Method and apparatus for measuring the concentration of optically active substances

The concentration of optically active substances is determined by measuring the polarization of light passed through the substance using a light source, a polarizer and a modulator operated at a predetermined modulation frequency f.sub.F, as well as a measuring cell, an analyzer and a detector. The output signal from the detector 16 is alternately integrated during each half period of the modulation frequency to form voltage values U.sub.I+ and U.sub.I-. These voltage values are stored and the quotient Q of these stored voltage values is formed. Subsequently, an adjustable constant voltage is subtracted from the quotient. The measuring arrangement can have a miniature design for implantation. No mechanically moving parts and only a single detector are used. The measurement is accomplished by a simple, miniature linear ray path having high resolution.

FIELD OF THE INVENTION 
The invention relates to polarimeters for measuring the concentration of 
optically active substances and, more particularly, polarimeters which can 
be used to measure the glucose concentration in body liquids. The 
apparatus measures the polarization of polarized light fed to a detector 
through the substance to be analyzed. The polarized light passes through a 
modulator which is operated at a predetermined modulation frequency. From 
the modulator, the light passes through a measuring cell, which contains 
the substance, and an analyzer before reaching the detector. 
BACKGROUND OF THE INVENTION 
A prior known polarimeter operates in accordance with the principle of 
automatic optical null balance. The prior polarimeter contains two line 
radiators, a mercury and a sodium vapor lamp, as well as five optical 
filters arranged on a filter wheel. A tilting mirror is coupled to the 
filter wheel shaft. The mirror allows the radiation of the corresponding 
light source to be inserted into the ray path of the polarimeter at the 
same time the measuring wavelength is selected. Further, a quartz-iodine 
and a deuterium lamp are provided to furnish continuous radiation. A grid 
monochromator is provided to select the desired wavelength. 
In this known design, the monochromatic light travels through the 
polarizer, the cell containing the sample, and the analyzer before 
arriving at a photo multiplier. The polarizer and analyzer are formed by 
rotatably arranged "glan" prisms made of calcite. The polarizer, including 
the respective plane of polarization of the transmitted light, vibrates 
about the optical longitudinal axis of the system at an excursion of about 
.+-.0.7 radians at 50 Hz. The 50 Hz signal is generated in the photo 
multiplier, in the unbalanced state of the system. The 50 Hz signal is 
amplified and fed, with the correct sign, to the power input of a servo 
motor. The servo motor is mechanically coupled to the analyzer for 
rotating the analyzer until the 50 Hz signal becomes zero. 
An optically active sample inserted into the ray path causes rotation of 
the plane of polarization. The analyzer is turned by means of the servo 
system into the new balanced position. The angular difference between the 
new and the original balanced position corresponds to the optical 
capability of rotation of the sample. This type of apparatus, such as the 
Perkin Elmer model 241 MC, requires mechanical movement of the polarizer, 
a mechanically acting modulator and a motor rotated analyzer thus making 
the device unsuitable for miniaturization and/or implantation. 
A further prior known method for determining the blood glucose using 
polarimetry operates by feeding polarized light via a Faraday modulator, 
operated at a predetermined modulation frequency, through the sample and 
an analyzer to the detector. In this known method, a further detector is 
provided because the ray is divided into both measuring and reference 
signals. Subsequently, the quotient is formed from the two output signals. 
However, methods using ray division, such as that shown in German Patent 
DE-OS No. 2944113, require suitable outlays for the optical system. 
Particularly, the two detectors must meet synchronization requirements. 
There is therefore a need for a method and apparatus for measuring the 
concentration of optically active substances while allowing 
miniaturization and consequently, implantation into a living body. 
SUMMARY OF THE INVENTION 
The present invention solves this problem through the use of clocked, 
integrated signal processing in conjunction with a modulator and a single 
ray path to obtain a resolution of 5.times.(10.sup.-4) for an angle of 
rotation .alpha..sub.M of the plane of polarization. The apparatus of the 
present invention further operates without the use of any moving parts. 
For example, a relative resolution of 4% is obtained for a cell length of 
2.7 cm and a resolution for a glucose concentration C of 34 mg/l (referred 
to the physiological standard value C.sub.0 =800 mg/l).

