Concept

Refractive index — where it appears

The ratio of the speed of light in a vacuum to its speed in a medium, which for a gas exceeds one by an amount proportional to its density. That proportionality, the Gladstone–Dale relation, is what lets schlieren, shadowgraph and interferometry measure density by how light is bent or delayed.

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

$Three instruments, three derivatives, one field. A density field — a shock, smoothed to its own thickness — and what each of the three optical techniques records across it, each scaled to its own peak so the shapes can be compared. Interferometry follows the density itself; schlieren follows its first derivative and peaks where the density is changing fastest; shadowgraph follows the second and is a light-and-dark pair straddling the same place. None of them is looking at the flow: the refractive index of a gas is linear in its density, so every one of them is a densitometer and the differences between them are differences of calculus rather than of apparatus.$

An instrument that takes a derivative

Dye, smoke and seeded particles mark the fluid and read the marks. The optical ones mark nothing — light passes through and is bent — and what a plate records is not the flow but a derivative of its density. Two of the three are therefore exactly blind to a uniform stream, at any speed it happens to have.

misconceptions · Visualisation

One per cent of noise on the image, 1.43 on the axis. The field recovered by onion peeling on 50 rings from one view carrying noise of one per cent of the instrument's own peak reading, from an interferometer's projection and from a schlieren system's deflection, against the true field. On the axis, where the truth is 1, the projection gives 1.431 and the deflection 0.876; over the whole radius their root-mean-square errors are 0.0742 and 0.0219, so the deflection is the quieter route here. Near the edge both are clean, and the error gathers towards the axis — where the field is largest and the flow usually most interesting.

One view is enough, and the axis pays for it

An axisymmetric flow — a jet, a plume, a flame — can be reconstructed from a single optical view, because Abel's integral inverts exactly. The inversion runs from the outside in, every error made on the way reaches the axis, and whether it arrives multiplied depends on which instrument took the picture.

misconceptions · Visualisation

Named alongside it

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

Density Instrument Measurement Misconception Model limit Visualisation Gradient Ill-posed Inverse problem Optics Sampling Shock

All concepts