Signal processing method and signal processing device

Abstract

The present invention makes it possible to reduce the burden of calculation for FFT analysis and efficiently perform measurement processing in an optical interference measurement device for performing measurement on the basis of phase spectrum information and amplitude spectrum information acquired through the FFT analysis from interference signals of two optical combs. An FFT algorithm, which performs DFT of order N, is used from data S (v) of the number of samples of kN shown in Equation (6) to obtain spectral components in the frequency domain from time series waveform data obtained by digitizing a time domain interference signal, and calculate an absolute distance D to a measurement surface of an object to be measured 50 from a reference point that is obtained by defining the position of a beam splitter 22A of a measurement interference system 22 as the reference point.

Description

Signal processing method and signal processing device

[0001] The present invention relates to a signal processing method and signal processing device for obtaining frequency domain spectral components from waveform data obtained by digitizing a signal having a periodic or periodic envelope, and is applicable to, for example, an optical interference measurement device that performs measurements based on phase spectrum information and amplitude spectrum information obtained by FFT analysis from the interference signal of two optical combs. This application claims priority based on Japanese Patent Application No. 2024-46168, filed in Japan on March 22, 2024, which is incorporated herein by reference.

[0002] Interfering two optical combs generates an optical interference pattern, which is formed by the difference in the frequency components of the optical frequency combs. Changes in the interference pattern depend on physical quantities (e.g., distance, changes in refractive index, etc.). Optical interferometry measures these physical quantities based on phase spectrum information obtained by FFT analysis of the interference signal between the two optical combs. Optical interferometry is used in many application fields, including precise distance measurement, interference fringe analysis, gas detection, refractive index measurement, and precise time measurement.

[0003] There is known a technique for irradiating a measurement object with coherent measurement light and measuring the distance, speed, vibration, etc. of the measurement object based on an interference signal between the reflected light (return light) and a reference light (see, for example, Patent Documents 1, 2, 3, 4, 5, 6, 7, and 8).

[0004] Patent Document 1 describes OCT based on an interference signal between reflected light (return light) and reference light, and Patent Document 2 describes an interferometer.

[0005] Laser distance meters are known as devices that measure the absolute distance from a given point to a measurement point with high accuracy. For example, Patent Documents 3 and 4 describe distance meters that measure the distance from the time difference between the interference signal of a measurement light and the interference signal of a reference light.

[0006] With conventional absolute distance meters, it was difficult to create a practical absolute distance meter that could measure long distances with high accuracy, and the only option available was to use a method that required returning to the origin, such as a laser displacement meter, which is not suitable for measuring absolute distances, in order to achieve high resolution.

[0007] The present inventors have previously proposed a distance meter, distance measurement method, and optical three-dimensional shape measuring instrument that can perform measurements with high accuracy and in a short time by detecting, with a reference light detector, interference light between reference light irradiated onto a reference surface and measurement light irradiated onto a measurement surface, and detecting, with a measurement light detector, interference light between the reference light reflected by the reference surface and the measurement light reflected by the measurement surface, and determining the difference between the distance to the reference surface and the distance to the measurement surface from the time difference between the two interference signals obtained by the reference light detector and the measurement light detector (see, for example, Patent Document 4).

[0008] The time difference between the two interference signals, i.e., the difference between the distance to the reference surface and the distance to the measurement surface, can be calculated based on phase spectrum information obtained by FFT analysis from the interference signals of the two optical combs.

[0009] Dual Comb spectroscopy has also been proposed as a technology for performing high-precision, high-speed spectroscopic measurements by utilizing the interference signals of two femtosecond lasers with slightly different repetition rates (see Patent Documents 9 and 10, and Non-Patent Documents 1 and 2).

[0010] Dual-comb spectroscopy can be used to characterize the physical properties of solid samples. In dual-comb spectroscopy, a sample (solid, gas, liquid, etc.) is placed in the path of one or both of two optical frequency combs, and an interference waveform between the optical frequency combs that pass through the sample and the optical frequency combs that do not is obtained. By performing Fourier analysis on the phase-corrected and coherent integration of the interference waveform in real time, amplitude and phase spectral information containing the characteristics of the solid sample can be detected. By analyzing the detected amplitude and phase spectral information, information on the physical properties of the sample can be obtained.

[0011] The applicant of the present application has also previously proposed a vibration measuring device and a vibration measuring method that, in a vibrometer that analyzes vibration information on a measurement surface of an object by detecting interference light between reference light and measurement light, which are spectra at a predetermined frequency interval and are phase-synchronized and coherent with each other, and determining the phase difference between the reference light and measurement light, uses a spectroscopic / multiplexing head that separates the measurement light into frequency components and irradiates the measurement light onto multiple points on the measurement surface of the object, thereby making it possible to simultaneously measure vibration information at multiple points on the measurement surface (see, for example, Patent Documents 5 to 7).

[0012] Japanese Patent Publication No. 2017-046739 Japanese Patent Publication No. 2021-143995 U.S. Patent No. 8,558,993 Japanese Patent No. 5,231,883 Japanese Patent No. 5,336,921 Japanese Patent Publication No. 2010-203860 Japanese Patent No. 5,363,231 Japanese Patent Publication No. 2021-056090 U.S. Patent No. 9,557,219 Japanese Patent Publication No. 2017-138129

[0013] S. Schiller, “Spectrometry with frequency combs”, OPTICS LETTERS Vol.27, No.9,May 1, 2002.Microresonator soliton dual-comb spectroscopy | Sciencehttps: / / www.ni.com / docs / ja-JP / bundle / labwindows-cvi / page / advancedanalysisconcepts / lvac_low_sidelobe.html

[0014] In an optical interference measurement device that performs measurements using the interference signals of two optical combs, the time-domain interference signals are digitized by an AD converter to obtain time-series waveform data, which is then converted into a Fourier transform as shown in the following equation (1): (where f ｎ is the nth frequency component, Δf ｃ is the offset frequency and Δf ｒ A commonly used method is to obtain frequency domain spectral components from interference signals occurring at frequencies smaller than 100 kJ / s, where n is the discrete index or frequency component number (0, 1, 2, . . . ).

[0015] One method of calculating spectral components using the Fourier transform is the fast Fourier transform (FFT), which is an algorithm that quickly calculates the discrete Fourier transform (DFT) on a computer. However, this method still poses the problem of a large number of calculations when the number of samples is large.

