International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2006). Vol. D, ch. 1.4, pp. 102-103

Section 1.4.3.3. Optical methods (interferometry)

H. Küppersa*

aInstitut für Geowissenshaften, Universität Kiel, Olshausenstrasse 40, D-24098 Kiel, Germany
Correspondence e-mail: kueppers@min.uni-kiel.de

1.4.3.3. Optical methods (interferometry)

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The basic principle of measuring thermal expansion by interferometry consists of converting sample-length changes into variations of optical path differences of two coherent monochromatic light beams, which are reflected from two opposite end faces of the sample (or planes corresponding to them). An He–Ne laser usually serves as a light source. A beam expander produces a parallel beam and interference by two planes, which are slightly inclined to each other, produces fringes of equal thickness. Thermal expansion causes a movement of this fringe pattern, which is detected by photodiodes. The number of fringes passing a reference mark is counted and gives a measure of the relative movement of the two planes.

As examples for various realizations of interferometric devices (Hahn, 1998[link]), two basic designs will be described.

  • (i) Fizeau interferometer (Fig. 1.4.3.1[link]). The sample S is covered by a thin plate [P_{2}] (with a polished upper surface and a coarsely ground and non-reflecting lower surface) and is placed in between a bottom plate [P_{3}] and a wedge-shaped plate [P_{1}] (wedge angle of about [1^{\circ}]). The upper surface of [P_{1}] reflects the incident beam (i) to a reflected beam (r) so that it is removed from the interference process. The relevant interference takes place between ray (1) reflected by the lower surface of [P_{1}] and ray (2) reflected by the upper surface of [P_{2}]. A cylindrical tube T, which defines the distance between [P_{1}] and [P_{3}] as well as [P_{2}], is usually made of fused silica, a material of low and well known thermal expansion. The measured dilatation is caused, therefore, by the difference between thermal expansion of the sample and a portion of the fused silica tube of equal length. The whole apparatus is mounted in a thermostat.

    [Figure 1.4.3.1]

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    Schematic diagram of a Fizeau interferometer.

  • (ii) Michelson interferometer (Fig. 1.4.3.2[link]). The reference mirror M and the beam-splitter B are placed outside the thermostat. The upper face of the sample S is one interference plane and the upper surface of the bottom plate is the other. The interference pattern IP is divided into two fields corresponding to the two ends of the sample. The difference of fringe movements within these two fields yields the absolute thermal expansion of the sample.

    [Figure 1.4.3.2]

    Figure 1.4.3.2 | top | pdf |

    Schematic diagram of a Michelson interferometer.

References

Hahn, T. A. (1998). Thermal expansion measurements using optical interferometry. In Thermal expansion of solids, edited by C. Y. Ho, ch. 6. Materials Park, Ohio: ASM International.








































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