Apparatus and method for optically measuring concentrations of components

What is claimed is:

1. An apparatus for optically measuring concentrations of components, comprising:

a cell for containing a sample therein;

means for presenting different optical path lengths to light transmitted through said cell;

a light irradiator for emitting light of a selected wavelength to the cell;

means for changing the wavelength of light emitted by said light irradiator;

a photodetector for receiving light that has been transmitted through the cell to detect a quantity of transmitted light; and

an arithmetic unit for calculating and storing, for each wavelength, an optimum optical path length of said different optical path lengths at which a peak value of quantity-of-light measuring sensitivity with respect to the quantity of transmitted light detected by the photodetector occur, for calculating a concentration of a component contained in the sample based on values of the quantity of transmitted light at the optimum optical path length, the values having been stored for each wavelength emitted by said light irradiator, and for outputting calculation results.

2. The apparatus for optically measuring concentrations of components according to claim 1, wherein said cell simultaneously presents continuously or stepwise different optical path lengths.

3. The apparatus for optically measuring concentrations of components according to claim 2, wherein different portions on said photodetector correspond to different optical path lengths simultaneously presented by said cell.

4. The apparatus for optically measuring concentrations of components according to claim 3, wherein a slope of an input face of said photodetector is parallel to a slope of an output face of said cell, such that a distance traversed by the transmitted light from said cell to said photodetector remains constant for light being transmitted through different optical path lengths internally in said cell.

5. The apparatus for optically measuring concentrations if components according to claim 1, wherein said cell has variable optical path length.

6. The apparatus for optically measuring concentrations of components according to any one of claims 1, 2 or 5, wherein said light irradiator is a laser.

7. The apparatus for optically measuring concentrations of components according to claim 6, wherein said laser is a variable-wavelength laser.

8. The apparatus for optically measuring concentrations of components according to any of claims 1, 2 or 5, wherein said light irradiator comprises a variable-wavelength laser, and a measuring system for enlarging and collimating a laser beam output from the variable-wavelength laser.

9. The apparatus for optically measuring concentrations of components according to any one of claims 1, 2 or 5, wherein said light irradiator comprises a rotatable mirror for, upon reception of a laser beam, changing a direction in which the laser beam is reflected, and a measuring system for directing the reflected laser beam toward a specified direction.

10. The apparatus for optically measuring concentrations of components according to any one of claims 1, 2 or 5 wherein said light irradiator comprises a light emitter for emitting light including different wavelengths, and a measuring system for collimating the emitted light and including a filter means for allowing light only of a selected wavelength out of the light including different wavelengths to be incident upon the cell.

11. The apparatus for optically measuring concentrations of components according to any one of claims 1, 2 or 5, further comprising a quantity-of-light detection means for detecting quantity of light when said photodetector has received selected light.

12. The apparatus for optically measuring concentrations of components according to any one of claims 1, 2 or 5, wherein said photodetector comprises a spectrometer.

13. A method for optically measuring concentrations of components, comprising the steps of:

selecting a wavelength to be emitted;

emitting light of the wavelength selected to a cell which contains a sample;

presenting different optical path length over which light is transmitted through said cell;

detecting a quantity of transmitted light for each of said different optical path lengths when a photodetector has received light transmitted through the cell;

repeating the above steps for a plurality of wavelengths;

calculating and storing for each wavelength of said plurality of wavelengths an optimum optical path length at which a peak value of quantity-of-light measuring sensitivity with respect to the quantity of transmitted light detected by the photodetector takes place; and

calculating concentration of a component contained in the sample based on values of the quantity of transmitted light at the optimum optical path length at peak positions for each of said plurality of wavelengths, and outputting calculation results.

