Coherent-distance measuring method and coherent-distance measuring device

Abstract

In the present invention, light to be measured is output from a coherence-wavelength-swept light source, is split into signal light and reference light by a first optical coupler which are then recombined by a second optical coupler and then output as a first interference signal, a second interference signal, and a third interference signal having phases different by 120°, and each of the signals is detected by a photodetector. A correction matrix in which factors that vary over time is calculated, the factors relating to amplitudes due to the first optical coupler and the second optical coupler, the quantum efficiency of the photodetector, and phase due to the second optical coupler. The phase difference between the signal light and the reference light is calculated by using the first interference signal, the second interference signal, the third interference signal, and the correction matrix. The spectral width of light is calculated by using the phase difference, and the coherence-distance of light is calculated by using the spectral width.

Description

Method for measuring coherent distance, and apparatus for measuring coherent distance

[0001] This disclosure relates to a coherence distance measurement method and a coherence distance measurement apparatus.

[0002] To easily measure the oscillation linewidth of a coherent light source during wavelength sweeping, it is known that the light to be measured, which is coherent light whose oscillation wavelength changes periodically, is generated from the wavelength-swept light source, separated into a measurement unit and a reference unit with different optical path lengths, then combined in an interference unit to obtain interference light, detected in a photodetector unit to obtain an interference signal, the interference signal obtained by an analysis unit by performing a Fourier transform on the interference signal obtained by changing the optical path length difference between the measurement unit and the reference unit to obtain the measured value of the noise floor value of the point image distribution function for each optical path length difference, the measured amplitude value of the noise floor value which changes according to the optical path length difference is calculated, the estimated coherence time is determined so that the measured amplitude value and the calculated amplitude value match, and the oscillation linewidth of the coherent light source is measured based on the estimated coherence time (see Patent Document 1 below).

[0003] Japanese Patent Publication No. 2022-138828

[0004] Xi Zhang, Fei Yang, Zitong Feng, Fang Wei, Haiwen Cai, and Ronghui Qu, "Narrow-linewidth swept laser phase reconstruction and noise measurement technology and its applications," Opt. Express 26, 32958-32970 (2018)

[0005] For example, light sources used for fundus measurement require high coherence to widen the measurement range. Tunable VCSELs have recently attracted attention as light sources with long coherence lengths. However, in conventional coherence distance measurement methods, the method of observing the roll-off of the PSF (Point Spread Function) (a method different from the method described in Patent Document 1 above) has a high repetition frequency of wavelength sweep, making it difficult to evaluate Tunable VCSELs that operate in a very high frequency band, partly due to limitations in the frequency band of the detector in the measurement system.

[0006] The method described in Patent Document 1 (referred to for convenience as the "noise floor method") is a coherence length measurement method that utilizes the behavior of the noise floor of the PSF of an interference signal, which fluctuates with respect to the difference in optical path length. In this method, since only signals in the low-frequency range are used for measurement, the measurement distance and sweep speed are not electrically limited, making it suitable for measuring the coherence length of high-coherence light sources. However, there is also a demand for a method that directly observes the optical electric field output from the light source rather than from noise.

[0007] Therefore, this disclosure aims to measure the coherence distance of a coherence light source operating in a very high frequency band.

[0008] The coherence distance measurement method of this disclosure outputs light to be measured from a coherence wavelength-swept light source, separates the light to be measured into signal light and reference light using a first optical coupler, combines the signal light and reference light using a second optical coupler, and outputs them as a first interference signal, a second interference signal, and a third interference signal, each with a phase difference of 120°, respectively, which are detected by a photodetector, and calculates a correction matrix using the first, second, and third interference signals to correct the first, second, and third interference signals, in which factors related to amplitude changes by the first and second optical couplers, the photoelectric efficiency of the photodetector, and the phase change by the second optical coupler change change over time, calculates the phase difference between the signal light and the reference light using the first, second, and third interference signals and the correction matrix, calculates the spectral width of the light using the phase difference, and calculates the coherence distance of the light using the spectral width.

