Spectrometer, program, and spectrum measurement method

Abstract

To provide a technique for performing dual comb spectroscopy that is effective when the line width of an optical frequency comb is large.SOLUTION: A spectrometer measures a spectrum of a beat generated by causing two optical frequency combs having different free spectral ranges. A signal processing section to which the beat is input includes: Fourier transform means for performing Fourier transform on the beat to acquire a frequency spectrum; distribution function multiplication means for multiplying the frequency spectrum by a distribution function; numerical integration means for multiplying the frequency spectrum by the distribution function and then performing integration with respect to a frequency; and intensity acquisition means for acquiring intensities of the two optical frequency combs as solutions of simultaneous equations obtained as a result of performing the integration with respect to the frequency.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present invention relates to a spectrometer, a program, and a spectrum measurement method suitable for use in dual-comb spectroscopy. [Background technology]

[0002] Dual-comb spectroscopy is known as one of the methods for performing spectroscopic measurement. Dual-comb spectroscopy is a spectroscopic technique that uses light called an optical frequency comb (see, for example, Patent Document 1).

[0003] An optical frequency comb is a type of light with discrete, evenly spaced frequency components, as shown in Figure 1. It is called an optical frequency comb because the optical frequency spectrum resembles a comb in the frequency domain. The frequency of each component (also called a mode) is expressed by the following equation (1):

[0004]

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[0005] where n is an integer and f r is the free spectral range (FSR) that represents the interval between adjacent frequency components, and f CEO is called the Carrier Envelope Offset frequency.

[0006] Multi-heterodyne detection will be described with reference to Fig. 2. Fig. 2 is a schematic diagram for explaining multi-heterodyne detection.

[0007] When two optical frequency combs with slightly different FSRs interfere with each other, that is, an optical frequency comb whose frequency is given by the above equation (1) (denoted by I in Fig. 2) and an optical frequency comb whose frequency is given by the following equation (2) (denoted by II in Fig. 2), a beat whose frequency is given by the following equation (3) is generated between the nth modes of each comb (denoted by III in Fig. 2).

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[0010] In this way, the spectrum of the beat also has a comb-like spectral shape similar to that of the optical frequency comb. In other words, the spectrum of the optical frequency comb is "copied" onto the spectrum of the beat. Using the above principle, multi-heterodyne detection makes it possible to determine the spectrum of the optical frequency comb from the spectrum of the beat.

[0011] In dual-comb spectroscopy, two optical frequency combs with slightly different FSRs are prepared as described above, and one or both of the optical frequency combs are passed through a measurement sample. The absorption spectrum of the sample can then be determined by measuring the spectrum of the beat generated by the interference of the two optical frequency combs.

[0012] One light source for an optical frequency comb uses a narrow-linewidth continuous-wave laser and a ring resonator made of special materials (such as silica or silicon nitride) (see, for example, Non-Patent Document 1). In Non-Patent Document 1, a continuous-wave laser is injected into the ring resonator, and many modes are generated by nonlinear optical phenomena. [Prior art documents] [Patent documents]

[0013] [Patent Document 1] Japanese Patent Application Publication No. 2022-38579 [Non-patent literature]

[0014] [Non-Patent Document 1] M.-G. Suh et al., “Microresonator soliton dual-comb spectroscopy” Science 354, 600-603 (2016). Summary of the Invention [Problem to be solved by the invention]

[0015] Here, multi-heterodyne detection is based on the premise that each mode of the optical frequency comb has an infinitely narrow linewidth like a delta function. As disclosed in Non-Patent Document 1, by using a narrow-linewidth laser and a ring resonator made of silicon nitride or the like, it is possible to generate an optical frequency comb with a narrow linewidth through the nonlinear optical effect.

[0016] However, both narrow-linewidth lasers and ring resonators made of materials such as silicon nitride are expensive.

[0017] Therefore, the inventors of this application investigated generating an optical frequency comb using a relatively inexpensive broadband light source and a silicon ring resonator. In this case, an optical frequency comb is generated by extracting broadband light generated by the broadband light source at a fixed frequency interval using the ring resonator.