[0016] When the phase changes over time, such as when measuring vibration or the distance to a moving object, it is necessary to measure the time evolution of each spectral information in the optical comb. In this case, the so-called short-time Fourier transform is used, in which kN overlapping data pieces are extracted from an infinitely long data set while shifting N data pieces, and then the short-time Fourier transform is performed. A typical FFT (fast Fourier transform) algorithm, for example, extracts data with a width of k waveform sections from the interference waveform acquired sequentially in a time series, as shown in Figure 5(A). (Since the waveform section is kN, if one waveform section is 2 μs, data with a time width of k × 2 μs is used.) As shown in Figure 5(B), the waveform with a width of kN is multiplied by a window function (W() or W'()) to perform a kN-order Fourier transform. Next, the extracted waveform is shifted by one waveform section (N) at a time, and a Fourier transform is performed while shifting the range of the window function to analyze the phase evolution of time-varying signals such as vibration and distance. That is, when the waveform section of the FFT is k=4, waveform data arranged in the time series of the measurement interference signal in the same range (k=4) as the waveform data arranged in the time series of the reference interference signal is acquired, and a window function is applied to each data to improve the dynamic range and reduce crosstalk between each frequency component at the expense of the frequency resolution of the waveform data arranged in the time series, and a frequency domain data sequence is obtained by performing FFT processing of order kN of the number of samples kN in the waveform section extended by k times to improve the frequency resolution at the expense of the frequency resolution. Then, from the data sequence of the real part and the imaginary part of the reference interference signal converted into the frequency domain and the data sequence of the real part and the imaginary part of the measurement interference signal, a data sequence of the real part and the imaginary part of the phase difference for each frequency of the measurement interference signal is obtained by complex number calculation, and Δf between the reference interference signal and the measurement interference signal calculated by θ=arctan (imaginary part / real part) is calculated. ｒThe system outputs phase difference data for each frequency, as well as the product of the phase conjugate of the reference interference signal and the measurement interference signal, or the division (phasor product) of the measurement interference signal by the reference interference signal. For example, by performing division, amplitude and phase spectrum information calibrated with the amplitude spectrum of the reference signal can be obtained. Since a vibrometer can collect data continuously for hours or an infinite amount of time, calculations are performed in real time. Therefore, an FPGA is used for calculations. However, when performing an FFT of order kN, the larger k is, the greater the calculation volume becomes, placing a strain on the FPGA and causing it to overwhelm its computing power. Furthermore, the large amount of output data can potentially interfere with data transfer.

[0017] FIG. 6 is a diagram showing the number of calculations of an FFT calculation algorithm (with window function), with k on the horizontal axis and the number of calculations on the vertical axis.

[0018] As shown in Fig. 6, in the case of an FFT with a window function, the number of calculations (multiplications) required to calculate kN samples, which is k times the number of samples in one waveform section N (assuming N = 256 here), is minimized when the number is a power of 2, and is kNLog2(kN) + kN, where +kN is an additional calculation due to the multiplication of the window function and the signal.

[0019] FIG. 7 shows the frequency on the horizontal axis and the signal intensity on the vertical axis, and the waveform interval (1 / Δf ｒ 1 shows the signal strength and crosstalk when an FFT of order 256 is performed over one waveform section with a rectangular window, assuming a time delay of 2 μs, 256 samples (AD converter 128 MS / s), a beat frequency of 40 MHz, and a Doppler frequency due to vibration of 50 kHz.

[0020] As shown in Fig. 7, when k is small, the crosstalk becomes large, and a single waveform section cannot be used as a vibrometer.

[0021] Furthermore, in FIG. 8, the horizontal axis is frequency and the vertical axis is signal intensity, and a general FFT calculation algorithm (k=8, window function LowSidelobe) is used to calculate one waveform section (1 / Δf ｒThis figure shows the signal strength and crosstalk when an FFT of order 2048 is performed, assuming a frequency of 2 μs, 256 samples (AD converter 128 MS / s), a beat frequency of 40 MHz, a Doppler frequency due to vibration of 50 kHz, k = 8 waveform sections, and 2048 samples (AD converter 128 MS / s). The required frequency is every 8 intervals, i.e., 500 kHz intervals.

[0022] As shown in Figure 8, when the waveform interval is enlarged and a window function is applied, the crosstalk is extremely small (-120 dB or less in this case). Furthermore, because the waveform interval is wider, the noise bandwidth is smaller, improving the S / N ratio. However, even if an FFT is performed for k=8 waveform intervals with one waveform interval of N=256 samples, the required signal is only one every k=8 intervals, which means that frequencies other than those required for the signal are being calculated redundantly.

[0023] Therefore, an object of the present invention is to reduce the calculation burden and enable efficient measurement processing when obtaining frequency domain spectral components from waveform data obtained by digitizing a signal having a periodic envelope in, for example, an optical interference measurement device that performs measurements based on amplitude and phase spectrum information of the interference signal obtained by FFT analysis of the interference signal of two optical combs.

[0024] Other objects of the present invention and specific advantages obtained by the present invention will become more apparent from the following description of the embodiments.

[0025] That is, the present invention uses a discrete Fourier transform (DFT) algorithm to extract the frequency f shown in the above equation (1) from waveform data obtained by digitizing a signal having a periodic envelope. ｎ is the repetition frequency Δf ｒ The normalized frequency is given by the following equation (2): (where Δf o is the repetition frequency Δf ｒA signal processing method for obtaining a frequency domain spectrum component represented by (offset frequency normalized by nΔf ｒ , F(n) is the normalized frequency of ｎ = Δf o +n components, the following equation (3) is used to obtain the above spectral component F(n) from the discrete signal S(v): The discrete Fourier transform (DFT) F(n) is defined as follows: where N is the number of samples in one waveform section (one period of a signal having a periodic envelope), and v is a discrete index (0, 1, 2, 3, ..., N-1). The signal range is expanded to a waveform section k times (k is an integer of 2 or more, and the discrete index v is 0, 1, 2, 3, ..., kN-1) and a window function is applied to it. (W'(v) is the following equation (5) where v is a window function other than a rectangular window function with a width of kN multiplied by a term of an offset frequency with a width of kN.) The DFT shown in (6) is converted into the following DFT of N samples: The method is characterized in that the above-mentioned frequency domain spectral components are obtained from waveform data obtained by digitizing a signal having a periodic envelope using an algorithm for calculating the DFT of order N shown in equation (6).

[0026] The signal processing method according to the present invention is to convert F(n) into a normalized frequency p ｎ When the component of n is set to , the following equation (7) is obtained. The above-mentioned frequency domain spectral components can be obtained from waveform data obtained by digitizing a signal having a periodic envelope using an algorithm for calculating a DFT of order N shown by:

[0027] The signal processing method according to the present invention may also use a Fast Fourier Transform (FFT) algorithm to obtain spectral components in the frequency domain.

[0028] Furthermore, in the signal processing method according to the present invention, the waveform data obtained by digitizing the signal having the periodic envelope may be waveform data obtained by digitizing a time-domain interference signal obtained by converting the interference light of two optical combs into an electrical signal.

