Visual Plane
every picture states the point it is correct from
Concept

Sensor — where it appears

The plane the picture is finally recorded on, at a stated distance behind the lens and of a stated width. It is what turns a focal length in millimetres into an angle, and what converts a blur diameter on glass into a diameter in the picture a reader sees.

Named by 5 essays across one field — each of them below, with the objects they name alongside it.

a point at 1.5 mthe pupilthe sensorwhere it focusesf/2.8, focused at 3 m5.8 px across

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.

sensor · Aperture 00.50011.50-0.25000.2500.5000.750the blur a reader is prepared to call sharp, in pixels (powers of ten)near and far limits of the band, in metres (powers of ten)the focus distance2 pxone lens, one focus setting, five criteria5 bands

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.

sensor · Aperture the pupilan opaque edge120 mmf/1.4, focused at 6 m3 of 5 rays get past

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.

sensor · Aperture 00.2000.40005101520field angle, in degrees from the axislight lost, in stops0°10°17°23°one foreshortening, one tilt, two of distance0.48 stops at the corner

The corner sees an ellipse

A circular pupil viewed from off the axis is foreshortened by the cosine, so the blur patch a corner receives is an ellipse of axis ratio 0.920 at the edge of a full-frame picture with a 50 mm lens — and the light through it falls as the fourth power of the same cosine, 0.480 stops. Both are geometry, both happen to a perfect lens, and no design removes either.

sensor · Aperture at one depth — a stadium, to 1.8e-5receding — tapered, 4% outone point, one exposure, the whole pupil1.8e-5 against 4%

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.

sensor · Aperture

Named alongside it

The objects these essays reach for when they reach for this one.

ApertureCircle of confusionEntrance pupildepth of fieldinstrument limitChief rayConvolutionExit pupilExposureFocal lengthHyperfocal distancePinhole

All concepts