Illustrated Physics
physics, drawn
Concept

Sampling — where it appears

Reading a continuous signal or image at separated points in time or space. A pattern is captured faithfully only if there are at least two samples for each cycle of its finest detail, and anything finer folds into a false coarser pattern.

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

A tornado's winds, folded. The radial wind across a line through the centre of a tornado-like vortex 400 m across with peak winds of 60 m/s — towards the radar on one side, away on the other — as it truly is (grey) and as a radar with a Nyquist velocity of ±25 m/s reports it (red). Outside the core the winds are slower than 25 m/s and are reported correctly. Near the core they exceed it, and the reported speed folds over: the strongest inbound winds appear as outbound and the outbound as inbound, so the tight pair of opposite velocities that marks a tornado — the velocity couplet — is turned inside out. Forecasters and the algorithms they use learn to read the sharp jumps between neighbouring gates as folds rather than winds, and to unfold them by continuity from the slower winds around.

The speeds a pulsed radar folds into one

A weather radar measures the wind inside a storm by the Doppler shift of its echoes, but it never hears the shift itself. It listens in pulses, and between pulses it notes only how far the echo's phase has turned — which is known only to within a whole turn. So speeds that differ by a fixed amount give identical echoes, and every speed is folded into a window. Make the window wider by pulsing faster, and the echoes from distant rain arrive after the next pulse has gone and land at the wrong range. The two limits multiply to a constant the designer cannot touch.

waves · Doppler A facet too wide and a facet too narrow. The blur of an insect's compound eye of radius 1 mm against the width of one facet, in green light. A wide facet looks at a wide patch of sky compared with its neighbours, so the eye's sampling is coarse, and that blur rises with the width. A narrow facet is a small aperture, so diffraction spreads what it collects, and that blur falls with the width. Added in quadrature they make a minimum at D = √(λR), here 22 µm, and that is close to the facets of real insects with an eye of that size. No choice of facet width can get below about 1.8°: that figure is forced by the size of the head. Horace Barlow worked this out in 1952 and compared it with bee eyes.

The eye a fly cannot afford

A compound eye is built from thousands of tiny straws, each looking in one direction. Wide straws look coarsely at the world, and narrow ones blur what they collect by diffraction, so there is a best width, and it depends only on the size of the head. To see as sharply as a person, an eye of this kind would need to be about twelve metres in radius. A single-lens eye gets the same result with a pupil of under two millimetres.

optics · Diffraction

Named alongside it

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

AliasingAmbiguityAngular resolutionCompound eyeDiffraction limitDoppler effectLens eyeNyquist frequencyOmmatidiumPhasePulse repetition frequencyRadar

All concepts