[0029] The present invention is a signal processing device, comprising: an AD conversion unit that digitizes an analog signal having a periodic envelope in the time domain; and a discrete Fourier transform (DFT) algorithm that calculates a time series waveform data obtained by the AD conversion unit, the time series waveform data being calculated based on the following equation (1). (where f ｎ is the nth frequency component, Δf ｃ is the offset frequency and Δf ｒ where n denotes the discrete index or frequency component number (0, 1, 2, ...). ｎ is the repetition frequency Δf ｒ The normalized frequency is given by the following equation (2): (where Δf o is the repetition frequency Δf ｒ a signal processing unit for obtaining a frequency domain spectrum component represented by a normalized offset frequency p ｎ = Δf o +n components, the signal processing unit uses the following equation (3) to obtain the spectral component F(n) from the discrete signal S(v): The discrete Fourier transform (DFT) F(n) is defined as follows: where N is the number of samples in one waveform section (one period of a signal having a periodic envelope), and v is a discrete index (0, 1, 2, 3, ..., N-1). The signal range is expanded to a waveform section k times (k is an integer of 2 or more, and the discrete index v is 0, 1, 2, 3, ..., kN-1) and a window function is applied to it. (W'(v) is the following equation (5) where v is a window function other than a rectangular window function with a width of kN multiplied by a term of an offset frequency with a width of kN.) The DFT shown in (6) is converted into the following DFT of N samples: The method is characterized in that the above-mentioned frequency domain spectral components are obtained from waveform data obtained by digitizing a signal having a periodic envelope using an algorithm for calculating the DFT of order N shown in equation (6).

[0030] In the signal processing device according to the present invention, the signal processing unit converts F(n) into a normalized frequency p ｎ When the component of n is set to , the following equation (7) is obtained. The above-mentioned frequency domain spectral components can be obtained from waveform data obtained by digitizing a signal having a periodic envelope using an algorithm for calculating a DFT of order N shown by:

[0031] In the signal processing device according to the present invention, the signal processing unit may obtain spectral components in the frequency domain using a Fast Fourier Transform (FFT) algorithm.

[0032] Furthermore, in the signal processing device according to the present invention, the analog signal having a periodic envelope in the time domain can be a time domain interference signal obtained by converting interference light of two optical combs into an electrical signal.

[0033] In the present invention, a DFT algorithm is used to calculate the following equation (1) from waveform data obtained by digitizing a signal having a periodic envelope. (where f ｎ is the nth frequency component, Δf ｃ is the offset frequency and Δf ｒ where n denotes the discrete index or frequency component number (0, 1, 2, ...). ｎ is the repetition frequency Δf ｒ The normalized frequency is given by the following equation (2): (where Δf o is the repetition frequency Δf ｒ To obtain the frequency domain spectral components represented by the offset frequency normalized by p ｎ = Δf o +n components, the following equation (6) By obtaining the above frequency domain spectral components from waveform data obtained by digitizing a signal having a periodic envelope using an algorithm for calculating a DFT of order N, the number of "multiplications" required for DFT processing can be reduced to 1 / k. Furthermore, by obtaining the frequency domain spectral components using a Fast Fourier Transform (FFT) algorithm, the number of "multiplications" required for FFT processing can be reduced to NLog2(N)+kN, as shown in FIG.

[0034] Therefore, according to the present invention, it is possible to reduce the number of "multiplications" required for DFT processing, and it is possible to provide a signal processing method and signal processing device that can reduce the calculation burden and perform measurement processing efficiently, for example, in an optical interference measurement device that performs measurements based on phase spectrum information obtained by FFT analysis from the interference signal of two optical combs, and that applies a window function to each piece of waveform data obtained by digitizing a signal having a periodic envelope to improve the dynamic range at the expense of frequency resolution and to improve crosstalk between frequency components, and obtain frequency domain spectral components from a signal that has been extended to a waveform section that is extended by a factor of k to improve the frequency resolution at the expense of frequency resolution.

[0035] Fig. 1 is a schematic diagram showing the configuration of an optical interferometry device that performs measurements based on phase spectrum information obtained by FFT analysis from the interference signals of two optical combs to which the present invention is applied. Fig. 2 is a state transition diagram showing the transition of the modulation states of the two optical combs output from the light source in the optical interferometry device. Figs. 3(A) and 3(B) are schematic diagrams showing an example of calculation using an FFT algorithm according to the signal processing method of the present invention, used in the signal processing section of the optical interferometry device, with k=4. Fig. 3(A) shows how waveform data of a width of k waveform sections arranged in the time series of the measurement interference signal in the same range (k=4) as the waveform data arranged in the time series of the reference interference signal are extracted. Fig. 3(B) shows how the extracted waveforms are shifted by one waveform section (N) at a time, and a window function (W() or W'()) is applied to each waveform data of a width of kN to improve the dynamic range and reduce crosstalk between each frequency component at the expense of frequency resolution, thereby analyzing changes in the phase of time-varying signals such as vibration and distance. Fig. 4 shows the calculation results of the above-mentioned FFT algorithm with k = 8 and a window function, with the horizontal axis representing frequency and the vertical axis representing signal strength. Fig. 5(A) and Fig. 5(B) are schematic diagrams illustrating a typical FFT (fast Fourier transform) algorithm used in the signal processing unit of an optical interferometer. Fig. 5(A) shows how data (data of a width of k waveform sections) is extracted from interference waveforms acquired sequentially in time series. Fig. 5(B) shows how the extracted waveform is shifted by one waveform section (N) at a time, shifting the range over which the window function is applied, and then Fourier transforming the waveform to be extracted to analyze changes in the phase of a time-varying signal such as vibration or distance. Fig. 6 shows the number of calculations for a typical FFT calculation algorithm (with a window function), with k on the horizontal axis and the vertical axis representing the number of calculations. Fig. 7 shows the signal strength and crosstalk when an FFT is performed using a typical FFT calculation algorithm (simplest k = 1, rectangular window function), with frequency on the horizontal axis and signal strength on the vertical axis. FIG. 8 is a diagram showing signal strength and crosstalk when FFT is performed using a general FFT calculation algorithm (k=8, window function LowSidelobe), with the horizontal axis representing frequency and the vertical axis representing signal strength.FIG. 9 shows the number of calculations (multiplications) when one waveform section is assumed to have N=256 samples, with the horizontal axis representing k and the vertical axis representing the number of calculations, and the order kN FFT calculation of k times that number, kN samples, is performed using equation (4), and the order N FFT calculation is performed using equation (6).

[0036] Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. Common components will be described by using common reference numerals in the drawings. Furthermore, the present invention is not limited to the following examples, and can be modified as desired without departing from the spirit of the present invention.

[0037] The present invention is implemented, for example, by an optical interference measurement apparatus 100 shown in FIG.

[0038] FIG. 1 is a schematic diagram showing the configuration of an optical interference measurement apparatus to which the present invention is applied, which performs measurement based on phase spectrum information acquired by FFT analysis from the interference signals of two optical combs.

