JP2011174798A - Spectrum analyzer and spectrum analysis method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a spectrum analyzer capable of analyzing highly accurately a spectrum of a measuring object. <P>SOLUTION: This spectrum analyzer for analyzing the spectrum of the measuring object includes: a measuring part for measuring the spectrum of the measuring object; an operation part for determining each inner product between each basis vector in an orthogonal system generated from linearly-independent n-th dimensional vectors to the number of n including a reference vector, and a measured vector, assuming that a vector acquired by expressing the spectrum measured by the measuring part as an n-th dimensional vector is the measured vector, and that a vector acquired by expressing a reference spectrum as an n-th dimensional vector is the reference vector; and an output part for outputting the inner product determined by the operation part. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a spectrum analysis apparatus and a spectrum analysis method for analyzing a spectrum of a measurement object.

  In order to obtain the characteristics of the measurement object, a method of measuring the spectrum of the electromagnetic wave when the measurement object is irradiated with the electromagnetic wave is used. For example, when the object to be measured is a gas, a method of measuring the gas concentration using an infrared absorption spectrum when the gas is irradiated with infrared light has been proposed (Patent Document 1).

JP 2007-309800 A

In general, the spectrum shape of the measurement object is often a unique shape depending on the characteristics of the measurement object. On the other hand, the spectrum intensity of the measurement object often depends on the measurement conditions.
For example, when an infrared absorption spectrum is measured when a gas is irradiated with laser light in the infrared region, it is possible to determine whether or not a predetermined gas (for example, NO ₂ ) is included from the shape of the spectrum. . However, the intensity of the spectrum decreases as the gas concentration decreases. In addition, when other types of gas (for example, CO ₂ ) are included or when moisture is included, the shape of the spectrum can change. Therefore, it may be difficult to determine whether or not a predetermined gas is included from the shape of the spectrum.
In recent years, in an actual field where it is not always easy to maintain a good measurement environment, for example, a technique for measuring the concentration of a gas such as NO ₂ with high accuracy is desired.

  Therefore, an object of the present invention is to provide a spectrum analysis apparatus and a spectrum analysis method that can analyze a spectrum of a measurement object with high accuracy.

  The spectrum analyzer of the present invention is a spectrum analyzer for analyzing the spectrum of a measurement object, a measurement unit for measuring the spectrum of the measurement object, and a vector expressing the spectrum measured by the measurement unit as an n-dimensional vector Is a measurement vector, and a vector in which a reference spectrum is represented by an n-dimensional vector is a reference vector, each orthogonal base vector generated from n linearly independent n-dimensional vectors including the reference vector, the measurement vector, And an output unit for outputting the inner product obtained by the operation unit.

  Further, if a basis vector generated based on the reference vector among the basis vectors of the orthogonal system is a reference basis vector, it is determined whether or not an inner product of the reference basis vector and the measurement vector is larger than a predetermined value. It is preferable that an analysis unit for determination is provided, and the output unit outputs a result determined by the analysis unit.

  Further, the analysis unit uses the information indicating the relationship between the magnitude of the inner product of the reference basis vector and the measurement vector and the physical quantity of the measurement object, to calculate the inner product of the reference basis vector and the measurement vector. It is preferable to obtain the physical quantity of the measurement object from the size.

  The reference spectrum is preferably a spectrum obtained by measuring a known measurement object by the measuring unit.

  Further, the measurement unit receives an electromagnetic wave transmitted through the measurement object, an electromagnetic wave irradiation unit that irradiates the measurement object with an electromagnetic wave, a control unit that adjusts a wavelength of the electromagnetic wave irradiated by the electromagnetic wave irradiation unit, It is preferable that the measurement unit measures the spectrum by irradiating the object to be measured with electromagnetic waves having different wavelengths.

  The measurement object is a gas, and the analysis unit preferably determines whether or not the measurement object includes a predetermined gas using an inner product of the reference basis vector and the measurement vector. .

