Helmholtz reciprocity
Encyclopedia
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.
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 larger 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).
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 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.
For example, incoming and outgoing light can be considered as reversals of each other, without affecting the bidirectional reflectance distribution function
Bidirectional reflectance distribution function
The bidirectional reflectance distribution function is a four-dimensional function that defines how light is reflected at an opaque surface...
(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
Flux
In the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks.* In the study of transport phenomena , flux is defined as flow per unit area, where flow is the movement of some quantity per time...
would remain equal.
In the larger scheme of global illumination
Global illumination
Global illumination is a general name for a group of algorithms used in 3D computer graphics that are meant to add more realistic lighting to 3D scenes...
, the Helmholtz reciprocity principle is important if the global illumination algorithm reverses light paths (for example Raytracing versus classic light path tracing).
Physics
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 KirchhoffGustav Kirchhoff
Gustav Robert Kirchhoff was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects...
and by Planck
Max Planck
Max Karl Ernst Ludwig Planck, ForMemRS, was a German physicist who actualized the quantum physics, initiating a revolution in natural science and philosophy. He is regarded as the founder of the quantum theory, for which he received the Nobel Prize in Physics in 1918.-Life and career:Planck came...
.
As cited by Kirchhoff in 1860, the principle is translated as follows:
A ray of light proceeding from point 1 arrives at point 2 after suffering any number of refractions, reflections, &c. At point 1 let any two perpendicular planes a1, b1 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 similar planes a2, b2 in the ray at point 2; then the following proposition may be demonstrated. If when the quantity of light i polarized in the plane a1 proceeds from 1 in the direction of the given ray, that part k thereof of light polarized in a2 arrives at 2, then, conversely, if the quantity of light i polarized in a2 proceeds from 2, the same quantity of light k polarized in a1 [misprint here corrected by Wikipedia editor] will arrive at 1.
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
Kirchhoff's law of thermal radiation
In thermodynamics, Kirchhoff's law of thermal radiation, or Kirchhoff's law for short, is a general statement equating emission and absorption in heated objects, proposed by Gustav Kirchhoff in 1859, following from general considerations of thermodynamic equilibrium and detailed balance.An object...
, Planck makes repeated and essential use of the Stokes-Helmholtz reciprocity 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.