(>Journal of Microscopy, Vol. 108, P t 3, December 1976, pp. 251-259. Revised paper accepted 18 October 1976

Methods for the measurement of polarization optical properties I. Birefringence

by D. LANSING TAYLOR and ROBERT M. ZEH,* The Biological Laboratories, Harvard University, 16 Divinity Avenue, Cambridge, Massachusetts 02 138, and *Custom Instrumentation, Ravena, New York, U.S.A.

SUMMARY A simple birefringence detection system has been developed that can be used

with any standard polarizing microscope. A Foster prism is utilized in separating the orthogonal components of the resultant linearly polarized light coming from a properly oriented h/4 plate. The light intensities of the orthogonal components are measured simultaneously and a mathematical manipulation yields a direct read-out of phase retardation (nm). The theory and practical use of this technique is discussed, as well as the present and future applications.

I N T R O D U C T I O N Polarized light analyses have the potential for quantifying the orientation and

conformation of biological structures in vivo as well as in vitro (Allen et al., 1963, 1966; Ruch, 1956; InouC, 1953; Taylor, 1973, 1976a; West, 1970). Measurements of birefringence have been the most commonly utilized form of polarized light analysis for microscopic specimens. Measurements of birefringence have been applied successfully to the investigations of macromolecular alignments in vertebrate striated muscle (No11 & Weber, 1934; Eberstein & Rosenfalck, 1963; Taylor, 1976a, 1975), sperm nucleii (Inout & Sato, 1962), mitotic spindles (Inout, 1953; Salmon, 1975; Sat0 et al., 1975; Stephens, 1973), membranes (Bear et al., 1937), amoeba cytoplasm (Allen, 1972; Taylor et al., 1973, 1976; Taylor, 1976b, c; Francis & Allen, 1972), and extracellular products (Taylor et al., 1974; Dreizel & Pfleidener, 1959), and many other biological systems (see Ruch (1956) for discussion). These studies have demonstrated that ultrastructural information can be obtained without damaging the cellular organization in vivo.

Polarized light microscopes were rather insensitive instruments until InouC & Dan (1951), as well as Swann & Mitchison (1950), developed ways to increase the extinction factor. In polarized light microscopy the sensitivity of the measurements are related directly to the extinction factor. However, the development of ‘rectifiers’, Inoui & Hyde (1957) and Huxley solved the problems of the diffraction anomaly and the stray light caused by the rotation of light at the surfaces of lenses (Inoui & Kubota, 1958; Kubota & Inout, 1959; Inoui, 1961).

Correspondence : Dr D. Lansing Taylor, The Biological Laboratories, Harvard University, 16 Divinity Avenue, Cambridge, Massachusetts 02138, U.S.A.

25 1

D. Lansing Taylor and Robert M. Zeh

Rapid and reproducible measurements of birefringence were made possible by the development of the phase modulation microspectrophotometer (Allen et al., 1966; Taylor, 1973). However, simultaneous viewing and measurements of transient changes in birefringence (i.e. transient changes in birefringence during muscle contraction) required a technique that was not limited by the time of a modulation cycle or the time of manually setting a compensator. In addition, the high light intensities required in the standard extinction methods of birefringence measure- ments are detrimental to many types of cells.

The present paper describes an inexpensive, simple technique designed to measure polarization properties very rapidly while utilizing minimum light intensities. The present discussion will be limited to the measurement of linear birefringence in birefringent specimens. However, measurements of linear dichroism, optical rotation, difluorescence, and circular dichroism are possible even in complex structures. The characterization of complex polarization properties will be discussed in future publications.

THEORY OF B I R E F R I N G E N C E MEASUREMENTS: T H E POLAR EYE The 'Polar Eye' is a special polarizing analyser which utilizes a Foster prism

with its fast and slow axes set at & 45" to the plane of incident polarization (0" or North-South). When the polarizer is set at 0" the prism divides the light into spatially separated orthogonal components. Two photodetectors (photodiodes or photomultipliers) are mounted directly or via light pipes to the exit faces of the prism (Fig. 1). Therefore, when the incident plane of polarization is 0", the two photodetectors receive the same intensity of light. However, when the plane of polarization is rotated by a phase retarding specimen followed by a destnarmont compensator one photo-detector receives more light than the other (block diagram of optical and electronic components Fig. 1). The two photodetectors are balanced initially to compensate for any differences in the light intensities from the two exit faces of the Foster prism at 0" phase retardation or from differences in the sensitivity of the photodetectors.