DETAILED DESCRIPTION 
Referring to FIG. 1, there is shown an apparatus for carrying out the 
method of determining the glucose concentration in body liquids, 
particularly in blood serum. A light source 2, preferably a light-emitting 
diode LED, emits light which passes through a polarizer 4, and a modulator 
6 such as a Faraday modulator. This modulator 6 includes a coil 7 and a 
crystal 8. The apparatus further includes a lens 10 which may, for 
example, be made of glass or plastic, a measuring cell 12 for containing a 
liquid substance to be measured, an analyzer 14 and a detector 16. In the 
measuring cell 12, the plane of vibration of the light is rotated by an 
angle .alpha..sub.M because of the optically active substance (not shown). 
The light is at least approximately linearly polarized. The analyzer is 
adjusted to a permeability minimum with the modulator 6 disconnected and 
in absence of any optically active substance in the measuring cell 12. 
An oscillator 20 controls the light source 2, a frequency divider 21 and a 
counting circuit 22 with its output signal U.sub.20 having a frequency 
f.sub.0. The modulator 6 and the counting circuit 22 are controlled by the 
modulator frequency f.sub.F of the output signal U.sub.21 from the 
frequency divider 21. One output signal U.sub.22 from the counting circuit 
22 is sent as a logical control signal for an integrator 26. An output 
signal U.sub.16 from the detector 16 is fed, preferably via an amplifier 
25 as input to the integrator 26. Two further output signals U.sub.23 and 
U.sub.24 from the counting circuit 22 are fed into one input of memories 
27 and 28, respectively. The memories 27, 28 also have a second input 
which receives the output signal U.sub.26 from the integrator 26. The 
memories 27 and 28 are preferably of the sample-and-hold type. The output 
signals U.sub.27 and U.sub.28 from the memories 27 and 28 are fed into a 
divider 30. The divider 30 further has an additional summing input. This 
additional input is provided with a given constant voltage U.sub.K from a 
constant-voltage source 29. 
In operation of the embodiment of FIG. 1, the measuring cell 12 receives a 
liquid substance that is to be measured. It should be noted that the 
invention can also be used for measuring a solid substance, for example, 
an organic substance having asymmetric carbon bonds, or any general 
optically active crystal such as quartz, cinnabar, or one of the sulfuric 
acid double salts from the alkali metals. The solid substance would be 
placed in the measuring cell 12 for carrying out the measurement. 
Referring to FIG. 2, there is shown a diagram plotting the output voltage 
U.sub.20 from the oscillator 20 as a function of the time t. The 
oscillator 20 supplies a constant output frequency f.sub.O. 
According to the diagram of FIG. 2A, there is shown the output signal from 
the frequency divider 21. The output signal U.sub.21 has a modulation 
frequency f.sub.F which is preferably at least one, and in particular, 
about two orders of magnitude smaller than the oscillator frequency 
f.sub.0. 
The photo current U.sub.16 from the detector 16 is shown in the diagram of 
FIG. 2B. The diagram indicates the noise of the photo current, or the 
voltage U.sub.16 proportional to the noise of the photo current, as well 
as the different mean amplitudes of the photo currents during both phases 
of the Faraday current. Using a vanishing angle of rotation .alpha..sub.M 
=0 within the measuring cell 12 allows both amplitudes to have the same 
value. 
After amplification of the photo current U.sub.16 and its integration, an 
output signal from the integrator 26 is obtained as shown in the diagram 
of FIG. 2D. The output signal U.sub.26 is reset, at times t.sub.3 and 
t.sub.7 by resetting pulses U.sub.22 having a length .tau..sub.R from 
t.sub.3 to t.sub.4 and from t.sub.7 to t.sub.8 as shown in FIG. 2C. 
According to the diagrams of FIGS. 2E and 2F, at times t.sub.1 to t.sub.2 
and t.sub.4 to t.sub.6, the control pulses U.sub.23 and U.sub.24 from the 
counting circuit 22 alternately switch the memories 27 and 28 into the 
sampling state. 
