Reciprocity (electromagnetism) - Optical Reciprocity in Radiometric Terms

Optical Reciprocity in Radiometric Terms

Apart from quantal effects, classical theory covers near-, middle-, and far-field electric and magnetic phenomena with arbitrary time courses. Optics refers to far-field nearly-sinusoidal oscillatory electromagnetic effects. Instead of paired electric and magnetic variables, optics, including optical reciprocity, can be expressed in polarization-paired radiometric variables, such as spectral radiance, traditionally called specific intensity.

In 1856, Hermann von Helmholtz wrote:

"A ray of light proceeding from point A arrives at point B after suffering any number of refractions, reflections, &c. At point A let any two perpendicular planes a₁, a₂ be taken in the direction of the ray; and let the vibrations of the ray be divided into two parts, one in each of these planes. Take like planes b₁, b₂ in the ray at point B; then the following proposition may be demonstrated. If when the quantity of light J polarized in the plane a₁ proceeds from A in the direction of the given ray, that part K thereof of light polarized in b₁ arrives at B, then, conversely, if the quantity of light J polarized in b₁ proceeds from B, the same quantity of light K polarized in a₁ will arrive at A."

This is sometimes called the Helmholtz reciprocity (or reversion) principle. When there are magnetic fields or optically active materials in the path of the ray, the principle does not apply in its simple form. When there are moving objects in the path of the ray, the principle may be entirely inapplicable. Historically, in 1849, Sir George Stokes stated his optical reversion principle without attending to polarization.

Like the principles of thermodynamics, this principle is reliable enough to use as a check on the correct performance of experiments, in contrast with the usual situation in which the experiments are tests of a proposed law.

The most extremely simple statement of the principle is 'if I can see you, then you can see me'.

The principle was used by Gustav Kirchhoff in his derivation of his law of thermal radiation and by Max Planck in his analysis of his law of thermal radiation.

For ray-tracing global illumination algorithms, incoming and outgoing light can be considered as reversals of each other, without affecting the bidirectional reflectance distribution function (BRDF) outcome.