To measure phase retardation due to birefringence, a quarter wave plate is inserted before the Polar Eye analyser with its slow (y) axis parallel to the plane of polarization of the polarizer (0") as in the classical destnarmont compensation method (destnarmont, 1840; Bennett, 1950). Under these conditions the super- position of elliptically polarized light coming from the specimen with the circularly polarized light introduced by the quarter wave plate produces a resultant linearly polarized light which is rotated relative to the transmission plane of the polarizer (Fig. 2). The angular phase retardation of the object is twice the rotation angle of the resultant linearly polarized light.

The intensity of light incident to the 'Polar Eye' detector ( l o ) is equal to the light intensity incident to photodetector- 1 (ZI) plus the light intensity incident to photodetector-2 (ZZ).

l o = 11 + I z (1)

11=Zo (3082 (45 * 4) (2)

1 2 = l o sin2 (45 4) (3)

The intensity of light incident to photodetector-1 (ZI) is given by:

while the intensity of light reaching photodetector-2 (Zz) is given by:

where 4 is equal to the number of degrees the plane of polarization has been rotated by the retardation of the specimen passing a destnarmont compensator (Fig. 3) .

252

A new birefringence detection system

, w Signal output

F i l t e r omp l i f i e r 4 Summing amDlif ier

Ampli f iers

Photodetectors

Fos!er p r i sm

I D i v i d e r

I 1 I

Difference amplifier

n Microscope opt ics

l -7- l O0 P o l a r i ze r

Aper tu re

Monochromator u I I L i g h t source

Fig. 1. Block diagram showing the major optical and electronic com- ponents used in the birefringence mode of the Polar Eye. The Foster beam splitting prism is made from pure calcite with a wavelength range from 300 to 2700 nm. The extinction factor is 105-106 on both beams.

253

D. Lansing Taylor and Robert M . Zeh The polarity of 5, is dependent upon whether the plane of polarization is rotated clockwise or counter-clockwise.

The electronic components of the polar eye performs a mathematical manipula- tion in which the differences of the light intensities measured by photodetector-1 ( I I ) and photodetector-2 ( 1 2 ) divided by their sum gives a measured value (Im).

I1 - I2

* - Z l + I z I -

Substituting with equations (l), (2) and (3) :

Zm = cos2 (45 & 4) - sin2 (45 & 4)

I I

Pho tode tec to r 2

'.

P ho todetector 1

Separated orthogonal components

Foster p r ism

Plane polarized light ( rotated)

h / 4 P l a t e

Ell iptically p o l a r i z e d l ight

Birefringent specimen

I L O0

4 50

Polar izer I T 1 O0 ~ ~~ ~

Fig. 2. Diagram showing the placement of optical components in the birefringence mode and the individual effect of these components on the state of polarization. In the general case a birefringent specimen will convert plane polarized light into elliptically polarized light. A properly oriented quarter-wave plate will convert elliptically polarized light into plane polarized light with some degree of rotation. The Foster prism will separate the plane polarized light into orthogonal components. The intensity of light exciting from each face of the prism is a function of the plane of polarization entering the prism.

(4)

254

A new birefringence detection system

By trigonometric identity : Z,=COS~ (45k4)

The measured value (I,) is linear over the range of k 18 degrees or k 54.6 nm with less than 0.1 nm noise after careful adjustment (Fig. 4).

This method of measuring birefringence has at least four major advantages : (a) the measuring speed of the instrument if limited only by the method of recording the signals. The present instrument permits a time constant of ca. 0.1 ms; (b) each photodetector receives approximately half of the total light intensity, thereby greatly reducing dark current errors associated with the standard extinction methods; (c) the output voltage of the Polar Eye varies linearly with a linear change in retardation of a birefringent specimen. The polarity of the output is a function of the direction in which the plane of polarization is rotated; (d) the Polar Eye can be used with any polarizing microscope.

S E T T I N G U P T H E M I C R O S C O P E The Polar Eye analyser can be used with any microscope equipped with standard

polarized light optics. Centred polarized light optics (rectified optics, Nikon or matched strain free Pol objectives, Zeiss) are placed on the microscope and Kohler illumination is obtained. Monochromatic light is selected with interference filters or a monochromater. Apertures or slits placed at the field diaphragm or at the primary image plane of the objective (Zeiss photometer head) are used to select the region of interest in the specimen. Too large an aperture will cause an error since the instrument yields a reading over the total area of the aperture. The specimen

Intensity wlth zero phase retardat ion

Photodetector 2

l2 = ro sin2 (45t 0 )

0 75

I I I

0 1 I

45 90

Degrees

Fig. 3. The Polar Eye is linear over a range of k 1/10 wavelength phase retardation. The two photodetectors can be balanced over this same range.