[0018] However, when an optical frequency comb is generated using a broadband light source and a silicon ring resonator, the linewidth of each mode of the optical frequency comb tends to be thicker than with the technique disclosed in Non-Patent Document 1.

[0019] Multi-heterodyne detection when the linewidth of each mode is increased will be described with reference to Fig. 3. Fig. 3 is a schematic diagram for explaining multi-heterodyne detection when the linewidth of each mode is increased.

[0020] When optical frequency combs with slightly different FSRs interfere with each other, i.e., an optical frequency comb (denoted by I in Figure 3) whose frequency is given by the above equation (1) and an optical frequency comb (denoted by II in Figure 3) whose frequency is given by the above equation (2), a beat is generated from the nth modes of each comb (denoted by III in Figure 3) whose frequency is given by the above equation (3). In this case, a discrepancy occurs between the spectrum of the optical frequency comb shown by curve I and the spectrum of the beat shown by curve III. This is because the linewidth of the frequency comb spectra shown by curves I and II is thickened, and therefore the linewidth of the beat spectrum shown by curve III is even thicker, resulting in overlap between the modes.

[0021] The present invention has been made in consideration of the above-mentioned problems, and aims to provide a spectrometer, program, and spectrum measurement method suitable for use in dual-comb spectroscopy, which is effective when the linewidth of the optical frequency comb is wide, for example, when an inexpensive broadband light source and a ring resonator made of ordinary silicon are used. [Means for solving the problem]

[0022] In order to achieve the above-mentioned object, the spectrometer of the present invention is a spectrometer that measures the spectrum of a beat signal generated by interfering with two optical frequency combs with different free spectral ranges, and includes a signal processing unit to which the beat signal is input, which includes: Fourier transform means that performs a Fourier transform on the beat to obtain a frequency spectrum; distribution function multiplication means that multiplies the frequency spectrum by a distribution function obtainable from the two optical frequency combs; numerical integration means that multiplies the frequency spectrum by the distribution function and then integrates it with respect to frequency; and intensity acquisition means that acquires the intensities of the two optical frequency combs as solutions to simultaneous equations obtained as a result of integrating it with respect to frequency.

[0023] According to a preferred embodiment of the spectrometer of the present invention, the two frequency combs are a signal light and a local oscillator light that are approximated by a Lorentz distribution, and the spectrum S of the signal light is S (f) and the spectrum S of the local oscillator light LO(f) is given by the following equations (1a) to (3a), and the spectrum S of the beat signal is RF (f) is given by the following equation (4a), the simultaneous equations are given by the following equation (5a), and the intensity acquisition means obtains the signal light intensity P s,n and the intensity of the local oscillator light P LO,n Get.

[0024]

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[0025] According to a further preferred embodiment of the spectrometer of the present invention, the spectrometer includes an optical unit that generates the beat signal. The optical unit includes a broadband light source that generates broadband light, an optical demultiplexer that splits the broadband light into the first light and the second light, a first ring resonator and a second ring resonator to which the first light and the second light are respectively input, an optical multiplexer that multiplexes the signal light generated by the first ring resonator and the local oscillator light generated by the second ring resonator, and a photodetector that photoelectrically converts the interference light multiplexed by the optical multiplexer to generate the beat signal, which is an electrical signal, and sends the beat signal to the signal processing unit. The free spectral range of the first ring resonator and the free spectral range of the second ring resonator are different from each other.

[0026] According to still another preferred embodiment of the spectrometer of the present invention, there is provided an optical unit for generating the beat signal, the optical unit including a broadband light source for generating broadband light, an optical demultiplexer for branching the broadband light into the first light and the second light, a first ring resonator and a second ring resonator to which the first light and the second light are respectively input, and a spectrometer having a free spectral range of f r and a signal light having a free spectral range f r +Δf r and a photodetector that photoelectrically converts the interference light multiplexed by the optical multiplexer to generate the beat, which is an electrical signal, and sends it to the signal processing unit.

