Helmholtz reciprocity

The Helmholtz reciprocity principle describes how a ray of light and its reverse ray encounter matched optical adventures, such as reflections, refractions, and absorptions in a passive medium, or at an interface. It does not apply to moving, non-linear, or magnetic media.

For example, incoming and outgoing light can be considered as reversals of each other, without affecting the bidirectional reflectance distribution function (BRDF) outcome. If light was measured with a sensor and that light reflected on a material with a BRDF that obeys the Helmholtz reciprocity principle one would be able to swap the sensor and light source and the measurement of flux would remain equal.

In the computer graphics scheme of global illumination, the Helmholtz reciprocity principle is important if the global illumination algorithm reverses light paths (for example Raytracing versus classic light path tracing).

The Stokes-Helmholtz reversion-reciprocity principle was stated in part by Stokes (1849) and with reference to polarization on page 169 of Helmholtz's Handbuch der physiologischen Optik of 1856 as cited by Kirchhoff and by Planck.

As cited by Kirchhoff in 1860, the principle is translated as follows:

The most extremely simple statement of the principle is 'if I can see you, then you can see me'. Rayleigh stated the basic idea of reciprocity as a consequence of the linearity of propagation of small vibrations, light consisting of sinusoidal vibrations in a linear medium.

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.

In his magisterial proof of the validity of Kirchhoff's law of equality of radiative emissivity and absorptivity, Planck makes repeated and essential use of the Stokes-Helmholtz reciprocity principle.

When there are magnetic fields in the path of the ray, the principle does not apply. Departure of the optical medium from linearity causes departure from Helmholtz reciprocity. When there are moving objects in the path of the ray, the principle may be entirely inapplicable.

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