Patent Publication Number: US-11385168-B2

Title: Spectroscopic analysis apparatus, spectroscopic analysis method, and readable medium

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a National Stage of International Application No. PCT/JP2015/006225 filed Dec. 14, 2015, claiming priority based on Japanese Patent Application No. 2015-071618 filed Mar. 31, 2015, the contents of all of which are incorporated herein by reference in their entirety. 
     TECHNICAL FIELD 
     The present invention relates to a spectroscopic analysis apparatus, a spectroscopic analysis method, and a readable medium, and more particularly, to a spectroscopic analysis apparatus, a spectroscopic analysis method, and a readable medium that perform an analysis using spectra obtained by dispersing light generated in a sample. 
     BACKGROUND ART 
     Patent Literature 1 discloses a spectroscopic analysis apparatus in which DNA testing is performed using spectral data. In Patent Literature 1, a sample including DNA fragments labeled by fluorescent substances is irradiated with excitation light. By spectroscopically measuring the fluorescence generated in the sample, an observed spectrum is measured. By performing a matrix operation using a generalized inverse on spectral data, concentrations of the fluorescent substances are obtained. 
     CITATION LIST 
     Patent Literature 
     Patent Literature 1: International Patent Publication No. WO 2014/045481 
     SUMMARY OF INVENTION 
     Technical Problem 
     However, there is a problem that, when noise components are included in the spectral data, an accurate analysis cannot be performed. 
     The present invention aims to provide a spectroscopic analysis apparatus, a spectroscopic analysis method, and a readable medium capable of appropriately analyzing the sample. 
     Solution to Problem 
     A spectroscopic analysis apparatus according to an aspect of the present invention includes: a light source configured to generate light to be incident on a sample including a plurality of substances labeled by a plurality of labeled substances; a spectrometer configured to disperse observed light generated in the sample by the light incident on the sample; a detector configured to detect the observed light dispersed by the spectrometer to output observed spectral data; and a processor configured to analyze the plurality of substances included in the sample based on the observed spectral data output from the detector, the processor analyzing the substances included in the sample from the observed spectral data using a generalized inverse of a matrix having, as elements, reference spectral data set for the plurality of labeled substances and data of a noise component. 
     A spectroscopic analysis method according to an aspect of the present invention includes: irradiating a sample with light, the sample including a plurality of substances labeled by a plurality of labeled substances; dispersing observed light generated in the sample by the light incident on the sample; detecting the observed light that has been dispersed to output observed spectral data; obtaining a generalized inverse of a matrix having, as elements, a reference spectral data set for the plurality of labeled substances and data of a noise component; and analyzing the substances included in the sample using the generalized inverse and the observed spectral data. 
     A readable medium according to an aspect of the present invention is a readable medium storing a program for causing a computer to execute a spectroscopic analysis method for analyzing a sample using observed spectral data obtained by spectroscopically measuring light generated in the sample including a labeled substance, in which the spectroscopic analysis method includes: obtaining a generalized inverse of a matrix having, as elements, a reference spectral data set for a plurality of labeled substances and data of a noise component; and analyzing the substances included in the sample using the generalized inverse and the observed spectral data. 
     Advantageous Effects of Invention 
     According to the present invention, it is possible to provide a spectroscopic analysis apparatus, a spectroscopic analysis method, and a readable medium capable of appropriately analyzing the sample. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a diagram schematically showing a configuration of a spectroscopic analysis apparatus according to an embodiment of the present invention; 
         FIG. 2  is a graph showing spectra of fluorescence generated from fluorescent substances that label DNA and spectra of noise components; 
         FIG. 3  is a diagram showing a matrix calculation expression for performing DNA analysis; 
         FIG. 4  is a diagram showing a matrix calculation expression for performing the DNA analysis; 
         FIG. 5  is a diagram showing a matrix calculation expression for performing the DNA analysis; 
         FIG. 6  is a diagram showing data of a generalized inverse of a matrix A; and 
         FIG. 7  is a block diagram showing a configuration of a spectroscopic analysis apparatus according to another embodiment. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     With reference to the accompanying drawings, an embodiment of the present invention will be described. The embodiment described below is examples of the present invention and the present invention is not limited to the following embodiment. Throughout the specification and the drawings, the same components are denoted by the same reference symbols. 
