Entrance pupil — where it appears
Named by 18 essays across 6 fields — each of them below, with the objects they name alongside it.
A turn of the head is not a step sideways
The textbook says a short baseline makes reconstruction ill-conditioned. Measured, the algebra does not notice — a two-millimetre baseline recovers the courtyard to nine digits from exact marks. What fails is the ratio of baseline to reading error, and it fails without refusing.
The eye is a place, not a point
Rotate a camera about the wrong point and the sky still stitches perfectly while the foreground slides. The misregistration falls as one over the distance, exactly — which is what says the fault is the pivot and not the lens.
The port that is not there
A flat window into water costs a lens a third of its field. A sphere centred on the entrance pupil costs nothing at all — not nearly nothing, exactly nothing — and six millimetres off centre costs 0.635°.
The dome knows its offset in units of itself
A dome port centred on the entrance pupil bends nothing at all, exactly. One that is not bends rays by an amount that depends on the decentring over the radius and on nothing else, so a ten-centimetre dome six millimetres off centre and a twenty-centimetre dome twelve millimetres off centre are the same instrument, bit for bit. The picture carries the ratio, which means it never carries the radius.
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.
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.
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 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.
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.
One depth per sample is not enough
A depth buffer keeps a single distance at each sample, so a post-process blur can only ask how far away the thing at this pixel is. Across an occluding edge that answer is two depths and an occlusion, and the gather it produces differs from the pupil's own integral by 70 per cent of full scale over a band eleven pixels wide.
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.
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.
The pivot that is not the eye
A camera bolted to a tripod turns about the screw under its baseplate, and the light crosses somewhere else. Every ray of the panorama that results passes the pivot by e sin γ — the offset times the sine of how far off its own frame's axis the ray points — so the picture has a radius where a projection would have a point.
The parallax you cannot shoot away
A stitched panorama's parallax has two halves and they do not behave alike. The one across the seam falls as the sine of half a frame spacing, so more frames buy it off; the one up the frame is the sine of half the frame's own height, and no quantity of shooting touches it. They cross at π over β, which has no pivot error in it at all.
The camera that is a cylinder
A swing-lens camera turns its lens about its own entrance pupil and sweeps a slit across film bent into a circle concentric with it. Compute where the light lands, unroll the film, undo the pinhole's inversion, and the result is not similar to the cylindrical picture surface — it is the same map, to the arithmetic floor. What it pays instead is detail, and a shear on anything that moves.
The eye is a picture surface too
A retinal sphere behind an off-centre nodal point takes every measurement this collection puts to a lens or a screen, and answers all of them. It is the equal-area fisheye to within 110 micrometres of retina rather than the equidistant one everybody draws it as, and a flat picture at its own correct distance leaves the identical arc on it, to 1.4e-14 degrees.
The hole a rig cannot fill
A two-lens spherical rig covers every direction between its two lenses and still cannot see 0.470 per cent of the sphere directly beneath it, reaching 12.8 degrees from straight down — its own tripod, standing exactly where neither lens can look. No arrangement of lenses removes it, because it is not a gap in coverage; it is the rig occluding itself.
Named alongside it
The objects these essays reach for when they reach for this one.
instrument limitParallaxcentre of projectionAperturePanoramaCircle of confusionChief rayFocal lengthSensordepth of fieldPinholeStitching