Method for generating raman spectrum

Abstract

Provided is a method for generating a Raman spectrum with a high SN ratio using spectral data in a quenching process, wherein the Raman spectrum is generated by separating Raman scattered light from fluorescence by a method free of arbitrariness.　The method for generating a Raman spectrum comprises: a step for repeating a procedure in which a sample is irradiated with laser light, Raman scattered light that is scattered from the sample and fluorescence that is radiated from the sample are received, and a spectrum that contains the Raman scattered light and the fluorescence is obtained, and recording a first spectrum, a second spectrum, ..., and an nth spectrum; a step for determining, for each of the n recorded spectra, the intensity of the Raman scattered light as the product of an exposure time and the power of the laser light with which the sample is irradiated; a step for determining the intensity of the fluorescence for each of the n recorded spectra; and a step for using the intensity of the determined Raman scattered light and the intensity of the determined fluorescence to determine a Raman spectrum by the least squares method.

Description

How Raman spectra are generated

[0001] The present disclosure relates to a method for generating a Raman spectrum.

[0002] Raman spectroscopy is used to identify materials, evaluate crystals, measure stress, and more. A Raman spectrometer is used for Raman spectroscopy analysis, and laser light is irradiated onto the sample to be measured. The Raman scattered light emitted from the sample is separated into spectra by a spectroscope and received by a detector to obtain a Raman spectrum. By comparing the obtained Raman spectrum with a known Raman spectrum, it is possible to identify the materials contained in the sample. By analyzing the shape of the Raman spectrum, it is possible to evaluate the crystalline state of the material and the stress acting on the material.

[0003] In Raman spectroscopy, fluorescence interference occurs in many samples. A method for circumventing this problem is to utilize fluorescence quenching (also known as bleaching). Quenching is a phenomenon in which the intensity of fluorescence emitted from a sample gradually decreases when the sample is irradiated with light.

[0004] In measuring Raman spectra, a laser beam is used as a light source, and quenching occurs when the sample is irradiated with the laser beam. In this case, fluorescence is quenched by irradiating the sample with laser beam, but the intensity of the Raman scattered light does not change. Therefore, if the Raman spectrum is measured after quenching, the intensity of the Raman scattered light is relatively greater than when the Raman spectrum is measured before quenching, making it easier to detect the Raman spectrum. To reduce interference caused by fluorescence by utilizing fluorescence quenching and increase the intensity of the Raman scattered light to easily detect the Raman spectrum, it is generally sufficient to irradiate the sample with laser beam before measuring the Raman spectrum, and then measure the Raman spectrum after quenching, which has the advantage that any Raman spectrometer can be used.

[0005] When measuring Raman spectra using fluorescence quenching, spectral data from the quenching process has not been utilized in the past. However, by utilizing the spectral data without waste, it is possible to improve the signal-to-noise ratio of the observed Raman scattered light. Such a technique is proposed in Patent Document 1. Specifically, Patent Document 1 describes a Raman scattered light observation method that irradiates a sample with laser light over multiple consecutive time intervals, collects the Raman scattered light and the fluorescence emitted from the sample for each of the multiple time intervals, and records a spectrum containing the Raman scattered light and the fluorescence. From the spectra recorded for each of the multiple time intervals, multivariate analysis is used to extract the time dependence of the intensity of the Raman scattered light and the intensity of the fluorescence, and separate the spectrum of the Raman scattered light from the spectrum of the fluorescence. The method describes a method for separating the spectrum of the Raman scattered light from the spectrum of the fluorescence, using the spectral data from the quenching process and the alternating least squares method (MCR-ALS). It is described that this method can improve the signal-to-noise ratio of Raman scattered light without wasting the Raman scattered light signal, compared to a method in which a laser is irradiated before measurement and measurement is performed after the fluorescence has quenched.

[0006] Furthermore, Non-Patent Document 1 describes a technique for separating a Raman signal from a strong fluorescent background using principal component analysis (PCA).

[0007] JP 2017-129389 A

[0008] T. Hasegawa, J. Nishijo, J. Umemura, Chemical Physics Letters 317 (2000) 642-646

[0009] Patent Document 1 describes that the signal-to-noise ratio of Raman scattered light can be improved by using the alternating least squares method and utilizing spectral data of the extinction process. However, the inventors' investigations revealed that there is room for further improvement in the signal-to-noise ratio of the Raman spectrum.

