0208.1 - Chapter 8 Interference Version 0208.1 20 November...

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Chapter 8 Interference Version 0208.1, 20 November 2002 Please send comments, suggestions, and errata via email to [email protected] and to [email protected], or on paper to Kip Thorne, 130-33 Caltech, Pasadena CA 91125 8.1 Overview In the last chapter, we considered superpositions of waves that pass through a (typically large) aperture. The foundation for our analysis was an expression for the field at a chosen point P as a sum of contributions from all points on a closed surface surrounding P . The spa- tially varying field pattern resulting from this superposition of many different contributions was called diffraction . In this chapter, we continue our discussion of the effects of superposition, but for the more special case where only two or at most several discrete beams are being superposed. For this special case one uses the term interference rather than diffraction. Interference is important in a wide variety of practical instruments designed to measure or utilize the spatial and temporal structures of electromagnetic radiation. However interference is not just of practical importance. Attempting to understand it forces us to devise ways of describing the radiation field that are independent of the field’s origin and independent of the means by which it is probed; and such descriptions lead us naturally to the concept of coherence (Sec. 8.2). The light from a distant, monochromatic point source is effectively a plane wave; we call it “perfectly coherent” radiation. In fact, there are two different types of coherence present: lateral or spatial coherence (coherence in the angular structure of the radiation field), and temporal or longitudinal coherence (coherence in the field’s temporal structure, which clearly must imply something also about its frequency structure). We shall see in Sec. 8.2 that for both types of coherence there is a measurable quantity, called the degree of coherence, that is the Fourier transform of either the angular intensity distribution or the spectrum of the radiation. After developing a formalism to describe coherence, we shall go on in Sec. 8.3 to apply it to the operation of radio telescopes, which function by measuring the spatial coherence of the radiation field. Temporal coherence is probed by a Michelson interferometer, or its 1
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2 a a F F max F min F max + F min arg ( ) (c) (b) (a) F max F min = θ θ θ - F θ Fig. 8.1: a) Young’s Slits. b) Interference fringes observed from a point source on the optic axis. c) Interference fringes observed from an extended source. practical implementation, a Fourier transform spectroscope, which we discuss in Sec. 8.2. In Sec. 8.4 we shall turn to multiple beam interferometry, in which incident radiation is split many times into several different paths and then recombined. A simple example is a Fabry-Perot etalon , which is essentially two parallel, highly reflecting surfaces. A cavity resonator (e.g. in a laser), which traps radiation for a large number of reflections, is essen- tially a large scale etalon. These principles find exciting application in laser interferometer
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