Calculating Webcam Focal Length and Distortion: A Comprehensive Guide

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Discussion Overview

The discussion revolves around calculating the required focal length for webcams based on the width of the field of view and the distance from the subject. Participants also explore the relationship between focal length and image distortion, particularly 'fish-eyedness'. The scope includes theoretical calculations and practical considerations related to webcam specifications.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants inquire about a formula for calculating the required focal length based on the field of view and distance to the subject.
  • Others suggest that webcam specifications typically provide the focal length, negating the need for calculations.
  • A participant emphasizes the need for additional information, such as the size of the imaging chip, to determine the appropriate focal length.
  • One participant presents a formula derived from similar triangles to calculate focal length, indicating that it depends on the width of the imaging plane and the desired width of the viewable area.
  • There is a discussion on the relationship between focal length and radial distortion, with some participants noting that wider fields of view tend to exhibit more distortion, but the relationship is not strictly geometric.
  • A participant raises concerns about the accuracy of sensor size specifications and their implications for focal length and viewing angles.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of calculating focal length versus relying on specifications. There is no consensus on the best approach to determine focal length or the implications of sensor size on image quality.

Contextual Notes

Participants note that the accuracy of sensor size specifications can vary, and there may be discrepancies between claimed and actual measurements, which could affect calculations.

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).
 

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