[0009] Furthermore, the coherence distance measurement method of the present disclosure is a coherence distance measurement device comprising: a coherence wavelength sweep light source that outputs light to be measured; a first optical coupler that separates light to be measured into signal light and reference light; a second optical coupler that, after combining the signal light and reference light, outputs a first interference signal, a second interference signal, and a third interference signal, each with a phase difference of 120°; and a photodetector that detects the first interference signal, the second interference signal, and the third interference signal, respectively, wherein the analysis unit analyzes the first interference signal, the second interference signal, Using the third interference signal, a correction matrix is ​​calculated in which factors related to amplitude changes due to the first and second optical couplers, the photoelectric efficiency of the photodetector, and the phase change due to the second optical coupler change over time, correcting the first, second, and third interference signals. Using the first, second, and third interference signals and the correction matrix, the phase difference between the signal light and the reference light is calculated. Using the phase difference, the spectral width of the light is calculated, and using the spectral width, the coherence distance of the light is calculated.

[0010] According to the present disclosure using the above solution, there is a benefit in measuring the coherence distance of a coherence light source operating in a very high frequency band.

[0011] This figure shows a conventional measurement system for measuring coherence distance. This figure shows a system assembled to measure phase difference using a 3x3 coupler. This figure shows static correction matrices and formulas for each factor in calculating the phase difference using three interference signals. This figure shows correction matrices and formulas for each factor that change with time in order to calculate the phase difference using three interference signals. This shows a Hilbert transform of the three interference signals. This shows a figure calculating the phase shift between the three interference signals. This is a flowchart showing the processing flow of the coherence distance measurement method of this disclosure. This figure shows the intermediate processing results when calculated using a static correction matrix and when calculated using a time-varying correction matrix. This is a table showing the calculated spectral width.

[0012] In this disclosure, the coherence distance (hereinafter also referred to as coherence length as appropriate) is measured using a 3x3 coupler. However, in order to facilitate understanding of this disclosure, a brief explanation will also be given of conventional methods for observing the roll-off of the PSF using 1x2 and 2x2 couplers.

[0013] Figure 1 shows a conventional measurement system for measuring coherence distance. The measurement device 1 comprises a wavelength-swept light source 10, an optical branching unit 20, a reference unit 70, a measurement unit 30, an interference unit 40, a photodetector 50, and an analysis unit 60. Light emitted from the wavelength-swept light source 10 propagates through an optical guide path 11a, which is made of an optical fiber or the like, and reaches the optical branching unit 20. The optical branching unit 20 splits the light emitted from the wavelength-swept light source 10 into light to be measured and reference light, and is, for example, a 1x2 optical coupler for optical path splitting. The light branched by the optical branching unit 20 propagates to the reference unit 70 via the optical guide path 11b and to the measurement unit 30 via the optical guide path 11c, respectively.

[0014] The reference unit 70 is a system that serves as a reference for the light being measured in the measurement unit 30. Light propagating through the reference unit 70 is emitted from the light guide path 11f via the light circulator 71, shaped into parallel light by an optical element 72 such as a collimating lens, and reflected by a reference mirror 73, for example, a metal mirror surface. The reflected reference light (return light of the reference light) is guided to the interference unit 40 via the light guide path 11d through the optical element 72, which is also the light receiving system of the reference unit 70.

[0015] In the measurement unit 30, the light to be measured is emitted from the light guide path 11g via the light circulator 31, and is shaped into parallel light by an optical element 32 such as a collimating lens. Similar to the reference unit 70, the light to be measured is directed toward the moving mirror M by the optical element 32 such as a collimating lens. The moving mirror M can move in one axis direction on the stage 34, thereby creating an optical path length difference of distance Z from the reference unit 70. The light returned from the moving mirror M (light including reflected and scattered light from the moving mirror M) is guided to the interference unit 40 via the optical element 32, which is also the light receiving system of the measurement unit 30, through the light guide path 11e.

[0016] The interference unit 40 is a system that combines the light to be measured, which has been reflected or scattered by each mirror, with the reference light to generate interference light. The reflected light from the measurement unit 30 and the reference unit 70 is coupled by an optical coupling unit 41, which is, for example, a 2x2 optical coupler for optical path combination, and interferes with each other to become interference light, which is then guided to the light detection unit 50 by optical guide paths 11h and 11i.

