ray tracing: "size" of the field of depth

Question

How do I actually define the depth of the field, that is, the range of z-values where my objects would be in focus. That is, I want objects with z-coords in [f-w,f+w] to be in focus (camera coords), where f is the focal length and w is some predefined constant.

The way I do it now is I find a primary ray from lens center to P (point on the focal plane, z=-f), then shoot rays from random points L on the lens to P.

What I am seeing is that the implicit value w is very small, so there is a very visible band where things are in focus, and everything near it and further is blurred. Now, I could play with d (distance from lens to image plane) and aperture values to make a specific scene look OK, but I wanted to see some maths on how to solve this issue properly.

I've looked at several ray tracing books and they all skirt this issue.

Answer 1

In case anyone else will look, a 1995 paper by Kolb, Mitchel, Hanrahan - A Realistic Camera Model for Computer Graphics describes a lens model of thickness t and how to control the depth of the field itself.

Link to paper