Signal processing method and signal processing device

Abstract

To mitigate the burden of calculation for FFT analysis and enable measurement processing to be performed efficiently in an optical interference measurement device that performs measurement on the basis of phase spectrum information and amplitude spectrum information acquired from the interference signal of two optical combs by FFT analysis.SOLUTION: The present invention obtains a spectrum component of frequency domain from time-series waveform data in which a time domain interference signal is digitized, by using an FFT algorithm that performs N-order DFT from data S (v) of kN samples indicated by formula (6), and determines an absolute distance D from a reference point to the measurement surface of a measurement object 50, with the position of the beam splitter 22A of an interference system 22 for measurement adopted as the reference point.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a signal processing method and signal processing device that obtains frequency domain spectral components from waveform data obtained by digitizing a signal that is periodic or has a 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. [Background technology]

[0002] By interfering with two optical combs, an optical interference pattern is generated, 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 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 distance from the time difference between the interference signal of measurement light and the interference signal of 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, the 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, the 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 is obtained between the optical frequency combs that pass through the sample and the optical frequency combs that do not. By performing Fourier analysis on the phase-corrected and coherent integration of the interference waveform in real time, amplitude and phase spectral information, including 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 a measurement 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 measurement object, thereby making it possible to simultaneously measure vibration information at multiple points on the measurement surface (see, for example, Patent Documents 5-7). [Prior art documents] [Patent documents]

[0012] [Patent Document 1] Japanese Patent Application Laid-Open No. 2017-046739 [Patent Document 2] Patent Publication No. 2021-143995 [Patent Document 3] U.S. Patent No. 8,558,993 [Patent Document 4] Patent No. 5231883 [Patent Document 5] Patent No. 5336921 [Patent Document 6] Japanese Patent Application Laid-Open No. 2010-203860 [Patent Document 7] Patent No. 5363231 [Patent Document 8] Patent Publication No. 2021-056090 [Patent Document 9] U.S. Patent No. 9,557,219 [Patent Document 10] Japanese Patent Application Laid-Open No. 2017-138129 [Non-patent literature]

[0013] [Non-Patent Document 1] S. Schiller, “Spectrometry with frequency combs”, OPTICS LETTERS Vol.27, No.9,May 1, 2002. [Non-patent document 2] Microresonator soliton dual-comb spectroscopy | Science [Non-patent document 3] https: / / www.ni.com / docs / ja-JP / bundle / labwindows-cvi / page / advancedanalysisconcepts / lvac_low_sidelobe.html Summary of the Invention [Problem to be solved by the invention]

[0014] In an optical interference measurement device that uses the interference signal of two optical combs for measurement, the time-series waveform data obtained by digitizing the interference signal in the time domain using an AD converter is converted into Fourier transform data as shown in the following equation (1):

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[0015] One method of calculating spectral components using 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, as in 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 intervals from the interference waveform acquired sequentially in a time series, as shown in Figure 5(A). (Since the waveform interval is kN, if one waveform interval is 2 μs, data with a time width of k × 2 μs is used.) Then, as shown in Figure 5(B), a window function (W() or W'()) is applied to the kN-width waveform to perform a kN-order Fourier transform. Next, the extracted waveform is shifted by one waveform interval (N), 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 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 of kN in the waveform section expanded by k times to improve the frequency resolution at the expense of 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, complex number calculation is performed to obtain data sequence of the real part and the imaginary part of the phase difference for each frequency of the measurement interference signal, and Δf of the reference interference signal and the measurement interference signal calculated by θ=arctan (imaginary part / real part). rIt 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 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. 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 making it unable to keep up. 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 Figure 6, in the case of an FFT with a window function, the number of calculations (multiplications) required to calculate k times that number, kN samples, for a data string of N samples in one waveform section (here, N = 256) is minimal when the number is a power of 2, and is kNLog2(kN) + kN. Here, +kN is added as a calculation because there is a multiplication of the window function and the signal.

[0019] In addition, Figure 7 shows the frequency on the horizontal axis and the signal strength on the vertical axis, and the time domain (1 / Δf r This figure 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 interval 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 Figure 7, when k is small, crosstalk increases. A single waveform section alone cannot be used as a vibrometer.

