Rayleigh-Sommerfield Diffraction vs Fresnel-Kirchhoff, Fourier Propagation and Poisson's Spot
Formal rept. Jun 2003-Jun 2004
NAVAL RESEARCH LAB WASHINGTON DC
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The boundary conditions imposed on the diffraction problem in order to obtain the Fresnel-Kirchhoff FK solution are well-known to be mathematically inconsistent and to be violated by the solution when the observation point is close to the diffracting screen 1-3. These problems are absent in the Rayleigh- Sommerfeld RS solution. The difference between RS and FK is in the inclination factor and is usually immaterial because the inclination factor is approximated by unity. But when this approximation is not valid, FK can lead to unacceptable answers. Calculating the on-axis intensity of Poisson s spot provides a critical test, a test passed by RS and failed by FK. FK fails because a convergence of the integral depends on how it is evaluated and b when the convergence problem is xed, the predicted amplitude at points near the obscuring disk is not consistent with the assumed boundary conditions.
- Statistics and Probability
- Fluid Mechanics