[0010] Furthermore, when using the alternating least-squares method to separate Raman scattered light and fluorescence, the solution obtained depends on various calculation conditions. For example, the solution obtained varies depending on various calculation conditions, such as how to select the initial value in the alternating calculation, what weighting (coefficient) value is assigned to the regularization term, what constraints are assigned, and what convergence conditions are used. Therefore, it is desirable to have a method that is free from arbitrariness and can separate Raman scattered light and fluorescence. On the other hand, the method described in Non-Patent Document 1 has limited applicability and requires careful examination of the results obtained, limiting its practical use.

[0011] The problem to be solved by the present disclosure is to provide a method for generating a Raman spectrum with a high S / N ratio by separating Raman scattered light and fluorescence in a non-arbitrary manner when using spectral data from the quenching process.

[0012] The present disclosure is as follows: [1] A method for generating a Raman spectrum, comprising: repeating the steps of irradiating a sample with laser light, receiving Raman scattered light and fluorescence emitted from the sample, and obtaining spectra including the Raman scattered light and the fluorescence, and recording a first spectrum, a second spectrum, ..., an n-th spectrum; determining, for each of the n recorded spectra, the product of the power of the laser light irradiated onto the sample and the exposure time as the intensity of the Raman scattered light; calculating the intensity of the fluorescence for each of the n recorded spectra; and calculating a Raman spectrum by the least squares method using the determined intensity of the Raman scattered light and the calculated intensity of the fluorescence, where n is an integer of 2 or greater. [2] A method for generating a Raman spectrum, comprising: a step of irradiating a sample with laser light, receiving Raman scattered light and fluorescence emitted from the sample, and repeatedly obtaining a spectrum containing the Raman scattered light and the fluorescence, thereby recording a first spectrum, a second spectrum, ..., an n-th spectrum; a step of selecting m spectra from the recorded n spectra, determining, for each of the selected m spectra, the product of the power of the laser light with which the sample was irradiated and the exposure time as the intensity of the Raman scattered light, and calculating the intensity of the fluorescence, and repeating the step of obtaining a Raman spectrum by the least squares method using the determined intensity of the Raman scattered light and the calculated intensity of the fluorescence, thereby obtaining a first Raman spectrum, a second Raman spectrum, ..., a k-th Raman spectrum; and a step of calculating an S / N ratio for each of the obtained k Raman spectra, and selecting a maximum S / N ratio Raman spectrum having the highest S / N ratio from the k Raman spectra. [wherein n represents an integer of 2 or more, m represents an integer of 2 or more and n or less, and k represents an integer of 2 or more.[3] The method according to [2], wherein, instead of selecting the highest S / N ratio Raman spectrum from the k Raman spectra, the S / N ratio of each of the k Raman spectra is calculated, an average S / N ratio is calculated by arithmetic averaging, and a high S / N ratio Raman spectrum having an S / N ratio equal to or greater than the average S / N ratio is selected from the k Raman spectra. [4] The method according to any one of [1] to [3], wherein, in the step of calculating the Raman spectrum, the Raman spectrum is calculated using a regularized least squares method. [5] The method according to any one of [1] to [4], wherein the fluorescence intensity is calculated in a wavenumber range that does not include a Raman peak.

[0013] According to the present disclosure, the Raman spectrum is calculated by the least-squares method using the spectral data of the quenching process and the intensities of the Raman scattered light and the fluorescence. As a result, Raman scattered light and fluorescence can be separated using a method with little arbitrariness and wide applicability. Furthermore, the signal-to-noise ratio of the Raman spectrum can be further improved by adding an appropriate regularization term.

[0014] Figure 1 is a graph showing 30 spectra recorded with a Raman microscope. Figure 2 shows the vector S representing the Raman spectrum calculated by the least squares method. Ｒ and a vector S representing the fluorescence spectrum generated by the least squares method. Ｆ FIG. 3 is a graph showing 10 spectra selected from 30 spectra. FIG. 4 is a graph showing Raman spectra and fluorescence spectra. FIG. 5 is a graph showing Raman spectra. FIG. 6 is a graph showing fluorescence spectra when the parameter λ indicating the strength of regularization in the regularized least squares method is changed. FIG. 7 is a graph showing Raman spectra when the parameter λ indicating the strength of regularization in the regularized least squares method is changed.