14. A method for optically measuring concentrations of components, comprising the steps of:

(i) measuring quantity of transmitted light of a wavelength .lambda. that has been emitted from a light source and transmitted through a cell which does not contain a sample, and calculating a quantity of incident light I.sub.o by the following equation:

.sub.t =I.sub.o t.gamma.

wherein

I.sub.o =quantity of light incident upon the cell,

I.sub.t =quantity of light transmitted through the cell,

.gamma.=e x p (-.SIGMA..alpha..sub.i C.sub.i L-.alpha..sub.c l)

l=l.sub.1 +l.sub.2

t:t.sub.1 t.sub.2 t.sub.3 t.sub.4 =(n.sub.o, n.sub.c n)

t.sub.i =transmissivity at i interface,

.alpha..sub.i =extinction coefficient of i component (a function of wavelength),

.alpha..sub.c =extinction coefficient of the cell (a function of wavelength),

l.sub.1, l.sub.2 =wall thicknesses on both sides of the cell, and

n, n.sub.o, n.sub.c =refractive indexes of sample, air, and cell, respectively;

(ii) calculating a transmissivity t.sub.s that depends on a refractive index of the light of wavelength .lambda. in a reference concentration sample;

(iii) measuring a quantity of transmitted light I.sub.to of the light of wavelength .lambda. when an optical path length L within the cell is set to a reference optical path length L.sub.0, in a state that the cell contains the reference concentration sample;

(iv) calculating a value .gamma..sub.o of .gamma. or light with the reference optical path length L.sub.o and the wavelength .lambda. by the following equation:

I.sub.t =I.sub.o t.gamma.

(v) calculating an optical path length ratio k.sub.p corresponding to an optical path length L.sub.p at which quantity-of-light measuring sensitivity S reaches a maximum with the wavelength .lambda., by the following equation:

k=-1/log.sub.e (.gamma..sub.o.sup..delta.)

where

.delta.=e x p (.alpha..sub.c l)

the quantity-of-light measuring sensitivity S being defined by the following equation:

S=d I.sub.t /dC.sub.i

where

S=quantity-of-light measuring sensitivity,

dI.sub.t =variation of quantity of transmitted light I.sub.t based on variation dC.sub.i of i component concentration, and

dC.sub.i =variation of i component concentration,

(vi) calculating an optimum optical path length L.sub.p.lambda. at which the quantity-of-light measuring sensitivity S reaches a maximum with the wavelength .lambda., by the following equation:

k=L/L.sub.o

repeating the above steps a plurality of times with the wavelength .lambda. varied, to calculate values of quantity of transmitted light at positions of optimum optical path lengths L.sub.p.lambda. corresponding to the varied wavelengths .lambda., wherein concentration of a component contained in the sample is calculated by multivariate analysis based on the calculated values of quantity of transmitted light.

15. A method for optically measuring concentrations of components, comprising the steps of:

(i) measuring quantity of transmitted light of a wavelength .lambda. that has been emitted from a light source and transmitted through a cell wherein a sample is not contained and calculating a quantity of incident light I.sub.o by the following equation:

I.sub.t =I.sub.o t.gamma.

wherein

I.sub.o =quantity of light incident upon the cell,

I.sub.t =quantity of light transmitted through the cell,

.gamma.=e x p (-.SIGMA..alpha..sub.i C.sub.i L-.alpha..sub.c l)

l=l.sub.1 +l.sub.2

t:t.sub.1 t.sub.2 t.sub.3 t.sub.4 =(n.sub.o, n.sub.c n)

t.sub.i =transmissivity at i interface,

.alpha..sub.i =extinction coefficient of i component (a function of wavelength),

.alpha..sub.c =extinction coefficient of the cell (a function of wavelength),

C.sub.i =concentration of i component in the sample,

l.sub.1, l.sub.2 =wall thicknesses on both sides of the cell, and

n, n.sub.o, n.sub.c =refractive indexes of sample, air, and cell, respectively,

(ii) calculating a transmissivity t.sub.s that depends on a refractive index of the light of wavelength .lambda. in a reference concentration sample,

(iii) measuring a quantity of transmitted light I.sub.tL of the light of wavelength .lambda. when an optical path length L within the cell containing the reference concentration sample,