According to the diagrams of FIGS. 2G and 2H, the output voltages U.sub.27 
and U.sub.28 from the memories 27 and 28 change only during corresponding 
sample pulses .tau..sub.S + and .tau..sub.S -. The difference or the 
quotient Q from output voltages U.sub.27 and U.sub.28 furnish, after 
subtracting the constant volta U.sub.K, the measuring signal U.sub.A. The 
measuring angle U.sub.A is proportional to the angle of rotation 
.alpha..sub.M of the plane of polarization and thereby, to the 
concentration of the optically active substance contained in the measuring 
cell 12. 
This embodiment of the measuring apparatus produces a resolution for the 
angle of rotation of the plane of polarization given by the equation: 
EQU .DELTA..alpha..sub.M =5.times.(10.sup.-4) 
Referring to FIG. 3, there is shown another embodiment for an implantable 
glucose measuring polarimeter. In this embodiment, the light source 2, 
polarizer 4 and Faraday crystal 8 are cemented to each other. Imaging of 
the radiating crystal surface from the light source 2 on the detector 16 
is accomplished exclusively by the lens action obtained by the convex back 
surface 9 of the Faraday crystal 8. The transmission of the surface 9 is 
preferably enhanced by a .lambda./4 layer of silicon oxide SiO or a more 
highly oxidized mix of SiO.sub.x with 1&lt;x&lt;2. The measuring cell 12, having 
a length L, for example, L=27 mm, is closed off on its input side with a 
window 32. The window 32 is preferably a neutral glass window. The output 
side of the measuring cell 12 is closed off by the analyzer 14. Two holes 
34, 35 serve to allow the measuring liquid to flow through the cell 12. 
The liquid typically may be a filtered blood serum. Two pairs of electric 
terminals 36, 37 and 38, 39 are provided for coupling to the light source 
2 and the detector 16, respectively. The terminals used for the Faraday 
coil 7 are not shown in the figure for simplification. The indicated ray 
bundle is limited by the maximum usable angle opening 2 .nu..sub.max for 
the radiation emitted by the light source 2. 
In the embodiment of FIG. 3, in which the light source 2, the polarizer 4 
and the Faraday crystal 8 are cemented together by immersion layers, 
practically no reflection losses are obtained. Further, a mechanically 
strong assembly results. 
A relatively small, inexpensive and stable light source 2, preferably a 
light-emitting diode LED, can be provided which furnishes monochromatic 
radiation which can be modulated at high frequency. 
Because the light source 2 can be imaged on the detector 16 through the use 
of lenses, the maximum amplitude of the photo current and therefore, a 
favorable signal-to-noise ratio, are obtained. The convex back surface 9 
of the Faraday crystal 8 produces an immersion lens action with respect to 
the light source 2. This allows the utilization of the high index of 
refraction, for example, n=3.4 for gallium phosphide GaP when using a 
wavelength .lambda.=575 mm (yellow). By this means, the cost of the lenses 
for imagining the light source 2 on the detector can be saved altogether 
or at least partially reduced. A semiconductor laser diode is also 
suitable for use as the light source because of its high radiation output 
and the maximum measuring sensitivity achievable thereby. 
Preferably suited for the optical medium of the Faraday crystal 8 in the 
modulator 6 is an A.sub.III B.sub.V semiconductor crystal. These compounds 
have a large Verdet constant V, i.e., a strong Faraday effect is obtained 
with a relatively small magnetic field in the Faraday coil 7. An 
especially well suited compound is gallium phosphide having a Verdet 
constant V=4.5.times.10.sup.3 min/(T.times.cm) at a wavelength 
.lambda.=665 nm and a constant V=6.7.times.10.sup.3 min/(T.times.cm) for a 
wavelength .lambda.=560 nm. Preferably suited for the detector 16 is a 
silicon photo diode or a silicon photo cell. 