[0027] Furthermore, in implementing the spectrometer of the present invention, the first ring resonator may be replaced with a first Fabry-Perot filter, and the second ring resonator may be replaced with a second Fabry-Perot filter.

[0028] Furthermore, according to the program of the present invention, the signal processing unit is caused to realize each of the above-mentioned functional means.

[0029] Furthermore, a method for measuring the spectrum of a beat signal generated by interfering with two optical frequency combs having different free spectral ranges according to the present invention includes the steps of: performing a Fourier transform on the beat signal to obtain a frequency spectrum; multiplying the frequency spectrum by a distribution function; multiplying the frequency spectrum by the distribution function and then integrating with respect to frequency; and obtaining the intensities of the two optical frequency combs as solutions to simultaneous equations obtained as a result of integrating with respect to frequency.

[0030] According to a preferred embodiment of the spectrum measuring method of the present invention, the two frequency combs are a signal light and a local oscillator light that are approximated by a Lorentz distribution, and the spectrum S of the signal light is S (f) and the spectrum S of the local oscillator light LO (f) is given by the above formulas (1a) to (3a), and the spectrum S of the beat RF (f) is given by the above equation (4a), the simultaneous equations are given by the above equation (5a), and in the process of acquiring the intensities of the two optical frequency combs, the signal light intensity P s,n and the intensity of the local oscillator light P LO,n Get.

[0031] Furthermore, according to a further preferred embodiment of the spectrum measurement method of the present invention, the method includes the steps of: generating broadband light; splitting the broadband light into the first light and the second light; generating signal light in a first ring resonator; generating local oscillator light in a second ring resonator; combining the signal light and the local oscillator light to generate interference light; and performing photoelectric conversion on the interference light to generate the beat, which is an electrical signal, wherein the first ring resonator and the second ring resonator have different free spectral ranges.

[0032] According to still another preferred embodiment of the spectrum measuring method of the present invention, the method further comprises the steps of: splitting the broadband light into the first light and the second light; and determining whether a free spectral range is f r The process of generating a signal light with a free spectral range of f r +Δf r a step of generating local oscillator light, which is a signal light and a local oscillator light, to generate interference light; and a step of photoelectrically converting the interference light to generate the beat, which is an electrical signal.

[0033] Furthermore, in carrying out the spectrum measurement method of the present invention, a configuration may be adopted in which a first Fabry-Perot filter is used instead of the first ring resonator, and a second Fabry-Perot filter is used instead of the second ring resonator. [Effects of the Invention]

[0034] According to the spectrometer, program, and spectrum measurement method of the present invention, when measuring the spectrum of a beat generated by the interference of two optical frequency combs with different free spectral ranges, the beat frequency spectrum is multiplied by a distribution function and numerically integrated to obtain the intensity. This enables accurate dual-comb spectroscopy even when the optical frequency comb linewidth is wide, such as when using an inexpensive broadband light source and a ring resonator made of ordinary silicon. [Brief explanation of the drawings]

[0035] [Figure 1] FIG. 1 is a schematic diagram for explaining an optical frequency comb. [Figure 2] FIG. 1 is a schematic diagram (1) for explaining multi-heterodyne detection. [Figure 3] FIG. 2 is a schematic diagram (2) for explaining multi-heterodyne detection. [Figure 4] FIG. 2 is a schematic diagram for explaining a spectrometer. [Figure 5] FIG. 1 is a schematic diagram for explaining an Airy distribution. [Figure 6] FIG. 10 is a diagram showing verification results by numerical calculation. DETAILED DESCRIPTION OF THE INVENTION

[0036] Hereinafter, embodiments of the present invention will be described with reference to the drawings. However, the shape, size, and positional relationship of each component are merely shown in a schematic manner to enable understanding of the present invention. Furthermore, while preferred configuration examples of the present invention will be described below, the materials and numerical conditions of each component are merely preferred examples. Therefore, the present invention is not limited to the following embodiments, and many changes and modifications can be made that achieve the effects of the present invention without departing from the scope of the configuration of the present invention.

