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Chapter 2:
A Statistical Introduction to Temporal Coherence Effects in Interferometers
Editor(s): H. John Caulfield
Author(s): Jonathan, Jean-Michel C., Institut d'Optique Graduate School; Chavel, Pierre H., Institut d'Optique Graduate School
Abstract
In paying tribute to the many contributions of Adolf Lohmann to optical science, we must highlight his inspiring talent as a lecturer and teacher as well as his ability to introduce original concepts and ideas.We have chosen to devote our contribution to one aspect of the teaching of physical optics. When teaching interferences, the lecturer always encounters the question:Why do two different frequencies never interfere? A two-beam interferometer illuminated by light of a different frequency on each arm does not show fringes. Or to be more precise, in the quite common case of thermal light sources,1 common experience shows that interferences between two different frequencies of the source spectrum cannot be observed. Interferences with light that is not strictly monochromatic are observed but merely result from the incoherent superposition of all component monochromatic interference intensities. Providing a convincing explanation of this fact in an elementary course is not easy because statistical tools are required that are only available to the students at a more advanced level—typically, senior undergraduate or graduate. However, a full account of the phenomenon based on solid statistical grounds is not even commonly found in textbooks designed for such advanced students. Such is the aim of the present chapter. Indeed, the superposition of two different frequencies should be expected to show a beat phenomenon in time. Nevertheless, common experience shows that interference effects are stationary in time and show no beat effect. If we start from the definition of interferences as the phenomenon whereby the intensity resulting from the superposition of two light beams differs from the sum of the two intensities, we are led to clarifying the temporal aspects in the detection of light beams. First, the common situation of describing the effect at a less advanced level is examined, together with the difficulties that automatically arise. After a review of the necessary statistical concepts such as, in particular, the Wiener-Khintchin theorem, the issue of what exactly is meant by average intensity and the associated “classical detection noise” is addressed, leading to a complete model of temporal coherence in thermal light.