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Let's say I want to photograph a piece of paper (letter size, 8.5 inches by 11 inches, or 215.9 mm × 279.4 mm). I want to use a regular digital camera of sorts, and get about 10 megapixels of resolution, or let's just say 1 megapixels for the sake of argument.

Using any off-the-shelf components, how could I build my setup such that the distance between the page (the surface to be photographed) and the camera is MINIMAL? And how small would that distance be?

I imagine I would want to use some kind of lens (a fresnel lens maybe?), but I am open to using computation to process the image.

But this cannot just be a "flatbed scanner" because the camera must not move. And the entire page must be captured in one go without human intervention.

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migrated from physics.stackexchange.com Jun 7 '13 at 8:21

This question came from our site for active researchers, academics and students of physics.

    
What are you looking for? if you clarify your goal, what you are wondering about / what you want to test, it could be easier to find out an answer or possibly to figure a different approach to solve your doubts. That is: I understand your question but I am a bit puzzled as to what you are really wondering about. –  Francesco Jun 7 '13 at 9:46
2  
What ist the purpose of the close distance? What do you want to achieve? –  Hermann Klecker Jun 7 '13 at 10:21
1  
Why not a flatbed scanner? Why is "in one go" so important? –  mattdm Jun 7 '13 at 11:24

3 Answers 3

Minimum focus distance is related to several aspects (e.g. sensor size, lens type, etc). I will try to give you a general answer however, I do not guarantee any exact results (use it at your risk!).

Here is a basic formula to calculate focus length, given the size and distance of the object (you can try to minimize the value by trying different parameters).

Dist: distance from object in meters (this is what you should minimize)

Width: subject size in meters (this is the size of the paper. I assume you have aligned longer side of the paper with longer side of the sensor)

Sensor longer size of sensor in meters (e.g. for 1.6 cropped body this would be ~0.0225 and 0.036 for a full frame)

Given this data, the required focal length can be calculated as (in millimeters):

FL=1000 * Sensor * Dist ÷ (Width + Sensor)

Example: If you want to take a photo of paper (0.2794 meters) from 20 cm distance (0.2 m) with a 1.6 cropped body (e.g. canon 450d) you need a lens with focal length of:

1000*0.0225*0.2 ÷ (0.2794+0.0225) = 14.9 mm

P.S. This formula does NOT work with extension tubes.

P.P.S. I personally think physics website was a better place to ask!

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  1. Use a wide angle lens that has a close near-focal distance. You will have a distance of around or less than 50cm from Paper to Camera. The closest that I think could be feasible would still be around 20cm, you are clearly not going to get 4cm...

  2. Use multiple cameras. You could get OmniVision camera modules or other mini cameras. They are cheap, you can get very close and you can sync them to take pictures at the same time. If your object is perfectly flat, you won't have any parallax errors.

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"Minimum" is not a good term here as there is no hard minimum distance. For a practical solution that may meet your (incompletely stated) need , try this:

  • Take a photo of the page with a camera positioned at height h above surface and lens centre distance d from a short edge.
    angle camera and zoom until page just fits from top to bottom.

For large h (say several page lengths) and small d (`= 0) you get a normalish photo with the lens vertically above the end of the page, slightly rotated, and slight keystone effect.
As you reduce h and increase d the camera must be angled increasingly to fit the page within the image area and keystoning increases.
Probably more importantly the ratio of the distances to nearest and furthest short edges increases, making it harder to keep the whole sheet in focus. With a real camera and lens there will be some camera position that gives an adequately recoverable image and which minimises overall height and length in a way that most closely suits your needs.

Adding a tilt-shift lens (really just the ability to move the lens around and change its plane relative to the camera sensor) will allow you to focus well enough along the whole length of paper when the minimum to maximum distances are large. ie at the close end of the image the focus distance is short and at the far end it is large, to match sheet dimemsions.

If you explained what you were trying to achieve and how-high-is-too-high,-and-why, you'd probably get better answers

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