     In this embodiment, a DNA base sequence analysis is performed using a plurality of fluorescent substances having emission wavelengths different from one another. Specifically, DNA is extracted from human cells. DNA fragments are amplified by a polymerase chain reaction (PCR) and are labeled by the fluorescent substances. The fluorescent substances may be, for example, 5-FAM, JOE, NED, and ROX. As a matter of course, the fluorescent substances used for the labeling are not particularly limited. In this example, a plurality of fluorescent substances having peak wavelengths different from one another are used for the labeling. Different bases are labeled by different fluorescent substances. 
     Different PCR products labeled by fluorescence are supplied to a capillary and are electrophoresed in gel. In a state in which a voltage is applied by electrophoresis, the migration velocity varies depending on the size of the DNA fragment. The migration distance increases as the number of bases decreases. It is therefore possible to separate the DNA fragments by size. When PCR products in the capillary are irradiated with excitation light emitted from a light source, fluorescence is generated from fluorescent substances. The fluorescence generated from the fluorescent substances is spectroscopically measured to obtain observed spectral data. The observed spectral data is obtained for each size of the DNA fragments. By analyzing these observed spectral data, it is possible to quantify DNA of a particular sequence and to execute DNA testing. 
     While the spectroscopic analysis apparatus is used for DNA testing in this embodiment, the spectroscopic analysis apparatus according to this embodiment is not limited to being applied to the DNA testing. This embodiment can be applied to a spectroscopic analysis apparatus that analyzes the spectrum of the fluorescence generated from the sample that has labeled the substances by a fluorescence probe. It is possible, for example, to analyze nucleic acid, proteins and the like. The spectroscopic analysis apparatus may be used to identify the substances, for example. Further, it is possible to label the substances included in the sample by labeled substances other than the fluorescent substances. The labeled substances may be preferably substances having different light peak wavelengths. 
     With reference to  FIG. 1 , the spectroscopic analysis apparatus according to the present invention will be described.  FIG. 1  is a diagram showing a configuration of the spectroscopic analysis apparatus. The spectroscopic analysis apparatus includes an injection part  11 , a capillary  12 , a light source  13 , a spectrometer  14 , a detector  15 , a processor  16 , a microchip  20 , and optical fibers  31 . In this example, an analysis is performed using capillary electrophoresis. 
     PCR products including DNA fragments labeled by fluorescent substances are injected into the injection part  11 . In this example, the DNA fragments, which correspond to the sample, are labeled by a plurality of fluorescent substances. For example, fluorescent substances such as 5-FAM, JOE, NED, and ROX are used depending on the base sequence of the DNA fragments. As a matter of course, the type and the number of the fluorescent substances used for the labeling are not particularly limited. 
     The injection part  11  is communicated with the capillary  12  on the microchip  20 . Electrodes (not shown) are arranged on the respective ends of the capillary  12  provided in the microchip  20  and voltages are applied to the electrodes. The capillary  12  and the injection part  11  are filled with an electrophoresis medium such as agarose gel. Accordingly, since the electrophoretic velocity becomes low in accordance with the number of bases of the DNA fragments, the DNA fragments are separated by size. 
     The light source  13  generates light to be incident on the medium in the capillary. The light source  13  may be, for example, an argon ion laser light source that emits excitation light having a wavelength of 488 nm or 514.5 nm. 
     The light emitted from the light source  13  is incident on the capillary  12 . In this example, 8-lane capillaries  12  are provided in parallel in the microchip  20 . When the 8-lane capillaries  12  are irradiated with excitation light, the fluorescent substances that label the DNA fragments in the capillary  12  generate fluorescence. The fluorescence generated by the fluorescent substances becomes observed light. 
     The fluorescence generated by the fluorescent substances in the sample propagates through the optical fiber  31  and is then input to the spectrometer  14 . The spectrometer  14  includes, for example, a prism or diffraction grating, and disperses the fluorescence. In summary, the fluorescence is spatially dispersed in accordance with the wavelength. The fluorescence spatially dispersed by the spectrometer  14  is input to the detector  15 . Accordingly, the fluorescence generated by the fluorescent substances becomes observed light observed by the detector. 
     The detector  15  is, for example, a photodetector such as a CCD sensor, and pixels are arranged along a dispersion direction. Specifically, the detector  15  is a two-dimensional array photodetector in which pixels are arranged along X and Y directions. The X direction and the Y direction are directions perpendicular to each other. The X direction corresponds to a spectroscopic direction and the Y direction corresponds to the direction perpendicular to the spectroscopic direction. Accordingly, fluorescence having wavelengths different from one another is detected for each of the pixels arranged in the dispersion direction (spectroscopic direction). 