[0015] The contents of the present disclosure will be specifically explained below based on the embodiments, but the present disclosure is not limited to the following embodiments, and it is of course possible to make modifications within the scope that is compatible with the intent described above and below, and all of these modifications are included in the technical scope of the present disclosure.

[0016] The method for generating a Raman spectrum according to the present disclosure includes a first embodiment and a second embodiment, which have in common the use of spectral data from the quenching process and the determination of the Raman spectrum by the least squares method using the intensity of the Raman scattered light and the intensity of the fluorescent light.

[0017] A first embodiment of the method for generating a Raman spectrum includes the steps of: irradiating a sample with laser light, receiving Raman scattered light and fluorescence emitted from the sample, and repeatedly obtaining spectra containing the Raman scattered light and the fluorescence to record a first spectrum, a second spectrum, ..., an n-th spectrum (hereinafter sometimes referred to as a spectrum recording step); determining, for each of the n recorded spectra, the product of the power of the laser light irradiated onto the sample and the exposure time as the intensity of the Raman scattered light (hereinafter sometimes referred to as a Raman scattered light intensity determining step); calculating the intensity of the fluorescence for each of the n recorded spectra (hereinafter sometimes referred to as a fluorescence intensity determining step); and calculating a Raman spectrum by the least squares method using the determined intensity of the Raman scattered light and the calculated intensity of the fluorescence (hereinafter sometimes referred to as a first Raman spectrum generating step), where n is an integer of 2 or greater.

[0018] A second embodiment of the method for generating a Raman spectrum includes: a step of irradiating a sample with laser light, receiving Raman scattered light and fluorescence emitted from the sample, and repeating the procedure of obtaining a spectrum including the Raman scattered light and the fluorescence to record a first spectrum, a second spectrum, ..., an n-th spectrum (hereinafter sometimes referred to as a spectrum recording step); a step of selecting m spectra from the recorded n spectra, determining the product of the power and exposure time of the laser light with which the sample was irradiated and the exposure time as the intensity of the Raman scattered light for each of the selected m spectra, and calculating the intensity of the fluorescence, and repeating the procedure of calculating a Raman spectrum by the least squares method using the determined intensity of the Raman scattered light and the calculated intensity of the fluorescence to obtain a first Raman spectrum, a second Raman spectrum, ..., a k-th Raman spectrum (hereinafter sometimes referred to as a second Raman spectrum generating step); and a step of calculating an S / N ratio for each of the k Raman spectra thus calculated, and selecting the Raman spectrum having the highest S / N ratio from the k Raman spectra (hereinafter sometimes referred to as a Raman spectrum selection step), where n is an integer of 2 or more, m is an integer of 2 or more and n or less, and k is an integer of 2 or more.

[0019] First, the first embodiment will be described, and then the second embodiment will be described, with the explanation of common steps being omitted.

[0020] [First embodiment] (Spectrum recording step) In the spectrum recording step, a laser beam is irradiated onto a sample, and Raman scattered light and fluorescence emitted from the sample are received to obtain a spectrum including the Raman scattered light and fluorescence, thereby measuring the spectrum during the quenching process. In the spectrum recording step, the procedure of irradiating the sample with laser beam and obtaining a spectrum including the Raman scattered light and fluorescence is repeated n times to record a first spectrum, a second spectrum, ..., and an nth spectrum, where n is an integer of 2 or greater.

[0021] The power of the laser light irradiated onto the sample may be changed as appropriate or may be kept constant each time. The exposure time when irradiating the sample with the laser light may be changed as appropriate or may be kept constant each time. The power of the laser light is the light intensity and is expressed in W.

[0022] The position at which the laser light is irradiated on the sample is not particularly limited, and the laser light may be irradiated at a specific position on the sample, or at multiple positions on the sample. For example, the laser beam may be focused at one point, may be irradiated in a line, or may be irradiated at multiple point-like spots simultaneously. Other irradiation methods are also acceptable. A method of measuring multiple positions on a sample sequentially is sometimes called imaging measurement. In imaging measurement, the order of measurements does not matter. In other words, one point may be measured continuously and then moved to the next measurement point, or the operation of measuring each measurement point once in order may be repeated. Other orders are also acceptable.

[0023] Since quenching occurs when a sample is irradiated with laser light, it is preferable to fix the position where the laser light is irradiated to a specific position on the sample, thereby increasing the degree of quenching.

