Recording Polarization of Fluorescence Spectrometer-A Unique Application of Piezoelectric Birefringence Modulation John E. Wampler and Richard J. DeSa Department of Biochemistry, University of Georgia, Athens, Ga. 30602
This paper describes the action and application of an optical train which can be used to obtain a continuous measure of polarization of fluorescence when incorporated into a fluorimeter. The optical train consists of a piezoelectric birefringence modulator (variable retardance waveplate) and an analyzing polarizer. Theoretical analysis using Mueller calculus of the action of this optical train on partially polarized fluorescence shows that the intensity is modulated in time as the cosine of a sine function and that subsequent components (e.g., the detector) see a light flux of varying intensity but fixed polarization. The optical train has been incorporated into a complete on-line computer-controlled instrument system, which has been programmed to obtain polarization of fluorescence excitation spectra or polarization dependence on the temperature-to-viscosity ratio. The computer allows automated control, such as wavelength stepping, scan averaging, comparison among spectra, etc. Each spectrum is represented by up to 500 data points. The effective fluorescence bandwidth is greater than 25 nm over a range of 380-700 nm. Circuitry suitable for analog signal processing is described and details of hardware and computer software are presented with examples of the performance of the whole system.
Fluorescence measurements have become increasingly useful in chemical and biochemical research because of their sensitivity, selectivity, and precision. One very useful analytical fluorescence parameter is emission polarization which aids in the analysis of electronic structure and the molecular movements of biomolecules. However, polarization excitation fluorimetry has been exploited by only a few investigators, presumably because of the requirement for specialized instrumentation. In this paper, we describe a simple instrument capable of collecting high precision polarization of fluorescence spectra. Our instrument uses a piezo-optical birefringence modulator in an arrangement not previously described; no moving or rotating parts are used and only one photomultiplier is required. Significantly, the sample cell is bracketed by fixed excitation and emission polarizers making the polarization sensitivity of other components ( e . g . , monochromators, filters, photomultiplier, etc.) irrelevant. The optical components of the system could readily be adapted to most scanning fluorimeters without in any way altering their normal function. We have used an on-line digital computer system (1, 2) to control the instrument described here, but we also present analog circuitry suitable for processing the signal from the fluorimeter to give a direct readout of polarization. (1) J. E. Wampler and R. J. DeSa, A p p l . Spectrosc.. 25, 623 (1971). (2) R. J. DeSa, in "Computers in Chemical and Biochemical Research," Vol. I C. Klopfenstein and C . Wilkins, Ed.. Academic Press, New
York, N.Y.. 1972. (3) J. Lavonel, C. Vernotte. E. Arrio, and F. Rocher, Biochimie. 54, 161 (1972).
THEORETICAL Polarization of fluorescence emission can be measured by analyzing the vertical and horizontal components of emission caused by excitation with polarized light. One simple way to do this is to place a linear polarizer on the optical axis between the detector and the emission source (usually the emission is viewed a t 90" to the axis of excitation). Under steady illumination, the analyzer is alternately set vertical or horizontal to obtain readings for the two components of the emission intensity. The polarization, P,is defined by Equation 1 as
where I, is the vertical intensity component and I h is the horizontal intensity component. Determining the polarization of fluorescence in this way, however, is not readily compatible with continuous measurement of a spectrum since the polarizer must be turned from vertical to horizontal a t each wavelength a t which P is to be determined. Mechanical rotation of the polarizer could be used to automate these measurements, a procedure employed by some workers (3, 4 ) . The main limitations of this technique are limited time resolution and dependence upon the polarization sensitivities of analyzing components. Another approach t o measuring P is to use two photomultipliers (4-8), one analyzing the vertical and one the horizontal component of the fluorescence. This technique requires careful matching of the photomultipliers and the precision of the results can be dependent upon the polarization sensitivity of other components of the optical system. In addition, such instruments are generally limited to making polarization measurements. Another possible method to measure P would be to fix the analyzer in the horizontal position and periodically interpose a half-wave plate between the fluorescent sample and the analyzer. Since a half wave plate in effect rotates the plane of polarization go", Ih would be measured without the plate in place and I , with it. This method would be impractical because of the wavelength dependence of half-wave plates; also, it would require mechanical components if spectra were t o be automatically scanned. The following theoretical analysis will demonstrate that the unique method employed in our instrument is somewhat analogous to this hypothetical half-wave plate method, but results in an instrument with no moving parts and with simple, electronic compensation for wavelength dependence. When a fluorescent sample is excited with vertically polarized light, the emission is depolarized because of Brownian rotation of the emitter, the degree of anisotrophy of the emitting transition and other factors (9). The emission can be rep(4) (5) (6) (7) (8) (9)
R . H . McKay, A r c h . Biochem. Biophys.. 16, 438 (1969) D.A . Deranleau, Anal. Biochem.. 16, 438 (1966). G. Weber and E. Bablouzian, J. Bioi Chem.. 241, 2558 (1966). S. Ainsworth and E. Winter. Appi. O p t . . 3, 371 (1964). B. Witholt and L. Brand, Rev. Sci. Instrum. 39, 1271 (1968). P. P. Feofilov, "The Physical Basis of Polarized Emission," Consultants Bureau, New York, N . Y . , 1961 ~..
