Illustrated Physics
physics, drawn
Concept

Signal-to-noise — where it appears

The ratio of a measurement's wanted content to the fluctuations competing with it, which decides whether the measurement exists rather than how precise it is. Improving it by averaging works only when the noise is uncorrelated between samples.

Named by 3 essays across 3 fields — each of them below, with the objects they name alongside it.

The same source measured by amplitude and by intensity. The degree of coherence of a 47 milliarcsecond disc at 550 nm, and its square, against the separation of two apertures. A Michelson interferometer measures the upper curve, because fringe contrast is |γ|. Correlating the intensities at the two apertures instead measures the lower one, because the excess correlation of two thermal beams is |γ|² — the same information about the source, since one curve determines the other, and reaching zero at the same baseline of 2.94 m. What is lost is the phase of γ, which the intensity correlation never sees; what is bought is that a path error of many wavelengths does not matter, because the quantity being correlated is a slow fluctuation of brightness rather than a wave. The half-coherence baselines differ — 1.71 m against 1.25 m — which is the practical statement that the squared curve is the steeper one to measure against.

The correlation that survives what the phase does not

Two telescopes can measure a star's diameter by interfering the light, which requires holding two paths equal to a fraction of a wavelength through an atmosphere that will not hold still. Or they can throw the phase away entirely and correlate the brightness fluctuations, which needs the paths equal to a few metres and works.

optics · Coherence Where the instrument can hear. The response of an L-shaped interferometer to the plus polarisation, over the whole sky: azimuth across, cosine of the polar angle up, so that equal areas of the picture are equal areas of the sky. The plus pattern is largest directly overhead and underfoot and along the arms, and vanishes on four lines where a wave stretches both arms equally and the interferometer has nothing to compare. The average of the square over the whole sky is 0.2333, summed over a hundred and sixty thousand directions, and the two polarisations' averages add to 0.4000 — two fifths exactly, whatever the polarisation angle. Averaged over that angle as well, each polarisation contributes a fifth, and that fifth is what turns a strain sensitivity into a range: it is why a detector's quoted reach is substantially less than what it would manage for a source overhead. There is no direction in which the instrument is deaf to both polarisations at once, and none in which it is fully sensitive either.

What the instrument actually hears

A gravitational-wave detector is not a ruler laid against a stretching space. It is a clock comparison, its response falls to nothing at frequencies where the wave turns over while the light is still in the arm, and there are directions in the sky where it is deaf.

astrophysics · Gravitational waves A field that oscillates faster than any of its components. The oscillation of (cos x + i·2·sin x) to the power 10 over half a period, with its changing size divided out so that only the turning of its phase shows, beside the fastest wave it contains, cos 10x (dashed). Multiplied out, the function is a sum of waves e^(inx) with n running from −10 to 10 and no further. Yet in the shaded window, |x| < 0.62, it oscillates faster than cos 10x — near the origin like cos 20x, 2 times faster — completing 3.0 cycles there where its fastest component completes 2.0. Outside the window it slows down, and the next figure shows what happens to its size there.

The wiggle faster than any wave in it

Light passing through a lens carries no detail finer than half a wavelength, because no travelling wave in it varies faster than that. It would seem to follow that the light itself cannot vary faster anywhere. It can. A sum of slow waves can be arranged to wiggle faster than any of them over a stretch of any length chosen — and to focus to a spot as narrow as wanted — provided the stretch sits between side lobes that grow exponentially with every extra wiggle.

waves · Huygens

Named alongside it

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

Angular diameterAntennaAntenna patternAntibunchingBandwidthBaselineCoherenceCorrelationDegeneracy parameterDetectorDiffraction limitEvanescent wave

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