[0039] The optical interference measurement device 100 is an optical comb distance meter that measures the distance to a measurement object 200 based on phase spectrum information obtained by FFT analysis from an interference signal of two optical combs output from a light source 10. The optical comb distance meter 10 includes a light source 10 that outputs two optical combs, and a measuring light L that outputs one of the two optical combs. Ｓ The measurement object is irradiated with the measurement light L200 as the measurement light L200, which is reflected by the measurement object 200 and returns. Ｓ ', the other of the two optical combs is the reference light L Ｒ and an interference optical system 20 for causing interference as the measurement interference light L obtained by the interference optical system 20. ＲＳ and a signal processing unit 50 that acquires amplitude and phase spectral information from frequency domain spectral components based on the time domain interference signal converted into an electrical signal obtained by the optical comb interferometer 40.

[0040] The light source 10 includes two optical comb generators 13 and 14 to which laser light of frequency ν output from a laser light source 11 with single frequency oscillation (oscillation wavelength 1554.94 nm) is split by a splitter 12 and input.

[0041] The two optical comb generators 13 and 14 are electro-optic modulation type optical comb generators (OFCG1, OFCG2). The optical comb generator (OFCG2) 14 receives the laser light of frequency ν split by the beam splitter 12 and converts it into f ａ (=40 MHz) and input, and the modulation frequency f ｍ The optical comb output from the optical comb generator (OFCG1) 13 driven by the drive signal is converted into the measurement light L Ｓ is input to the optical comb interferometer 40, and the modulation frequency f ｍ +Δf ｒ The optical comb output from the optical comb generator (OFCG2) 14 driven by the drive signal of Ｒ and inputs it to the optical comb interferometer 40.

[0042] The interference optical system 20 of the optical comb interferometer 40 receives the measurement light L input from the light source 10. Ｓ and reference light L Ｒ The interference light detecting unit 30 comprises a reference interference light detector 31 to which the reference interference light obtained by the reference interferometry system 21 is input, and a measurement interference light detector 32 to which the measurement interference light obtained by the measurement interferometry system 22 is input.

[0043] The reference interference system 21 receives the measurement light L input from the light source 10. Ｓ into transmitted light and reflected light, and the reference light L input from the light source 10. Ｒ The beam splitter 21B splits the reflected light into transmitted light and reflected light.

[0044] The beam splitter 21A splits the measurement light L Ｓ is input to the measurement interferometer 22 as transmitted light, and the measurement light L Ｓ is input to the beam splitter 21B as reflected light.

[0045] The beam splitter 21B splits the reference light L Ｒis input to the measurement interference system 22 as transmitted light, and the measurement light L is input as reflected light by the beam splitter 21A. Ｓ is used as the transmitted light, and the reference light L Ｒ is used as the reflected light, and the reference light L Ｒ and the measurement light L Ｓ The reference interference light L ＲＳ is input to the reference interference light detector 31 of the interference light detection unit 30.

[0046] The measurement interferometer 22 also receives the measurement light L input from the reference interferometer 21. Ｓ into transmitted light and reflected light, and the reference light L input from the reference interference system 21. Ｒ The beam splitter 22B splits the reflected light into transmitted light and reflected light.

[0047] The beam splitter 22A splits the measurement light L Ｓ is input as transmitted light to the measurement surface of the measurement object 200, and the measurement light L is reflected by the measurement surface of the measurement object 200 and returned. Ｓ ' is input to the beam splitter 22B as reflected light.

[0048] The beam splitter 22B splits the measurement light L reflected by the beam splitter 21A into Ｓ ' is the transmitted light, and the reference light L Ｒ is used as the reflected light, and the reference light L Ｒ and the measurement light L Ｓ ' are superimposed and interfered with each other, and the measurement interference light L ＲＳ ' is input to the measurement interference light detector 32 of the interference light detection section 30.

[0049] Here, the time waveform of the optical comb is a pulse train with a period that corresponds to the inverse of the modulation frequency, and the pulse detected by the measurement interference light detector 32 contains a group delay or a phase delay of the periodic pulse compared to the pulse detected by the reference interference light detector 31 that does not travel back and forth through the measurement section.

[0050] In direct detection, the time resolution expected from a short pulse width cannot be obtained due to band limitations of the detector and signal processing. Ｒ and the measurement light L Ｓ The reference interference light L ＲＳ is detected by the reference interference light detector 31, and the reference light L Ｒ and the measurement light L Ｓ ' are superimposed and interfered with each other, and the measurement interference light L ＲＳ The interference light ' is detected by the measurement interference light detector 32 of the interference light detecting section 30 to obtain an interference signal including a group delay, thereby avoiding the band problem.

[0051] The reference light L Ｒ and the measurement light L Ｓ are pulse trains with a constant repetition frequency, the interference signal also repeats the same waveform at a constant cycle. ｒ If is too large, the time during which the light pulses overlap becomes short, making it difficult to obtain an interference signal. Ｒ and the measurement light L Ｓ To avoid this, for example, ｍ is 25 GHz, while the repetition frequency difference Δf ｒ is 500 kHz, and f ｍ It is orders of magnitude smaller than Δf ｒ <<f ｍ , and the frequency intervals are slightly different, so that the phases of multiple wavelengths can be detected simultaneously while compressing the frequency band.

[0052] The measurement light L output from the two optical comb generators 13 and 14 Ｓ and the reference light L Ｒ is input to the optical comb interferometer 40. １２ is common to the reference interference light detector 31 and the measurement interference light detector 32, and is the measurement interference light L input to the measurement interference light detector 32. ＲＳ ' contains the delay time difference T １２ In addition to the above measurement light L Ｓincludes a group delay time T caused by the light traveling back and forth between the beam splitter 22A of the measurement interferometer 22 and the measurement surface of the measurement object 200.

[0053] That is, the reference interference light detector 31 detects the reference interference light L ＲＳ The reference interference signal S obtained by detecting Ｒ and the measurement interference light detector 32 detects the measurement interference light L ＲＳ ', the measurement interference signal S Ｓ has a phase difference corresponding to the group delay time T.

[0054] In the signal processing unit 50, an AD converter converts the time domain reference interference signal S Ｒ and the measurement interference signal S Ｓ The waveform data of each time series obtained by digitizing the above signals is subjected to frequency analysis by real-time signal processing using Fourier transform, and the above two interference signals S are obtained as described later. Ｒ , S Ｓ The phase difference between them is calculated as 2πf ｍ By replacing it with T, the measurement interference light L ＲＳ Calculate the group delay time T of

[0055] f ｍ The half wavelength of the modulated signal of 25 GHz is about 6 mm, and the distance is the ambiguity distance (La = c / 2f ｍ c: the speed of light), and in one measurement, only the distance within that range can be obtained. The measured distance is ｍ When the wavelength exceeds half of the wavelength, the distance of an integer multiple of the half wavelength becomes unclear due to the periodicity of the object light, and the distance cannot be determined uniquely. Therefore, for example, measurements are taken four times using reference light pulses and measurement light pulses set to the four modulation frequencies shown in Table 1, and the same processing is performed in the signal processing unit 50. Using each phase difference obtained, an ambiguous distance equivalent to half the wavelength (La = c / 2f ｍ Calculate the distance exceeding the speed of light (c).

