Interferometer

Michelson Interferometer

Theoretical background

The design of many interferometers used for infrared spectrometry today is based on that of the two-beam interferometer originally designed by Michelson in 1891. Many other two-beam interferometers have subsequently been designed that may be more useful than the Michelson interferometer for certain specific applications. Nevertheless, the theory behind all scanning two-beam interferometers is similar, and the general theory of interferometry is most readily understood by first acquiring an understanding of the way in which a simple Michelson interferometer can be used for the measurement of infrared spectra.

The Michelson interferometer is a device that can divide a beam of radiation into two paths and then recombine the two beams after a path difference has been introduced. A condition is thereby created under which interference between the beams can occur. The variation of intensity of the beam emerging from the interferometer is measured as a function of path difference by a detector. The simplest form of the Michelson interferometer is shown in the next figure.

michelsolinterferoemter.jpg

Michelson interferometer. The median ray is shown by the solid line, and the extremes of the collimated beam are shown by the dashed line.

It consists of two mutually perpendicular plane mirrors, one of which can move along an axis that is perpendicular to its plane.

Bisecting the fixed mirror and the movable mirror is a beamsplitter, where a collimated beam of radiation from an external source can be partially reflected to the fixed mirror (at point F for the median ray) and partially transmitted to the movable mirror (at point M). When the beams return to the beamsplitter, they interfere and are gain partially reflected and partially transmitted. Because of the effect of interference, the intensity of each beam passing to the detector and returning to the source depends on the difference in path of the beams in the two arms of the interferometer. The variation in the intensity of the beams passing to the detector and returning to the source as a function of the path difference ultimately yields the spectral information in a Fourier transform spectrometer.

The beam that returns to the source is rarely of interest for spectrometry, and usually only the output beam traveling in the direction perpendicular to that of the input beam is measured. Nevertheless, it is important to remember that both of the output beams contain equivalent information. The main reason for measuring only one of the output beams is the difficulty of separating the output beam that returns to the source from the input beam. On rare occasions, both output beams are measured with the use of two detectors or by focusing both beams onto the same detector. In other measurements, separate beams can be passed into each arm of the interferometer and the resulting signal measured using one or two detectors.

The movable mirror can either be moved at a constant velocity (a continuous-scan interferometer) or be held at equally spaced points for fixed short periods and stepped rapidly between these points (a step-scan interferometer). When the mirror of a continuous-scan interferometer is moved at a velocity greater than $~0.1 cm/s$ (the usual case for most commercial instruments), the interferometer is often called a rapid-scan interferometer.

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