[0024] When irradiating the sample with laser light, light other than the laser light used as the light source for Raman measurement may be simultaneously irradiated. Irradiating the sample with light other than the laser light used as the light source for Raman measurement can promote quenching. Examples of such light sources include incandescent lamps, halogen lamps, LEDs, and lasers other than the light source for Raman measurement.

[0025] (Raman scattered light intensity determination step) In the Raman scattered light intensity determination step, the product of the power of the laser light irradiated onto the sample and the exposure time is calculated for each of the n spectra recorded in the spectrum recording step, and this is determined as the intensity of the Raman scattered light.

[0026] (Fluorescence Intensity Determining Step) In the fluorescence intensity determining step, the fluorescence intensity is determined for each of the n spectra recorded in the spectrum recording step. The fluorescence intensity may be determined by a known method.

[0027] (First Raman spectrum generation step) In the first Raman spectrum generation step, a Raman spectrum is obtained by the least squares method using the Raman scattered light intensity determined in the Raman scattered light intensity determination step and the fluorescence intensity determined in the fluorescence intensity determination step. The procedure for obtaining a Raman spectrum is as follows.

[0028] The data of the i-th spectrum obtained in the spectrum recording process is represented by a vector d ｉ Then, the vector d ｉ is a vector S that represents the fluorescence spectrum Ｆ and a vector S representing the spectrum of the Raman scattered light. Ｒ This is expressed by the following equation (1) as a linear sum of the above: In the following equation (1), vector e represents the residual.

[0029]

[0030] In the above formula (1), the coefficient C Ｆ(ｉ) represents the intensity of fluorescence when the sample is irradiated with the i-th laser beam, and the coefficient C Ｒ(ｉ) represents the intensity of the Raman scattered light when the sample is irradiated with the laser light for the i-th time.

[0031] The n pieces of spectral data D recorded in the spectrum recording step can be expressed as a matrix as in the following equation (2).

[0032]

[0033] When the intensity (concentration) C is expressed by the following formula (3) and the spectrum S is expressed by the following formula (4), the spectrum data D is expressed by the following formula (5). Ｆ is the fluorescence intensity, and vector C Ｒ and represent the intensities of the Raman scattered light. In the following formula (5), E represents the residual matrix.

[0034]

[0035]

[0036] D=CS Ｔ + E ... (5)

[0037] If the number of spectral data points is M, the spectral data D is an N×M matrix, the intensity C is an N×2 matrix, and the spectrum S Ｔ is a 2×M matrix. The residual E is an N×M matrix.

[0038] In the above formula (5), the intensity C or the spectrum S Ｔ If one of the two is obtained, the other can be obtained by the least squares method. For example, the spectrum S Ｔ can be calculated by the following formula (6): Ｔ = (C Ｔ C) －１ C Ｔ D...(6)

[0039] Of the intensity C, the intensity of the Raman scattered light is proportional to the intensity of the laser light, so the vector C Ｒ The intensity of the laser light represents the product of the power of the laser light and the exposure time. For example, when the intensity of the laser light irradiating the sample is kept constant and the spectrum is measured, a vector C Ｒ is constant. Vector C indicating the intensity of fluorescence Ｆ is the baseline intensity of the measured spectrum. Vector C Ｒ and vector C Ｆ may be normalized as appropriate.

[0040] Since the intensity C can be obtained easily in this way, the Raman spectrum S can be obtained in a non-arbitrary way. Ｒ Furthermore, since the calculation is not performed using the alternating least squares method as in Patent Document 1, the calculation process can be performed at high speed.

[0041] Second Embodiment (Spectrum Recording Step) For an explanation of the spectrum recording step in the second embodiment, refer to the explanation of the spectrum recording step in the first embodiment.

[0042] (Second Raman Spectrum Generation Step) In the second Raman spectrum generation step, first, m spectra are selected from the n spectra recorded in the spectrum recording step, and for each of the selected m spectra, the product of the power of the laser light irradiated on the sample and the exposure time is determined as the intensity of the Raman scattered light, and the intensity of the fluorescence is calculated. m is an integer between 2 and n. Next, a Raman spectrum is calculated using the determined intensity of the Raman scattered light and the calculated intensity of the fluorescence using the least squares method. For the process of calculating a Raman spectrum using the least squares method, see the description of the first Raman spectrum generation step above. Next, the procedure of calculating a Raman spectrum using the determined intensity of the Raman scattered light and the calculated intensity of the fluorescence is repeated k times to calculate a first Raman spectrum, a second Raman spectrum, ..., the k-th Raman spectrum. k is an integer greater than or equal to 2.

