DOF Fundamentals

Tightening things up

So far we've been using the lens wide open, using a large diaphragm aperture such as f/1 or f/1.2. Now let's narrow the aperture so that only the central portion of the lens can pass light. We see what happens in Fig. 4:

Fig. 4. Close-up of camera, narrow aperture

Most photons arriving from each point in the scene are blocked from traveling on to the film/sensor plane. Those that do make it through the aperture travel on paths that are closer to being parallel to the centre-line of the camera. Technically, their angle of incidence is shallower:

Fig. 5. Narrower aperture means smaller circles of confusion

Acceptable confusion

Film frames and sensors are typically much smaller than prints. Let's say our camera is a so-called full frame digital or 35mm film, which has a frame size of roughly 1 by 1.5 inches, or 24 by 36 mm. If I make a 11 x 16.5 inch print from 35mm film, I've magnified the image 11 times. It follows that a COC that is 1/11th of a millimeter in diameter on the film will be a full millimeter in diameter in the print – which is certainly big enough to be seen. Nevertheless, there will be some COC diameter that is small enough such that it is still too small to be seen (or better too small to be printed as more than a single dot) for a given size print.

We can see, then, that some degree of misconvergence can be tolerated. This tolerance is what gives us our depth of field:

Fig. 6. Acceptable DOF

In Fig. 6 we see a possible depth of field, resulting from a particular combination of lens focal length, lens aperture, subject distance, print magnification, and print viewing distance. Notice that the red-shaded region extends twice as far behind the plane of focus as it does in front of the plane of focus. This is because photon paths from more distant objects have a narrower angle of incidence than those from closer objects. Notice also that the red-shaded region tapers off as it gets further from the exact plane of focus. This signifies that the circles of confusion are getting larger the further we get from the plane of focus, and therefore the less precisely focused each corresponding point on the print will be.