It is preferable to use a garnet, which can be produced in large crystals 
according to the Czochralski method, IG for the optical medium of the 
Faraday crystal 8. The garnet should have great purity and a large Faraday 
constant. One such garnet has a gadolinium-gallium base. These garnets are 
transparent throughout the entire visible spectral range. Also highly 
suited are iron garnets of the type M.sub.3 Fe.sub.4 O.sub.12, where M is 
one of the rare earth metals, particularly ytterbium, thulium, yttrium, 
erbium or holmium. These rare earth metals have a very large Faraday 
constant below the magnetic saturation, for example, V=4.times.10.sup.4 
min/(T.times.cm) for the yttrium--iron garnet (Y.sub.3 Fe.sub.5 O.sub.12) 
for a wavelength of .lambda.=1 .mu.m. Therefore, very short Faraday 
crystals 8 less than 1 mm in length can be used. The coil 7 surrounding 
the crystals 8 can thus be very small which again decreases the amount of 
electric energy required for generating the magnetic field. This is 
particularly important for the implantable glucose sensor, since only 
very-low-power supplies can be employed. 
In conjunction with iron garnets, an infrared light-emitting diode of 
gallium-indium-arsenide-phosphide Ga.sub.x In.sub.1-x As.sub.y P.sub.1-y 
is preferably used as the light source. This LED has an emission 
wavelength in the range 0.9 .mu.m.ltoreq..lambda..ltoreq.1.4 .mu.m and, 
more preferably, in the range of 1.0 .mu.m.ltoreq..lambda..ltoreq.1.11 
.mu.m. In this range, the radiation penetration depth in water is larger 
than 60 mm, so that cell lengths of this order of magnitude can be 
employed. Thereby, correspondingly low concentrations of the optically 
active substance, particularly glucose, can be measured. In conjunction 
with iron garnets, a germanium photo diode or a germanium photocell can be 
employed as the detector 16, especially for wavelengths in the range 1.0 
.mu.m.ltoreq..lambda..ltoreq.1.7 .mu.m. 
The Faraday coil's 7 control voltage U.sub.21, having the modulation 
frequency f.sub.F, is a symmetrical squarewave voltage as seen from the 
diagram of FIG. 2A. With this control voltage U.sub.21, the largest 
possible detector signal U.sub.16, for a given amplitude of the coil 
current, is obtained. The oscillator frequency f.sub.0 becomes 
approximately 100.times.f.sub.F and the modulation frequency f.sub.F is 
chosen .ltorsim.500 Hz. 
The oscillator frequency f.sub.0, representing the clock frequency f.sub.L 
of the light source 2, is preferably chosen to be substantially larger 
than the modulating frequency f.sub.F, as seen from the diagrams of FIGS. 
2 and 2A. The modulation frequency f.sub.F is preferably chosen to be in 
the range 50 Hz.ltoreq.f.sub.F .ltoreq.500 Hz. The clock frequency f.sub.L 
provides an increased light yield in conjunction with an LED light source 
2 by utilizing the nonlinear emission-operating current characteristic of 
the LED, especially in the visible range of the spectrum. Thereby, an 
improved signal-to-noise ratio is obtained and thus a higher measuring 
sensitivity. Using an oscillator frequency f.sub.0 as the clock frequency 
f.sub.L for the light source 2, the exact same number of radiation pulses 
from the light source 2 is obtained in each integration period without any 
additional circuitry cost. The integration period has a duration of 
1/(2.times.f.sub.F). This provides a measuring signal which is a highly 
stable measuring signal. 
The starting times t.sub.1 and t.sub.5 for the sample pulse time intervals 
.tau..sub.s+ and .tau..sub.s- of the sample-and-hold memories 27 and 28 
as well as the starting times t.sub.3 and t.sub.7 of the resetting time 
intervals .tau..sub.R for the integrator 26 are determined by counting out 
f.sub.O and f.sub.L periods during each period f.sub.F. Thereby, very 
accurate and equal integration times for each of the integral values to be 
stored in the two memories 27 and 28 are obtained. 