[0037] The spectrometer of the present invention will be described with reference to Fig. 4. Fig. 4 is a schematic diagram for explaining the spectrometer of the present invention.

[0038] The spectrometer comprises an optical section 100 and a signal processing section 200 .

[0039] The optical unit 100 includes a broadband light source 110 , an optical demultiplexer 120 , a first ring resonator 130 , a second ring resonator 140 , an optical multiplexer 150 , and a photodetector 160 .

[0040] The broadband light source 110 generates broadband light. Any suitable conventional light source capable of generating light with a white spectrum, such as an ASE (Amplified Spontaneous Emission) light source that amplifies and emits spontaneous emission light, or a halogen lamp, can be used as the broadband light source 110. The broadband light generated by the broadband light source 110 is sent to the optical demultiplexer 120.

[0041] As the optical demultiplexer 120, any suitable conventionally known element having the function of splitting input light into two, such as a beam splitter (BS), can be used. The optical demultiplexer 120 splits the broadband light generated by the broadband light source 110 into a first light and a second light. The first light is sent to the first ring resonator 130, and the second light is sent to the second ring resonator 140.

[0042] The ring resonator amplifies and outputs light of a frequency that matches the resonant frequency. The first ring resonator 130 amplifies the input light of a predetermined frequency of the first light to generate and output signal light. The second ring resonator 140 amplifies the input light of a predetermined frequency of the second light to generate and output signal light. The FSRs of the first ring resonator 130 and the second ring resonator 140 are slightly different. Here, the FSR of the first ring resonator 130, i.e., the FSR of the signal light, is defined as f r The FSR of the second ring resonator 140, that is, the FSR of the local oscillator light, is set to f r +Δf r Let's say.

[0043] Instead of the ring resonator, a Fabry-Perot filter may be used.

[0044] The signal light output from the first ring resonator 130 and the local oscillator light output from the second ring resonator 140 are multiplexed by the optical multiplexer 150 and undergo heterodyne interference for each mode. The optical multiplexer 150 can be any suitable conventionally known element that has the function of multiplexing two lights input to two ports. The optical multiplexer 150 can be configured with a BS similar to the optical demultiplexer 120. The optical multiplexer 150 is arranged in the opposite direction to the optical demultiplexer 120 with respect to the light propagation direction. The interference light output from the optical multiplexer 150 is sent to the optical receiver 160.

[0045] The optical receiver 160 is configured with any suitable conventionally known element, such as a photodiode (PD), that has the function of photoelectrically converting an input optical signal into an electrical signal and outputting it. The optical signal input to the optical receiver 160 is photoelectrically converted by the optical receiver 160 and sent to the signal processing unit 200 as a beat signal, which is an analog electrical signal.

[0046] The signal processing unit 200 is configured to include, for example, an analog-to-digital converter (ADC) 210 and an arithmetic unit 220. The ADC 210 has a function of converting an input analog electrical signal into a digital electrical signal and can have any suitable conventionally known configuration. The arithmetic unit 220 is a device having a function of processing digital electrical signals and can have any suitable conventionally known configuration, such as a personal computer (PC), except for the functional means realized by the arithmetic unit 220. The functional means of the arithmetic unit 220 are realized by executing a program stored in any suitable storage device.

[0047] Because the first and second lights undergo heterodyne interference in combiner 150, when the signal sent to processor 220 is Fourier transformed, if each mode of the optical frequency comb has an infinitely thin linewidth like a delta function, it will become the beat signal shown by curve III in Fig. 2. However, when broadband light source 110 and silicon ring resonators 130 and 140 are used, the linewidth of each mode of the optical frequency comb becomes thick, resulting in the spectrum shown by curve III in Fig. 3.

[0048] Therefore, in the spectrometer of the present invention, the arithmetic unit 220 includes, as functional means, a Fourier transform means 222, a distribution function multiplication means 224, a numerical integration means 226, an intensity acquisition means 228, and an analysis means 230.

[0049] Here, we assume that the spectrum of the optical frequency comb is a superposition of Lorentzian distributions, which is justified for the following reasons.

