What is the relation between FOV, Focal Length and Sensor size in a Pin hole Camera Model?

Question

I aim to recreate the camera parameters of my camera in the Unity rendering system, which has the following variables:

1) I tweaked the focal length and saw that the Field of View is changing (inversely) which makes intuitive sense. But I also notice that the FOV is changing when I am changing Sensor size - how is that possible? FOV should be fixed for a fixed focal length, right?

2) Is the Sensor size related to cx, cy - principal point in the Pin Hole Camera model? Ref

3) The camera parameters I have are of this format:

where fx,fy are the focal length in pixel units. Unity though needs the actual focal length(in meters). Is there a way to mathematically deduce focal length from fx, fy?

Answer 1

The field of view can be shown to be $$ \theta = 2 \tan^{-1} \frac{D}{2f} $$ where $D$ is the dimension of the sensor (width or height) and $f$ is the focal length.

You can derive this easily using similar triangles as in the figure below, where $\phi$ is the half field of view. Since the sensor is typically rectangular, do this twice (once for sensor width, once for height) to get the horizontal and vertical field of view angles.