Other methods of measuring birefringence

Glazer, A. M.; Cox, K. G.

doi:10.1107/97809553602060000633

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

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International Tables for Crystallography (2006). Vol. D. ch. 1.6, p. 160

Section 1.6.4.10. Other methods of measuring birefringence

A. M. Glazer^a ^* and K. G. Cox^b ^‡

^a Department of Physics, University of Oxford, Parks Roads, Oxford OX1 3PU, England, and ^bDepartment of Earth Sciences, University of Oxford, Parks Roads, Oxford OX1 3PR, England
Correspondence e-mail: glazer@physics.ox.ac.uk

1.6.4.10. Other methods of measuring birefringence

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While the use of compensating plates is convenient, more precise techniques have been developed for the measurement of linear birefringence, both in an absolute and in a relative sense. The main methods of making absolute measurements use commercially available compensators mounted on a microscope. The main types are used with a polarizing microscope with crossed polars:

(i) Babinet compensator: This is mounted instead of the eyepiece of the microscope, and uses two quartz wedges sliding in opposite directions to each other. The wedges are so designed that when they fully overlap, but without a birefringent specimen in the microscope, a black compensation band is seen in the centre of the field of view. Then when the specimen is placed on the microscope stage in one of the two possible 45° positions, the compensation band is shifted. When in the correct 45° position, as found by trial, the lower wedge is then screwed out to recentre the compensation band, and the distance moved is read from an internal scale. This distance is calibrated in terms of relative retardation .
(ii) Berek and Ehringhaus compensators: These use a rotating birefringent crystal to change their effective retardation in order to compensate against the retardation of the specimen. The Berek compensator uses a calcite plate 0.01 mm thick, whereas the Ehringhaus compensator has compound compensating plates of either quartz or calcite, made of two sections of equal thickness cut parallel to the optic axes and cemented above one another at right angles. The compensator is inserted in the slot used for accessory plates with the specimen in one of the two 45° positions. Then by tilting the compensator plate, the apparent retardations are varied until the combined retardation matches that of the specimen, thus giving rise to the compensation band appearing in the centre of the field of view. The angle of tilt can then be converted to relative rotation by the use of suitable tables provided by the manufacturer.

In order to measure birefringence in a relative sense, the following techniques have been devised. All are capable of phenomenal precision in measuring changes in birefringence, in some instances to one part in 10⁷.

(i) Sénarmont compensator: A $[\lambda/4]$ plate is inserted above the specimen, with one of its principal vibration directions, say the slow direction, parallel to the vibration direction of the polarizer. The analyser is rotatable with a divided circle so that the angle of rotation can be measured. It can be shown that the phase shift of the light $[\delta]$ is given in terms of the angle $[\theta]$ through which the analyser is turned to achieve extinction by $[\delta = {2\pi \over \lambda} \Delta n z = 2 \theta.]$ Thus if the birefringence, or more correctly the relative retardation , of the specimen is changed, say by altering the temperature, one can follow the change simply by monitoring the angle $[\theta]$ . This can be done either manually, or electronically using a phase meter attached to a photomultiplier to measure the intensity as a function of the angle of the analyser, which is rotated at some frequency by a motor.
(ii) Intensity between crossed polars: In this case the specimen is placed in the 45° position between crossed polars and the intensity of the light through the system is measured by a photomultiplier and presented typically on a recorder. On changing the retardation of the specimen, say by heating, this intensity changes according to $[I = I_o \sin^2 \delta/2.]$ Thus on heating a set of sin² fringes is drawn out, and by counting the fringes exact measurements of $[\delta]$ can be made. This technique is of great sensitivity, but suffers from the fact that the specimen must be maintained throughout in the 45° position.

(iii) Rotating analyser: In this system (Wood & Glazer, 1980), a $[\lambda/4]$ plate is inserted below the substage but above the polarizer in order to produce circularly polarized light. On passing through a birefringent crystal specimen, this is generally converted to elliptical polarization. This then passes through a Polaroid analyser set to rotate about the axis of the light at a predetermined frequency $[\omega]$ . The resulting intensity is then given by $[I = (I_o/2) \left[1 + \sin(2\omega t - 2\varphi) \sin \delta\right],]$ where $[\varphi]$ is the angle between the analyser at any time and an allowed vibration direction of the specimen. Thus by measuring the light intensity with a photomultiplier and then by using, say, phase-sensitive detection to examine the signal at $[2\omega]$ , a plot of $[\sin \delta]$ can be made as the specimen's retardation is changed. The fact that circularly polarized light is incident on the specimen means that it is not necessary to align the specimen to any particular angle. Recently, a new type of optical microscope (Glazer et al., 1996) has been developed using this principle, in which false colour images representing [I_o] , $[\varphi]$ and $[|\sin \delta|]$ can be formed (Fig. 1.6.4.7).

Figure 1.6.4.7 | top | pdf |

Three birefringence images of industrial diamond viewed along [111] taken with the rotating analyser system. (a) [I_0] ; (b) $[|\sin\delta|]$ ; (c) orientation $[\varphi]$ of slow axis with respect to horizontal.

References

Glazer, A. M., Lewis, J. G. & Kaminsky, W. (1996). An automatic optical imaging system for birefringent media. Proc. R. Soc. London Ser. A, 452, 2751–2765.Google Scholar

Wood, I. G. & Glazer, A. M. (1980). Ferroelastic phase transition in BiVO₄. I. Birefringence measurements using the rotating-analyser method. J. Appl. Cryst. 13, 217–223.Google Scholar

International Tables for Crystallography (2006). Vol. D. ch. 1.6, p. 160