[0021] Furthermore, in Figure 8, the horizontal axis is frequency and the vertical axis is signal strength, and a general FFT calculation algorithm (k=8, window function LowSidelobe) is used to calculate one waveform section (1 / Δf r This figure shows the signal strength and crosstalk when performing an FFT of order 2048, assuming a time interval 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 intervals, 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 and the S / N ratio is improved. 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. [Means for solving the problem]

[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):

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[0026] The signal processing method according to the present invention is to convert F(n) into a normalized frequency p n =n, the following equation (7)

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[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 can 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).

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[0030] In the signal processing device according to the present invention, the signal processing unit converts F(n) into a normalized frequency p n =n, the following equation (7)

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[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. [Effects of the Invention]

[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.

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[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, in which waveform data obtained by digitizing a signal having a periodic envelope is used to improve the dynamic range at the expense of frequency resolution, and a window function is applied to each data in order to improve crosstalk between each frequency component, and frequency domain spectral components are obtained from the signal extended to a waveform section extended by a factor of k to improve the crosstalk at the expense of frequency resolution. [Brief explanation of the drawings]

[0035] [Figure 1]FIG. 1 is a schematic diagram showing the configuration of an optical interference measurement device to which the present invention is applied, which performs measurement based on phase spectrum information acquired by FFT analysis from the interference signal of two optical combs. [Figure 2] 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 interference measurement device. [Figure 3] 3A and 3B are diagrams showing schematic diagrams of calculation examples in which the FFT algorithm according to the signal processing method of the present invention, used in the signal processing section of the optical interferometry device, is set to k=4. FIG. 3A shows how waveform data of a width of k waveform intervals arranged in the time series of the measurement interference signal over the same range (k=4) as the waveform data arranged in the time series of the reference interference signal is extracted. FIG. 3B shows how the extracted waveform is shifted by one waveform interval (N) at a time, and a window function (W() or W'()) is applied to each waveform data of the kN width in order to improve the dynamic range at the expense of frequency resolution and reduce crosstalk between frequency components, thereby performing FFT processing to analyze changes in the phase of time-varying signals such as vibration and distance. [Figure 4] FIG. 4 is a diagram showing the calculation results of the above FFT algorithm in the case where k=8 and a window function is used, with the horizontal axis representing frequency and the vertical axis representing signal intensity. [Figure 5] Figure 5 (A) and (B) are diagrams showing a typical FFT (fast Fourier transform) algorithm used in the signal processing section of an optical interferometer. (A) shows how data of the width of k waveform sections (waveform sections) are extracted from the interference waveforms acquired sequentially in time series. (B) shows how the extracted waveform is shifted by one waveform section (N) at a time, and the Fourier transform is performed while shifting the range to which the window function is applied, thereby analyzing changes in the phase of time-varying signals such as vibration and distance. [Figure 6] FIG. 6 is a diagram showing the number of calculations of a general FFT calculation algorithm (with window function), with k on the horizontal axis and the number of calculations on the vertical axis. [Figure 7] FIG. 7 is a diagram showing signal strength and crosstalk when FFT is performed using a general FFT calculation algorithm (simplest k=1, rectangular window function), with the horizontal axis representing frequency and the vertical axis representing signal strength. [Figure 8] 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. [Figure 9] 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 FFT calculation of order kN of k times that number, kN samples, is performed using equation (4), and the FFT calculation of order N is performed using equation (6). DETAILED DESCRIPTION OF THE INVENTION

[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 device to which the present invention is applied, which performs measurement based on phase spectrum information acquired by FFT analysis from the interference signal 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 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 L 200 and is reflected by the measurement object 200 and returned. 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. RSThe optical comb interferometer 40 includes an interference light detector 30 that receives the interference signal ' and converts it into an electrical signal, and a signal processor 50 that acquires amplitude and phase spectral information from the 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 that oscillates at a single frequency (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 and OFCG2), and the laser light of frequency ν split by the beam splitter 12 is input to the optical comb generator (OFCG2) 14 via an acousto-optic frequency shifter 15 to be converted into f a (=40MHz) 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 used as the measurement light L S is input to the optical comb interferometer 40 as a 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 input it to the optical comb interferometer 40 as

