Helmholtz Reciprocity: its validity and application to reflectometry

Many measurements of reflection properties of materials or components depend for their validity on the Helmholtz Reciprocity Principle. Yet this principle is widely misunderstood, and is stated in textbooks in various forms which have different meanings. This paper examines Helmholtz's own statements of his Reciprocity Principle, which restrict its applicability to corresponding states of polarization for incident and emergent fluxes. This interpretation contrasted with those of more generalised statements, which either allow any incident and emergent states of polarization or which merely require an interchange of unrestricted incident and emergent states of polarization. A comprehensive set of measurements on five matt and two glossy white standard materials has enabled luminance factors to be compared for (0°/45°) and (45°/0°) conditions as well as for the special conditions (0°/57°) and (57°/0°) involving Brewster's Angle for the glossy samples. Each of these nine comparisons has been carried out with all 15 possible combinations of s- and p-plane polarized and unpolarized light. The 135 tests of reciprocity demonstrate that significant and sometimes large discrepancies occur for non-corresponding states of incident and emergent polarizations, whereas no significant discrepancies occur for corresponding states of polarization.