Single-slit diffraction at three slit widths

At its defaults it draws single-slit diffraction at three slit widths. Intensity against angle behind a single slit, evaluated from the integral across the aperture, for slits two, six and twenty wavelengths wide. A wide slit throws a nearly sharp shadow; a narrow one spreads light through a wide angle.

single-slit is one function in lib/figures/optics.js — rays, lenses, mirrors and what light does to a surface. Everything below came out of it during this build, at parameters taken from the essays rather than invented for this page. A figure here is the figure a reader meets in an essay, and if the generator changes, this page changes with it.

Intensity against angle behind a single slit, evaluated from the integral across the aperture, for slits two, six and twenty wavelengths wide. A wide slit throws a nearly sharp shadow; a narrow one spreads light through a wide angle.

Intensity against angle behind a single slit, evaluated from the integral across the aperture, for slits two, six and twenty wavelengths wide. A wide slit throws a nearly sharp shadow; a narrow one spreads light through a wide angle.

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.

The point-spread function of the same aperture with increasing spherical aberration, on a logarithmic intensity axis. The core keeps very nearly its width and loses its height, and everything lost from it appears in the wings — at a fifth of a wave of error the peak is down by a factor of 6.8 and the light outside the core is up by 8. That is the difference between an aberration and a stop: stopping an aperture down makes the core wider and the total the same, and aberrating it leaves the core where it was and scatters the light into a halo. Which matters more depends entirely on the measurement — a halo is fatal for seeing something faint next to something bright and nearly harmless for measuring the position of an isolated point.

The point-spread function of the same aperture with increasing a polishing ripple, on a logarithmic intensity axis. The core keeps very nearly its width and loses its height, and everything lost from it appears in the wings — at a fifth of a wave of error the peak is down by a factor of 8.0 and the light outside the core is up by 16. That is the difference between an aberration and a stop: stopping an aperture down makes the core wider and the total the same, and aberrating it leaves the core where it was and scatters the light into a halo. Which matters more depends entirely on the measurement — a halo is fatal for seeing something faint next to something bright and nearly harmless for measuring the position of an isolated point.

The Strehl ratio of a mirror with a fixed surface roughness, against the wavelength it is used at, for three roughnesses. Nothing about the mirror changes along any curve; what changes is what a nanometre is worth. A surface bump of a given height costs twice that in wavefront, because the light crosses it and comes back, and the cost in waves is that divided by the wavelength. So a mirror ground to 25 nanometres is far from diffraction-limited in the blue, at a Strehl of 0.54, and is essentially perfect at five micrometres, at 0.996. That is why an infrared telescope can be built to a tolerance a visible one could not use, why the same optic is specified differently for different instruments behind it, and why a surface specification quoted without a wavelength says nothing at all.

physicscheck asserts something about single-slit that could fail — it draws it and measures the result against a value reached some other way.

Across the library: 100 interrogated, 2 exercised only, 1 untouched, of 103. Read out of the gate's source by the gate's own two patterns — and the gate's last claim fails the build if that read disagrees with what it was handed while running.