[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 beam 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. Sa beam splitter 21A for splitting the reference light L input from the light source 10 into transmitted light and reflected light; 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 R is 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 above reference light L R is used as the reflected light, and the above reference light L R and the above 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 detects the measurement light L input from the reference interferometer 21. S a beam splitter 22A that splits the reference light L input from the reference interference system 21 into transmitted light and reflected light; 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 above reference light LR is used as the reflected light, and the above reference light L R and the above measurement light L S The measurement interference light L is obtained by overlapping and interfering RS ' is input to the measurement interference light detector 32 of the interference light detecting 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 pulses detected by the measurement interference light detector 32 contain a group delay or a phase delay of the periodic pulses compared to the pulses detected by the reference interference light detector 31 that do 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 the band limitations of the detector and signal processing. R and the above 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 above measurement light L S The measurement interference light L is obtained by overlapping and interfering RS The band problem is avoided by detecting the interference signal ' by the measurement interference light detector 32 of the interference light detecting section 30 and obtaining an interference signal including a group delay.

[0051] The above reference light L R and the above measurement light L S are pulse trains with a constant repetition frequency, the interference signal also repeats the same waveform at a constant period. r If is too large, the time for overlapping of the optical pulses becomes short, making it difficult to obtain an interference signal. R and the above measurement light L S To avoid this, for example, m is 25GHz, while the repetition frequency difference Δf r is set to 500kHz, 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 above reference light L R The delay time difference T 12 is common to the reference interference light detector 31 and the measurement interference light detector 32, and the measurement interference light L input to the measurement interference light detector 32 is RS ', the delay time difference T 12 In addition to the above measurement light L S includes a group delay time T due to the light traveling back and forth between the beam splitter 22A of the measurement interferometer 22 and the measurement surface of the object 200 to be measured.

[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 obtained by detecting S There is 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 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 Calculate the phase difference between them and convert it to 2πf m By replacing T 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 at 25 GHz is about 6 mm, and the distance is the ambiguity distance (La = c / 2f mc: the speed of light), and in one measurement, only the distance within that range can be obtained. The measured distance is modulated at a frequency f 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). [Table 1]

[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 m The 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 judgment is Δf m , the driving frequency difference for generating the optical comb interference is Δf r For example, Δf r =500kHz, Δf m = 10MHz, 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. The horizontal axis shows time, and the vertical axis shows the selection state of settings #1 to #4 shown in Table 1 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 driving frequencies of the two optical comb generators 13 and 14 by B are transitioned as shown in Table 2 below. [Table 2]

[0059] 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 the signal processing unit 50 generates 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 S The 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] Note that the measurement 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 way, 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 a vacuum, n g Calculate the distance beyond which the reflection wavelength exceeds the atmospheric refractive index.

[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 between the two optical comb generators 13 and 14 is determined by the modulation frequency 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 f m +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 phase difference (-2πf m T) is in the form φ+2βπ where β is an integer, and only the φ part can be calculated, 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 T and #2 settingsR and the measurement interference signal S S Phase difference of -2π(f m +Δf m )T is 2πΔfmT, and the reference interference signal S in the setting of #3 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 #4 setting R and the measurement interference signal S S Phase difference of -2π(f m +Δf m +Δf r )T difference is 2πΔf m T and 1 / Δf m The distance equivalent to the wavelength of (Δf m = 10MHz, La is 15m), the phase is determined uniquely.

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

[0065] In this optical interference measurement device 100, the reference interference signal S obtained by measuring at four different modulation frequencies shown in Table 1 above is 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 rThe frequency is 500 kHz, while the absolute distance measurement requires frequency switching, which includes the frequency switching time and the absolute distance calculation time. m 1,F m 2,F m 3,F m 4 are cyclically switched to rapidly 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 for the reference interference signal, which is obtained by simultaneously sampling each waveform using an AD converter and converting them into digital signals, and the waveform data arranged in time series for the measurement interference signal in the same range are subjected to FFT processing using the FFT algorithm shown in Figure 3 (A) and (B).

