Illustrated Physics
physics, drawn
Concept

Astigmatism — where it appears

An imaging fault in which a lens or mirror has different powers in two perpendicular directions. Light from a point then focuses to two short lines at different distances instead of a point; the eye's version is corrected with a cylindrical lens.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The bowl a lens actually focuses onto. Where a lens of 50 mm focal length brings each part of a flat scene to a focus, against distance from the centre of the field, out to 21.6 mm — the corner of a 35 mm frame. The surface of best focus is a sphere of radius 76 mm curving towards the lens, and the corner of the frame sits 3.13 mm in front of the plane the centre is focused on. The shaded band is the depth of focus at f/8, which is 0.070 mm — 45 times smaller than the sag it has to cover. The curvature is not an error in the lens. It is what Σ1/nf comes to for this stack, and it depends on the powers and the glasses and on nothing else: bending the surfaces, moving the stop or stopping down changes every other aberration and leaves this one exactly where it was.

The flat scene that comes back curved

A lens does not image a plane onto a plane. It images it onto a bowl, and the curvature of that bowl is fixed by the powers and the glasses alone — not by the shapes of the surfaces, not by where the stop is, and not by stopping down. Everything a designer usually plays with leaves it exactly where it was.

optics · Imaging Sturm's conoid: a line, a circle, a line. The cross-section of a parallel beam after a lens whose focal length is 100 mm in its vertical meridian and 125 mm in its horizontal one, traced ray by ray through a round aperture, at seven distances behind the lens: 60.0, 100.0, 105.6, 111.1, 118.1, 125.0, 135.0 mm. There is no point focus anywhere. At 100 mm the vertical meridian has focused and the beam is a horizontal line; at 125 mm the horizontal meridian has, and it is a vertical line. Between them the beam is an ellipse that turns from wide to tall, and at 111.1 mm — the harmonic mean of the two focal lengths — it is a circle, the circle of least confusion, of diameter 22.2 per cent of the aperture's.

The focus that is two lines

A lens curved more steeply in one direction than the other has no focus. It brings light to a short line at one distance, to a line at right angles at another, and in between to an ellipse that turns from wide to tall and is round at exactly one place. Most eyes are built this way to some degree, so do mirrors used at an angle, and the best any ordinary lens can do for them is to put that round patch on the retina. A cylinder, curved in one direction only, can do what no sphere can: move one line onto the other.

optics · Imaging

Named alongside it

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

AberrationDepth of focusFocal lengthApertureBlurCircle of least confusionCylindrical lensDetectorDioptreField curvatureImage planeLens

All concepts