[0056] Table 1 shows the drive signals F of the two optical comb generators 13 and 14 in the settings #1 to #4. ｍ A, F ｍThe transition state and phase difference of the frequency of B are shown, and the fundamental frequency is f ｍ , the deviation of the fundamental frequency required for distance determination is Δf ｍ , the driving frequency difference for generating the optical comb interference is Δf ｒ For example, Δf ｒ = 500 kHz, Δf ｍ = 10 MHz, f ｍ =F ｍ 1 (25000MHz), f ｍ +Δf ｍ =F ｍ 2 (25010MHz), f ｍ +Δf ｒ =F ｍ 3 (25000.5MHz), f ｍ +Δf ｍ +Δf ｒ =F ｍ 4 (25010.5MHz).

[0057] FIG. 2 is a state transition diagram showing the transition of the modulation state of the measurement light LS and reference light LR output from the light source 10 in this optical interference measurement device 100, in which the horizontal axis is time and the vertical axis shows the selection state of settings #1 to #4 shown in Table 1 of the optical comb of the optical comb, although the modulation frequencies of the optical comb are different.

[0058] That is, in this optical interference measurement device 100, the drive signals F supplied to the two optical comb generators 13 and 14 are ｍ A, F ｍ The drive frequencies of the two optical comb generators 13 and 14 by B are transitioned as shown in Table 2 below.

[0059] Here, in the optical comb distance measurement device 100, coherent reference light and measurement light pulsed from two optical comb generators 13 and 14 driven by two types of modulation signals with different frequencies in principle are used, and an interference signal obtained by the reference interference light detector 31, i.e., a reference interference signal S Ｒ and the measurement interference signal S obtained by the measurement interference light detector 32. Ｓ and based on the state signal, a reference interference signal S Ｒ and the measurement interference signal S ＳA frequency analysis is performed on the reference interference signal S Ｒ and the measurement interference signal S Ｓ The same normalized frequency p ｎ The phase difference between the modes is calculated to cancel out the optical phase difference during the optical comb generation and transmission process from the optical comb generator to the reference point, and then the increment of the phase difference per order 1 on the frequency axis is calculated to determine the phase difference of the signal pulse, thereby calculating the distance from the reference point to the measurement object surface 50.

[0060] The measured distance is modulated at a frequency f ｍ When the frequency exceeds half the wavelength of the object light, the distance of an integer multiple of the half wavelength becomes unclear due to the periodicity of the object light, and the distance cannot be determined uniquely. Therefore, measurements are performed four times using reference light and measurement light set to the four modulation frequencies shown in Table 1, and the reference light and measurement light are taken in the signal processing unit 50 and processed in the same manner, and the phase differences obtained are used to determine the ambiguous distance equivalent to half the wavelength (La = c / (2f ｍ n ｇ ) c: speed of light in vacuum, n ｇ Calculate the distance beyond which the reflection wavelength exceeds the atmospheric refractive index (refraction index: the group refractive index of the atmosphere).

[0061] That is, the reference interference signal S obtained by measuring the modulation frequencies set to the four types shown in Table 1 above is Ｒ and the measurement interference signal S Ｓ The phase difference is determined by the modulation frequency of the modulation signals driving the two optical comb generators 13 and 14 being f ｍ and f ｍ +Δf ｒ In the setting of #1, the modulation frequency of the modulating signal is f ｍ +Δf ｍ and f ｍ +Δf ｍ +Δf ｒ In the setting of #2, -2π(f ｍ +Δf ｍ ) T, and the modulation frequency of the modulating signal is f ｍ +Δf ｒ and f ｍ In the setting of #3, -2π(f ｍ + Δf ｒ ) T, and the modulation frequency of the modulating signal is f ｍ +Δf ｍ +Δf and fｍ +Δf ｍ In the setting of #4, -2π(f ｍ +Δf ｍ +Δf ｒ ) T. The sign of the phase difference is corrected for sign inversion due to the reversal of the magnitude relationship between the modulation frequencies that drive the two optical comb generators 13 and 14.

[0062] Ambiguity distance (La=c / (2f ｍ n ｇ ), the reference interference signal S Ｒ and the measurement interference signal S Ｓ The phase difference (-2πf ｍ T) is in the form of φ+2βπ where β is an integer, and only the φ part can be found by calculation, but the integer value β is unknown.

[0063] On the other hand, the reference interference signal S Ｒ and the measurement interference signal S Ｓ Phase difference of -2πf ｍ Reference interference signal S at settings T and #2 Ｒ and the measurement interference signal S Ｓ Phase difference of -2π(f ｍ +Δf ｍ ) The difference between the reference interference signals S Ｒ and the measurement interference signal S Ｓ Phase difference of -2π(f ｍ +Δf ｒ ) T and the reference interference signal S in the setting of #4 Ｒ and the measurement interference signal S Ｓ Phase difference of -2π(f ｍ +Δf ｍ +Δf ｒ ) The difference in T is 2πΔf ｍ T and 1 / Δf ｍ The distance equivalent to the wavelength of (Δf ｍ = 10 MHz, La is 15 m), the phase is determined uniquely.

[0064] where f ｍ = 25 GHz, Δf ｒ = 500 kHz, Δf ｍ = 10 MHz, Δf ｒ= 500 kHz, distance measurement can be performed up to La = 300 m.

[0065] In this optical interference measurement device 100, the reference interference signal S Ｒ and the measurement interference signal S Ｓ That is, after holding one state for a certain period of time, the system switches to another state, measures the signal phase of that state for a certain period of time, and then uses the phases of the set states #1, #2, #3, and #4 to perform calculation processing of the absolute distance D from the reference point, which is the position of the beam splitter 22A of the measurement interferometer 22, to the measurement surface of the measurement object 50.

[0066] The measurement speed of this optical interference measurement device 100 is Δf ｒ In absolute distance measurement, which requires frequency switching, the frequency switching time and absolute distance calculation time are included. ｍ 1. F ｍ 2. F ｍ 3. F ｍ 4 can be cyclically switched to quickly transition the driving states of the two optical comb generators 13 and 14. Ｒ and the measurement interference signal S Ｓ and the reference interference signal S Ｒ and the measurement interference signal S Ｓ The absolute distance can be calculated reliably and quickly while clearly understanding the waveform location and the frequency setting of the optical comb at that location.

[0067] The signal processing unit 50 detects, for example, two interference signals S obtained by the photodetectors 31 and 32 of the interference light detecting unit 30. Ｒ , S Ｓ The system can be configured with an AD converter that simultaneously samples each waveform and converts it into a digital signal, and an FPGA (Field-Programmable Gate Array) that performs real-time signal processing using Fourier transform.