[0017] The photodetector 50 is for detecting interference light and is a balanced photodetector (BPD) that outputs a differential using, for example, two photoelectric conversion elements such as two photodiodes. The photodetector 50 outputs an interference signal, which is input to the analysis unit 60 via the filter 51. As shown in Figure 1, the measurement light (signal light) and the reference light reach the optical coupling unit 41 at different times τ0 (delay time) due to the difference in optical path length, and the frequency difference is the beat frequency f ｂ This is how it appears. The interference signal is processed by FFT (Fast Fourier Transform) in the analysis unit 60 and output as a calculation result. The FFT converts the interference signal from the time domain to the frequency domain. Note that since a wavelength-swept light source whose wavelength (frequency) changes with time is used as the light source, it is essentially a conversion from the frequency domain to the time domain.

[0018] A window function is applied to the interference signal to obtain a Point Spread Function (PSF). The coherence distance is then measured according to whether the peak value in the PSF (vertical axis: dB) decreases to a predetermined ratio of intensity (roll-off) relative to the Depth (horizontal axis: mm).

[0019] However, due to the frequency bandwidth limitations of balanced photodetectors (BPDs) that output differential signals, it is difficult to acquire differential signals in very high frequency ranges, making it difficult to measure coherence distance using the roll-off method in high bandwidths. For example, in a Tunable VCSEL, the sweep speed can reach 100 to 400 kHz. For instance, when measuring the coherence length with a sweep wavelength of 90 nm, a sweep speed of 400 kHz, and a depth of 100 mm, the frequency of the interference signal can reach 15 GHz.

[0020] Therefore, while referring to Non-Patent Document 1 above, the inventors considered a method for measuring the coherence distance by a different method. Non-Patent Document 1 discloses a method for obtaining three interference signals using a 3x3 coupler and measuring the coherence distance. FIG. 2 is a diagram showing a system configured to measure the phase difference using a 3x3 coupler. In this figure, for example, a light source 100 which is a coherent wavelength sweeping light source using a Tunable VCSEL, a first optical coupler 110 which is a 2x2 coupler, a signal coil 120, a reference coil 130, and a second optical coupler 140 which is a 3x3 coupler are provided. The optical path is constituted by an optical fiber, and the signal coil 120 and the reference coil 130 are coils of optical fiber, not metal coils for safety. The light emitted from the light source 100 is split by the first optical coupler 110, passes through the optical path (signal arm) of the signal coil 120 which is the measurement object and the optical path (reference arm) of different optical path lengths of the reference coil 130, and is combined and interfered by the second optical coupler 140, and then output respectively. Hereinafter, these three signals are also referred to as three output signals and three interference signals (interference signal 1, interference signal 2, interference signal 3).

[0021] The second optical coupler 140 is designed so that the three output signals have a phase difference of 120 degrees. Therefore, the three output signals are independent interference signals respectively, and are represented as a sine wave function of the optical path length difference between the signal arm and the reference arm. The three output signals include the complex electric field vector components representing the amplitude and phase of the electric field when light propagates. That is, such a system can also be said to be a 120-degree phase difference interferometer in which the three output signals have a phase difference of 120 degrees. The analysis unit 160 may be a computing terminal or a dedicated processing device provided with one or more processors.

[0022] In photodetectors 150A, 150B, and 150C using a photodiode (PD) or the like at the signal output destination, the intensity (square of the amplitude) of the electric field component E is measured, and this is detected as the light intensity I. Since the three output signals are detected as single interference signals respectively, they can be detected without band limitation like a BPD.

[0023] First, the process by which the analysis unit 160 calculates the spectral width from these three output signals will be briefly described. From these three output signals, the phase difference of the interference signal is obtained using a correction matrix described later. Unwrapping processing is performed on this phase difference. From the unwrapped phase difference of the interference signal, the time derivative of the instantaneous phase of the light is reconstructed. While differentiating the reconstructed instantaneous phase with respect to time, it is divided by 2π. Thereby, the instantaneous frequency is obtained. Also, using polynomial fitting, a quasi-linear function of the frequency sweep is obtained. Then, the residual frequency error is obtained by subtracting the quasi-linear function from the instantaneous frequency. Then, using the residual frequency error, the power spectral density (PSD) of the frequency variation within a specific observation time window is estimated. Here, the PSD is not treated as the absolute value of the spectrum, but is used as information representing the fluctuation (shift) of the frequency centered on the sweep frequency. Using the obtained PSD, the spectral width is calculated.

