanks

    bernard_L: Thanks. No, there won't be any macro going on! and yes, I realise the need for DOF, and I do realise the need for minimising error. However, this is a "fun foamcore" project, as I have no workshop, woodworking tools or indeed skills, and thus none of the things of most of the LF community take for granted. I really just want to know how much wiggle room I have, if any. I'm not sure whether your final remark is for me or for spijker - for my part, I simply used a CoC number that seems commonly used for calculating DOF on 10x8 (at Dofmaster.com for instance).

  6. #6
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    Try this ( based on Hansma):

    N = D / (2 * c)

    N = f stop
    D = depth at film plane; (mm)
    c = circle of confusion size (mm)

  7. #7

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    Hi, I sort of dislike using formulas that I don't understand, so my first approach is to consider how things work. You've stated both the lens' focal length and aperture (150mm and f/45). So we can act as though any given image point on the film originates from a disc of 3.3mm diameter (150mm/45) at the lens, which is 150mm away from the film. In other words, imagine a cone of light coming to a point at the film. If there were no film in place, then the cone would continue to expand on the other side.

    The diameter of the light cone at any position limits the finest detail. For example, if the cone had a diameter of 1 mm, it would not be possible to resolve any finer, for example, a one-half mm image point could not be resolved. (Diffraction will further degrade the image, but nothing will make finer detail than the cone of light allows.)

    If you sketch this out, you can see that this cone's diameter expands at a rate of 3.3 mm per 150mm = 0.022 mm per mm. In other words, for each 1 mm error you have in locating your image plane, the cone-of-light's diameter increases by 0.022mm. So your specific question is, "How much locating error is allowed before the cone of light reaches a diameter of 2mm?" The answer is 2/0.22 = 9mm.

    In other words, your allowable error in locating the film plane would be a maximum of +/- 9 mm. The total range of possible error is from -9 to +9 = 18mm, roughly the same as a couple other people (especially bernard_L) have mentioned.

    Sorry if I made it sound complicated, but the concept is actually pretty simple. Once one understands the concept of the cone, it's probably quicker to calculate by hand than it is to use an on-line calculator.

    Personally, I would try to build the camera more precisely, something like the +/- 2 or 3mm you originally thought, in order to improve the focus. If you make your lens mount so that it screws onto a stack of shims, this would let you have any arbitrary amount of precision that you desire. Good luck on the project.

  8. #8
    AgX
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    Quote Originally Posted by pdeeh View Post
    Do please note this is NOT a question about depth of field!
    My understanding is that depth of focus and depth of field mean the same.

    (My photographic encyclopediae and dictionaries confirm this.)

  9. #9

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    ic-racer: thanks

    Mr Bill: That is one of the most beautiful explanations - I want to say visualisations - I have ever seen of this issue, and one which moreover makes it pellucidly clear how theory and application mesh. Thank you!
    I'm certainly going to try and make it as tight in tolerance as possible, and even with my limited skills 2 or 3mm is achievable. I'd even thought about shims

    AgX: Field and focus are distinguished in both my Focal/Ilford Manual (6th ed) and Focal Encyclopedia (3rd ed) with the latter devoting several pages to each concept

  10. #10

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    Quote Originally Posted by AgX View Post
    My understanding is that depth of focus and depth of field mean the same.

    (My photographic encyclopediae and dictionaries confirm this.)
    As far as I know, depth of field is related to the subject while depth of focus relates to the film plane. See image below.

    So if the subject is a plane, say a brick wall, parallel to the film plane, then the film plane can move within the depth of focus area and the subject is still perceived as in-focus.

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