[0069] 3A and 3B are diagrams showing an example of calculations in which k=4 using an 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 string in the frequency domain for each 256 samples in one waveform section is obtained. Then, from the data strings of the real and imaginary parts of the reference interference signal converted into the frequency domain and the data strings of the real and imaginary parts of the measurement interference signal, a data string of the real and imaginary parts of the phase difference for each frequency of the measurement interference signal is 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, as well as 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 large dynamic range and are used to efficiently reduce crosstalk, Blackman-based window functions are effective when k is 8 or greater, such as the Blackman-Harris window function, Blackman-Nuttall window function, 7-Term Blackman window function, and 4-Term Blackman window function. Non-Blackman-based window functions that are effective when k is 8 or greater include the Harris window function, low sidelode window function, and flat top window function. When k is an integer of 4, the Parzen window function is effective (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 a DFT algorithm according to the following equation (1):

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

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[0074] Equation (9) can be replaced by equation (7) above, 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.

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[0075] When an FFT algorithm is used to perform a DFT of kN samples multiplied by a kN-wide window function W(v), the number of "multiplications" is kNLog2(kN)+kN in equation (9), but is reduced to NLog2(N)+kN in equation (7), if the kN-wide window function W(v) is not a rectangular window function.

[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 signals, and calculates 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, in the signal processing unit 50, waveform data S(v) obtained by digitizing a signal having an envelope with a periodic envelope is used, and f shown in the above formula (1) is obtained from S(v). n Signal processing for obtaining amplitude and phase spectrum information of the frequency component of is executed. [Number]

[0078] Here, f n is the nth frequency component (n ranges from 0 to ∞, but in the cases of FIGS. 3 and 5, the valid frequency component range is 0 ≤ n min from n max to n <0OO0213> is the offset frequency, and the component of n = 0 which is smaller than Δf c r <N / 2. In Patent Document 8 and Non-Patent Document 1, a detection method for the case where n is a negative frequency component is shown. This patented technology can also be applied when n is negative.). Δf r indicates the repetition frequency.

[0079] The waveform data S(v) extracted from a large amount of continuous waveform data in a width of kN has a linearly changing phase with a pulse (with a carrier) for each period. It is the same as the carrier envelope offset frequency in optical communication. v ranges from 0 to kN - 1. [[ID=3o]]

[0080] Equation (1) is normalized by Δf r by performing the following calculation of Equation (10). [Number]

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

[0082] In the signal processing for obtaining the amplitude and phase spectrum information of the frequency component of f from the waveform data S(v), the sampling frequency is set to be an integer N and one cycle. Generally, to prevent aliasing, N is set to 2n n < N. If aliasing is allowed, it is not limited to this. max

[0083] To obtain the information of the frequency component with the discrete index of n, it is necessary to perform the calculation of at least one waveform section (one cycle) shown by the above formula (3). [Number]

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

[0085] When the waveform section is expanded by an integer multiple of k and multiplied by a window function W(v) other than the rectangular window function with a width of kN, the above formula (4) is obtained. [Number] Here, W’(v) is the above formula (5) in which v is multiplied by the term of the offset frequency with a width of kN for a window function W(v) other than the rectangular window function with a width of kN. Here, the discrete index v is 0, 1, 2, 3,..., kN - 1). [Number] is

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

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[0087] Using the algorithm for calculating the DFT of equation (6), the spectral components in the frequency domain can be obtained from the waveform data obtained by digitizing the 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.

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[0089] Therefore, the signal processing unit 50 uses an FFT algorithm that performs a DFT shown in the above equation (7) to obtain frequency domain spectral components, i.e., discrete frequency signals F(n), from a discrete time signal S(v), which is 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 is 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 is a diagram showing the calculation results of the above FFT algorithm in the case where k=8 and a window function is used, with the horizontal axis representing frequency and the vertical axis representing signal intensity.

[0092] Figure 4 shows the same conditions as in Figure 8, that is, k=8, window function (LowSidelobe), and one waveform section (1 / Δf r = 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 intervals as the FFT interval, and an FFT algorithm that performs DFT as shown in equation (7) are shown in the figure, which shows the signal strength and crosstalk when FFT is performed.