  Moreover, it is preferable that the said analysis part calculates | requires the density | concentration of the said measurement target object from the magnitude | size of the inner product of the said reference basis vector and the said measurement vector.

  The spectrum analysis method of the present invention is a spectrum analysis method for analyzing a spectrum of a measurement object, a measurement process for measuring the spectrum of the measurement object, and an n-dimensional vector representing the spectrum measured in the measurement process. As a measurement vector and a vector expressing a reference spectrum as an n-dimensional vector as a reference vector, each orthogonal base vector generated from linearly independent n n-dimensional vectors including the reference vector And an output step for outputting an inner product obtained in the operation step.

  Further, if a basis vector generated based on the reference vector among the basis vectors of the orthogonal system is a reference basis vector, it is determined whether or not an inner product of the reference basis vector and the measurement vector is larger than a predetermined value. It is preferable to have an analysis step for discrimination, and the output step outputs the result discriminated in the discrimination step.

  Further, the analysis step uses the information indicating the relationship between the magnitude of the inner product of the reference basis vector and the measurement vector and the physical quantity of the measurement object, to calculate the inner product of the reference basis vector and the measurement vector. It is preferable to obtain the physical quantity of the measurement object from the size.

  The reference spectrum is preferably a spectrum obtained by measuring a known measurement object.

  In addition, the measurement step includes an electromagnetic wave irradiation step of irradiating the measurement object with an electromagnetic wave, a wavelength adjustment step of adjusting a wavelength of the electromagnetic wave irradiated in the electromagnetic wave irradiation step, and an electromagnetic wave transmitted through the measurement object. It is preferable to measure the spectrum by irradiating the object to be measured with electromagnetic waves having different wavelengths.

  The measurement object is a gas, and the analysis step preferably determines whether or not the measurement object contains a predetermined gas using an inner product of the reference basis vector and the measurement vector. .

  Moreover, it is preferable that the said analysis process calculates | requires the density | concentration of the said measurement target object from the magnitude | size of the inner product of the said reference basis vector and the said measurement vector.

  According to the present invention, the spectrum of the measurement object can be analyzed with high accuracy.

It is a figure which shows an example of schematic structure of the spectrum analyzer of embodiment. It is a figure which shows an example of a reference spectrum. It is a figure which shows an example of a measurement spectrum. It is a figure which shows an example of the inner product ( _wk * x) which an output part outputs. It is a flowchart which shows an example of the spectrum analysis method of embodiment. (A) is a diagram showing a measurement spectrum of NO ₂ of 1000 ppm, a diagram illustrating a (b) is the inner product _(w k · x). (A) is a diagram showing a measurement spectrum of NO ₂ in 593Ppm, a diagram illustrating a (b) is the inner product _(w k · x). (A) is a diagram showing a measurement spectrum of NO ₂ in 393Ppm, a diagram illustrating a (b) is the inner product _(w k · x). (A) is a diagram showing a measurement spectrum of NO ₂ of 197 ppm, a diagram illustrating a (b) is the inner product _(w k · x). (A) is a diagram showing a measurement spectrum of NO ₂ of 98 ppm, a diagram illustrating a (b) is the inner product _(w k · x). Is a diagram showing the relationship between NO ₂ concentration and the inner product _(w 2 · x).

Hereinafter, a spectrum analysis apparatus and a spectrum analysis method of the present invention will be described based on embodiments.
<First Embodiment>
In the present embodiment, a predetermined gas (for example, NO ₂ ) is measured by measuring an infrared absorption spectrum when the gas (measurement object) is irradiated with laser light in the infrared region and analyzing the measured spectrum. A spectrum analysis apparatus and a spectrum analysis method for obtaining the presence / absence and the concentration of a predetermined gas will be described.

(Schematic configuration of spectrum analyzer)
First, the schematic configuration of the spectrum analyzer of the present embodiment will be described with reference to FIG. FIG. 1 is a diagram illustrating an example of a schematic configuration of a spectrum analysis apparatus according to the present embodiment. As shown in FIG. 1, the spectrum analysis apparatus according to the present embodiment includes a measurement unit 100, a calculation unit 120, an output unit 130, and an analysis unit 140.