(iv) calculating absorbances to the light of wavelength .lambda. at portions of the cell corresponding to different optical path lengths L, by the following equation:

log.sub.e (I.sub.o /I.sub.t) -log.sub.e (1/t)-.alpha..sub.c 1=A.sub.c

where

A.sub.c =.SIGMA.,.alpha..sub.i C.sub.i L

(v) determining an absorbance A.sub.c.lambda.p equal to log.sub.e e from among the absorbances A.sub.c.lambda. to the light of wavelength .lambda., and

(vi) storing an optical path length L.sub.p corresponding to the absorbance A.sub.c.lambda.p to the light of wavelength .lambda.

repeating the above steps a plurality of times with the wavelength .lambda. varied, to calculate values of quantity of transmitted light at positions of optimum optical path lengths L.sub.p.lambda. corresponding to the varied wavelengths .lambda., wherein concentration of a component contained in the sample is calculated by multivariate analysis based on the calculated values of quantity of transmitted light.

16. An apparatus for optically measuring concentrations of components comprising:

a light irradiator for emitting light of a selected wavelength towards a cell containing a sample therein, where the light is collimated into a plurality of light beams by a light collimating means, before entering said cell;

wherein said cell presents simultaneous multiple optical path lengths where each one of the collimated light beams simultaneously traverses a different one of the simultaneous multiple optical path lengths;

means for changing the wavelength of light emitted by said light irradiator;

a photodetector for receiving said light beams which have transmitted through said cell to detect a quantity of the transmitted light beams;

an arithmetic unit for calculating and storing, for each wavelength of the emitted light, an optimum optical path length, based on said simultaneous multiple optical path lengths, at which a peak value of quantity-of-light sensitivity with respect to the quantity of transmitted light beams at the optimum optical path length, the values having been stored for each wavelength omitted by said light irradiator, and for outputting calculation results.

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BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an apparatus and a method for measuring concentrations of light-absorbing substances in an aqueous solution. More specifically, the invention relates to an apparatus and a method for optically measuring concentrations of components, which are applicable to measurement of, for example, concentrations of glucose and hemoglobin in blood, and concentrations of protein, bilirubin and saccharide in urine as well as concentrations of components in beverages.

2. Description of the Prior Art

It is well known that the relation between concentration of a solution and light absorption can be expressed by the following Lambert-Beer's law:

A.sub.c =Log.sub.e (I.sub.o /I.sub.t)=.SIGMA..alpha..sub.i C.sub.i L(1)

where

A.sub.c =absorbance,

I.sub.o =quantity of incident light,

I.sub.t =quantity of transmitted light,

.alpha..sub.i =extinction coefficient of i component in the sample,

C.sub.i =concentration of i component in the sample, and

L=optical path length within the cell containing the sample.

With regard to this equation, the concentration can be determined by performing multivariate analysis based on measured values of quantity of transmitted light on multiple wavelengths.

Since the concentrations of each component is determined based on measured values obtained by a measuring system, the accuracy of the concentration is limited by the measurement accuracy of the measuring system. Therefore, to determine the concentrations of components, particularly accurate concentrations of trace amounts of components out of the components to be measured, the measuring system is required to have an enhanced accuracy of measurement. Thus, the accuracy of the concentrations determined has a close relation to the S/N ratio of the measuring system.

Japanese Patent Laid-Open Publication No. 63-144237 (1988) has disclosed a method for measuring absorbances and an apparatus for the same, which are applicable to quantitative determination of trace amounts of organic and inorganic components in a sample solution.

This apparatus comprises a cell for a spectrophotometer having different cell lengths (i.e., optical path lengths, which herein mean distances over which light travels within a cell), a feeder for feeding a sample solution to the cell, a switching unit for switching over the optical path length, and a controller for controlling the feeder and the switching unit. According to this apparatus, measurement of absorbances of sample solutions is carried out based on the quantity of transmitted light at a portion of the cell corresponding to the short optical path length for high concentration samples or the quantity of transmitted light at another portion of the cell corresponding to the long optical path length for low concentration samples.