[0068] In the signal processing section 50, two interference signals S obtained by the photodetectors 31 and 32 of the interference light detecting section 30 are Ｒ , S Ｓ The waveform data arranged in time series of the reference interference signal and the waveform data arranged in time series of the measurement interference signal in the same range are obtained by simultaneously sampling each waveform using an AD converter and converting them into digital signals. FFT processing is performed using the FFT algorithm shown in Figures 3(A) and 3(B).

[0069] 3A and 3B are diagrams showing an example of calculations in which k=4 using the FFT algorithm according to the signal processing method of the present invention used in the signal processing unit 50. In FIG.

[0070] That is, in the signal processing unit 50, when the waveform interval of the FFT is k=4 as shown in FIG. 3A, waveform data of a width of k waveform intervals arranged in the time series of the measurement interference signal in the same range (k=4) as the waveform data arranged in the time series of the reference interference signal is extracted, and as shown in FIG. 3B, a window function is applied to each waveform data of a width of kN in order to improve the dynamic range at the expense of frequency resolution and to improve crosstalk between each frequency component, and one waveform interval (1 / Δf ｒ ) By performing FFT processing of order N on waveform data with the same number of samples, a data sequence in the frequency domain for each 256 samples in one waveform section is obtained. Then, from the data sequence of the real part and the imaginary part of the reference interference signal converted into the frequency domain and the data sequence of the real part and the imaginary part of the measurement interference signal, a data sequence of the real part and the imaginary part of the phase difference for each frequency of the measurement interference signal are obtained by complex number calculation, and Δf of the reference interference signal and the measurement interference signal calculated by θ = arctan (imaginary part / real part) is obtained. ｒ It outputs phase difference data for each frequency, and also outputs the results of calculations such as the product of the phase conjugate of the reference interference signal and the measurement interference signal, and the division of the measurement interference signal by the reference interference signal (phasor product). For example, by performing division, amplitude and phase spectrum information calibrated with the amplitude spectrum of the reference signal can be obtained.

[0071] Here, in the present invention, a window function other than a rectangular window function is used as the window function. As window functions that allow a wide dynamic range and are used for the purpose of efficiently reducing crosstalk, Blackman-based window functions, such as the Blackman-Harris window function, Blackman-Nuttall window function, 7-Term Blackman window function, and 4-Term Blackman window function, are effective when k is 8 or greater; non-Blackman-based window functions, such as the Harris window function, low sidelode window function, and flat top window function, are effective when k is 8 or greater; and Parzen window function is effective when k is an integer of 4 (see, for example, Non-Patent Document 3).

[0072] In the FFT algorithm used in the signal processing unit 50, the time-series waveform data obtained by digitizing the time-domain interference signal, i.e., the discrete-time signal S(v), is calculated using the DFT algorithm according to the following equation (1): (where f ｎ is the nth frequency component, Δf ｃ is the offset frequency and Δf ｒ (in the case of FIG. 1, it is 0), where n indicates a discrete index or frequency component number (0, 1, 2, ...) or normalized frequency. ｎ When n is the component, the DFT of one waveform section is defined as the following equation (8): Δf at each time sample point v, expressed as exp(-i2πnv / N) ｒ The frequency component p ｎ is given as the sum of the components of

[0073] Here, the DFT with N samples per waveform interval to obtain the frequency domain spectrum component, i.e., the discrete frequency signal F(n), from the discrete time signal S(v) is used, where v is normalized at one sample point, and n is Δf rLet n be normalized integer values ​​0, 1, 2, . . . , N-1, and the number of samples in one waveform section be N. The definition of n is left as it is, and the signal range is expanded to a waveform section k times larger. The DFT of kN samples multiplied by a window function W(v) with a width of kN is given by the following equation (9): It is defined as:

[0074] Equation (9) can be substituted into the above equation (7) because exp(-i2πnv / N), a function of the variable v, is periodic with a width of N for any value, even if n is greater than N or even if it is a negative value, as long as n is an integer.

[0075] When an FFT algorithm is used for a DFT of kN samples multiplied by a kN-wide window function W(v), if the kN-wide window function W(v) is other than a rectangular window function, the number of "multiplications" is kNLog2(kN)+kN in equation (9), whereas it is reduced to NLog2(N)+kN in equation (7).

[0076] Therefore, the signal processing unit 50 uses an FFT algorithm that performs DFT shown in the above equation (7) to obtain frequency domain spectral components, i.e., discrete frequency signals F(n), from discrete time signals S(v), which are time-series waveform data obtained by digitizing the time domain interference signal, and determines the absolute distance D from the reference point, which is the position of the beam splitter 22A of the measurement interferometry system 22, to the measurement surface of the measurement object 50.

[0077] As described above, the signal processing unit 50 digitizes a signal having a periodic envelope to obtain waveform data S(v), and calculates f(v) from S(v) using the above equation (1). ｎ Then, signal processing is performed to obtain amplitude and phase spectrum information of the frequency components.

[0078] where f ｎ is the nth frequency component (n is 0 to ∞, but in the cases of Figures 3(A), 3(B), 5(A), and 5(B), the range with valid frequency components is 0≦n ｍｉｎ From n ｍａｘ<N / 2. Patent Document 8 and Non-Patent Document 1 show detection methods when n is a negative frequency component. This patented technology can also be applied when n is negative.), Δf ｃ is the offset frequency and Δf ｒ The smaller n=0th component (this is because it is assumed that even if the envelope is periodic, the phase changes in each period), n is the discrete index or frequency component number or normalized frequency, Δf r indicates the repetition frequency.

[0079] The waveform data S(v) extracted from a large amount of continuous waveform data with a width of kN has a linear phase change with each pulse (carrier) in each period. This is the same as the carrier envelope offset frequency in an optical comb. v ranges from 0 to kN-1.

[0080] Equation (1) can be calculated using the following equation (10): Δf r is normalized by

[0081] Here, the normalized offset frequency Δf ｏ = Δf ｃ / Δf r n is nΔf r is the normalized frequency of Δf, which corresponds to n in the above formulas (1) to (4) and (6) to (10). r The normalized frequency component p ｎ is shown in the above formula (2). (where Δf o is the repetition frequency Δf ｒ offset frequency normalized by

[0082] Waveform data S(v) to f ｎ In signal processing to obtain amplitude and phase spectrum information of frequency components, the sampling frequency is set so that one period is an integer N. Generally, to prevent aliasing, N is set to 2n ｍａｘ < N. This is not the case if aliases are allowed.

[0083] To obtain information on frequency components having n discrete indexes, it is necessary to perform calculations for at least one waveform section (one period) shown in the above equation (3).

[0084] The range here is from 0 to N-1.

[0085] When the waveform section of equation (3) is expanded by an integer factor k and multiplied by a window function W(v) other than a rectangular window function having a width of kN, equation (3) becomes equation (4) above. Here, W'(v) is the above equation (5) where v is a window function W(v) other than a kN-wide rectangular window function multiplied by a kN-wide offset frequency term, where the discrete index v is 0, 1, 2, 3, ..., kN-1). is.

