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

Chief ray — where it appears

The ray from a world point that passes through the centre of the aperture stop. All of them are concurrent on the object side, at the entrance pupil, which is what makes a picture through a real lens a projection from a definite point rather than from the glass.

Named by 5 essays across 2 fields — 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 the entrance pupilthe stopthe glassthe chief rays, from four object distances3.6e-15 mm apart

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.

lens · Pupil 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 paraxial pupilthe stopa curved front elementcrossings 15.0 · 14.5 · 13.5 · 11.6 mm

The entrance pupil walks with the angle

The place a picture is a projection from is not a point in a wide-angle design. Chief rays traced through a strongly curved front element cross the axis 15.07 mm behind its front vertex when they are nearly on the axis, and 4.23 mm nearer the front at 80° of field. So no pivot makes a wide panorama seam clean: at one metre, pivoting at the paraxial pupil leaves 4.39 arcminutes of misregistration along a seam, and the best pivot still leaves 1.41.

lens · Pupil 0.313100510how far away the subject is, in metreshow far the pupil moves forward, in millimetres0.50 mthe whole walk with field anglea 50 mm lens, focused as one pieceequal at 0.50 m

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.

lens · Pupil

Named alongside it

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

Entrance pupilinstrument limitAperturecentre of projectionFocal lengthParallaxThin lensVignettingCircle of confusionExit pupilPanoramaPinhole

All concepts