Recently I was working on a ray tracer and came to implement depth of field. I looked at a few "tutorials" on how to do it and must admit I had some difficulties understanding them. They often introduce the concept of a lens and try to explain how actual physics work. Sort of. Well, I didn't like these explanations so I decided to share my own.
Have a look at the picture:
It shows a side view of the view frustum. There is the eye along with the "plane" (let's call it eye plane) the eye is on, the near plane at near plane distance (you could also call it film plane) and the focal plane at focal plane distance.
The point of depth of field is to make the image appear blurry everywhere where the generated rays don't intersect scene at focal plane distance. To achieve this, instead of ray tracing only one regular pinhole ray (the black ray in the picture), we generate a bunch of rays (let's call them depth of field rays) that originate at random places on the eye plane (one of these rays is the red ray in the picture). So, we know where the new ray originates. Now what we need to know is its direction. Since our image cannot be blurry at the focal plane, all of the depth of field rays must meet at the same point on the focal plane. This intersection point is simply calculated by finding the intersection point of the regular pinhole ray (the black ray in the picture) with the focal plane. So now, for each depth of field ray you have its origin (random point on the eye plane; the bigger the variance of those rays the bigger the DOF effect) and point it passes through (on the focal plane) hence the ray's direction is easy to be calculated. Once you've traced all DOF rays and got their radiances you just average them and get a nice depth of field effect.
That was it!
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