(Measurement part)
First, the measurement unit 100 will be described. The measurement unit 100 measures the spectrum of the measurement object. As shown in FIG. 1, the measurement unit 100 of this embodiment includes an electromagnetic wave irradiation unit 102, a control unit 104, a gas cell 106, and a reception unit 108. The electromagnetic wave irradiation unit 102 of the present embodiment is a quantum cascade laser (QCL) that irradiates laser light in the infrared region. The electromagnetic wave irradiation unit 102 can irradiate laser light in a wavelength band including, for example, a wavelength of 6.1 μm.

The control unit 104 controls the wavelength of the electromagnetic wave emitted by the electromagnetic wave irradiation unit 102. The control unit 104 of this embodiment includes a temperature adjustment unit that controls the temperature of the electromagnetic wave irradiation unit 102. The wavelength of the laser beam can be controlled by adjusting the temperature of the quantum cascade laser by the temperature adjusting unit. The control unit 104 controls the timing at which the electromagnetic wave irradiation unit 102 irradiates the electromagnetic wave. For example, the control unit 104 can control the electromagnetic wave irradiation unit 102 so that the electromagnetic wave irradiation unit 102 emits pulsed electromagnetic waves.
In addition, the control part 104 can also apply the structure which controls the wavelength of the electromagnetic waves which the electromagnetic wave irradiation part 102 irradiates by controlling the voltage of the electromagnetic wave irradiation part 102.

The gas cell 106 is a container that accommodates a gas that is an object to be measured. In the present embodiment, the gas that is the measurement object contains NO ₂ . The gas cell 106 may be a sealed container or a non-sealed container. For example, the gas cell 106 may be provided with a gas inlet and a gas outlet, and the concentration of the measurement object may be measured while flowing the gas as the measurement object through the gas cell 106.
Note that NO ₂ has a strong absorption line in the vicinity of 6.1 μm.

The receiving unit 108 receives an electromagnetic wave that has passed through a measurement object accommodated in the gas cell 106. The receiving unit 108 of the present embodiment is an infrared sensor having InSb as a light receiving surface. The receiving unit 108 may be, for example, a PIN diode (p-intrinsic-n diode) or a photoconductive element (MCT element: Mercury Cadmium Telluride element) having HgCdTe as a light receiving surface.
The spectrum data of the measurement object measured by the measurement unit 100 described above is supplied to the calculation unit 120. Here, the spectrum data of the measurement object is the intensity of the electromagnetic wave received by the receiving unit 108 with respect to the wavelength of the electromagnetic wave irradiated by the electromagnetic wave irradiation unit 102.

(Calculation unit)
Next, the calculation unit 120 will be described. Here, a vector expressing the spectrum measured by the measurement unit 100 as an n-dimensional vector is taken as a measurement vector. A vector representing a known reference spectrum by an n-dimensional vector is used as a reference vector. At this time, the arithmetic unit 120 obtains an inner product of each base vector of the orthogonal system generated from the n linearly independent n-dimensional vectors including the reference vector and the measurement vector. Here, before describing the calculation performed by the calculation unit 120, a reference vector, an orthogonal system generated from n linearly independent n-dimensional vectors including the reference vector, and a measurement vector will be described.

First, reference vectors will be described with reference to FIG. FIG. 2 is a diagram illustrating an example of a reference spectrum. In the present embodiment, the measurement object is known and the spectrum of the measurement object whose spectrum shape is sufficiently clear is used as the reference spectrum. The reference spectrum of the example shown in FIG. 2 is a spectrum obtained by the measurement unit 100 measuring NO ₂ having a known concentration (1000 ppm). The horizontal axis of FIG. 2 indicates the temperature of the quantum cascade laser (QCL), and the vertical axis indicates the amplitude of the laser beam received by the receiving unit 108. Since the wavelength of the laser light emitted from the quantum cascade laser is controlled by the temperature of the quantum cascade laser, the horizontal axis in FIG. 2 corresponds to the wavelength of the laser light emitted from the quantum cascade laser.

