Exposure — where it appears
Named by 9 essays across one field — each of them below, with the objects they name alongside it.
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.
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 rolling frame on a bend is right at its centre
Read a camera car's frame row by row as it rounds a bend and every still point moves — except the bend's centre, at every height, and the horizon row, at every depth. Each mark's displacement is its streak scaled by its row time, so the rolling frame is undistorted wherever the global one is sharp. And the usual repair makes it worse: a gyroscope that undoes the turn row by row puts 0.73 px back into the centre and is a net loss everywhere nearer than twice the bend's radius.
A rolling frame on a bend is a coarse curvature gauge
Read row by row on a bend, a frame leans every vertical by an amount proportional to one over its range less one over the bend's radius, so posts at several ranges lie on a straight line that crosses zero at the radius — exactly, to a thousandth of a metre. Off the axis the zero moves to R·cos of the bearing, the circle on which a camera on a bend is sharp. As a gauge it is coarse: one frame's eight posts read a 50 m bend as 45 m (35–74) with tops placed to half a pixel, and sixteen frames as 51 m (47–55). The slower the sensor reads, the better it measures the road.
A tracked post reads the bend, if the speed is known
A rolling camera aimed at a bend's centre passes across its roadside posts rather than towards them: in half a second a post twelve metres out moves from 12.0 to 12.8 metres away and its lean changes by five per cent. Followed through those sixteen frames it is one lean read sixteen times, and one lean is a ratio of the car's speed to the bend's radius. With the speed known it reads the radius as 49.9 metres (48.1–52.9), closer than eight posts in a single frame; with it unknown, it reads nothing. Aimed forty-five degrees ahead, the camera closes on the post, its lean doubles, and one post gives both.
A followed post's own lean is read as the bend
A rolling camera on a bend reads the bend from how its roadside posts lean, and a post that leans by itself adds its own tilt to every frame, unchanged. That tilt is indistinguishable from the bend's curvature: a tenth of a degree on a post twelve metres out turns a 50-metre bend into 58. No number of frames removes it, and fitting each post's own lean along with the bend loses the bend — a sideways camera's reading widens from ±7 metres to ±29. A followed post has to be plumb to six hundredths of a degree, finer than a well-set steel column; timber posts at a quarter of a degree help only in their dozens.
A post read both ways sets its own lean aside
A rolling camera reads a bend from how its roadside posts lean, and a post's own tilt is read as bend: a quarter of a degree leaves a 50-metre bend read to ±12 metres. Followed again by a car coming the other way, the same post shows the same tilt and the opposite shutter lean. Half the sum of the two passes is the tilt and half the difference is the bend, and a timber pole read both ways gives the bend to ±1.7 metres — better than a plumb steel column read one way, at ±2.3.
Frames read up and down part a post's lean in one drive
A rolling camera reads a bend from how its roadside posts lean, and a post's own tilt is read as bend unless a second car drives the road the other way. A sensor that reads alternate frames from the bottom row up reverses the shutter's lean without reversing the car. Thirty-two such frames of one drive read the 50-metre bend from a timber pole to ±1.8 metres, against ±1.7 for two passes of sixteen — and a post swaying in the wind, which costs two passes three metres, costs one drive a quarter of one.
One pair of frames reads the speed and the bend from the roadside
A camera that reads one frame from the top down and the next from the bottom up turns every roadside pole's rolling-shutter lean round and leaves its own tilt where it was. Half the difference of each pole's two leans is the shutter's alone, and across a row of poles it lies on one straight line in one over the range: its slope is the car's speed and its crossing is the bend. So one pair of frames, a fifteenth of a second, reads both — the speed to 3 per cent and the bend to ±5.6 m from sixteen timber poles, whatever they lean. With the speed known, sixteen poles read the bend to ±2.4 m, a little better than one plumb post followed for sixteen frames. The nearest pole decides most of it.
Named alongside it
The objects these essays reach for when they reach for this one.
Sensorcamera trackMoving viewpointleast squaresIdentifiabilityMotion blurModel errorApertureCircle of confusiondepth of fieldEntrance pupilHyperfocal distance