[0043] In the Raman spectrum selection step, the S / N ratio of each of the k Raman spectra obtained in the second Raman spectrum generation step is calculated, and the Raman spectrum with the highest S / N ratio (hereinafter sometimes referred to as the maximum S / N ratio Raman spectrum) is selected from the k Raman spectra, and this maximum S / N ratio Raman spectrum is used as the Raman spectrum to be generated in the present disclosure. This allows the generation of a Raman spectrum with a high S / N ratio.

[0044] In the Raman spectrum selection step of the second embodiment, instead of selecting the highest S / N ratio Raman spectrum from among the k Raman spectra obtained in the second Raman spectrum generation step, the S / N ratios of the k Raman spectra obtained in the second Raman spectrum generation step may be calculated, the S / N ratios may be arithmetically averaged to obtain an average S / N ratio, and a Raman spectrum having an S / N ratio equal to or greater than the average S / N ratio (hereinafter, sometimes referred to as a high S / N ratio Raman spectrum) may be selected from among the k Raman spectra. In other words, the embodiment of the generation method in the present disclosure is not limited to generating a Raman spectrum having the highest S / N ratio, and a Raman spectrum having an S / N ratio equal to or greater than the average S / N ratio may also be generated. For example, the spectrum having the second or third highest S / N ratio may be selected as the Raman spectrum.

[0045] In the first Raman spectrum generating step in the first embodiment and the second Raman spectrum generating step in the second embodiment, the Raman spectrum may be obtained by the regularized least squares method. In the spectral separation of fluorescence and Raman scattered light using the least squares method, regularization can be performed to further increase the signal-to-noise ratio of the Raman spectrum. In the regularized least squares method, a spectrum S that satisfies the following formula (7) is obtained. In the following formula (7), the first term is the least squares term and the second term is the regularization term.

[0046]

[0047] In the above formula (7), D is the spectrum data, C is the intensity, and S Ｔ is the spectrum, ||·|| Ｆ denotes the Frobenius norm. As the regularization term R, for example, the following formula (8) may be used.

[0048]

[0049] In the above formula (8), λ is a parameter representing the strength of regularization and is a positive real number, D ｄ is a dth-order differential operator, d is an integer equal to or greater than 1, and vector S Ｆ is the fluorescence spectrum, ||·|| ｐis the Lp norm, and p represents the order of the norm and is a positive real number. p is commonly set to 1 or 2, and when p is 1 it is called the L1 norm, and when p is 2 it is called the L2 norm. The regularization term shown in equation (8) reduces the intensity difference between adjacent pixels in the fluorescence spectrum, which has the effect of smoothing the fluorescence spectrum. The spectral shape changes depending on d and p when the regularization parameter is increased.

[0050] In the fluorescence intensity determination step in the first embodiment and the second Raman spectrum generation step in the second embodiment, the fluorescence intensity is determined in a wavenumber range that does not include a Raman peak (hereinafter, λ baseline It is preferable to measure the Raman spectrum using the Raman spectrum detector. This allows the fluorescence spectrum and the Raman spectrum to be separated. The wavenumber range that does not include the Raman peak is the silent region, 1800 to 2700 cm －１ It is preferable to use the above wavenumber range, but other wavenumber ranges may also be used.

[0051] This application claims the benefit of priority based on Japanese Patent Application No. 2024-135782, filed on August 15, 2024. The entire contents of the specification of Japanese Patent Application No. 2024-135782 are incorporated herein by reference.

[0052] The contents of the present disclosure will be explained in more detail below using examples, but the present disclosure is not limited to the following examples, and it is of course possible to make appropriate modifications within the scope that is compatible with the intent described above and below, and all of these modifications are included in the technical scope of the present disclosure.