[0086] When the equation (4) is transformed into the DFT of the following N samples, it becomes the above equation (6).

[0087] Using the algorithm for calculating the DFT of equation (6), it is possible to obtain frequency domain spectral components from waveform data obtained by digitizing a signal.

[0088] In addition, in the above formula (4), exp(-i2πnv / N) is a periodic function of the variable v with a width of N, since n is an integer, and the above formula (4) can be expressed as the above formula (6). ｃ If = 0, Δf ｏ = 0, so exp(-i2πΔf ｏ Since (v+mN) / N)=1, the following equation (7) is obtained.

[0089] Therefore, the signal processing unit 50 uses an FFT algorithm that performs DFT shown in the above equation (7) to obtain frequency domain spectral components, i.e., discrete frequency signals F(n), from discrete time signals S(v), which are time-series waveform data obtained by digitizing the time domain interference signal, and can calculate the absolute distance D from the reference point, which is the position of the beam splitter 22A of the measurement interferometry system 22, to the measurement surface of the measurement object 50.

[0090] Here, the FFT algorithm is a DFT algorithm that reduces the number of operations, and is an algorithm that can be obtained with a computational complexity of O(NlogN) when the order N is a power of 2. More generally, when the order N=Πn ｉ When it can be factorized as O(NΣn ｉ ) The calculation time is the fastest when the degree is a power of 2, and the algorithm is simpler, so the degree is sometimes adjusted by padding with zeros. Therefore, N does not need to be a power of 2.

[0091] FIG. 4 shows the calculation results of the above FFT algorithm when k=8 and a window function is used, with the horizontal axis representing frequency and the vertical axis representing signal intensity.

[0092] FIG. 4 shows the same conditions as in FIG. 8, that is, k=8, window function (LowSidelobe), and one waveform section (1 / Δf ｒ 10 shows the signal strength and crosstalk when FFT is performed using the FFT algorithm shown in equation (7) above, assuming a time delay of 2 μs, 256 samples (AD converter 128 MS / s), a beat frequency of 40 MHz, a Doppler frequency due to vibration of 50 kHz, and an FFT interval of k=8 waveform intervals.

[0093] In the case of FIG. 8, one necessary signal is obtained at intervals of k=8, which means that calculations are being performed on signals other than the necessary signals, whereas in FIG. 4, calculations on the unnecessary signals are not performed.

[0094] In this manner, in the optical interference measurement device 100, the two optical comb generators 13 and 14 of the light source 10 provide an interference signal nΔf ｒ The signal processing method of the present invention is executed by generating a signal at a frequency domain of 100 kHz, and the signal processing unit 50 uses an FFT algorithm that performs a DFT shown in equation (7) above to obtain frequency domain spectral components from time series waveform data that has been digitized from the time domain interference signal. This reduces the calculation burden for FFT analysis and enables efficient measurement of absolute distance.

[0095] Here, depending on the configuration of the two optical comb generators 13 and 14 of the light source 10, the interference signal obtained in the optical comb interferometer 40 may be nΔf ｒ rather than Δf ｃ +nΔf ｒ This may produce signals at frequencies below 100 kHz.

[0096] For example, when an octave comb is used for the two optical comb generators 13 and 14 of the light source 10, the carrier envelope frequency of the optical comb can be set to nΔf as an interference signal obtained in the optical comb interferometer 40 by setting the carrier envelope frequency of the optical comb. Also, when an electro-optical modulator (EO modulator) is arranged in an optical resonator and an EO comb is used for the two optical comb generators 13 and 14 of the light source 10, the acousto-optical frequency shifter 15 can be set to nΔf as an interference signal obtained in the optical comb interferometer 40. ｒ rather than Δf ｃ This produces a signal at a frequency of +nΔf.

[0097] In the optical interference measurement device 100, the interference signal obtained in the optical comb interferometer 40 is nΔf ｒ rather than Δf ｃ +nΔf ｒ When a signal is generated at a frequency of 100 kHz, the signal processing unit 50 cannot use the FFT algorithm that performs the DFT shown in equation (4) above in the calculation process of obtaining frequency domain spectral components from time series waveform data obtained by digitizing the time domain interference signal.

[0098] In this case, the signal processing unit 50 uses the window function W(v) other than the rectangular window function with a width of kN, as shown in the above equation (5), which adds a term of the offset frequency to the window function W(v). (where Δf ｏ is the normalized offset frequency) Calculation processing can be performed using the window function W(v)'. ｃ +nΔf ｒ Since the signal moves by nΔf, the FFT algorithm that performs the DFT shown in the above equation (4) can be applied.

[0099] That is, the interference signal obtained in the optical comb interferometer 40 is nΔf ｒrather than Δf ｃ +nΔf ｒ When generating a signal, the signal processing unit 50 can use an FFT algorithm to perform a DFT shown in the above equation (6) using a window function W′(v) obtained by adding a term of an offset frequency to a window function W(v) other than the kN-width rectangular window function, to obtain spectral components in the frequency domain from waveform data obtained by digitizing a signal having a periodic envelope.

[0100] The optical interference measurement device 100 described above functions as an optical comb rangefinder that measures the distance to the measurement surface of the measurement object 200 based on phase spectrum information obtained by FFT analysis from the interference signals of the two optical combs output from the light source 10. However, the present invention is not limited to optical comb rangefinders, and can be used in many application fields, such as velocity measurement and vibration measurement of the measurement surface of the measurement object 200, analysis of interference fringes, gas detection, refractive index measurement, and precise time measurement, based on the phase spectrum information obtained by FFT analysis from the interference signals of the two optical combs output from the light source 10.

[0101] For example, in measurements using dual comb spectroscopy, a solid sample is placed in the path of one of two optical frequency combs, and interference waveforms between the optical frequency combs that pass through the solid sample and the optical frequency combs that do not are obtained. By performing phase correction and coherent integration of the interference waveforms in real time, amplitude and phase spectral information containing the characteristics of the solid sample can be detected. Analysis of the detected amplitude and phase spectral information provides information on the physical properties of the solid sample.

[0102] In the technology disclosed in Non-Patent Document 1, (where f ｎ is the nth frequency component, Δf ｃ is the offset frequency and Δf ｒ n is the discrete index or frequency component number or normalized frequency, Δf rThe interference signal generated in the gas analyzer is analyzed using a spectrum analyzer or Fourier transform, and the interference signal, which is time-series data, is then analyzed to determine the gas.

[0103] The interference signal of two optical frequency combs used in measurements using the Dual Comb spectroscopy is a time-domain interference signal generated at the frequency of the above formula (1). Therefore, the signal processing unit 50 can use an FFT algorithm to calculate amplitude and phase spectral information from time-series waveform data obtained by digitizing the time-domain interference signal. By using an FFT algorithm that performs the DFT shown in the above formula (4), calculations can be performed efficiently with a small number of "multiplications."