->c v)
2
c Y
5 0 W
E 0 g 0 0
3 Y Y
2
5
oz Y
1
1
I
0
EXCITING
iiGnr I
Figure 1. Complete polarization module of the polarization of
fluorescence spectrometer A, Analyzer; C. sample cuvette: CH, thermostated cuvette holder, piezoelectric birefringence modulator; P, polarizer
M,
resented by the combination of a polarized and a depolarized component; thus, the Stokes vector for a fluorescence intensity, I F , is {IF,-PIF,O,Ol where the brackets indicate a column vector and P is the polarization. In our system, this emission is passed through an "analyzing train" and the resultant light is detected by a photomultiplier (Figure 1). The analyzing train consists of a piezo-electric modulator and an analyzing polarizer. The modulator acts as a rapidly varying (50 KHZ) variable wave plate; the retardance, 6, produced by it is proportional to the voltage driving it and varies sinusoidally according to the following equation,
6
= 6o sin (ut)
For a given applied voltage, the maximum retardance, 60, is proportional to the ratio of this voltage to the wavelength of light being modulated. [See Kemp (IO) for a full discussion of this device.] The action of the modulator on the fluorescence emission can be analyzed rigorously using Mueller calculus as described by Shurcliff ( 1 1 ) . Thus the effect of both modulator and polarizer on the fluorescent emission can be expressed in terms of a matrix which is the product of the matrices for each of the two devices. This matrix, MT, has the form shown where 6 varies with time as indicated by Equation 2 above.
polarizer
I
Figure 2. Variation of fluorescence intensity with time calculated from Equation 5 The piezoelectric modulator is operated at 50 KHz. The soiid line is for a maximum retardance, do. of T radians while the dashed line is for do = 1.22 T. This latter value gives the largest value for the integrated area under the curve
tor of the incident light and is characterized by a time dependent product vector:
[IF - cos (6) IFP
+ 0 +ol
The detector sees only a time variant plane polarized light beam with an intensity, Id,given by Equation 4.
Id
=
O H F - 0.51FP cos [do sin (at)]
(5)
The amplitude variation expressed by Equation 5 is shown in Figure 2 for a polarization value, P, of 0.5 and for maximum retardance values, 60, of x and 1.22 x . The peaks and troughs (for 60 = x ) represent Z, and Ib, respectively, and their values could be used in Equation 1 to calculate polarization. Obviously, any conventional analog demodulation circuit (e.g., a lock-in amplifier) used to process this waveform would need to take account of its marked asymmetry; a simpler analysis can be employed, however. By using a photocurrent-to-voltage transducer at the photomultiplier anode, a time dependent voltage, V, is obtained. V is determined by the gain of the transducer, k , and the sensitivity of the photomultiplier, S ; thus the working form of Equation 5 is given by Equation 6.
modulator
$/o
1 cos 6 0 sin 6 0 0 0
Lo
0 0
A mean voltage, V,, defined as the average of V when it is examined for a time much longer than the cycle time of the modulator, is given by Equation 7,
01
The light beam which is seen by the detector is, then, the product of the matrix of this train and the Stokes vec(10) J . C . Kemp, J . Opt. SOC.Arner. 59, 950 (1969). (11) N. A. Shurcliff, "Polarized Light," Harvard University Press, Cambridge, Mass., 1966.
564
7-l
PHASE ANGLE OF D R I V I N G VOLTAGE ( u t )
ANALYTICAL CHEMISTRY, VOL. 46, NO. 4 , APRiL 1974
The integral in Equation 7 can be solved by numerical integration to give a constant mean value, C. Figure 3 shows C as a function of 60. If the modulator is switched off, the quartz becomes isotropic and the detector sees only the component of the
i
1 1
2
2 8
L-
-1-
2 c.
t
+I
0
60
360
WAVELENGTH ( n m l
560
"
-;6 ,/'
/'
I
cp
c:
0-
;L-200
-05
MAXIMUM R E T A R O A N C I
Figure 3. The mean value of cos [& sin
'60)
( u t ) ]as
ZIT
a function of
60
This value, C. goes to a minimum at 1.22 ?T retaro'ance corresponding to the maximum difference between the modulated and unmodulated slgnals
incident light beam which can pass through the horizontal polarizer, the 1, component, which gives a voltage, VO,
Vo
=
0.5kSIF - 0.5kSIFP
v, v,
1 - CP 1 - P
400
500
600
WAVELENGTH l n m l
Figure 4. The required control voltage necessary to maintain 1.22 K retardance as a function of wavelength (solid line). Since the calculation of polarization involves a retardance dependent term, c, the bandwidth of the calculation is limited. The dashed lines show the bandwidth allowed for a maximum calculation error of 1%. The inset shows this bandwidth as a function of wavelength for 1 % and 5% maximum calculation error
(8)
It can readily be seen that if the ratio V,/Vo is taken, the gain, sensitivity, and intensity components of Equations 7 and 8 cancel and the working equation becomes - =
I] 300
WLARIZAT
(9) MEATH
When rearranged to give polarization, Equation 9 becomes
P =
v, - vo v, - cvo
(10)
V , can most readily be obtained by simply using a long time constant in the feedback circuit of the photocurrer.ttto-voltage transducer and VOis obtained when the driving voltage to the modulator is turned off. The data of Figure 3 show that the optimum value of 60 for this analysis is 1.22 K , corresponding to a C value of -0.402. This value of 60 gives the largest absolute difference between V , and VO,and the widest bandwidth in terms of the wavelength dependence of 60 (Figure 4 ) . Figure 4 shows the control voltage required to give 1.22 K maximum retardance from our modulator. The dashed lines of either side of this curve show the envelope of wavelengths of light which correspond to values of C (from Figure 3) which gave an error in the calculated polarization of 1% or less. From curves of this type, the bandwidth for a particular wavelength and a given acceptable error can be determined (Figure 4 inset). An examination of these data clearly indicates that the bandwidth for
