Calculating Webcam Focal Length and Distortion: A Comprehensive Guide

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joeyar
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Is there a formula for calculating the required focal length for a webcam given the width of the field of view and the distance away from the subject the camera is?

Also is there a relationship between the focal length of a webcam and the 'fish-eyedness' or distortion of the picture?
 
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Most webcams say the specs right around the lens, so you shouldn't need to calculate anything if you just want to know what is focal length is.
 
No, I want to know what focal length webcam I will need to fit an object of a given width from a given distance away into shot
 
joeyar said:
No, I want to know what focal length webcam I will need to fit an object of a given width from a given distance away into shot

I think you're confused as to the technical meaning of 'focal length' in photography
 
joeyar said:
No, I want to know what focal length webcam I will need to fit an object of a given width from a given distance away into shot
That's not quite enough, you would also need to know the size of the imaging chip.
 
joeyar said:
Is there a formula for calculating the required focal length for a webcam given the width of the field of view and the distance away from the subject the camera is?

Yes of course, because the triangle formed between the imaging plane (having a distance f) is similar to the triangle formed by the view frustum. f = focal length
d = distance to object
W = desired width of viewable area at distance to object
w = width of imaging plane (CCD size)

(W/2) / d = (w/2) / f

So,

f = (w/2) / ((W/2) / d)
= w*d / W

Of course, you need to know w but this should be something you can look up in the camera specifications. Focal length is adjustable.

Also is there a relationship between the focal length of a webcam and the 'fish-eyedness' or distortion of the picture?

Yes, radial distortion is more pronounced with wider field of view. However radial distortion is an effect of low quality lenses so it doesn't follow a particular geometric relationship. Typically removing for radial distortion requires calibration against known images of straight lines and then minimizing some energy function to find the radial coefficients that cause the lines to appear straight, which can then be used to apply an inverse transformation to undo the effects in future images.
 
junglebeast said:
w = width of imaging plane (CCD size)
Sensor size specifications are misleading:

http://www.dpreview.com/news/0210/02100402sensorsizes.asp

Also there's no guarantee that a camcorder claimed sensor size of 1/3" is really 4.8 by 3.6 mm (if the camcorder has a 4:3 sensor size). I have a Sony HC1 HDV camcorder that claims a sensor size of 1/3" and focal length of 5.1 to 51 mm. The Sony specs also includes 4 different 35 mm "equivalents". None of the specs correspond to what I acually see, which is a viewing angle that ranges from about 45 degrees down to 4.7 degrees ("10x" optical zoom lens).