The above measuring method and apparatus incorporate a cell for a spectrophotometer, actually a triangular cell, having different optical path lengths, wherein the optical path length is switched over so that the absorbance falls within a range suited for measurement. Thus, the measuring method and apparatus are intended to accomplish a wide range of concentration measurement from low concentration sample solutions to high concentration sample solutions without necessitating dilution of the sample solution or exchange of the cell.

In the above measuring method and apparatus, the optical path length is switched to a path length such that the absorbance falls within a range suited for measurement depending on differences in concentration among sample solutions, without changing the wavelength of light applied to samples. However, for example, when one component contained in the samples is of almost the same concentration among the samples, like glucose in blood, the method and apparatus have a disadvantage that they could not enhance the measurement accuracy of the concentration of this component.

SUMMARY OF THE INVENTION

The present invention has been accomplished to solve the above problems of the prior art. An object of the invention is therefore to provide an apparatus and a method for optically measuring concentrations of components, which are capable of enhancing the measurement accuracy of concentrations, regardless of whether the differences in concentration of one component contained in samples are large or small.

To achieve the above object, according to a first aspect of the present invention, there is provided an apparatus for optically measuring concentrations of components, which comprises: a cell for containing a sample therein, the cell being capable of changing its internal optical path length; a light irradiator for irradiating light of a selected wavelength to the cell, the light irradiator being capable of changing the wavelength of to be irradiated; a photodetector for receiving light that has been transmitted through the cell to detect quantity of the transmitted light; and an arithmetic unit for calculating and storing for each wavelength an optical path length at which a peak value of quantity-of-light measuring sensitivity with respect to the quantity of transmitted light detected by the photodetector takes place, and calculating concentration of a component contained in the sample based on values of the quantity of transmitted light and values of the optical path length at peak positions, the values having been stored for each wavelength, and for outputting calculation results.

As a second aspect of the present invention, the cell has a continuously or stepwise different optical path lengths.

As a third aspect of the present invention, the cell has a variable optical path length.

As a fourth aspect of the present invention, the light irradiator has a laser generator capable of generating laser beams of different wavelengths.

As a fifth aspect of the present invention, the laser generator is a variable-wavelength laser generator.

As a sixth aspect of the present invention, the light irradiator comprises a variable-wavelength laser generator, and a measuring system for making laser beams from the variable-wavelength laser generator incident upon the cell in such a form that the laser beam has been enlarged in its beam cross-sectional area and formed into collimated light.

As a seventh aspect of the present invention, the light irradiator comprises a rotatable mirror for, upon reception of a laser beam, changing a direction in which the laser beam is reflected, and a measuring system for directing the reflected laser beam toward a specified direction.

As an eighth aspect of the present invention, the light irradiator comprises a light emitter for emitting light including different wavelengths, and a measuring system for allowing light only of a selected wavelength out of the light to become incident on the cell in the form of collimated light.

As a ninth aspect of the present invention, the apparatus for optically measuring concentrations of components further comprises a quantity-of-light detection means for detecting quantity of light when said photodetector has received selected light.

As a tenth aspect of the present invention, the photodetector comprises a spectrometer.

As an eleventh aspect of the present invention, there is provided a method for optically measuring concentrations of components, which comprises: a step for irradiating light of a wavelength selected by a light emitter capable of generating light of different wavelengths, to a cell which contains a sample therein and which is capable of changing optical path length over which light is transmitted; a step for detecting quantity of transmitted light for each optical path length when the photodetector has received light transmitted through the cell, the above steps being repeatedly performed for a plurality of wavelengths; and a step for calculating and storing for each wavelength an optical path length at which a peak value of quantity-of-light measuring sensitivity with respect to the quantity of transmitted light detected by the photodetector takes place, and calculating concentration of a component contained in the sample based on values of the quantity of transmitted light and values of the optical path length at peak positions, and for outputting calculation results, the step being performed by an arithmetic unit.

