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I'm planning on building a scanner camera. The principle of which is simple: everything's built like a large format camera, except the film is a simple scanner controlled by computer.

Now, building such a thing may take time, but doesn't seem too complicated... Except when you need to pick a lens.

This is what I want to do: make an image circle fill a space of 216x297mm (A4). The diagonal of my scanner (the film) thus being 311,7mm big.

This is what I don't know how to do: calculate the focal length/lens width I'd need to fill such a space.

I have tried a few ways... None of which are really conclusive. The main one being to modelize the lens as an isosceles triangle. Its base's identical to the width of the lens glass, its height, to the focal length + focus distance on the "film" (with a 135mm lens, that would be 2x135mm, no ?). I have found that with a lens of 120mm width, and 135mm focal length, I'd only cover 240mm. And it's already a pretty big lens ! (found available online, scraped from a projector).

Well, you can see, the struggle is there: finding the fitting lens, knowing the calculations needed in order to do so. Any help would be appreciated !

PS: sorry if I'm unclear regarding mathematics. I don't practice them often anymore.

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  • \$\begingroup\$ Why not use a large format lens? 8x10" is a fairly common format and almost matches the dimensions of A4. \$\endgroup\$
    – Kahovius
    Commented Aug 24, 2022 at 16:57
  • \$\begingroup\$ Hi, I wasn't aware of such a format until very recently. Do you have any recommendation ? \$\endgroup\$
    – Zmaragdinae
    Commented Aug 24, 2022 at 17:26
  • \$\begingroup\$ Not really, I'm afraid, as I don't do large format myself. But I was hoping you might be able to find a used large-format lens that might suit your needs. (Beware though that 4x5" is more common, but too small.) Perhaps others with more experience with large format gear will chime in. \$\endgroup\$
    – Kahovius
    Commented Aug 24, 2022 at 18:31
  • \$\begingroup\$ "This is what I don't know how to do: calculate the focal length/lens width I'd need to fill such a space." There's no direct correspondence between focal length and image circle size. You can have a 24mm lens that projects a very small image circle, such as 11mm for 2/3" format, and another 24mm lens that projects a very large image circle, such as 325mm for Large Format 8x10 (inches). The entire 11mm image circle of the 2/3" format lens would project the same image as the 11mm diameter of the very center of the 325mm diameter LF lens' image circle. \$\endgroup\$
    – Michael C
    Commented Aug 30, 2022 at 5:50
  • \$\begingroup\$ This is kind of confusing. Do you mean that focal length isn't related to angle of projection ? (rather than to image circle size, because it is). Thus according to your example, a 24mm for 2/3" and a 325mm for 8x10 would have the same angle, but not the same circle size. \$\endgroup\$
    – Zmaragdinae
    Commented Aug 31, 2022 at 14:48

3 Answers 3

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Alternatively to an enlarger lens, you could use a lens from an 8x10 large format camera. The image circle is probably close enough to mostly work.

You might also try adding a fresnel lens or similar, such as a page-magnifier, to straighten out axis of the light going into the microlenses and filters on the sensor.

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The focal length --- same or slightly greater than the diagonal measure. Better to use an enlarger lens. This type of lens is optimized to work flat surface to flat surface.

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  • \$\begingroup\$ Thanks ! Why does a focal length equal to the diagonal measure cover the full frame of my film ? \$\endgroup\$
    – Zmaragdinae
    Commented Aug 24, 2022 at 14:58
  • \$\begingroup\$ Such a lash-up will deliver a circle of good definition large enough to cover the image with minimal vignette. \$\endgroup\$
    – Alan Marcus
    Commented Aug 24, 2022 at 15:02
  • \$\begingroup\$ Thank you very much :) For my own instruction, I would be very interested in understanding the maths behind that. Do you have a web link or an explanation ? \$\endgroup\$
    – Zmaragdinae
    Commented Aug 24, 2022 at 16:30
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A quick web search reveals that full frame sensors have a diagonal of about 43 mm, APS-C sensors of about 27 mm.

We know that full frame ultra-wide rectilinear lenses typically have a focal length of 16 mm, APS-C of 10 mm. So that is 1/2.7 of their diagonals for both of them. 1/2.7 of 311.7 mm is approximately 115 mm, so that is likely approximately where lenses for A4 size sensors would start; if you want a narrower field of view you need even higher, the other answer is right that a "normal" field of view is typically around the diagonal, i.e. 312 mm.

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