Interferometers

Abstract

Among tremendous variety of geometries that interferometry as a science acquired during centuries, this chapter focuses on only few selected configurations that became practical standards. Section one introduces indispensable plane-wave Michelson configuration, and discusses effects of polarization, beamsplitter transmittance, and tilts of the mirrors on interference pattern. In simple vector interpretation, these effects become clear, and optimal conditions for fringe contrast, spatial frequency, and beamsplitter ratio are established. The most frequently used fringe counting technique is introduced here in generalized configuration, later explained in full detail in the next section, considering heterodyne interferometry. Analytical formula is derived for the signal variation as a function of mirrors angular misalignment. Fundamental property of invariance of the interference integral is explained. From these theoretical basics, practical rules of aligning Michelson interferometer become straightforward, and pictures of real interference patterns in various consequitive phases of alignment are presented. The effect of temporal coherence on visibility of fringes is analyzed rigorously in analytical form, introducing the visibility function. Experimental results presented in a series of images recorded in spatial steps of ten micrometers corroborate theoretical conclusion. This effect has clear influence on the design of the mechanism for adjustment of mirrors, and the best solution is explained. The solution that does not require angular adjustment of mirrors implements corner cube reflectors—the optical element explained in Chap. 1. The absence of interference fringes in this type of the interferometer is portrayed in a series of experimental pictures that can hardly be found elsewhere. Such pictures are better observed with telecentric lenses (Chap. 1), and important practical know-how is explained. Chapter 1 already briefly introduced polarization properties of a corner cube, and in this section, these effects are presented in a series of impressive experimental pictures. Practical recommendations of how to avoid images of chamfers of the cube corners in the field of view may be useful. The second section gives detailed understanding of functionality and geometry of the heterodyne interferometers— devices widely used in industry to control nano-scale positioning. The self-explanatory figure and real oscilloscope traces give necessary impression about this technology. Various configurations are possible with standard high-quality modules available on the market. Some scientific applications require another peculiar configuration that may be composed with the help of the energy separator cube explained in Chap. 1. The shear interferometer for controlling parallelicity of laser beams is the most simple and common device in optical laboratory, but its theory is rather complicated and can be understood fully only with the help of detailed three-dimensional mathematical analysis and computer simulation that are left for the Chap. 12. Without experimental pictures presented in the third section it is not easy to realize this technique, but when the idea is grasped it is only a pleasure to use shear interferometer for perfect adjustment of laser collimators. Besides, with the help of theoretical analysis presented in this section, it turns out to be possible to estimate aberrations. However, this approach requires three-dimensional numerical ray-tracing routines that are summarized in Chap. 12. Imaging interferometers, freely available in the form of Mireau and Michelson interference objectives, are much more than an ordinary microscope objectives, and require special practice to handle them in order to avoid common mistakes. All that is described in the fourth section, starting from the generalized concept of an imaging interferometer and theoretical requirements for image contrast. A series of experimental interference patterns obtained on images of incoherent tungsten halogen lamp (Chap. 2) clearly explain these requirements. The newly purchased interference objective never works on the microscope without special, often tedious alignment. This process is carefully explained and the explanation is supported by detailed figures and photographs. The last section of this chapter is devoted to spectral interferometry. It starts with clear graphical explanation of the concept of this simple and reliable technique, followed by experimental spectrum obtained with very primitive experimental means, always available in any optical laboratory. Interference oscillations in the spectrum of a broad-band light source (Chap. 2) are clearly connected with the optical path difference of a transparent stratified sample. The fast Fourier transform performed on the spectrum can compute absolute values of thicknesses of layers if some non-trivial mathematical transformations are made. Explicit mathematical formulas are given.