As a twelfth aspect of the present invention, the method comprises:

(i) a step for measuring quantity of transmitted light of a wavelength .lambda. that has been emitted from a light source and transmitted through a cell which does not contain a sample and calculating a quantity of incident light I.sub.o by the following equation:

I.sub.t =I.sub.o t.gamma.

where

I.sub.o =quantity of light incident upon the cell,

I.sub.t =quantity of light transmitted through the cell,

.gamma.=exp (-.SIGMA..alpha..sub.i C.sub.i L-.alpha..sub.c 1)

l=l.sub.1 +l.sub.2

t:t.sub.1 t.sub.2 t.sub.3 t.sub.4 =t(n.sub.o, n.sub.c n)

t.sub.i =transmissivity at i interface,

.alpha..sub.i =extinction coefficient of i component (a function of wavelength),

.alpha..sub.c =extinction coefficient of the cell (a function of wavelength),

C.sub.i =concentration of i component in the sample,

l.sub.a, l.sub.2 =wall thicknesses on both sides of the cell, and

n, n.sub.o, n.sub.c refractive indexes of sample, air, and cell, respectively,

(ii) a step for calculating a transmissivity t.sub.s that depends on the refractive index of a reference concentration sample to the light of wavelength .lambda.,

(iii) a step for measuring a quantity of transmitted light I.sub.to of the light of wavelength .lambda. when an optical path length L within the cell is set to a reference optical path length L.sub.o, in a state that the cell contains the reference concentration sample,

(iv) a step for calculating a value .gamma..sub.o of .gamma. for light with the reference optical path length L.sub.o and the wavelength .lambda. by the following equation:

I.sub.t =I.sub.o t.gamma.

(v) a step for calculating an optical path length ratio k.sub.p corresponding to an optical path length L.sub.p at which quantity-of-light measuring sensitivity S reaches a maximum with the wavelength .lambda., by the following equation:

k=-1/log.sub.e (.gamma..sub.o .delta.)

where

.delta.=exp(.alpha..sub.c l)

the quantity-of-light measuring sensitivity S being defined by the following equation:

S=dI.sub.t /d C.sub.i

where

S =quantity-of-light measuring sensitivity,

dI.sub.t =variation of quantity of transmitted light I.sub.t based on variation dC.sub.i of i component concentration, and

dC.sub.i =variation of i component concentration,

(vi) a step for calculating an optimum optical path length L.sub.p.lambda. at which the quantity-of-light measuring sensitivity S reaches a maximum with the wavelength .lambda., by the following equation:

k=L/L.sub.o

the above steps being performed repeatedly a plurality of times with the wavelength .lambda. varied, to calculate values of quantity of transmitted light at positions of optimum optical path lengths L.sub.p.lambda. corresponding to the varied wavelengths .lambda., wherein concentration of a component contained in the sample is calculated by multivariate analysis based on the calculated values of quantity of transmitted light.

As a thirteenth aspect of the present invention, the method comprises:

(i) a step for measuring quantity of transmitted light of a wavelength .lambda. that has been emitted from a light source and transmitted through the cell which does not contain a sample and calculating a quantity of incident light I.sub.o by the following equation:

I.sub.t =I.sub.o t.gamma.

where

I.sub.o =quantity of light incident upon the cell,

I.sub.t =quantity of light transmitted through the cell,

.gamma.=exp(-.SIGMA..alpha..sub.i C.sub.i L-.alpha..sub.c l).

l=l.sub.1, l.sub.2

t:t.sub.1 t.sub.2 t.sub.3 t.sub.4 =t(n.sub.o, n.sub.c, n)

t.sub.i =transmissivity at i interface,

.alpha..sub.i =extinction coefficient of i component (a function of wavelength),

.alpha..sub.c =extinction coefficient of the cell (a function of wavelength),

C.sub.i =concentration of i component in the sample,

l.sub., l.sub.2 =wall thicknesses on both sides of the cell, and

n, n.sub.o, n.sub.c =refractive indexes of sample, air, and cell, respectively,

(ii) a step for calculating a transmissivity t.sub.s that depends on the refractive index of the light of wavelength .lambda. in a reference concentration sample,

