depth of field — where it appears
Named by 5 essays across one field — each of them below, with the objects they name alongside it.
The centre has an area
Every theorem of perspective follows from a projection through a point, and no instrument has one. Give the pupil a radius and each world point images as a disc — whose centre is the pinhole's mark to 5.7 × 10⁻¹⁴ millimetres, at every aperture, every distance and every field angle. The geometry survives exactly; only the sharpness is spent.
The sharp band is a decision
One 50 mm lens at f/2.8 focused at three metres has a sharp band half a metre deep or an unbounded one, and nothing about the optics changes between them — only how large a blur disc a reader is prepared to ignore. Every quantity usually quoted about depth of field is that acceptance restated, including the rule that a third of the band lies in front, which is true at one distance and nowhere else.
A pupil sees around an edge
Two backgrounds identical everywhere a pinhole can see, differing only in the strip an occluder hides from it, produce identical pinhole pictures and pupil pictures 42 per cent apart. So no function of the sharp image — no kernel, no depth-dependent kernel, nothing — produces the picture a real lens makes, and the reach behind the edge is R(Z₂/Z₁ − 1), which is 120 mm here.
The disc and the streak
A frame integrates over the pupil and over the exposure at once. Hold the point's depth and the patch is exactly the streak of its centres with one disc slid along it, to 1.8 × 10⁻⁵ of its own width. Let it recede over the same exposure and the disc's radius falls by 3.7 along the streak, and the patch departs from any single kernel by 16 pixels.
A close picture carries its own distance
A 50 mm lens focused at one metre stands 2.632 mm beyond its focal length, and a picture records where the lens stood. Recover that from two vanishing points, put in the engraved focal length, and the focus distance comes back — to 0.7 per cent at 1 m, 3.7 at 5 m, and as an interval 28 per cent wide at 30 m. A single picture has given a scale. What it has given is where the lens was focused, and the subject can be anywhere in a sharp band two to fifteen times wider.
Named alongside it
The objects these essays reach for when they reach for this one.
Circle of confusionApertureEntrance pupilSensorFocal lengthinstrument limitConvolutionExit pupilExposureHyperfocal distancePinholePoint spread function