In the method of the present invention, an output signal is obtained having 
low noise and drift U.sub.A =(U.sub.27 /U.sub.28).times.U.sub.N -U.sub.K 
=Q-U.sub.K. The output signal U.sub.A is zero by a suitable choice of the 
constant voltage U.sub.K at a zero or background angle of rotation of the 
polarization plane in the measuring cell 12. The output signal is thus 
proportional as a measure for the desired concentration of the optically 
active substance to the angle of rotation .DELTA..alpha..sub.M caused by 
this substance. Therefore, U.sub.A .about..DELTA..alpha..sub.M. U.sub.N is 
the constant internal normalizing voltage of the divider 30. 
The primary measurement signal is the photo current i.sub.ph generated in 
the detector 16. The principal passage directions of the polarizer 4 and 
the analyzer 14 are perpendicular to each other, i.e., they are adjusted 
for minimum transmission. The direction of vibration corresponding to the 
situation when the polarized radiation strikes the analyzer 14 is 
characterized by the angle of rotation .alpha.=0 for the plane of 
vibration. The plane of polarization of the radiation leaving the 
polarizer 4 is alternately rotated the maximum angles .+-..alpha..sub.F of 
the same magnitude, by the a-c current of the frequency f.sub.F flowing 
through the Faraday coil 7. In the cell 12, the optically active substance 
causes a further rotation by the angle .alpha..sub.M proportional to the 
concentration C of the substance. Thereby, the photo current i.sub.ph 
oscillates with the frequency f.sub.F between a minimum value depending on 
the degree of polarization and the alternately generated extreme values as 
shown by Eq. (1). 
EQU i.sub.ph .+-.=sin.sup.2 (.+-..alpha..sub.F +.alpha..sub.M)+i.sub.u 
.times.cos.sup.2 (.+-..alpha..sub.F .+-..alpha..sub.M)=i.sub.u +(i.sub.o 
-i.sub.u).times.sin.sup.2 (.+-..alpha..sub.F +.sub.M). Eq. (1) 
With an alternating squarewave current in the Faraday coil 7, only the 
values i.sub.ph+ and i.sub.ph- are alternately generated. 
An ideal case has completely linear polarization of the radiation reaching 
the analyzer 14. In this case, the "depolarization component" i.sub.u =0. 
When the Faraday modulator 6 is turned off and the optically active 
substance in the measuring cell 12 is absent, i.e., with .alpha..sub.F 
=.alpha..sub.M =0, then the photo current i.sub.ph disappears. 
For the general case of incomplete polarization 0&lt;i.sub.u &lt;i.sub.o, the 
formation of the total current U.sub.16, having different amplitudes 
i.sub.ph+ and i.sub.ph-, is shown in FIG. 4. The depolarization component 
i.sub.u is shown exaggerated such that i.sub.u =i.sub.o /4. With 
commercially available polarizers, i.sub.u can be less than i.sub.o /100. 
If the ratio: 
EQU .epsilon.=iu/io=(1-p) Eq. (2) 
of Eq. (2) is introduced as a measure for the degree of polarization p of 
the radiation reaching the detector 16, then Eq. (1) for the two photo 
currents which are generated by the Faraday coil 7, assume the following 
form: 
EQU i.sub.ph .+-.=i.sub.o [.epsilon.+(1-.epsilon.).times.sin.sup.2 
(.+-..alpha..sub.F +.alpha..sub.M)]. Eq. (3) 
The photo current i.sub.ph is amplified in the amplifier 25 to form the 
voltage U.sub.v =v.times.i.sub.ph and is subsequently integrated by 
integrator 26 to form the two voltages 
##EQU1## 
where .tau..sub.J is the effective integration time. .tau..sub.J is fixed 
by the oscillator 20, the frequency divider 21 and the counting circuit 22 
and is equal to the time difference t.sub.5 -t.sub.4 between the end of a 
resetting pulse U.sub.22 at time t.sub.4 and the next following storage 
pulse U.sub.24 at time t.sub.5. The integrator 26 acts in a manner known 
per se as a mean value amplifier having adjustable gain. 
The integral values U.sub.I .+-. of alternately generated voltage U.sub.26 
are stored separately during the time intervals .tau..sub.s + and 
.tau..sub.S - defined by the voltage pulses U.sub.23 and U.sub.24. The 
changing contents of the memory and the additive constant voltage U.sub.K 
from the constant voltage source 29, allows the output voltage (U.sub.A) 
to be finally generated in the divider 30 as follows: 
##EQU2## 
The bars over i.sub.ph+ and i.sub.ph- in Eq. (5) indicate that each of the 
two photo currents are averaged over the corresponding period .tau..sub.J. 
