Focus, aperture and depth of field
The thin-lens relation drawn as an optical bench: object distance, image distance and focal length, with the circle of confusion that sets how much of the scene is acceptably sharp.
Try this
Stop the aperture down from f/4 to f/22 and watch the in-focus band widen. That band is the whole of depth of field, and nothing about the lens moved but one number.
Where this lab comes from
Lenses and Depth of Field: What You Buy With Light, and What It CostsLesson 2 of the Image Formation unit. A lens buys the brightness a pinhole cannot have and charges a plane of focus for it. Worked on a published scene: 93 mm at f/4 focused at 1.52 m is sharp from 1.500 m to 1.550 m, a band 5 cm deep. Stopping down to f/22 widens it to 0.277 m, a factor of 5.54 against an aperture ratio of 5.50, and the circle of confusion behind those numbers comes out at 0.0248 mm.
More in cameras and geometry
- Four ways a fisheye maps angle to radius — Plot r(θ) for the classical designs against a fitted curve.
- The scene, and what the camera sees — Orbit a 3-D scene on the left; the pinhole view updates on the right.
- Straight lines that bow — Brown–Conrady radial and tangential terms on a pixel grid.