     The detector  15  detects the fluorescence from the fluorescent substances that have labeled the DNA fragments and outputs the detection signal to the processor  16 . For example, spectra in a wavelength region of 200 to 800 nm are measured by the spectrometer  14  and the detector  15 . The number of pieces of data included in the spectral data varies in accordance with the dispersion performance or the like of the spectrometer  14 . As a matter of course, the wavelength region that can be spectroscopically measured by the spectrometer  14  and the detector  15  is not particularly limited. The wavelength region can be appropriately set in accordance with the fluorescent substance used as a label and the excitation light wavelength. 
     The detector  15  outputs to the processor  16  the light intensity in each wavelength in the wavelength region that can be observed as observed spectral data. The number of pieces of data included in the observed spectral data varies in accordance with the dispersion performance or the like of the spectrometer  14 . 
     The processor  16  is an information processing device such as a personal computer, and performs processing in accordance with a control program. Specifically, the processor  16  stores an analysis program that analyzes the observed spectral data output from the detector  15 . The processor  16  executes processing in accordance with the analysis program. The processor  16  analyzes the plurality of substances included in the sample based on the observed spectral data output from the detector  15 . The concentrations of the DNA fragments are thus obtained. It is therefore possible to perform DNA testing. 
     The processing in the processor  16  is one of the characteristics of the spectroscopic analysis method according to this embodiment. The processor  16  analyzes the substances included in the sample from the observed spectral data using a generalized inverse of a matrix having, as elements, reference spectral data set for the plurality of fluorescent substances and data of noise components. 
     In the following description, the processing in the processor  16  will be described.  FIG. 2  is a diagram schematically showing the spectra of the fluorescent substances that have labeled the DNA fragments. In this example, a case in which the DNA fragments are labeled using five fluorescent substances will be described. 
       FIG. 2  shows spectral data of the five fluorescent substances and the noise components. The horizontal axis indicates a wavelength (nm) and the vertical axis indicates a signal intensity. The spectra obtained from the five fluorescent substances are denoted by reference spectra  51 - 55 . That is, the fluorescent spectra when the excitation light is incident on the respective fluorescent substances are denoted by the reference spectra  51 - 55 . That is, the fluorescent spectra of the first fluorescent substance to the fifth fluorescent substance are denoted by the reference spectra  51 - 55 . 
     Further, a spectrum in a case in which there is no fluorescent substance is denoted by a stray light noise  56 . That is, the stray light noise  56  includes the spectral data spectroscopically measured in the state in which there is no fluorescent substance. The reference spectra  51 - 55  and the stray light noise  56  are normalized in such a way that the peak values (maximum values) thereof become 1. Further, data which has a fixed value irrespective of the wavelength is denoted by an offset noise  57 . Since the offset noise  57  is normalized in a similar way, the offset noise  57  has a value of 1, which is a fixed value. 
     The reference spectra  51 - 55  of the fluorescent substances are known and vary for each fluorescent substance. That is, the reference spectra have peak wavelengths different from one another. For example, the reference spectrum  51  has its peak at about 280 nm. The reference spectrum  52  has its peak at about 350 nm. The reference spectrum  53  has its peak at about 410 nm. The reference spectrum  54  has its peak at about 570 nm. The reference spectrum  55  has its peak at about 610 nm. Further, the stray light noise  56  has its peak at 420 nm. 
     The observed spectrum detected by the detector  15  is obtained by overlapping the spectra obtained by multiplying the reference spectra  51 - 55  shown in  FIG. 2  in accordance with the concentrations of the fluorescent substances. Accordingly, by analyzing the observed spectral data to obtain the concentration of each fluorescent substance, the distribution of the concentration of each base can be obtained. 
     Further, the observed spectrum detected by the detector  15  is obtained by overlapping the stray light noise  56  and the offset noise  57 . Further, the level of the stray light noise  56  and that of the offset noise  57  vary with time. Therefore, the concentration of each fluorescent substance included in the sample is obtained after taking into consideration of the stray light noise  56  and the offset noise  57 . It is therefore possible to perform analysis more accurately. 
     In this example, two noises, i.e., the stray light noise  56  and the offset noise  57 , are used for the analysis as the noise components. The stray light noise  56  and the offset noise  57  vary with time. For example, the stray light noise  56  is scattered and reflected in a measurement environment and is based on the stray light that is incident on the detector  15 . Therefore, the stray light noise  56  varies in accordance with output fluctuations of the light source  13 . The offset noise  57  becomes a background noise which has a fixed value irrespective of the wavelength. 
     The observed spectrum is a total of the fluorescent intensities from the fluorescent substances and the noise components. When, for example, the fluorescent intensities of the five respective fluorescent substances are denoted by F1-F5, the intensity of the stray light noise  56  is denoted by N1, and the intensity of the offset noise is denoted by N2, the intensity I of the observed spectrum becomes the total sum of F1-F5, N1, and N2 as shown in the following (1).
 