U.sub.N, as mentioned above, is the internal normalizing voltage of the 
divider 30, for example, 10 V. If the constant voltage U.sub.K is set 
equal to the internal normalizing voltage U.sub.N, then one obtains: 
##EQU3## 
With the photo current calculated in accordance with Eq. (3), or the 
voltage U.sub.16 proportional thereto, the output signal normalized to the 
voltage U.sub.N is as follows: 
##EQU4## 
Similar to the integration of Eq. (4), the variables .alpha..sub.M, 
.alpha..sub.F and .epsilon. on the right side of Eq. (7) are interpreted 
as mean values over an integration period .tau..sub.J. Thereby, the output 
voltage U.sub.A and the normalized output signal y are also mean values 
having a corresponding reduced noise component. For a further reduction of 
the noise bandwidth, the divider 30 is preferably chosen to have a time 
constant .tau..sub.Q &gt;1/f.sub.F. 
For the case of small rotations in the plane of polarization (this is 
particularly important for determining glucose concentration) and a small 
Faraday rotation sin .alpha..sub.F &lt;&lt;1, for example, .alpha..sub.F 
=2.degree., sin .alpha..sub.F =0.035, then Eq. (7) simplifies to: 
##EQU5## 
In addition, if the radiation is linearly polarized to a sufficient 
degree, such that: 
##EQU6## 
then the fractional term in Eq. (8) can be neglected and the output signal 
becomes proportional to the angle of rotation .alpha..sub.M and therefore 
also to the concentration C of the optically active substance to be 
measured as shown by Eqs. (10) and (11), respectively. 
EQU y=4.times..alpha..sub.M /.alpha..sub.F Eq. (10) 
EQU U.sub.A =4.times.(.alpha..sub.M /.alpha..sub.F).times.U.sub.NEq. (11) 
According to the different possible algebraic representations of Eq. (5), 
as for example, shown in Eq. (5A) 
##EQU7## 
the output voltage U.sub.A can also be determined from the two output 
signals U.sub.27 and U.sub.28 in a manner known per se by a subtraction 
and subsequent division. Accurate adjustment of the null point for 
compensating small deviations between the photo currents i.sub.ph+ and 
i.sub.ph- or between the output signals U.sub.27 and U.sub.28 only 
requires the addition of a small offset voltage .gamma.U .gamma.U.sub.A 
=U.sub.N -U.sub.K when adjusting the analyzer 14 for minimum transmission. 
Therefore, the output circuitry of the two sample and hold memories 27 and 
28 in FIG. 1 can also be represented by an equivalent circuit diagram as 
shown in FIG. 5. 
In the circuit of FIG. 5, the difference voltage U.sub.31 =(U.sub.27 
-U.sub.29)/2 is formed in the subtractor 40. The subtractor 40 can 
include, for example, an inverter 31 and two resistors 42 and 43. 
Subsequently, the difference voltage U.sub.31 is divided by the output 
signal U.sub.28 in a divider 30, taking into consideration the factor 2. 
The constant-voltage source 44 only needs to supply the small offset 
voltage .gamma.U.sub.A, which for an ideal adjustment equals zero. 
In the embodiment according to FIG. 1, an analog signal processor is 
provided. The functional elements, shown in the lower part of FIG. 1 
however, can partially be replaced, for example, by a microprocessor. The 
microprocessor would function as the oscillator 20, the frequency divider 
21, the counting circuit 22 as well as the integrator 26, the 
sample-and-hold memories 27 and 28 and the divider 30 having the 
constant-voltage source 29. 
Further the embodiment according to FIG. 1 provides a Faraday modulator as 
the modulator 6. In some cases it may be advantageous to use a Kerr 
modulator in which an artificial birefringence is generated. Thereby, a 
rotation of the plane of polarization by the electric field strength also 
occurs.