[0050] When the spectrum of the broadband light input to the first ring resonator 130 and the second ring resonator 140 is completely flat, the spectrum of the output light is represented by the Airy distribution shown in Fig. 5. Fig. 5 is a schematic diagram showing an Airy distribution. In Fig. 5, the horizontal axis represents frequency (THz) and the vertical axis represents intensity (au).

[0051] The Airy distribution can be expressed as a superposition of the Lorentz distribution, as shown in the following equation (4).

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[0053] Even if the broadband light input to the first ring resonator 130 and the second ring resonator 140 is not completely flat, it can often be approximated as flat within the range of the linewidth of each mode. Therefore, the spectrum of the light output from the first ring resonator 130 and the second ring resonator 140 can be expressed as a superposition of Lorentzian distributions. In addition to the light output from a ring resonator that inputs broadband light, the spectrum of each mode of an optical frequency comb can often be approximated by a Lorentzian distribution. Therefore, the assumption that the spectrum of the optical frequency comb used in dual-comb spectroscopy is a superposition of Lorentzian distributions is justified.

[0054] When the spectrum of the optical frequency comb is a superposition of Lorentzian distributions, the spectrum S of the optical frequency comb of the signal light and the local oscillator light is S (f) and S LO (f) are expressed by the following equations (5) and (6), respectively.

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[0056]

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[0057] where f CEO is the carrier envelope offset frequency, f r and f r +Δf r are the FSRs of the signal light and the local oscillator light, respectively, n is an integer representing the mode, and P s,n and P LO,n are the intensities of each mode n of the signal light and the local oscillator light, respectively. Also, L(f; f0, α) is a Lorentz distribution with f0 as the mode and α as the linewidth (full width at half maximum), and is expressed by the following equation (7).

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[0059] When the signal light and the local oscillator light interfere with each other, a beat occurs according to the frequency difference between them. Considering that each mode of the signal light and the local oscillator light has a spectral spread, the spectrum of the beat S RF (f) is expressed by the following equation (8).

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[0061] The bandwidth of the photodiode that is the receiver 160 is f r Assuming that n = n', the beat is observed only when n = n'. Therefore, the observed beat signal is given by the following equation (9).

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[0063] The distribution function multiplication means 224 multiplies both sides of the above equation (9) by the distribution function, and the integration means 226 integrates with respect to f, to obtain the following equation (10). Here, the distribution function to be multiplied is, for example, the Lorentz function L(f;mΔf r ,2α).

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[0065] The left side of the above formula (10) can be calculated by numerical integration of the Lorentz function corresponding to each m and the spectrum of the beat, which is the measured value. s,n and P LO,n Therefore, the above equation (10) is a simultaneous equation and can be solved by numerical calculation.

[0066] where Δf rand α can be determined by approximation using any suitable conventionally known method such as the least squares method based on the outputs from the first ring resonator 130 and the second ring resonator 140 that have been measured in advance. r and α may be determined based on the interference light between the signal light and the local oscillator light.

[0067] The intensity acquisition means 228 solves the simultaneous equations given by the above formula (10) to obtain P s,n and P LO,n Ask for.

[0068] The analysis means 230 may, for example, determine P s,n and P LO,n and P when no sample is present s,n and P LO,n As a result, the absorbance of the sample can be determined. Note that the comparison when a sample is present and when it is not present can be arbitrarily and suitably set by a person skilled in the art. For example, in the configuration example shown in FIG. 4, before placing the sample at the measurement target location, P s,n and P LO,n After placing the sample at the measurement location, P when the sample is present is measured. s,n and P LO,n Alternatively, the output of the multiplexer can be split into two, and one of them can be used to measure P s,n and P LO,n The other optical path is used to measure the P when a sample is present. s,n and P LO,n It may be configured to measure the above.

[0069] The measurement location where the sample is placed may be between the first ring resonator 130 and the optical multiplexer 150, between the second ring resonator 140 and the optical multiplexer 150, or between the optical multiplexer 150 and the photodetector 160.