 I=F 1+ F 2+ F 3+ F 4+ F 5+ N 1+ N 2  (1)
 
     Ideally, the aforementioned Expression (1) is established in any wavelength. Further, the fluorescent intensities F1-F5 have values in accordance with the concentrations of the respective fluorescent substances. That is, the fluorescent intensities F1-F5 vary depending on the concentrations of the fluorescent substances. The fluorescent intensities F1-F5 can be expressed by the product of the reference spectra  51 - 55  and the coefficients indicating the concentrations of the respective fluorescent substances. For example, data of the reference spectra  51 - 55  in the wavelength λ are respectively denoted by A1(λ)-A5(λ) and the coefficients indicating the concentrations of the first fluorescent substance-the fifth fluorescent substance are respectively denoted by x1-x5. Then the fluorescent intensities F1(λ)-F5(λ) in the wavelength λ can be expressed as shown in the following Expression (2).
 
 F 1(λ)= A 1(λ)× x 1
 
 F 2(λ)= A 2(λ)× x 2
 
 F 3(λ)= A 3(λ)× x 3
 
 F 4(λ)= A 4(λ)× x 4
 
 F 5(λ)= A 5(λ)× x 5  (2)
 
     Further, the spectral data of the stray light noise  56  is denoted by A6(λ), the offset noise is denoted by A7(λ), the coefficient indicating the intensity fluctuations of the stray light noise  56  is denoted by x6, and the coefficient indicating the intensity fluctuations of the offset noise is denoted by x7. Further, the data of the offset noise A7(λ) may be, for example, 1, which is a fixed value, irrespective of the wavelength. Accordingly, the intensity N1 of the stray light noise and the intensity N2 of the offset noise can be expressed by the following Expression (3).
 
 N 1(λ)= A 6(λ)× x 6
 
 N 2(λ)= A 7(λ)× x 7=1× x 7  (3)
 