(iii) a step for measuring a quantity of transmitted light I.sub.tL of wavelength with an optical path length L within the cell containing the reference concentration sample,

(iv) a step for calculating absorbances A.sub.c.lambda. to the light of wavelength .lambda. at portions of the cell corresponding to different optical path lengths L, by the following equation:

log.sub.e (I.sub.o /I.sub.t)-log.sub.e (1/t)-.alpha..sub.c l=A.sub.c

where

A.sub.c =.SIGMA..alpha..sub.i C.sub.i L

(v) a step for determining an absorbance A.sub.c.lambda.p equal to log.sub.e e from among the absorbances A.sub.c.lambda. to the light of wavelength .lambda., and

(vi) a step for storing an optical path length L.sub.p corresponding to the absorbance A.sub.c.lambda.p to the light of wavelength .lambda., the above steps being performed repeatedly a plurality of times with the wavelength .lambda. varied, to calculate values of quantity of transmitted light at positions of optimum optical path lengths L.sub.p.lambda. corresponding to the varied wavelengths .lambda., wherein concentration of a component contained in the sample is calculated by multivariate analysis based on the calculated values of quantity of transmitted light.

with the above-described arrangements, it becomes possible to determine concentrations of components in a sample from the quantity of transmitted light in such a state that the S/N ratio reaches a maximum for each wavelength.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram showing the outline of an apparatus for optically measuring concentrations of components according to the first, second, fourth, fifth, sixth and ninth aspects of the present invention, to which a method for optically measuring concentrations of components according to the eleventh, twelfth, and thirteenth aspects of the invention is applied;

FIG. 2 is an enlarged sectional view of the cell the apparatus shown in FIG. 1;

FIG. 3 is a chart showing measurement results of the relation between variation of quantity of transmitted light and wave number in a glucose solution, measured by an apparatus as shown in FIG. 13;

FIG. 4 is a chart showing measurement results of the relation between variation of quantity of transmitted light and wave number in solutions containing hemoglobin at two kinds of concentrations, measured by the apparatus as shown in FIG. 13;

FIG. 5 is a chart showing the relation between optical path length ratio and variation ratio of quantity of transmitted light in a solution containing hemoglobin;

FIG. 6 is a chart showing the relation between optical path length ratio and variation ratio of quantity of transmitted light in a solution containing albumin;

FIG. 7 is a chart showing the relation between optical path length ratio and variation ratio of quantity of transmitted light in a solution containing glucose;

FIG. 8 is a diagram showing a modification example of the cell in the apparatus shown in FIG. 1;

FIG. 9 is a diagram showing the outline of an apparatus for optically measuring concentrations of components according to the first, third, fourth, fifth, and ninth aspects of the present invention, to which the method for optically measuring concentrations of components according to the eleventh, twelfth, and thirteenth aspects of the present invention is applied;

FIG. 10 is a diagram showing the outline of an apparatus for optically measuring concentrations of components according to the first, second, fourth, fifth, seventh, and ninth aspects of the present invention, to which the method for optically measuring concentrations of components according to the eleventh, twelfth, and thirteenth aspects of the present invention is applied;

FIG. 11 is a diagram showing a cell and a photodetector used instead of the cell and the photodetector shown in FIG. 10;

FIG. 12 is a diagram showing the outline of an apparatus for optically measuring concentrations of components according to the first, third, eighth, and ninth aspects of the present invention, to which the method for optically measuring concentrations of components according to the eleventh, twelfth, and thirteenth aspects of the present invention is applied;

FIG. 13 is a diagram showing the outline of an apparatus for optically measuring concentrations of components according to the first, third, eighth, and tenth aspects of the present invention, to which the method for optically measuring concentrations of components according to the eleventh, twelfth, and thirteenth aspects of the present invention is applied;

FIG. 14 is a diagram showing a light-irradiating means used instead of the lamp shown in FIG. 13 or the laser of FIGS. 1, 9, and 10; and

FIG. 15 is a diagram showing another light-irradiating means used instead of the lamp in the apparatus shown in FIG. 13.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

An embodiment of the present invention is now described with reference to the accompanying drawings.