255

D. Lansing Taylor and Robert M . Zeh

I .c

0 50

r o

0 50

1 0 0 45 90

Seqrees

Fig. 4. Diagram demonstrating the relative intensities of light received by photodetector-1 and photodetector-2 in the birefringence mode. At zero phase retardation an equal light intensity is received by both photodetectors.

can be viewed under the standard crossed polars during the measurements by the insertion of eye piece analysers.

C A L I B R A T I O N Calibrations are necessary for each wavelength and aperture size. The polarizer

is rotated 18" and the instrument is adjusted until the digital meter reads 1/10 the centre wavelength used. The polarizer is then rotated back to 0" (North-South) while the X/4 plate is rotated so that the slow axis is parallel to the transmission plane of the polarizer. Alternatively, the polarizer is set at O", while a X j l O Kohler com- pensator is set for a determined phase retardation. A calibration curve for the desinarmont compensator is shown in Fig. 5. The phase retardation (F) is plotted over a range from zero to 18" rotation. The calculated phase retardation is determined as in all applications of the desknarmont compensation method (Bennett, 1950) (Fig. 5).

degrees rotation x A 180" ~

r= ~~

r =phase retardation

O P E R A T I O N O F T H E I N S T R U M E N T A baseline value is established by measuring the phase retardation in the back-

ground region of the sample. The specimen is then centred in the measuring beam

256

A neu birefringence detection system

60-07 I

nm r

18 15 I 2 9 6 3 0 3 6 9 12 15 18 - t

Degrees rotation deSBnarmont compensation

Fig. 5. Sample calibration curve demonstrating that the instrument is linear over one-tenth wavelength.

and rotated until the specimen slow axis is +45" to the polarizer which yields the maximum output on the digital voltmeter. The phase retardation (I?) can be recorded directly on a strip chart recorder, stored on F M tape or any other suitable recording system.

P E R F O R M A N C E Sensitivity

The sensitivity of the Polar Eye with or without lenses is ca. 5.0 mV/nm unit of retardation. The response is linear over the range of f54.6nm for light with a wavelength of 546 0.2 nm. The use of rectified optics (Nikon) in conjunction with the Polar Eye permits the simultaneous realization of maximum contrast and sensitivity with rapid and reproducible measurements. Electronically, the measure- ments are a function of differences between two large numbers since ca. 50% of the incident light is utilized. Furthermore, the measured value Im (equation 4) is insensitive to changes in total light intensity since it is equal to the ratio of light intensities detected by the two photodetectors.

N O I S E The smallest retardation detectable depends on the noise level which is a function

257

D. Lansing Taylor and Robert M. Zeh of the light intensity, aperture size, and RC filtering. The minimum noise level obtainable after careful optical and electronic alignment is less than 0.1 nm over a range of 54.6 nm with a time constant of 0.1 ms and a 30-0 pm diameter measuring area.

The smallest region measured with the present system is 12 pm in diameter. Two photodiode detectors were used with a 150 W mercury arc light source. The noise level and the measuring area can be minimized by using either a higher light intensity with the present system or by using balanced photomultipliers for the light detectors. The latter approach is presently being investigated.

A P P L I C A T I O N S O F BIREFRINGENCE D E T E C T I O N The present birefringence detector has been used to measure the changes in

birefringence during the rigor to relax transition in vertebrate striated muscle, Taylor (1975, 1976a), as well as to characterize the organization of actin and myosin in the giant amoeba, Chaos carolinensis (Taylor, 1976b, c; Taylor et al., 1976).

FUTURE A P P L I C A T I O N S The ‘Polar Eye’ birefringence detector is a simple, relatively inexpensive method

for quantifying birefringence and its fluctuations in microscopic specimens. Accurate measurements are possible in single muscle fibres, motile non-muscle cells, mitotic spindles, nerve fibres and many other more weakly birefringent specimens in vivo or in vitro. In addition, very few changes in the optical and electronic components will permit the measurement of linear dichroism, difluor- escence, optical rotation, and circular dichroism. The specific analyses of these parameters and experimental results will be discussed in future publications.

ACKNOWLEDGMENTS The authors would like to thank Robert Chapman for machining several com-

ponents of the instrument, they are also indebted to Professor R. D. Allen for valuable discussions on polarized light microscopy over the last few years. Further- more, one of the authors (D.L.T.) has benefited from many discussions on polarized light microscopy with S . Inoue, E. Salmon, J. Fuseler and R. Hard. The experi- mental results obtained with the Polar Eye were supported by research grant AM 18111 from the National Institute of Arthritis and Metabolic Diseases.

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