     From the aforementioned (1)-(3), as long as x1-x5 can be obtained, the concentrations of the respective fluorescent substances can be obtained. The processor  16  calculates the generalized inverse of the matrix having, as elements, the light intensity data of the reference spectra  51 - 55  set for the plurality of labeled substances and the data of noise components. The processor  16  analyzes the DNA fragments included in the sample from the observed spectral data. In the following description, matrix calculations performed by the processor  16  to analyze the sample will be described. 
     The matrix composed of the light intensity data in each wavelength included in the observed spectral data is denoted by b. When the observed spectral data includes, for example, m (m is an integer larger than 2) pieces of light intensity data, the matrix b has m rows and one column. The elements included in the matrix b are denoted by b1, b2, . . . bm. 
     Further, the matrix composed of the data included in the reference spectra  51 - 55  of the five fluorescent substances, the stray light noise  56 , and the offset noise  57  is denoted by A. The matrix A has m rows and seven columns. The m pieces of light intensity data included in the reference spectrum  51  are denoted by A 11 , A 21 , A 31 , . . . A m1 . The m pieces of light intensity data included in the reference spectrum  52  are denoted by A 12 , A 22 , A 32 , . . . A m2 . The m pieces of light intensity data included in the reference spectrum  53  are denoted by A 13 , A 23 , A 33 , . . . A m3 , the m pieces of light intensity data included in the reference spectrum  54  are denoted by A 14 , A 24 , A 34 , . . . A m4 , and the m pieces of light intensity data included in the reference spectrum  55  are denoted by A 15 , A 25 , A 35 , . . . A m5 . The m pieces of data included in the spectral data of the stray light noise  56  are denoted by A 16 , A 26 , A 36 , . . . A m6 . The m pieces of data included in the data of the offset noise  57  are denoted by A 17 , A 27 , A 37 , . . . A m7 . A 17 , A 27 , A 37 , . . . A m7  all have the same value and may be, for example, 1. 
     The light intensity data A 11 , A 21 , A 31 , . . . A m1  are the elements of the first row and the light intensity data A 12 , A 22 , A 32 , . . . A m2  are the elements of the second row. Similarly, the data of the reference spectra  53 - 55  are the elements of the third to fifth rows, respectively. The spectral data A 16 , A 26 , A 36 , . . . A m6  of the stray light noise  56  are the elements of the sixth row, and the data of the offset noise A 17 , A 27 , A 37 , . . . A m7  are the elements of the seventh row. As a matter of course, the positions of the data in the matrix A are not specifically limited. For example, the order of the rows may be changed. 
     Since the number of fluorescent substances that label the sample is five and the number of noise components is two in this example, the matrix A has m rows and seven columns. However, the number of rows of the matrix A increases depending on the number of fluorescent substances to be used. When, for example, the sample is labeled by two fluorescent substances corresponding to the two bases, the matrix A has m rows and four columns. 
     Note that the number of pieces of light intensity data of the reference spectra  51 - 55 , the number of pieces of spectral data of the stray light noise, and the number of pieces of data of the offset noise are the same as the number of pieces of light intensity data included in the observed spectrum. That is, the wavelength where the data is present in the observed spectrum, that in the reference spectrum, that in the stray light noise, and that in the offset noise are all the same. As a matter of course, when the number of pieces of data of the reference spectra, that of the stray light noise, and that of the offset noise are different from the number of pieces of data of the observed spectrum, the number of pieces of data may be made the same by complementing data. 
     Further, the matrix composed of the concentrations of the fluorescent substances included in the sample and the coefficient in accordance with the fluctuations of the noise components is denoted by X. Since the number of fluorescent substances to be used for labeling is five and the number of noise components is two in this example, the matrix X has seven rows and one column. The elements included in the matrix X are denoted by x1-x7. The processor  16  executes processing for obtaining the matrix X. 
     In each wavelength, the following Expression (4) is established.
 
 b   j   =A   j1   ×x   1   +A   j2   ×x   2   +A   j3   ×x   3   +A   j4   ×x   4   +A   j5   ×x 5+ A   j6   ×x   6   +A   j7   ×x   7   (4)
 