FIG. 1 shows an apparatus for optically measuring concentrations of components according to the first, second, fourth, fifth, sixth, and ninth aspects of the present invention, to which a method for optically measuring concentrations of components according to the eleventh, twelfth, and thirteenth aspects of the invention is applied. This apparatus comprises a cell 1, a light irradiator 2, a photodetector 3, and an arithmetic unit 4.

The cell 1 is formed from a transparent member into a triangular shape in its cross section, and adapted to contain therein a sample 11 such as blood or urine. The cell 1 is arranged to be able to change its internal optical path length by changing the position in which the light is transmitted though the cell 1.

The light irradiator 2 comprises a variable-wavelength laser generator 12 capable of generating laser beams of different wavelengths, and a measuring system 15 composed of lenses 13, 14. A laser beam from the variable-wavelength laser generator 12 is focused on the focal point and then diverged by the lens 13 so that the laser beam is enlarged in cross-sectional area more than original, and further formed into collimated light by the lens 14. Then, the laser is incident upon the cell 1. It is noted that for the present invention the measuring system 15 is not limited to the combination of the lenses 13, 14 as far as the laser beam can be enlarged in cross-sectional area and formed into collimated light.

The photodetector 3 is provided by a quantity-of-light detection means 16, e.g. a CCD, composed of a multiplicity of quantity-of-light detection elements 16a, e.g. pixels, arranged in parallel to the surface of the cell 1 through which light goes out. Thus, it is possible to detect quantities of transmitted light that have traveled over different optical path lengths within the cell 1 at positions of an equal distance from the cell

The arithmetic unit 4 receives a signal of quantity of transmitted light from the quantity-of-light detection elements 16a while it is connected to the variable-wavelength laser generator 12. Thus, the arithmetic unit 4 is capable of obtaining correspondence among the signal of quantity of transmitted light, optical path length and wavelength of transmitted light. In this arrangement, the arithmetic unit 4 derives an optimum optical path, at which the quantity-of-transmitted-light measuring sensitivity shows peak value, based on the above-described Lambert-Beer's formula (1) and Fresnel's formula, and calculates concentrations of components in the sample 11, such as those of glucose, hemoglobin, protein, bilirubin, and saccharide, based on the value of quantity of transmitted light at the position resulting the peak value. Then, the arithmetic unit 4 outputs calculation results.

More specifically, the calculation of component concentrations is accomplished by the following equations:

The quantity of transmitted light I.sub.t can be expressed by the following equation:

I.sub.t =I.sub.o t.gamma. (2)

where

.gamma.=exp (=.SIGMA..alpha..sub.i C.sub.i L-.alpha..sub.c l)

l=l.sub.1 +l.sub.2

t:t.sub.i t.sub.2 t.sub.3 t.sub.4 =t (n.sub.o, n.sub.c, n)

t.sub.i =transmissivity at i interface,

.alpha..sub.i =extinction coefficient of i component (a function of wavelength),

.alpha..sup.c =extinction coefficient of the cell 1 (a function of wavelength),

C.sub.i =concentration of i component in the sample 11,

l.sub.1, l.sub.2 =wall thicknesses on both sides of the cell 1, as shown in FIG. 2, and

n, n.sub.o, n.sub.c =refractive indexes of sample, air, and cell 1, as shown in FIG. 2, respectively.

Note that the l, .alpha..sub.c, n.sub.o, and n.sub.c, are previously calculated. Also the t, .alpha..sub.i, and n are previously calculated by the measurement using a plurality of liquid samples whose concentrations are known. ##EQU1## where

A.sub.n =log.sub.e (1/t)+.alpha..sub.c l

A.sub.c =.SIGMA..alpha..sub.i C.sub.i L (4)

A:assumed absorbance

where A.sub.n is a function of the refractive indexes of the cell and aqueous solution, the extinct/on coefficient of the cell, and the wall thicknesses of the cell, while A.sub.c is a function of the extinction coefficient of the solution, concentrations of components in the solution, and the optical path length L as shown in FIG. 2. They are commonly called absorbances.

