# Depth of field

1. Sep 21, 2013

### Aelo

1. The problem statement, all variables and given/known data

A photographer is taking a portrait photo of a person at 6 m distance from his digital camera, which has a sensor pixel size of 10 μm and is equipped with a f = 100 mm thin lens. Image blur is supposed to be limited to the size of one pixel. Which of the following aperture stops: f/4, f/8, or f/16 should the photographer select in order to get a depth of field of about 0.5 m?

2. Relevant equations

Depth of field = δz = (2*l*ρ*D)/(D2 - ρ2)
ρ = -ρ'*l/l' = ρ'[(l/f) -1]
F# relates to f such that, if F# = 8, you have an f/8 aperture stop.
Using the paraxial approximation for a single lens, F# = f/D
For a single lens with diameter D and a stop at the lens, NA = D/(2*f)
F# = 1/(2*NA) by definition
For a general system, F# = f/(2*he) with he being the height of the entrance pupil

3. The attempt at a solution

We know ρ' = 1 pixel ≈ 0.26 mm. l = 6000 mm. I'm not sure what sensor pixel size describes - is it D? If it is, I'm confused about when I can use F# = f/D. I know the paraxial approximation is used only at very small angles, so maybe that equation isn't valid when we're 6 m away. Maybe I can't use that, but if the sensor pixel size is D, I could plug in to the NA equation - but again, I feel that this would be too simple, so I think I'm oversimplifying it. Since I'm given ρ', l, and f, I could find ρ, and maybe I'm supposed to find ρ for each of the different f's (using the given F#'s and multiplying by D)and just plug into the δz equation to see which gives me the result closest to 0.5 m. This confuses me somewhat as f was given to be 100 mm, so how could f be anything else?