[0104] In the above explanation, the present invention has been applied to an optical interference measurement apparatus 100 that performs measurements based on phase spectrum information acquired by FFT analysis from the interference signal of two optical combs. However, the present invention is not limited to Fourier analysis processing of the interference signal of the optical combs, but can also be applied to Fourier analysis processing of a signal having a periodic envelope made up of a fundamental frequency and its associated higher-order frequency components. Phase spectrum information and amplitude spectrum information can be calculated using an FFT algorithm from time-series waveform data obtained by digitizing the signal having a periodic envelope, and by using an FFT algorithm that performs the DFT shown in equation (4) above, calculation processing can be performed efficiently with a small number of “multiplications.”

[0105] In addition, in the above explanation, it has been stated that by using the FFT algorithm in the signal processing unit 50, calculation processing can be performed efficiently with a small number of "multiplications." However, the FFT algorithm is a DFT algorithm that reduces the number of operations, and even without using the FFT algorithm, the number of "multiplications" required for DFT processing can be reduced to 1 / k by using the DFT shown in the above equation (4).

[0106] That is, the signal processing unit 50 digitizes a signal having a periodic envelope, and from the waveform data obtained, the DFT algorithm is used to In order to obtain the frequency domain spectrum components from the signal generated in The signal range of the DFT in one waveform section defined as above is expanded to a waveform section k times larger than the above equation (6). By performing the DFT calculation shown in FIG. 9, the number of "multiplications" required for the DFT processing can be reduced by a factor of k, as shown in FIG.

[0107] 9 represent the number of "multiplications" when FFT calculation is performed on equation (4) or equation (9) with order kN, where kN is a power of 2, and the number of "multiplications" when FFT calculation is performed on equation (6) or equation (7) with order N, where N is a power of 2. Note that the window functions W() and W'() are not included in the number of "multiplications" because they can be calculated in advance as a sequence of kN constants.

[0108] REFERENCE SIGNS LIST 10 Light source, 11 Laser light source, 12 Beam splitter, 13, 14 Optical comb generator 15 Acousto-optic frequency shifter, 20 Interference optical system, 21 Reference interference system, 21A, 21B Beam splitter, 22 Measurement interference system, 22A, 22B Beam splitter, 30 Interference light detection unit, 31 Reference interference light detector, 32 Measurement interference light detector, 40 Optical comb interferometer, 50 Signal processing unit, 100 Optical interference measurement device, 200 Measurement object

Claims

1. From waveform data obtained by digitizing a signal having a periodic envelope, the following equation (1) is calculated using a discrete Fourier transform (DFT) algorithm. (where f ｎ is the nth frequency component, Δf ｃ is the offset frequency, and n is the discrete index or frequency component number (0, 1, 2, ...). ｎ is the repetition frequency Δf ｒ The normalized frequency is given by the following equation (2): (where Δf o is the repetition frequency Δf ｒ A signal processing method for obtaining a frequency domain spectrum component represented by a normalized offset frequency p ｎ = Δf o +n components, the following equation (3) is used to obtain the above spectral component F(n) from the discrete signal S(v): The discrete Fourier transform (DFT) F(n) is defined as follows: where N is the number of samples in one waveform section (one period of a signal having a periodic envelope). The DFT F(n) is expressed as follows: where v is a discrete index (0, 1, 2, 3, ..., N-1), the signal range is expanded to a waveform section k times (k is an integer equal to or greater than 2, and the discrete index v is 0, 1, 2, 3, ..., kN-1) and a window function is applied to the waveform section. (W'(v) is the following equation 5, where v is a window function other than a rectangular window function with a width of kN multiplied by a term of an offset frequency with a width of kN.) ) is converted into the following equation (6) of the DFT of the number of N samples: A signal processing method characterized by obtaining the above-mentioned frequency domain spectral components from waveform data obtained by digitizing a signal having a periodic envelope using an algorithm that calculates a DFT of order N shown in equation (6).

2. From the waveform data obtained by digitizing a signal with a periodic envelope, F(n) is calculated at a normalized frequency p ｎ When the component of n is set to , the following equation (7) is obtained.

2. The signal processing method according to claim 1, wherein the frequency domain spectral components are obtained from waveform data obtained by digitizing a signal having a periodic envelope using an algorithm for calculating a DFT of order N shown in 3. A signal processing method according to claim 1 or 2, characterized in that the spectral components in the frequency domain are obtained using a Fast Fourier Transform (FFT) algorithm.

4. The signal processing method according to claim 3, characterized in that the waveform data obtained by digitizing the signal having the periodic envelope is waveform data obtained by digitizing a time-domain interference signal obtained by converting the interference light of two optical combs into an electrical signal.

5. An AD conversion unit that digitizes an analog signal having a periodic envelope in the time domain, and from the time series waveform data obtained by the AD conversion unit, uses a discrete Fourier transform (DFT) algorithm to obtain the following equation (1): (where f ｎ is the nth frequency component, Δf ｃ is the offset frequency, and n is the discrete index or frequency component number (0, 1, 2, ...). ｎ is the repetition frequency Δf ｒ The normalized frequency is given by the following equation (2): (where Δf o is the repetition frequency Δf ｒ a signal processing unit for obtaining a frequency domain spectrum component represented by a normalized offset frequency p ｎ = Δf o +n components, the signal processing unit uses the following equation (3) to obtain the spectral component F(n) from the discrete signal S(v): The discrete Fourier transform (DFT) F(n) is defined as follows: where N is the number of samples in one waveform section (one period of a signal having a periodic envelope), and v is a discrete index (0, 1, 2, 3, ..., N-1). The signal range is expanded to a waveform section k times (k is an integer equal to or greater than 2, and the discrete index v is 0, 1, 2, 3, ..., kN-1) and a window function is applied to it. (W'(v) is the following equation (5) where v is a window function other than a rectangular window function with a width of kN multiplied by a term of an offset frequency with a width of kN.) ) is converted into the following equation (6) of the DFT of the number of N samples: A signal processing device characterized by obtaining the above-mentioned frequency domain spectral components from waveform data obtained by digitizing a signal having a periodic envelope, using an algorithm for calculating a DFT of order N shown in equation (6).

6. The signal processing unit converts F(n) into a normalized frequency p ｎ When the component of =n is set, the following equation (7) is obtained.

6. The signal processing apparatus according to claim 5, wherein the frequency domain spectral components are obtained from waveform data obtained by digitizing a signal having a periodic envelope using an algorithm for calculating a DFT of order N shown by:

7. The signal processing device according to claim 5 or 6, wherein the signal processing section uses a Fast Fourier Transform (FFT) algorithm to obtain spectral components in the frequency domain.

8. The signal processing device according to claim 7, wherein the analog signal having a periodic envelope in the time domain is a time domain interference signal obtained by converting interference light of two optical combs into an electrical signal.

9. The signal processing device according to claim 7, wherein the analog signal having a periodic envelope in the time domain is a time domain interference signal obtained by converting interference light of two optical combs into an electrical signal.

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