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The Resilience of an Inconsistent Model: Kirchhoff's Diffraction Theory of Light

I situate Kirchhoff’s theory of light diffraction in 1882 in a long-term development of wave optics from the early nineteenth to the late twentieth century. This development began in the 1820s when Fresnel came up with an empirically successful wave theory of diffraction based on a reinterpretation of Huygens’ principle. Then in 1856, Stokes showed that Huygens’ principle was derivable from the wave equation. Kirchhoff’s work marked a crucial point of the Huygens-Fresnel approach, for the German physicist produced Fresnel’s results as a solution of the wave equation under a specific boundary condition: unaltered field at the aperture and null field behind the obstacle. In the late 1880s, Poincaré found an inconsistency between Kirchhoff’s boundary condition and his solution. In spite of this inconsistency, researchers continued to use Kirchhoff’s diffraction theory—even after the 1930s when Sommerfeld developed a different and mathematically consistent theory of diffraction. The persistence of Kirchhoff’s problematic theory was owing to its empirical adequacy, which was not a surprise given his results were a product of the successful Huygens-Fresnel approach. While scientists admitted the error of Kirchhoff’s reasoning, they nonetheless viewed his formula as a valid approximation to reality. In 1964, Marchand and Wolf employed Maggie’s and Rubinowicz’s transformation of Kirchhoff’s surface diffraction integral into a contour integral and discovered a consistent boundary condition that produced this new formulation of Kirchhoff’s results. This move helped obtain at least a logically unproblematic theory for Kirchhoff’s diffraction formula.
 
 
I situate Kirchhoff’s theory of light diffraction in 1882 in a long-term development of wave optics from the early nineteenth to the late twentieth century.  This development began in the 1820s when Fresnel came up with an empirically successful wave theory of diffraction based on a reinterpretation of Huygens’ principle.  Then in 1856, Stokes showed that Huygens’ principle was derivable from the wave equation.  Kirchhoff’s work marked a crucial point of the Huygens-Fresnel approach, for the German physicist produced Fresnel’s results as a solution of the wave equation under a specific boundary condition: unaltered field at the aperture and null field behind the obstacle.  In the late 1880s, Poincaré found an inconsistency between Kirchhoff’s boundary condition and his solution.  In spite of this inconsistency, researchers continued to use Kirchhoff’s diffraction theory—even after the 1930s when Sommerfeld developed a different and mathematically consistent theory of diffraction.  The persistence of Kirchhoff’s problematic theory was owing to its empirical adequacy, which was not a surprise given his results were a product of the successful Huygens-Fresnel approach.  While scientists admitted the error of Kirchhoff’s reasoning, they nonetheless viewed his formula as a valid approximation to reality.  In 1964, Marchand and Wolf employed Maggie’s and Rubinowicz’s transformation of Kirchhoff’s surface diffraction integral into a contour integral and discovered a consistent boundary condition that produced this new formulation of Kirchhoff’s results.  This move helped obtain at least a logically unproblematic theory for Kirchhoff’s diffraction formula.【本講係全程以英文發表】
 
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