[0070] The results of verifying the operation of the spectrometer of the present invention through numerical calculations will be described with reference to Fig. 6. Fig. 6 is a diagram showing the results of the verification through numerical calculations. In Fig. 6, the horizontal axis represents frequency (unit: Hz) and the vertical axis represents absorbance (au). Curve I represents the original spectrum, Curve II represents the spectrum before signal processing, and Curve III represents the spectrum after signal processing.

[0071] Here, we assume a sample with a Lorentzian distribution type absorption line with a center frequency of approximately 193 THz and a full width at half maximum of 150 GHz. r =1.25GHz, f r =50GHz.

[0072] As shown in Figure 6, the spectrum (II) before using the distribution function multiplication means, numerical integration means, and intensity acquisition means (before signal processing) has a wider spectral width than the original spectrum (I). On the other hand, the spectrum (III) after using the distribution function multiplication means, numerical integration means, and intensity acquisition means (after signal processing) has a narrower spectral width than the spectrum (II) before signal processing, i.e., it has better accuracy. Furthermore, the spectrum (III) after signal processing can reproduce the spectral shape of the original spectrum (I), indicating that accurate absorption spectrum measurement is possible.

[0073] As described above, the spectrometer of the present invention can use an inexpensive broadband light source and a ring resonator made of silicon, without using an expensive narrow-linewidth laser and a ring resonator made of silicon nitride, etc. The signal processing unit included in the spectrometer of the present invention is not limited to the optical frequency comb generated from the broadband light source and ordinary ring resonator described above, but can also be applied when the linewidth of each mode is wide. 。

[0074] In the above-described embodiment, it is assumed that the spectrum of the optical frequency comb or beat is a superposition of Lorentzian distributions, but this is not limiting. Taking into account the influence of measurement noise and the like, it is also possible to assume that the spectrum is a Voigt distribution or the like. [Explanation of symbols]

[0075] 100 Optics Department 110 Broadband Light Source 120 Optical demultiplexer 130, 140 Ring resonator 150 Optical multiplexer 160 Receiver 200 Signal processing section 210 ADC 220 Arithmetic equipment 222 Fourier transform means 224 Distribution Function Multiplication Means 226 Numerical Integration Methods 228 Intensity acquisition means 230 Analysis Means

Claims

1. A spectrometer for measuring a spectrum of a beat signal generated by interfering two optical frequency combs with different free spectral ranges, comprising: a signal processing unit to which the beat signal is input, a Fourier transform means for Fourier transforming the beat signal to obtain a frequency spectrum; a distribution function multiplication means for multiplying the frequency spectrum by a distribution function; a numerical integration means for multiplying the frequency spectrum by the distribution function and then integrating with respect to frequency; and an intensity acquisition means for acquiring the intensities of the two optical frequency combs as a solution to a simultaneous equation obtained by integrating the frequencies; A spectrometer comprising:

2. the two frequency combs are a signal light and a local oscillator light that are approximated by a Lorentzian distribution, The spectrum SS(f) of the signal light and the spectrum SLO(f) of the local oscillator light are given by the following equations (1) to (3): The spectrum SRF(f) of the beat is given by the following equation (4): The simultaneous equations are given by the following equation (5): The intensity acquisition means acquires the intensity Ps,n of the signal light and the intensity PLO,n of the local oscillator light as solutions to the simultaneous equations.

10. The spectrometer of claim 1. [Equation 1]

3. an optical unit that generates the beat signal, The optical part is a broadband light source for generating broadband light; an optical demultiplexer that splits the broadband light into two, the first light and the second light; a first ring resonator and a second ring resonator to which the first light and the second light are respectively input; an optical multiplexer that multiplexes the signal light generated by the first ring resonator and the local oscillator light generated by the second ring resonator; a photodetector that photoelectrically converts the interference light multiplexed by the optical multiplexer to generate the beat, which is an electrical signal, and sends the beat to the signal processing unit; Equipped with The free spectral range of the first ring resonator and the free spectral range of the second ring resonator are different from each other.