The number of data included in the reference spectrum is n. Also, n pieces of data _{(amplitude) a 1, a 2, ...} , and _{a n.} At this time, the reference spectrum, n pieces of data _{a 1, a 2, ...,} n -dimensional vector _{{a 1, a 2, ...} , a n} whose components each of _{a n} is expressed as. Thus, a vector expressing the reference spectrum as an n-dimensional vector is defined as a reference vector. For convenience of explanation, the reference vector and v _2.

Here, as linear independent of n n-dimensional vector containing the reference vector v _2, defining the v ₁ to v _n as follows.

However, a ₂ ≠ 0. When a ₂ = 0, the reference vector v ₂ is determined so that a non-zero component among the components of the reference vector v ₂ is a ₂ .

Then, orthogonal system will be described which is generated from the reference vector v linearly independent of n n-dimensional vector v ₁ to v _n including _2. In the present embodiment, by using the Gram-Schmidt process, orthonormal system is generated from the n n-dimensional vector v ₁ to v _n.
If the basis vectors of the orthonormal system and _{w 1 ~w n, w 1 ~w} n is determined as follows.

As described above, orthonormal system is generated from the linear independent of n include a reference vector v ₂ n-dimensional vector v ₁ to v _n.

Next, the measurement vector will be described with reference to FIG. FIG. 3 is a diagram illustrating an example of a measurement spectrum. The measurement spectrum is a spectrum obtained by measuring the measurement object by the measurement unit 100 described above. Measurement spectrum example shown in FIG. 3 is a spectrum obtained by measuring unit 100 NO ₂ unknown concentration is measured. As is clear from comparison between FIG. 2 and FIG. 3, the amplitude of each data of the measurement spectrum is smaller than the amplitude of each data of the reference spectrum. Therefore, it is difficult to determine the spectrum in the measurement spectrum compared to the reference spectrum.

The number of data included in the measurement spectrum is n. Also, n pieces of data _{(amplitude) x 1, x 2, ...} , and _{x n.} In this case, the measurement spectrum, n pieces of data _{x 1, x 2, ...,} n -dimensional vector _{{x 1, x 2, ...} , x n} whose components each of _{x n} is expressed as. Thus, a vector expressing a measurement spectrum as an n-dimensional vector is defined as a measurement vector. Hereinafter, for convenience of explanation, it is assumed that the measurement vector is x.

The computing unit 120 obtains an inner product (w _k · x) between each of the orthogonal basis vectors w _k (k = 1, 2,..., N) and the measurement vector x. The inner product (w _k · x) obtained by the calculation unit 120 is supplied to the output unit 130 and the analysis unit 140.

(Output part)
Returning to FIG. 1, the output unit 130 will be described. The output unit 130 outputs the inner product (w _k · x) obtained by the calculation unit 120. The output unit 130 is, for example, a display device. Here, the output of the inner product (w _k · x) by the output unit 130 will be described with reference to FIG. FIG. 4 is a diagram illustrating an example of the inner product (w _k · x) output from the output unit 130. The horizontal axis in FIG. 4 indicates k (natural number), and the vertical axis indicates the value of the inner product (w _k · x). In the example shown in FIGS. 2 and 3 described above, n = 41. Therefore, FIG. 4 shows the value of the inner product (w _k · x) obtained by the calculation unit 120 for each k from k = 1 to k = 41. However, in FIG. 4, in order to improve the visibility, the value of the inner product (w _k · x) of k = 2 and k = 21 is switched. That is, from the left to the right in FIG. 4, the value of the inner product (w _k · x) is shown in the order of k = 1, 21, 3, 4,..., 20, 2, 22,. Has been.

