Article ID: CBB998174639

Kirchhoff’s Theory for Optical Diffraction, Its Predecessor and Subsequent Development: The Resilience of an Inconsistent Theory (2016)


Kirchhoff’s 1882 theory of optical diffraction forms the centerpiece in the long-term development of wave optics, one that commenced in the 1820s when Fresnel produced an empirically successful theory based on a reinterpretation of Huygens’ principle, but without working from a wave equation. Then, in 1856, Stokes demonstrated that the principle was derivable from such an equation albeit without consideration of boundary conditions. Kirchhoff’s work a quarter century later marked a crucial, and widely influential, point for he produced Fresnel’s results by means of Green’s theorem and function under specific boundary conditions. In the late 1880s, Poincaré uncovered an inconsistency between Kirchhoff’s conditions and his solution, one that seemed to imply that waves should not exist at all. Researchers nevertheless continued to use Kirchhoff’s theory—even though Rayleigh, and much later Sommerfeld, developed a different and mathematically consistent formulation that, however, did not match experimental data better than Kirchhoff’s theory. After all, Kirchhoff’s formula worked quite well in a specific approximation regime. Finally, in 1964, Marchand and Wolf employed the transformation of Kirchhoff’s surface integral that had been developed by Maggi and Rubinowicz for other purposes. The result yielded a consistent boundary condition that, while introducing a species of discontinuity, nevertheless rescued the essential structure of Kirchhoff’s original formulation from Poincaré’s paradox.

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Authors & Contributors
Levitt, Theresa
Kragh, Helge S.
Mollon, J. D.
Schirrmacher, Arne
Lombardi, Anna Maria
Magalhães, Gildo
Nuncius: Annali di Storia della Scienza
British Journal for the History of Science
Royal Society of London. Philosophical Transactions. Mathematical, Physical and Engineering Sciences
Historical Studies in the Physical and Biological Sciences
Science in Context
Archive for History of Exact Sciences
Oxford University Press
Harvard University
The Royal Danish Science Society
World Scientific
Pavia University Press
Philosophy of science
Electromagnetic waves; radiation
Methodology of science; scientific method
Kirchhoff, Gustav Robert
Arago, François Jean Dominique
Fresnel, Augustin Jean
Biot, Jean-Baptiste
Lorenz, Ludvig Valentin
Young, Thomas
Time Periods
19th century
20th century, early
18th century
Early modern
20th century
21st century
Great Britain

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