[0053] (Spectrum Recording Step) Using a RAMANTouch (Bruker Japan Co., Ltd.) as a Raman microscope, a polyimide film sample was irradiated with a laser having a wavelength of 532 nm as an excitation light source. The Raman scattered light and fluorescence emitted from the sample were separated and received by a detector, and a spectrum including the Raman scattered light and fluorescence was measured. This was repeated 30 times consecutively. The power of the laser light irradiated onto the sample was 4.36 mW, and the exposure time was 0.1 seconds. The spectrum measured when the laser light was irradiated onto the sample the first time was designated the first spectrum, the spectrum measured when the laser light was irradiated the second time was designated the second spectrum, ..., the spectrum measured when the laser light was irradiated the 30th time was designated the 30th spectrum, and spectra 1 to 30 were recorded. Note that when irradiating the sample with laser light, no light other than the laser light used as the light source for Raman measurement was irradiated.

[0054] The 30 recorded spectra are shown in Figure 1. In Figure 1, the horizontal axis represents the Raman shift, and the vertical axis represents the spectral intensity. Figure 1 shows that the fluorescence faded and the baseline gradually decreased each time the sample was irradiated with laser light.

[0055] A vector S representing the Raman spectrum is calculated by the least squares method using the intensity of the Raman scattered light determined in the Raman scattered light intensity determination step and the intensity of the fluorescence determined in the fluorescence intensity determination step. Ｒ is shown in Figure 2. In Figure 2, a vector S representing the fluorescence spectrum generated by the least squares method is shown. Ｆ The results are also shown.

[0056] Next, the procedure for generating a Raman spectrum from the spectrum shown in FIG. 1 will be described in more detail.

[0057] [Procedure Based on First Embodiment] (Spectrum Recording Step) The spectrum recording step in the first embodiment was the same as the procedure described above in the spectrum recording step.

[0058] In the following, for the sake of convenience, the first to tenth spectra will be used out of the 30 recorded spectra. For the sake of convenience, the Raman shifts of the ten spectra, from the first to the tenth spectra, will be calculated as 1776.4 to 1823.6 cm －１ Fifteen points were selected from the range of 15, and the spectral intensities at the selected 15 points were read. The spectral intensities read for each spectrum are shown in Table 1 below. Ten spectra are also shown in Figure 3.

[0059]

[0060] (Raman scattered light intensity determination step) In the Raman scattered light intensity determination step, the product of the power of the laser light irradiated on the sample and the exposure time was calculated for each of the 10 spectra recorded in the spectrum recording step, and the intensity of the Raman scattered light was determined. Since the product of the power of the laser light irradiated on the sample and the exposure time for each of the 10 spectra recorded in the spectrum recording step is constant, the vector C Ｒ All elements of are set to 1.

[0061] (Fluorescence Intensity Determination Step) In the fluorescence intensity determination step, the fluorescence intensity was determined for each of the 10 spectra recorded in the spectrum recording step. The fluorescence intensity was determined as the intensity of the spectrum in a wavenumber range that did not include a Raman peak. Specifically, of the intensities in each spectrum shown in Table 1 above, the average value of the intensities of the spectrum in the three columns from the right was taken as the fluorescence intensity. Because the Raman shift range of the three columns from the right is a region (wavenumber range) that does not include a Raman peak, the average value of the intensities of the spectrum in these three columns can be taken as the fluorescence intensity. Regarding the calculated fluorescence intensities, the fluorescence intensities of the first to ninth spectra were normalized so that the fluorescence intensity of the tenth spectrum was 1.0000. As a result, the fluorescence intensity of the first spectrum was 1.8059, the fluorescence intensity of the second spectrum was 1.4651, the fluorescence intensity of the third spectrum was 1.3158, the fluorescence intensity of the fourth spectrum was 1.2237, the fluorescence intensity of the fifth spectrum was 1.1686, the fluorescence intensity of the sixth spectrum was 1.1137, the fluorescence intensity of the seventh spectrum was 1.0804, the fluorescence intensity of the eighth spectrum was 1.0481, the fluorescence intensity of the ninth spectrum was 1.0194, and the fluorescence intensity of the tenth spectrum was 1.0000.

[0062] (First Raman spectrum generation step) In the first Raman spectrum generation step, a Raman spectrum is obtained by the least squares method using the intensity of the Raman scattered light determined in the Raman scattered light intensity determination step and the intensity of the fluorescence determined in the fluorescence intensity determination step. A vector C representing the intensity of the Raman scattered light determined in the Raman scattered light intensity determination step is used. Ｒ All elements of were 1, and the normalized fluorescence intensities determined in the fluorescence intensity determination step were 1.0000 to 1.8059. Using these, the Raman spectrum S Ｒ and the fluorescence spectrum S Ｆ The Raman spectrum S Ｒ Intensity and fluorescence spectrum S Ｆ The intensities of the Raman spectrum and the fluorescence spectrum are shown in Table 2 below. The Raman spectrum and the fluorescence spectrum are shown in Figure 4. As shown in Table 2 and Figure 4, the Raman spectrum can be generated.