For example, in the case of a glucose aqueous solution, where .SIGMA.C.sub.i =1, then ##EQU2##

Further, the quantity-of-light measuring sensitivity S for the i component in the sample 11 is defined as follows:

S=dI.sub.t dC.sub.i (5)

where

dI.sub.t =variation of quantity of transmitted light

I.sub.t based on variation of i component concentration dC.sub.i,

dC.sub.i =variation of i component concentration.

From Eq. (5), ##EQU3## where .eta.=dn/dC.sub.i

In this case, dC.sub.i is equal to -dC.sub.w since C.sub.i +C.sub.w =1.

Substituting S.sub.n for the first term of the right side of Eq. (6) and S.sub.c for the second term yields

S=S.sub.n +S.sub.c (7)

With respect to the quantity-of-light measuring sensitivity S, S.sub.n of the right side of Eq. (7) represents a term that depends on the refractive index and S.sub.c represents a term that depends on the light absorption of each component.

In the equation (3) representing the assumed absorbances A, A.sub.n denotes an apparent absorbance based on the refractive index of a measurement object and the material of the cell, and A.sub.c depends linearly on the concentration of the sample that is the measurement object. Similarly, also in the quantity-of-light measuring sensitivity S, S.sub.n is an apparent quantity-of-light measuring sensitivity. Therefore, S.sub.n can be treated as a term for correction in the processing by electric circuits or in data arithmetic operations, like A.sub.n.

Hence, the quantity-of-light measuring sensitivity that depends directly on the concentration of the measurement object is defined as

S.sub.c =S-S.sub.n (8)

With the quantity-of-light measuring sensitivity at a wavelength .lambda. assumed as S.sub.c.lambda., Eq. (8) is reduced to

S.sub.c.lambda. =S.sub..lambda. -S.sub.n.lambda. (9)

Then

S.sub.c.lambda. /S.sub.n.lambda. =f(L, n, .alpha..sub.w -.alpha..sub.i, .eta.) (10)

Thus, from Eqs. (6) and (9) ##EQU4## Since

dS.sub.c.lambda. /dL=0 (12)

the following equation results:

1-.SIGMA..alpha..sub.j.lambda. C.sub.j L=0

Hence, the following expression can be obtained:

L=1/.SIGMA..alpha..sub.i.lambda. C.sub.j (Let Lbe L.sub.p.lambda.)

At this point, the quantity-of-light measuring sensitivity S.sub.c.lambda. reaches a maximum, the maximum value being expressed as S.sub.c.lambda.max.

Also, the absorbance A.sub.p (=log.sub.e (I.sub.o /I.sub.p.lambda.)) at this point is

-A.sub.p =.multidot..SIGMA..alpha..sub.i C.sub.i =1

As shown above, with respect to light of one wavelength .lambda., there exists an optimum optical path length L.sub.p.lambda. that brings the quantity-of-light measuring sensitivity S.sub.c.lambda. to a maximum value S.sub.c.lambda.max.

More specifically, the optical path length L.sub.p.lambda. can be calculated from a ratio of quantity-of-light measuring sensitivities S.sub.c.lambda. at different optical path lengths, as shown below.

From the equation

S.sub.c.lambda.L =I.sub.o t(.alpha..sub.w -.alpha..sub.i).gamma.L(14)

the absorption-dependent term S.sub.c.lambda.Lo of the quantity-of-light measuring sensitivity at the reference optical path length L.sub.o can be expressed by the following equation:

S.sub.c.lambda.Lo =I.sub.o t(.alpha..sub.w -.alpha..sub.i).gamma..sub.o L.sub.l (15)

If the ratio of S.sub.c.lambda.L to S.sub.c.lambda.Lo is set to M, then ##EQU5## where

k=L/L.sub.o (17)

.delta.=exp (.alpha..sub.c l)

where .delta. is determined by the previously determined .alpha..sub.c and