Illustrated Physics
physics, drawn
Concept

Strehl ratio — where it appears

The peak brightness of an optical system's image of a point, as a fraction of the peak a perfect system of the same aperture would give. It measures how much aberrations, obstructions or turbulence have spread the light out of the central core.

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

The peak that is lost to a fraction of a wave. The height of the central peak, relative to a perfect pupil of the same size, against the root-mean-square error of the wavefront in waves, for four kinds of error — each computed from the transform and each normalised to the same rms. The dashed curve is the usual approximation, the exponential of minus the square of two pi times the error. What the figure shows is that to a good approximation it does not matter WHAT the error is, only how large it is in the mean square: four quite different shapes of wavefront give nearly the same peak. A fourteenth of a wave leaves 80 per cent of the peak, which is the conventional definition of diffraction-limited, and it corresponds to a quarter of a wave peak-to-valley for a simple defocus — which is where Rayleigh's quarter-wave rule comes from and why it is a convention laid over a computed number rather than a threshold in the physics.

How accurate a mirror has to be

The pupil's amplitude decides the rings; its phase decides the peak. A wavefront error of a fourteenth of a wave root-mean-square leaves eighty per cent of the peak intensity, which is the whole of what 'diffraction-limited' means — a convention laid over a computed number. And the number barely depends on what the error is, only on how large: four quite different aberrations of the same magnitude give nearly the same answer.

optics · Diffraction The spikes a star wears are the vanes that hold the mirror. The image of a single star — the squared Fourier transform of the pupil — for a telescope aperture with a central obstruction of 0.3 of its diameter and no vanes, four vanes in a cross, and three vanes at 120°, each vane 2 per cent of the aperture's diameter wide; shown on a logarithmic brightness scale over six decades, each panel spanning ±30 times the angle λ/D. The small pictures are the pupils. With no vanes the star is an Airy core and rings. Each vane adds a streak at right angles to itself, through the core, in both directions: the cross of four vanes, which is two straight bars, gives four spikes, and the three vanes, which are not opposite one another, give six — each vane's two spikes pointing in directions no other vane's do.

The spikes a bright star wears

Photographs of bright stars show them with spikes — four in most telescope pictures, eight in the James Webb Space Telescope's, none at all in some amateur images. The spikes are not in the sky and not in the camera. They are the shadows of whatever holds the telescope's secondary mirror, transformed by diffraction into streaks at right angles to themselves, and they can be counted, predicted and removed by reading a telescope's pupil the way diffraction reads it: as a pattern whose Fourier transform is the star's image.

optics · Diffraction

Named alongside it

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

DiffractionFourier transformPoint-spread functionAberrationAdaptive opticsAiry discApproximationBabinet principlePupil functionScatteringSpecificationSurface roughness

All concepts