[0093] In the case of Figure 8, the required signal is one at intervals of k=8, which means that calculations are being performed on signals other than the required signals, but in Figure 4, calculations on signals other than the required signals are not being 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 generate an interference signal nΔf r The signal processing method of the present invention is executed by using the signal processing unit 50 as a signal generating unit, and the signal processing unit 50 uses an FFT algorithm that performs DFT shown in the above equation (7) to obtain frequency domain spectral components from time series waveform data that has been digitized from the time domain interference signal, thereby reducing the calculation load for FFT analysis and enabling efficient measurement processing 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-optic frequency shifter 15 can be set to nΔf as an interference signal obtained in the optical comb interferometer 40. r rather than Δf c A signal is generated 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 an FFT algorithm that performs a 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 calculates the window function W(v) other than the rectangular window function having a width of kN by adding a term of an offset frequency to the window function W(v) as shown in the above equation (5).

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[0099] That is, the interference signal obtained in the optical comb interferometer 40 is nΔf r rather than Δf c +nΔf rWhen generating a signal in the range of 100 kHz to 100 kHz, the signal processing unit 50 can use an FFT algorithm to perform a DFT shown in equation (6) above, which uses a window function W'(v) obtained by adding a term for an offset frequency to a window function W(v) other than the rectangular window function with a width of kN, to obtain spectral components in the frequency domain from waveform data obtained by digitizing a signal having a periodic envelope.

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[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 comb that passes through the solid sample and the optical frequency comb that does not are obtained. By performing phase correction 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 solid sample can be obtained.

[0102] In the technology disclosed in Non-Patent Document 1,

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[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 calculate amplitude and phase spectral information using an FFT algorithm from time-series waveform data obtained by digitizing the time-domain interference signal. By using the 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. It can also be applied to Fourier analysis processing of a signal having a periodic envelope composed 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. 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 the above explanation, it has been stated that the use of an FFT algorithm in the signal processing unit 50 enables efficient calculation processing with a small number of "multiplications." However, the FFT algorithm is a DFT algorithm that reduces the number of operations. Therefore, 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

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[0107] Here, the two curves shown in Figure 9 represent the number of "multiplications" when FFT calculations are performed on equation (4) or equation (9) with order kN, where kN is a power of 2, and the number of "multiplications" when FFT calculations are 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. [Explanation of symbols]

[0108] 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, a discrete Fourier transform (DFT) algorithm is used to obtain the following equation (1): [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, ...). The frequency f ｎ is the repetition frequency Δf ｒ The normalized frequency is given by the following equation (2): [Equation 2] (where Δf o is the repetition frequency Δf ｒ offset frequency normalized by A signal processing method for obtaining a frequency domain spectrum component represented by F(n), 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): [Equation 3] 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. [Equation 4] (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.) [Equation 5] ) is converted into the following equation (6) of the DFT of the number of N samples: [Equation 6] 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 having a periodic envelope, F(n) is converted to a normalized frequency p ｎ When the component of n is set to , the following equation (7) is obtained. [Equation 7] 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. 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. 4. The signal processing method according to claim 3, wherein 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 converter that digitizes an analog signal having a periodic envelope in the time domain; From the time series waveform data obtained by the AD conversion means, a discrete Fourier transform (DFT) algorithm is used to obtain the following equation (1): [Equation 8] (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, ...). The frequency f ｎ is the repetition frequency Δf ｒ The normalized frequency is given by the following equation (2): [Equation 9] (where Δf o is the repetition frequency Δf ｒ offset frequency normalized by a signal processing unit for obtaining a frequency domain spectrum component represented by F(n) is the normalized 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): [Equation 10] 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. [0011] (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.) [0012] ) is converted into the following equation (6) of the DFT of the number of N samples: [0013] 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. [0014] 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. 7. The signal processing device according to claim 5, wherein the signal processing unit obtains spectral components in the frequency domain using a Fast Fourier Transform (FFT) algorithm.

8. 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. 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.

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