Here, the basis vector w ₂ generated based on the reference vector v ₂ is set as a reference basis vector. Further, as described above, since all the components of the vector v ₁ are 1, all the components of the basis vector w ₁ are equal. Referring basis vectors w ₂ from the reference vector v _2, it is generated by subtracting the basis vectors w ₁ all components equal. This means that those from the reference vector v ₂ to remove the offset is a reference base vector w _2. Therefore, as the shape of the measurement spectrum is similar to the shape of the reference spectrum, the value of the inner product (w ₂ · x) of the reference base vector w ₂ and the measurement vector x increases. On the other hand, since the basis vector w _k is an orthonormal basis vector, the inner product (w _k · x) of the basis vector w _k (k ≠ 1, 2) and the measurement vector x becomes a value close to zero.
Note that the inner product (w ₁ · x) of the base vector w ₁ and the measurement vector x indicates the magnitude of the offset of the measurement spectrum.

As in the example illustrated in FIG. 4, in the graph of the inner product (w _k · x) of the basis vector w _k and the measurement vector x output by the output unit 130, the inner product of the reference basis vector w ₂ and the measurement vector x The observation of a peak at the position (w ₂ · x) means that the shape of the measurement spectrum is similar to the shape of the reference spectrum. Therefore, by observing the presence or absence of a peak at the position of the inner product (w ₂ · x) of the reference basis vector w ₂ and the measurement vector x, the user can determine whether or not NO ₂ is included in the measurement object. I can know.

(Analysis Department)
Returning to FIG. 1, the analysis unit 140 will be described. The analysis unit 140 determines whether or not the inner product (w ₂ · x) of the reference basis vector w ₂ and the measurement vector x is larger than a predetermined value. The result determined by the analysis unit 140 is output by the output unit 130.
As described above, as the measurement object contains more NO ₂ , the inner product (w ₂ · x) of the reference basis vector w ₂ and the measurement vector x increases. Therefore, whether the measurement object contains NO ₂ by the analysis unit 140 determining whether or not the inner product (w ₂ · x) of the reference basis vector w ₂ and the measurement vector x is larger than a predetermined value. It becomes possible to detect whether or not.

(Spectrum analysis method)
Next, the spectrum analysis method of the present embodiment will be described with reference to FIG. FIG. 5 is a flowchart showing an example of the spectrum analysis method of the present embodiment.
First, the measurement part 100 measures the spectrum of a measurement object (step S101). Next, the calculation unit 120 obtains an inner product of each orthogonal base vector w _k generated from the linearly independent n n-dimensional vectors including the reference vector v ₂ and the measurement vector x (step S102).
Next, the analysis unit 140 determines whether or not the inner product (w ₂ · x) of the reference basis vector w ₂ and the measurement vector x is larger than a predetermined value (step S103). Further, the output unit 130 outputs the inner product (w _k · x) obtained by the calculation unit 120 and the result determined by the analysis unit 140 in step S103 (step S104).

Incidentally, from the graph of the inner product (w k _· x) to be output by the output unit 130, if whether contains NO ₂ in the measurement object user observes may skip Step S103.

As described above, according to the present embodiment, the inner product of the orthogonal basis vector w _k generated from the linearly independent n n-dimensional vectors including the reference vector v ₂ and the measurement vector x is obtained. The spectrum of the measurement object can be analyzed with high accuracy.

In the present embodiment, an example has been described in which the measurement unit 100 obtains a reference spectrum by measuring NO ₂ gas having a known concentration, but the method of obtaining a reference spectrum is not limited to this. For example, instead of using the measurement unit 100 to obtain a reference spectrum, data of orthogonal basis vectors w _k generated in advance from a reference spectrum and n linearly independent n-dimensional vectors including the reference vector v ₂ are obtained. The present invention can also be applied when the arithmetic unit 120 stores the information.

In the present embodiment, the reference spectrum has been described as a spectrum obtained by measuring NO _2. However, for example, reference spectra can be obtained for other gases such as CO ₂ . Therefore, even if the measurement object includes a plurality of gases, whether or not each of the plurality of gases is included in the measurement object by the calculation unit 120 performing the above-described calculation using each reference spectrum. Can be determined.

