How do I calculate the fixed copy-stand height for photographing an A5 page with a smartphone?
Asked 2/12/2022
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I want to build a DIY copy stand for a smartphone camera in its normal (non-macro) mode and set it to a fixed height so an A5 document fills the frame. I originally described this as "1:1 magnification," but I realize that is not the correct term unless the image on the sensor is life-size. What I really need is the camera-to-subject distance based on the phone camera’s field of view or focal length/sensor size. How can I calculate the required height?
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
4y ago
2 Answers
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If you want to have A5 to be 1:1 you need sensor with size A5. This is by definition 1:1 magnification ratio (object is projected on the sensor with the same size as reality).
The maximum size object you can reproduce with smartphone will be something like 6.17mm by 4.55mm (sensor 1/2.3).
If you want to get the entire object in the frame it depend of angle of view (focal length of the lens). For Samsung S20/OnePlus 8T (~120 degree angle of view) will be around 74mm (this is with wide angle lens where you can expect some geometric distortions). For standard lens of OnePlus 8T the distance is around 20cm
Originally by user34947. Source · Licensed CC BY-SA 4.0
user34947
4y ago
0
Generated from our catalog & community — verify before relying on it.
For a smartphone, "1:1 magnification" is not the right target for an A5 page unless the sensor itself were A5-sized. What you actually want is the distance at which an A5 sheet fills the frame.
To calculate that, you need the specific phone camera’s field of view (or focal length plus sensor size). Then use basic trigonometry:
- distance = (half of subject size) / tan(half of angle of view)
Use the page width with the horizontal angle of view, or page height with the vertical angle of view, and choose the larger distance so the whole page fits.
In practice, the required height depends entirely on the lens used:
- with an ultrawide smartphone lens, it may be only around 74 mm, but distortion can be significant
- with a more standard smartphone camera, it may be around 20 cm
So there is no single fixed height that works for all smartphones. First find your phone camera’s sensor size and focal length or published angle of view, then plug those values into a field-of-view calculator or the formula above.
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