Where is the image sensor located in a camera with a fixed-focus lens?

Question

I am working on some research on the Kinect for XBOX One. I am looking into the depth measurements of the device. I have read that the depth values are calculated from the devices focal plane. So i had to determine the exact position of the focal plane within the device. I did camera calibration to determine the devices focal length.
The thing i am confused about is the use of the term focal length. In some sources (http://www.sony.net/Products/di/en-us/Learnmore/knowledge/01.html) it is directly used as the distance between the lens and the image sensor and they also say that the image sensor is located at the focal plane. In other sources (http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/image.html) that are more physics focused the make a distinction between the focal length and the image distance.
I asked my advisor at the university and he said i could use the calculated focal length as distance to the image sensor and said that in fixed-focus cameras the image sensor is located at the focal length but could not really explain why.

So my question is can i use the focal length i got from the camera calibration as the distance from the lens to the image sensor or would that be wrong?

I am new here and hope that did this correctly and would be glad for all feedback!

Answer 1

The camera lens is a converging lens. Light rays from distant objects arrive as parallel rays. The lens turns these rays inward (refraction). The light rays now trace out the path of a cone. We focus the camera lens by changing the distance lens to sensor. The image will be in focus when the apex of the cone just kisses the surface of the sensor. If the lens is a simple one-element convex – convex, the focal length measurement is made from the center of the lens to surface of the sensor. Again, this measurement is made when the lens is imaging an object at infinity ∞ (as far as the eye can see).

Since a simple lens suffers from 7 major aberrations, we mitigate by designing the camera lens using an array of lenses. Some lens elements will be negative and some positive as to their power. Some will be low density material and some will be high density material. The net result is a lens array that mitigates but does not eliminate the aberrations. Now a complex lens grouping of lens elements will likely have an optical center that falls off-center. In some designs the measuring point can fall outside the lens barrel.

We make the focal length measurement from a point called the rear nodal. This point is difficult to determine as it will not be marked on the lens barrel. Generally finding this point requires an optical bench. As you know, if the object distance is less than infinity, the lens to sensor distance is elongated. At unity (1:1 otherwise life-size), the object to sensor distance is 4x the focal length. Thus we can set-up a 1:1 configuration to measure the focal length. Use a millimeter scale as the object. Focus the image of the scale on a screen or ground glass. With a millimeter scale, measure the length of the image at the focal plane. When a 1:1 set-up is realized, measure object to screen distance and divide by 4. The result is the focal length of the array.

Answer 2

Well the formula for a lens or a lens system (read a camera lens the inner one or in your case kinect lens) will be

1/f = 1/Dsource + 1/Dimage

where f is the focal length Dsource is distance of source from the lens DImage is the distance of image from the lens

Now each and every camera lens have multiple lenses so that they can focus and bring the image (value of Dimage) on the sensor. So when you have a sharp image the sensor in effect is at focal plane and the distance between sensor and its nearest lens is the focal length of the nearest lens. Just remember the key here is the sharp image.

That is the theory. Now if you are working on the Kinect and you want the 3 dimensional characteristics of the image seen by Kinect then I believe you have to invoke the appropriate API for it. The reason been Kinect can see depth and calculates is all the time.

I will update this post with the API link that can be used as soon as I get it but in the mean time this will give you a place to start looking.

In addition this link https://www.youtube.com/watch?v=1YIvvXxsR5Y explains focal plane and focal length very nicely from approximatly 8min onwards