     Note that j is any integer from 1 to m. That is, from the product of the coefficient of the concentration of the fluorescent substance used for labeling and the light intensity data of the reference spectrum in one wavelength, and the noise components and the coefficients indicating the fluctuations of the noise components, the light intensity data of the observed spectrum in this wavelength is calculated. Since Expression (4) is established for any desired wavelength, when Expression (4) is expressed using the matrix A, the matrix b, and the matrix X, Expression (5) in  FIG. 3  can be obtained. 
     In an ideal measurement, Expression (5) in  FIG. 3  is established. While there are seven elements x 1 ,x 2  of the matrix X to be obtained, the number of conditional expressions is m. Since m is larger than 7, the number of conditions is too large. In order to solve this problem, the approximate solution that minimizes the error r shown in Expression (6) in  FIG. 4  is obtained. This approximate solution is the least squares problem that minimizes |r|. 
     Since A is not a square matrix, there is no inverse matrix. It is also possible, however, to calculate a generalized inverse (or generalized inverse matrix). By using the generalized inverse, the matrix X can be calculated from Expression (6) shown in  FIG. 3 . In summary, the processor  16  obtains the least squares optimal solution by the generalized inverse. 
     It is assumed that the matrix A T  has seven rows and m columns. As shown in Expression (7) in  FIG. 5 , A T A is a square matrix (in this example, seven rows and seven columns), whereby it is possible to obtain the inverse matrix. When the inverse matrix of A T A is (A T A) −1 , the matrix X can be calculated by the following Expression (8) from Expression (7) in  FIG. 5 .
 
 X =( A   T   A ) −1   A   T   b   (8)
 
