Binocular vision

We have 2 cameras L and R, they are lined up with center to center distance $D$ . if an identified object is detected in both cameras, then we are able to use the position difference in between the 2 cameras to determine the distance. Let’s say the camera has a field of view(FOV) of $\theta$. Resolution wise $l\ast h$

let’s say the object has a coordination $(x_L,y_L)$ and $(x_R,y_R)$ in the 2 cameras respectively.

$${\theta }_L=\frac{(x_L-\frac{l}{2})}{l}\ast \frac{\theta }{2}$$ $${\theta }_R=\frac{(x_R-\frac{l}{2})}{l}\ast \frac{\theta }{2}$$

then we have 2 light path which could be described from the center of the 2 cameras as

$$f(d)=tan{\theta }_L\ast d-\frac{D}{2}$$ $$f(d)=tan{\theta }_R\ast d+\frac{D}{2}$$

where $d$ is the distance between object and camera plane, $f$ is the how far away it is from the center line between 2 cameras calculating the intersection will be

$$d=\frac{D}{tan{\theta }_R-tan{\theta }_L}$$