Interference The superposition principle for electromagnetic waves implies that, for example, two overlapping fields u1 and u2 add to give u1 + u2 . This is the basis for interference. Because of the slow response of practical detectors, interference phenomena are also a matter of averaging over time and space. Therefore the concept of coherence is intimately related to interference. In this chapter we will investigate both topics. A high degree of coherence is obtained from lasers, which therefore have been widely used as light sources in interferometry. In recent years, lack of coherence has been taken to advantage in a. | Optical Metrology. Kjell J. Gasvik Copyright 2002 John Wiley Sons Ltd. ISBN 0-470-84300-4 3 Interference INTRODUCTION The superposition principle for electromagnetic waves implies that for example two overlapping fields u1 and u2 add to give u1 u2. This is the basis for interference. Because of the slow response of practical detectors interference phenomena are also a matter of averaging over time and space. Therefore the concept of coherence is intimately related to interference. In this chapter we will investigate both topics. A high degree of coherence is obtained from lasers which therefore have been widely used as light sources in interferometry. In recent years lack of coherence has been taken to advantage in a technique called low-coherence or white-light interferometry which we will investigate at the end of the chapter. GENERAL DESCRIPTION Interference can occur when two or more waves overlap each other in space. Assume that two waves described by ui U1ei01 and U2 U-el overlap. The electromagnetic wave theory tells us that the resulting field simply becomes the sum viz. u u1 u2 The observable quantity is however the intensity which becomes I u 2 U1 U2 2 U2 U22 2U1U2 cos 1 - fa I1 I2 2y I1I2 cos A t where Aç 1 - 2 3-4 38 INTERFERENCE As can be seen the resulting intensity does not become merely the sum of the intensities I1 I2 of the two partial waves. One says that the two waves interfere and 2 VIi I2 cos A is called the interference term. We also see that when A 2n 1 n for n 0 1 2 . cos A 1 and I reaches its minima. The two waves are in antiphase which means that they interfere destructively. When A 2nn for n 0 1 2 . cos A 1 and the intensity reaches its maxima. The two waves are in phase which means that they interfere constructively. For two waves of equal intensity . I1 I2 I0 Equation becomes I 2I0 1 cos A 4I0 cos2 where the intensity varies between 0 and 4I0. COHERENCE Detection of light . intensity .