Van Cittert-Zernike theorem for introductory optics course using the concept of fringe visibility

Chandrasekhar Roychoudhuri; Kevin R. Lefebvre

doi:10.1117/12.224008

13 October 1995 Van Cittert-Zernike theorem for introductory optics course using the concept of fringe visibility

Chandrasekhar Roychoudhuri, Kevin R. Lefebvre

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Proceedings Volume 2525, 1995 International Conference on Education in Optics; (1995) https://doi.org/10.1117/12.224008
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

Abstract

Historically, the van Cittert-Zernike (vC-Z) theorem on the far-field degree of coherence due to a finite incoherent source was developed by using complex integral propagating mutual intensity function that is normally beyond the 'introductory' mathematical background for many students. In 1920, Michelson demonstrated his steller interferometer to measure the separation between a double-star (two point sources) using Young's double slit on his telescope. He observed that the visibility of the fringes oscillate with the change in the slit separation for a given double-star spacing. Then in 1957, Thompson & Wolf (TW) carried out an experiment to illustrate the physical meaning of the coherence function as the fringe visibility using Young's double-slit experiment. We propose to use Michelson and TW experiments as the starting point to introduce the vC-Z theorem. One can sum the cosine fringes due to each point of the extended incoherence source produced by the double-slit placed at the observation plane where the correlation is to be measured. The visibility of this resultant cosine fringes is precisely the correlation function derived by the customary vC-Z theorem. We use a double Fourier transform lens set up that eliminates the need to develop the rigorous Fraunhofer diffraction integral. One only need to sum the plane waves with regular tilt angles at the lens focal planes. The mathematical formulation becomes easily accessible and the physical meaning of limited increase in the spatial coherence due to the propagation of Huygens-Fresnel wavelets from incoherent source become physically meaningful.

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Chandrasekhar Roychoudhuri and Kevin R. Lefebvre "Van Cittert-Zernike theorem for introductory optics course using the concept of fringe visibility", Proc. SPIE 2525, 1995 International Conference on Education in Optics, (13 October 1995); https://doi.org/10.1117/12.224008

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KEYWORDS

Visibility

Chlorine

Correlation function

Fourier transforms

Interferometers

Stars

Wavelets

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