[0063]

[0064] [Procedure Based on the Second Embodiment] (Spectrum Recording Step) The spectrum recording step in the second embodiment was the same as the procedure described in the spectrum recording step in the first embodiment.

[0065] (Second Raman Spectrum Generation Step) In the second Raman spectrum generation step, m spectra were selected from the 10 spectra recorded in the spectrum recording step, and for each of the selected m spectra, the product of the power and exposure time of the laser light irradiated on the sample was determined as the intensity of the Raman scattered light, and the intensity of the fluorescence was calculated. This procedure of calculating the Raman spectrum by the least squares method using the determined intensity of the Raman scattered light and the calculated intensity of the fluorescence was repeated k times to obtain the first Raman spectrum, the second Raman spectrum, ..., the k-th Raman spectrum. Specifically, ten spectra (1st to 10th spectra), nine spectra (2nd to 10th spectra), and eight spectra (3rd to 10th spectra) were selected from the 10 spectra recorded in the spectrum recording step. For each of the three selected spectrum groups, a vector C representing the intensity of the Raman scattered light was calculated. Ｒ is a vector with all elements being 1.

[0066] The fluorescence intensity was determined for each of the three selected spectrum groups. Specifically, of the intensities in each spectrum shown in Table 1 above, the average value of the intensities of the spectra in the three columns from the right was taken as the fluorescence intensity. Because the Raman shift range of the three columns from the right does not include any Raman peaks, the average value of the intensities of the spectra in these three columns can be taken as the fluorescence intensity. The calculated fluorescence intensities were normalized so that the fluorescence intensity of the tenth spectrum was 1.0000. As a result, the fluorescence intensity of the first spectrum in the first spectrum group was 1.8059, the fluorescence intensity of the second spectrum was 1.4651, the fluorescence intensity of the third spectrum was 1.3158, the fluorescence intensity of the fourth spectrum was 1.2237, the fluorescence intensity of the fifth spectrum was 1.1686, the fluorescence intensity of the sixth spectrum was 1.1137, the fluorescence intensity of the seventh spectrum was 1.0804, the fluorescence intensity of the eighth spectrum was 1.0481, the fluorescence intensity of the ninth spectrum was 1.0194, and the fluorescence intensity of the tenth spectrum was 1.0000. In the second spectrum group, the fluorescence intensity of the second spectrum was 1.4651, the fluorescence intensity of the third spectrum was 1.3158, the fluorescence intensity of the fourth spectrum was 1.2237, the fluorescence intensity of the fifth spectrum was 1.1686, the fluorescence intensity of the sixth spectrum was 1.1137, the fluorescence intensity of the seventh spectrum was 1.0804, the fluorescence intensity of the eighth spectrum was 1.0481, the fluorescence intensity of the ninth spectrum was 1.0194, and the fluorescence intensity of the tenth spectrum was 1.0000. In the third spectrum group, the fluorescence intensity of the third spectrum was 1.3158, the fluorescence intensity of the fourth spectrum was 1.2237, the fluorescence intensity of the fifth spectrum was 1.1686, the fluorescence intensity of the sixth spectrum was 1.1137, the fluorescence intensity of the seventh spectrum was 1.0804, the fluorescence intensity of the eighth spectrum was 1.0481, the fluorescence intensity of the ninth spectrum was 1.0194, and the fluorescence intensity of the tenth spectrum was 1.0000.

[0067] For the first to third spectrum groups, the determined Raman scattered light intensities and the calculated fluorescence intensities were used to calculate the Raman spectra by the least squares method, which was repeated three times to obtain the first, second, and third Raman spectra. The intensities of Raman spectrum S are shown in Table 3 below. The three Raman spectra are also shown in Figure 5.