10. The spectrometer of claim 1.

4. an optical unit that generates the beat signal, The optical part is a broadband light source for generating broadband light; an optical demultiplexer that splits the broadband light into two, the first light and the second light; a first ring resonator and a second ring resonator to which the first light and the second light are respectively input; The free spectral range generated by the first ring resonator is f ｒ and a signal light having a free spectral range f generated by the second ring resonator. ｒ +Δf ｒ an optical multiplexer that multiplexes the local oscillator light; a photodetector that photoelectrically converts the interference light multiplexed by the optical multiplexer to generate the beat, which is an electrical signal, and sends the beat to the signal processing unit; Equipped with 3. The spectrometer of claim 2.

5. a first Fabry-Perot filter is provided instead of the first ring resonator; A second Fabry-Perot filter is provided in place of the second ring resonator. A spectrometer according to any one of claims 3 to 4.

6. A beat signal generated by interfering two optical frequency combs with different free spectral ranges is input to a signal processing unit. a Fourier transform means for Fourier transforming the beat signal to obtain a frequency spectrum; a distribution function multiplication means for multiplying the frequency spectrum by a distribution function; a numerical integration means for multiplying the frequency spectrum by the distribution function and then integrating with respect to frequency; and an intensity acquisition means for acquiring the intensities of the two optical frequency combs as a solution to a simultaneous equation obtained by integrating the frequencies; A program to make this happen.

7. the two frequency combs are a signal light and a local oscillator light that are approximated by a Lorentzian distribution, The spectrum S of the signal light Ｓ (f) and the spectrum S of the local oscillator light ＬＯ (f) is given by the following equations (1) to (3): The spectrum S of the beat ＲＦ (f) is given by the following equation (4): The simultaneous equations are given by the following equation (5): The intensity acquisition means obtains the signal light intensity P ｓ，ｎ and the intensity P of the local oscillator light ＬＯ，ｎ Get The program according to claim 6. [Equation 1]

8. A method for measuring the spectrum of a beat signal generated by interfering two optical frequency combs having different free spectral ranges, comprising: performing a Fourier transform on the beat signal to obtain a frequency spectrum; multiplying the frequency spectrum by a distribution function; multiplying the frequency spectrum by the distribution function and then integrating with respect to frequency; and obtaining the intensities of the two optical frequency combs as solutions to simultaneous equations obtained by integrating with respect to the frequencies. A spectrum measurement method comprising:

9. the two frequency combs are a signal light and a local oscillator light that are approximated by a Lorentzian distribution, The spectrum S of the signal light Ｓ (f) and the spectrum S of the local oscillator light ＬＯ (f) is given by the following equations (1) to (3): The spectrum S of the beat ＲＦ (f) is given by the following equation (4): The simultaneous equations are given by the following equation (5): In the process of acquiring the intensities of the two optical frequency combs, the signal light intensity P ｓ，ｎ and the intensity P of the local oscillator light ＬＯ，ｎ Get The spectrum measurement method according to claim 8. [Equation 1]

10. generating broadband light; splitting the broadband light into two beams, the first beam and the second beam; generating signal light in a first ring resonator; generating local oscillation light in a second ring resonator; a step of generating interference light by combining signal light and local oscillator light; A step of photoelectrically converting the interference light to generate the beat, which is an electrical signal. Equipped with The first ring resonator and the second ring resonator have different free spectral ranges. The spectrum measurement method according to claim 8.

11. splitting the broadband light into two beams, the first beam and the second beam; The first ring resonator has a free spectral range of f ｒ generating a signal light in which The free spectral range of the second ring resonator is f ｒ +Δf ｒ generating a local oscillator light having a wavelength of 1000 kHz; a step of generating interference light by combining signal light and local oscillator light; A step of photoelectrically converting the interference light to generate the beat, which is an electrical signal. Equipped with The spectrum measurement method according to claim 9.

12. a first Fabry-Perot filter is used instead of the first ring resonator; A second Fabry-Perot filter is used instead of the second ring resonator. The spectrum measuring method according to any one of claims 10 to 11.

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