<Second Embodiment>
In the first embodiment, the example in which the spectrum analyzer determines whether or not NO ₂ is included in the measurement object has been described. In the present embodiment, an example will be described in which the spectrum analyzer determines the concentration of NO ₂ contained in the measurement object.
Prior to describing the spectrum analyzer of the present embodiment, a measurement spectrum obtained by the measurement unit 100 measuring a plurality of known concentrations of NO ₂ will be described with reference to FIGS. The inner product (w _k · x) obtained by the arithmetic unit 120 at this time will be described.

FIGS. 6A to 10A are diagrams illustrating an example of a measurement spectrum obtained by the measurement unit 100 measuring NO ₂ having a plurality of known concentrations. FIGS. 6B to 10B are diagrams illustrating an example of the inner product (w _k · x) obtained by the calculation unit 120. The measurement result when the concentration of NO ₂ is 1000 ppm is shown in FIG. The concentration of NO ₂ is shown in Figure 7 the measurement results in the case of 593Ppm. The concentration of NO ₂ is shown in FIG. 8 the measurement results in the case of 393Ppm. The concentration of NO ₂ is shown in Figure 9 the measurement results in the case of 197 ppm. The concentration of NO ₂ is shown in FIG. 10 the measurement results in the case of 98 ppm.

Referring to FIG. 6A to FIG. 10A, it can be seen that the amplitude of the measurement spectrum decreases as the NO ₂ concentration decreases. It can also be seen that the shape of the measurement spectrum becomes less clear as the concentration of NO ₂ decreases.
On the other hand, referring to FIG. 6 (b) to FIG. 10 (b), even if the NO ₂ concentration is lowered, a peak appears at the position of the inner product (w ₂ · x) of the reference basis vector w ₂ and the measurement vector x. You can see that it is observed. Furthermore, it can be seen that the inner product (w ₂ · x) of the reference basis vector w ₂ and the measurement vector x decreases as the concentration of NO ₂ decreases.

Here, the relationship between the concentration of NO ₂ and the inner product (w ₂ · x) will be described with reference to FIG. FIG. 11 is a diagram in which the inner product (w ₂ · x) of FIGS. 6B to 10B is plotted against the NO ₂ concentration. As shown in FIG. 11, the inner product (w ₂ · x) is expressed by a linear function with respect to the NO ₂ concentration. Therefore, as in the example shown in FIG. 10 from FIG. 6, by calculating the inner product _(w 2 · x) with respect to NO ₂ in a plurality of known concentrations, NO ₂ concentration and the inner product _(w 2 · x) A calibration curve showing the relationship between

The analysis unit 140 according to the present embodiment obtains the concentration of NO ₂ (physical quantity of the measurement object) using the calibration curve described above from the magnitude of the inner product (w ₂ · x). Therefore, according to the present embodiment, even when the concentration of NO ₂ is low and it is difficult for the user to determine the shape of the measurement spectrum, it is detected whether or not NO ₂ is included in the measurement object. In addition, the concentration of NO ₂ can be determined. As a result, the spectrum of the measurement object can be analyzed with high accuracy.

  The spectrum analysis apparatus and the spectrum analysis method of the present invention have been described in detail above, but the present invention is not limited to the above embodiment. For example, the present invention can be applied to Fourier transform infrared spectroscopy (FT-IR). It goes without saying that various improvements and modifications may be made without departing from the spirit of the present invention.

DESCRIPTION OF SYMBOLS 100 Measurement part 102 Electromagnetic wave irradiation part 104 Control part 106 Gas cell 108 Reception part 120 Calculation part 130 Output part 140 Analysis part

Claims (14)

