Interferometry - Categories - Wavefront Splitting Versus Amplitude Splitting

Wavefront Splitting Versus Amplitude Splitting

• A wavefront splitting interferometer divides a light wavefront emerging from a point or a narrow slit (i.e. spatially coherent light) and, after allowing the two parts of the wavefront to travel through different paths, allows them to recombine. Fig. 5 illustrates Young's interference experiment and Lloyd's mirror. Other examples of wavefront splitting interferometer include the Fresnel biprism, the Billet Bi-Lens, and the Rayleigh interferometer.

• In 1803, Young's interference experiment played a major role in the general acceptance of the wave theory of light. If white light is used in Young's experiment, the result is a white central band of constructive interference corresponding to equal path length from the two slits, surrounded by a symmetrical pattern of colored fringes of diminishing intensity. In addition to continuous electromagnetic radiation, Young's experiment has been performed with individual photons, with electrons, and with buckyball molecules large enough to be seen under an electron microscope.
• Lloyd's mirror generates interference fringes by combining direct light from a source (blue lines) and light from the source's reflected image (red lines) from a mirror held at grazing incidence. The result is an asymmetrical pattern of fringes. Interestingly, the band of equal path length, nearest the mirror, is dark rather than bright. In 1834, Humphrey Lloyd interpreted this effect as proof that the phase of a front-surface reflected beam is inverted.

• An amplitude splitting interferometer uses a partial reflector to divide the amplitude of the incident wave into separate beams which are separated and recombined. Fig. 6 illustrates the Fizeau, Mach–Zehnder and Fabry–Pérot interferometers. Other examples of amplitude splitting interferometer include the Michelson, Twyman–Green, Laser Unequal Path, and Linnik interferometer.

• The Fizeau interferometer is shown as it might be set up to test an optical flat. A precisely figured reference flat is placed on top of the flat being tested, separated by narrow spacers. The reference flat is slightly beveled (only a fraction of a degree of beveling is necessary) to prevent the rear surface of the flat from producing interference fringes. Separating the test and reference flats allows the two flats to be tilted with respect to each other. By adjusting the tilt, which adds a controlled phase gradient to the fringe pattern, one can control the spacing and direction of the fringes, so that one may obtain an easily interpreted series of nearly parallel fringes rather than a complex swirl of contour lines. Separating the plates, however, necessitates that the illuminating light be collimated. Fig 6 shows a collimated beam of monochromatic light illuminating the two flats and a beam splitter allowing the fringes to be viewed on-axis.
• The Mach–Zehnder interferometer is a more versatile instrument than the Michelson interferometer. Each of the well separated light paths is traversed only once, and the fringes can be adjusted so that they are in focus in any desired plane. For a wind tunnel study, as illustrated in Fig. 6, the fringes would customarily be adjusted to lie in the same plane as the test object, so that fringes and test object can be photographed together. If it is decided to produce fringes in white light, then, since white light has a limited coherence length, on the order of microns, great care must be taken to equalize the optical paths or no fringes will be visible. A compensating cell would be placed in the path of the reference beam to match the test cell. Note also the precise orientation of the beam splitters. The reflecting surfaces of the beam splitters would be oriented so that the test and reference beams pass through an equal amount of glass. In this orientation, the test and reference beams each experience two front-surface reflections, resulting in the same number of phase inversions. The result is that light traveling an equal optical path length in the test and reference beams produces a white light fringe of constructive interference.
• The heart of the Fabry–Pérot interferometer is a pair of partially silvered glass optical flats spaced several millimeters to centimeters apart with the silvered surfaces facing each other. (Alternatively, a Fabry–Pérot etalon uses a transparent plate with two parallel reflecting surfaces.) As with the Fizeau interferometer, the flats are slightly beveled. In a typical system, illumination is provided by a diffuse source set at the focal plane of a collimating lens. A focusing lens produces what would be an inverted image of the source if the paired flats were not present; i.e. in the absence of the paired flats, all light emitted from point A passing through the optical system would be focused at point A'. In Fig. 6, only one ray emitted from point A on the source is traced. As the ray passes through the paired flats, it is multiply reflected to produce multiple transmitted rays which are collected by the focusing lens and brought to point A' on the screen. The complete interference pattern takes the appearance of a set of concentric rings. The sharpness of the rings depends on the reflectivity of the flats. If the reflectivity is high, resulting in a high Q factor (i.e. high finesse), monochromatic light produces a set of narrow bright rings against a dark background. In Fig. 6, the low-finesse image corresponds to a reflectivity of 0.04 (i.e. unsilvered surfaces) versus a reflectivity of 0.95 for the high-finesse image.

• It is interesting to note that Michelson and Morley (1887) and other early experimentalists using interferometric techniques in an attempt to measure the properties of the luminiferous aether, used monochromatic light only for initially setting up their equipment, always switching to white light for the actual measurements. The reason is that measurements were recorded visually. Monochromatic light would result in a uniform fringe pattern. Lacking modern means of environmental temperature control, experimentalists struggled with continual fringe drift even though the interferometer might be set up in a basement. Since the fringes would occasionally disappear due to vibrations by passing horse traffic, distant thunderstorms and the like, it would be easy for an observer to "get lost" when the fringes returned to visibility. The advantages of white light, which produced a distinctive colored fringe pattern, far outweighed the difficulties of aligning the apparatus due to its low coherence length. This was an early example of the use of white light to resolve the "2 pi ambiguity".