Thin lens — where it appears
Named by 7 essays across 2 fields — 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 hole a scene actually sees
The stop is not the centre of projection. Model a 50 mm lens with its stop 18 mm behind the glass and the chief rays from every object distance cross the axis at one point 28.1 mm on the other side of the lens — 10.1 mm from the stop and 1.56 times its size — to 3.6 × 10⁻¹⁵ mm. That point is the entrance pupil, and it is where a picture is a projection from.
Focusing is a zoom
A 50 mm lens focused at half a metre is not a 50 mm camera. It stands 55.56 mm from the sensor, its picture is a pinhole picture at that distance, and it covers 35.9° where the same lens at infinity covers 39.6°. Recover the camera from the picture and it reports 55.56 mm. Read the picture with the engraved 50 mm instead and a right angle comes back as 96.0°.
Focusing moves the pivot past its best place
Focusing a fifty-millimetre lens to one metre carries its entrance pupil 2.63 millimetres forward of the camera body, and to half a metre 5.56 — which is more than the whole 5.53 that the pupil walks with field angle, so past a subject at 502 millimetres the focus decides where the pupil is. A panorama head aligned at infinity and used at a metre leaves 7.46 arcminutes along its seam; aligned at four metres it leaves 2.21, better than pivoting at the pupil at all.
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.
A refocused panorama is six lenses
Refocus between the frames of a room panorama and each frame is its own camera: its pupil carried forward by its own extension, its picture made at its own principal distance. The best fixed pivot then leaves 12.9 arcminutes along the worst seam, and a head that slides the camera back as the lens extends leaves 2.82 — the lens's walk alone. The pivot's share is first order and worth a tracking head indoors. But a stitcher that reads all six frames with one focal length misregisters by up to 270 arcminutes, which is the larger mistake by ninety times.
One focus stopped down is as sharp as six in a deep room
Refocusing a room panorama frame by frame costs a seam of 12.9 arcminutes on a fixed head. One focus stopped down costs none of that, and at f/40 holds half a metre to four metres to 5.27 arcminutes — sharper than the fixed head's seam, blunter than a tracking head's 2.82. But the comparison flatters refocusing: the frame on the table also holds the wall behind it, so it cannot be held sharper than 5.27 however it is focused. Counted properly, one focus on a plain head comes within 2.4 per cent of the geared one, and pays for it in light.
Named alongside it
The objects these essays reach for when they reach for this one.
Focal lengthcentre of projectionEntrance pupilinstrument limitParallaxChief raydepth of fieldPanoramaStitchingApertureCamera calibrationCircle of confusion