A spectrum analyzer for analyzing a spectrum of a measurement object,
A measurement unit for measuring the spectrum of the measurement object;
Assuming that a vector representing the spectrum measured by the measurement unit as an n-dimensional vector is a measurement vector and a vector representing a reference spectrum as an n-dimensional vector is a reference vector, n linearly independent n-dimensional vectors including the reference vector An arithmetic unit for obtaining an inner product of each of the basis vectors of the orthogonal system generated from the measurement vector;
An output unit for outputting the inner product obtained by the arithmetic unit;
The spectrum analyzer characterized by having. If a basis vector generated based on the reference vector among the basis vectors of the orthogonal system is a reference basis vector, it is determined whether or not an inner product of the reference basis vector and the measurement vector is larger than a predetermined value. With an analysis unit,
The spectrum analysis apparatus according to claim 1, wherein the output unit outputs a result determined by the analysis unit.   The analysis unit uses the information indicating the relationship between the magnitude of the inner product of the reference basis vector and the measurement vector and the physical quantity of the measurement object, and the magnitude of the inner product of the reference basis vector and the measurement vector. The spectrum analyzing apparatus according to claim 1, wherein a physical quantity of the measurement object is obtained from   The spectrum analyzer according to any one of claims 1 to 3, wherein the reference spectrum is a spectrum obtained by the measurement unit measuring a known measurement object. The measuring unit is
An electromagnetic wave irradiation unit for irradiating the measurement object with an electromagnetic wave;
A control unit for adjusting the wavelength of the electromagnetic wave emitted by the electromagnetic wave irradiation unit;
A receiver for receiving electromagnetic waves transmitted through the measurement object;
With
The spectrum analyzer according to any one of claims 1 to 4, wherein the measurement unit measures a spectrum by irradiating the object to be measured with electromagnetic waves having different wavelengths. The measurement object is a gas,
The spectrum analysis according to any one of claims 2 to 5, wherein the analysis unit determines whether or not the measurement object includes a predetermined gas using an inner product of the reference basis vector and the measurement vector. apparatus.   The spectrum analysis apparatus according to claim 6, wherein the analysis unit obtains a concentration of the measurement object from a magnitude of an inner product of the reference basis vector and the measurement vector. A spectrum analysis method for analyzing a spectrum of a measurement object,
A measurement step of measuring a spectrum of the measurement object;
Assuming that a vector representing the spectrum measured in the measurement step as an n-dimensional vector is a measurement vector and a vector representing the reference spectrum as an n-dimensional vector is a reference vector, n linearly independent n-dimensions including the reference vector A calculation step of calculating an inner product of each basis vector of the orthogonal system generated from the vector and the measurement vector;
An output step of outputting the inner product obtained in the calculation step;
A spectrum analysis method characterized by comprising: If a basis vector generated based on the reference vector among the basis vectors of the orthogonal system is a reference basis vector, it is determined whether or not an inner product of the reference basis vector and the measurement vector is larger than a predetermined value. Has an analysis process,
The spectrum analysis method according to claim 8, wherein the output step outputs a result determined in the determination step.   The analysis step uses the information indicating the relationship between the magnitude of the inner product of the reference basis vector and the measurement vector and the physical quantity of the measurement object, and the magnitude of the inner product of the reference basis vector and the measurement vector. The spectrum analysis method according to claim 8 or 9, wherein a physical quantity of the measurement object is obtained from the measurement data.   The spectrum analysis method according to claim 8, wherein the reference spectrum is a spectrum obtained by measuring a known measurement object. The measurement step includes
An electromagnetic wave irradiation step of irradiating the measurement object with an electromagnetic wave;
A wavelength adjusting step for adjusting the wavelength of the electromagnetic wave irradiated in the electromagnetic wave irradiation step;
A receiving step of receiving electromagnetic waves transmitted through the measurement object;
Have
The spectrum analysis method according to claim 8, wherein the spectrum is measured by irradiating the object to be measured with electromagnetic waves having different wavelengths. The measurement object is a gas,
The spectrum analysis according to any one of claims 9 to 12, wherein the analysis step determines whether or not the measurement object contains a predetermined gas using an inner product of the reference basis vector and the measurement vector. Method. The spectrum analysis method according to claim 13, wherein the analysis step obtains the concentration of the measurement object from the magnitude of the inner product of the reference basis vector and the measurement vector.