     Expression (8) means obtaining the least square solution that minimizes the error r shown in Expression (6) in  FIG. 4 . Since the matrix A is composed of the known reference spectra  51 - 55 , the stray light noise  56 , and the offset noise  57 , it is possible to unambiguously calculate (A T A) −1 A T .  FIG. 6  shows the generalized inverse of the matrix A having, as an element, the data shown in  FIG. 2 . 
     It is possible to calculate the matrix X by multiplying the matrix b of the observed spectrum by (A T A) −1 A T . It is therefore possible to obtain the concentrations of the fluorescent substances. When C=(A T A) −1 A T , for example, C is the generalized inverse. The product of the generalized inverse C of A and the matrix b is then obtained. The elements of the generalized inverse (A T A) −1 A T  are generalized inverse data  61 - 67  shown in  FIG. 6 . In summary, the matrix has seven rows and m columns, the first row to the seventh row being the generalized inverse data  61 - 67 , respectively. By calculating the product of the matrix of the observed spectral data and the generalized inverse, it is possible to calculate the rate of the plurality of labeled substances included in the sample. The data of the generalized inverse can be obtained in advance from the data of the reference spectrum, the stray light noise, and the offset noise. 
     It is therefore possible to calculate the concentrations of the plurality of fluorescent substances used for the labeling in a simple way. In the matrix operation using the generalized inverse, the data of noise components is added as an element of the matrix. According to this configuration, even in a measurement environment in which there are noise components, the concentrations of the fluorescent substances can be appropriately obtained. Even when the excitation light output from the light source fluctuates or the electrical offset noise fluctuates, for example, the concentrations of the fluorescent substances can be appropriately obtained. When, in particular, the intensities of the noise components fluctuate, it becomes difficult to remove only the noise components from the observed spectrum. However, in the matrix operation described in this embodiment, the noise components can be easily removed. It is therefore possible to calculate the concentrations more accurately. 
     While the case in which the noise components include the stray light noise  56  and the offset noise  57  has been described in the aforementioned description, only one of them may be incorporated into the matrix operation. When the stray light noise  56  that is fluctuated in accordance with the wavelength is negligible in the observed spectral data, only the offset noise can be used. Further, when the offset noise  57  that is fixed irrespective of the wavelength is negligible in the observed spectral data, only the stray light noise  56  can be used. 
     Further, since windows  41 - 45  are not set unlike in the case shown in  FIG. 2 , it is possible to calculate the concentrations more accurately. For example, by setting the windows  41 - 45 , light intensity data of the observed spectrum outside the windows  41 - 45  is not used any more. In summary, the number of pieces of light intensity data to obtain the concentrations of the fluorescent substances becomes small, which causes degradation of the accuracy of the calculation. Meanwhile, in this embodiment, a larger number of pieces of light intensity data included in the observed spectrum can be used, whereby it is possible to decrease the noise and to improve the measurement accuracy. It is therefore possible to obtain the concentrations accurately and to perform a more appropriate analysis. 
     As described above, the processor  16  analyzes the plurality of substances included in the sample based on the observed spectral data output from the detector  15 . Accordingly, the processor  16  obtains the generalized inverse of the matrix having, as elements, the reference spectral data set for the plurality of labeled substances that label the plurality of substances and the data of the noise components. The processor  16  analyzes the substances included in the sample using the observed spectral data and the generalized inverse. If the generalized inverse of the matrix of the reference spectra and the noise components is calculated in advance, the processing can be executed in a shorter period of time. That is, the generalized inverse may be acquired by reading out the generalized inverse stored in a storage unit such as a memory in advance. As a matter of course, the generalized inverse may be obtained by calculating the generalized inverse using the data of stray light noise that has been measured. 
     It is therefore possible to perform an analysis using a larger number of observed spectral data. It is therefore possible to appropriately analyze the sample based on the spectrum of the fluorescence and to perform DNA testing with a small measurement error. 
     As described above, by electrophoresing the PCR amplified sample, the DNA fragments are separated by size. The DNA fragments in the capillary are irradiated with light to detect the observed spectrum in each size of the DNA fragments. The plurality of observed spectra are subjected to the above processing to calculate the concentration of each base. The distribution of the concentration of the base is obtained for each size of the DNA fragments. The DNA testing is carried out in accordance with the base sequence of the DNA fragment. It is therefore possible to perform DNA testing with higher accuracy. 
     Other Embodiments 
     With reference to  FIG. 7 , a spectroscopic analysis apparatus  100  according to another embodiment will be described.  FIG. 7  is a block diagram showing a configuration of the spectroscopic analysis apparatus  100 . The spectroscopic analysis apparatus  100  includes a light source configured to generate light to be incident on a sample comprising a plurality of substances labeled by a plurality of labeled substances; a spectrometer configured to disperse observed light generated in the sample by the light incident on the sample; a detector configured to detect the observed light dispersed by the spectrometer to output observed spectral data; and a processor configured to analyze the plurality of substances included in the sample based on the observed spectral data output from the detector, the processor analyzing the substances included in the sample from the observed spectral data using a generalized inverse of a matrix having, as elements, reference spectral data set for the plurality of labeled substances and data of noise components. According to this configuration, it is possible to analyze the sample appropriately. 
     The control for analyzing the above sample may be executed by a computer program. The control program described above can be stored and provided to a computer using any type of non-transitory computer readable media. Non-transitory computer readable media include any type of tangible storage media. Examples of non-transitory computer readable media include magnetic storage media (such as flexible disks, magnetic tapes, hard disk drives, etc.), optical magnetic storage media (e.g. magneto-optical disks), CD-ROM (Read Only Memory), CD-R, CD-R/W, and semiconductor memories (such as mask ROM, PROM (Programmable ROM), EPROM (Erasable PROM), flash ROM, RAM (Random Access Memory), etc.). The program may be provided to a computer using any type of transitory computer readable media. Examples of transitory computer readable media include electric signals, optical signals, and electromagnetic waves. Transitory computer readable media can provide the program to a computer via a wired communication line (e.g. electric wires, and optical fibers) or a wireless communication line. 
     Further, the embodiments of the present invention include not only the case in which the functions of the above embodiments are achieved by the computer executing the program that achieves the functions of the above embodiments but also a case in which this program achieves the functions of the above embodiments in collaboration with an application software or an operating system (OS) operated on the computer. 
     While the present invention has been described with reference to the embodiments, the present invention is not limited to the above embodiments. Various changes that can be understood by those skilled in the art may be made on the configuration and the details of the present invention within the scope of the present invention. 
     This application is based upon and claims the benefit of priority from Japanese Patent Application No. 2015-71618, filed on Mar. 31, 2015, the disclosure of which is incorporated herein in its entirety by reference. 
     REFERENCE SIGNS LIST 
     
         
           11  INJECTION PART 
           12  CAPILLARY 
           13  LIGHT SOURCE 
           14  SPECTROMETER 
           15  DETECTOR 
           16  PROCESSOR 
           20  MICROCHIP 
           31  OPTICAL FIBER 
           41 - 44  WINDOW 
           51 - 55  REFERENCE SPECTRUM 
           56  STRAY LIGHT NOISE 
           57  OFFSET NOISE 
           61 - 67  GENERALIZED INVERSE DATA