[0068]

[0069] (Raman spectrum selection step) In the Raman spectrum selection step, the S / N ratio of each of the three Raman spectra obtained in the second Raman spectrum generation step was calculated, and the Raman spectrum with the highest S / N ratio (the Raman spectrum with the highest S / N ratio) was selected from the three Raman spectra. This Raman spectrum with the highest S / N ratio was used as the Raman spectrum to be generated in the present disclosure. Specifically, since the Raman scattered light intensity corresponding to the signal in this example was constant, the standard deviation of the three columns from the right was calculated as the amount of noise in each of the three Raman spectra obtained in the second Raman spectrum generation step. As a result, the amount of noise in the first Raman spectrum was 118, the amount of noise in the second Raman spectrum was 127, and the amount of noise in the third Raman spectrum was 154.

[0070] The Raman spectrum with the highest S / N ratio, i.e., the Raman spectrum with the smallest amount of noise, was selected from the three Raman spectra. As a result, the first Raman spectrum was the Raman spectrum with the highest S / N ratio.

[0071] Next, an example will be described in which, in the first Raman spectrum generation step and the second Raman spectrum generation step, the Raman scattered light intensity determined in the Raman scattered light intensity determination step and the fluorescence intensity determined in the fluorescence intensity determination step are used to determine the Raman spectrum S by the regularized least squares method instead of the least squares method.

[0072] As the regularized least squares method, L2 norm regularization (d = 2, p = 2) of the second-order differentiated fluorescence spectrum was used, as shown in the following equation (9). The parameter λ, which represents the strength of regularization, was set to 0.01, 0.1, 1, or 10. The results are shown in Figures 6 and 7. Figure 6 shows the fluorescence spectrum when λ is varied. Note that in Figure 6, the spectra are offset by 2000 in the intensity direction to prevent overlapping. Figure 7 shows the Raman spectrum when λ is varied. Note that in Figure 7, the spectra are offset by 500 in the intensity direction to prevent overlapping.

[0073]

[0074] As is clear from Fig. 6, the fluorescence spectrum becomes smoother as the regularization parameter λ increases. As a result, as is clear from Fig. 7, the noise in the Raman spectrum is reduced and small peaks become visible.

Claims

1. A method for generating a Raman spectrum, comprising the steps of: irradiating a sample with laser light, receiving Raman scattered light and fluorescence emitted from the sample, and repeatedly obtaining spectra containing the Raman scattered light and fluorescence to record a first spectrum, a second spectrum, ..., an nth spectrum; determining the intensity of the Raman scattered light for each of the n recorded spectra as the product of the power of the laser light irradiated onto the sample and the exposure time; calculating the intensity of the fluorescence for each of the n recorded spectra; and calculating a Raman spectrum by the least squares method using the determined intensity of the Raman scattered light and the calculated intensity of the fluorescence, where n is an integer of 2 or greater.

2. A method for generating Raman spectra, comprising: a step of irradiating a sample with laser light, receiving Raman scattered light and fluorescence emitted from the sample, and repeatedly obtaining spectra containing the Raman scattered light and fluorescence to record a first spectrum, a second spectrum, ..., an nth spectrum; a step of selecting m spectra from the n recorded spectra, determining the product of the power and exposure time of the laser light irradiated onto the sample for each of the selected m spectra as the intensity of the Raman scattered light, and calculating the intensity of the fluorescence, and repeating the step of obtaining a Raman spectrum by the least squares method using the determined intensity of the Raman scattered light and the calculated intensity of the fluorescence to obtain a first Raman spectrum, a second Raman spectrum, ..., a kth Raman spectrum; and a step of calculating the signal-to-noise ratio for each of the k Raman spectra, and selecting the maximum signal-to-noise ratio Raman spectrum from the k Raman spectra. [wherein n represents an integer of 2 or more, m represents an integer of 2 or more and n or less, and k represents an integer of 2 or more.] 3. The method of claim 2, wherein instead of selecting the highest S / N ratio Raman spectrum from among the k Raman spectra, the S / N ratio of each of the k Raman spectra is calculated, and an average S / N ratio is calculated by arithmetically averaging the calculated S / N ratios, and a high S / N ratio Raman spectrum having an S / N ratio equal to or greater than the average S / N ratio is selected from among the k Raman spectra.

4. A method according to any one of claims 1 to 3, wherein the step of obtaining the Raman spectrum involves obtaining the Raman spectrum using a regularized least squares method.

5. A generation method according to any one of claims 1 to 3, wherein the intensity of the fluorescence is determined in a wavenumber range that does not include a Raman peak.

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