[0024] If the spectral width can be calculated, the coherence length can be calculated. It is known that the coherence length Lc is approximately obtained by the following formula. Lc ~ λ ２ / Δλ λ: center wavelength of the light source, Δλ: spectral width (full width at half maximum FWHM)

[0025] FIG. 3 is a diagram showing the static correction matrix and mathematical expressions for each factor for calculating the phase difference using three interference signals. Here, the phase difference between the signal light and the reference light is, as shown in the formula of FIG. 3, η(t) = φ(t - T) = arctan(X' ２ (t) / X' １ (t)). T is the delay time of the signal light with respect to the reference light. X' ２ (t) and X' １ (t) are derived from the three output signals of the 120-degree phase difference interferometer shown in FIG. 2.

[0026] I １ (t), I ２ (t), I ２ (t) each represent three interference signals, and X' １ (t), X' ２ (t), X' ３(t) represents its orthogonal component. Here, X′ is used in the calculation of the phase difference. １ (t), X' ２ It is sufficient to obtain the two values ​​of (t).

[0027] The values ​​of η, ζ, and ξ are parameters that constitute a 3x3 matrix, which is a correction matrix used to compensate for various factors in a real 120-degree phase difference interferometer. Specifically, it includes a combination of elements such as amplitude changes due to 2x2 and 3x3 couplers, photoelectric efficiency of the photodetector, and phase changes due to the 3x3 coupler.

[0028] Therefore, in actual measurements, the above parameters are set appropriately and corrections are applied to the three output signals, resulting in X' １ (t), X' ２ (t) can be obtained, and the phase difference between the signal light and the reference light can be calculated from this.

[0029] However, the correction matrix shown in Figure 3, also described in Non-Patent Document 1, has static values ​​for each of η, ζ, and ξ. In other words, the first and second couplers are wavelength-dependent, but they do not correspond to the change in wavelength in the wavelength-swept light source. Therefore, the amplitude due to the first and second optical couplers, the photoelectric efficiency of the photodetector, and the phase due to the second optical coupler, as described above, have properties that change over time, and accuracy cannot be high unless they change over time.

[0030] Furthermore, while photoelectric efficiency includes factors related to the coupling efficiency between, for example, an optical fiber and an optical coupler, this coupling efficiency is an extremely unreproducible value that changes each time operations such as reconnecting the coupler and fiber are performed.

[0031] For the reasons stated above, in order to improve the accuracy of the final spectral linewidth and coherence distance calculation, the correction matrix needs to be one in which factors related to amplitude changes due to the first and second optical couplers, the photoelectric efficiency of the photodetector, and the phase change due to the second optical coupler change over time.

[0032] Figure 4 shows mathematical formulas and other information to explain the correction matrix (hereinafter, for convenience, also simply called the time-varying correction matrix or time-varying matrix) that uses three interference signals to describe the factors related to the amplitude change due to the first and second optical couplers, the photoelectric efficiency of the photodetector, and the phase change due to the second optical coupler, which change over time.

[0033] We will now explain in detail how each parameter included in the time-change correction matrix relates to the factors mentioned above. As shown in Figure 4, η ｎ (t) = 2c １ｎ (t)c ２ｎ (t)r ｎ (t) cosφ ｎ (t) ζ ｎ (t) = 2c １ｎ (t)c ２ｎ (t)r ｎ (t) sinφ ｎ (t) ξ ｎ (t) = r ｎ (t)(c １ｎ (t) ２ +c ２ｎ (t) ２ ) and c １ｎ (t) is the value obtained by multiplying the amplitude change caused by outputting from the first optical coupler 110 to the signal coil 120 (output tap on that side) by the amplitude change of the signal input from the signal coil 120 and output from the nth (1 to 3) output tap of the second optical coupler 140, c ２ｎ (t) is the value obtained by multiplying the amplitude change caused by outputting to the reference coil 130 (side output tap) of the first coupler 110 by the amplitude change of the signal input from the reference coil 130 and output from the nth (1 to 3) output tap of the second optical coupler 140, r ｎ (t) is the photoelectric efficiency, cosφ ｎ (t) and sinφ ｎ (t) is a function of time of the phase change caused by the second coupler. Therefore, if these can be obtained from the three output interference signals, the time-change correction matrix can be obtained.

[0034] Here, within the wavelength band where the accuracy of the 3x3 coupler is guaranteed, the phase difference of the interference signals of each output is guaranteed to be 120°. Therefore, the distribution ratio of all couplers is set to the same value of 1 / 6 (c １ｎ = c ２ｎ (= 1 / 6). However, since the wavelength of a wavelength-swept light source changes with time, in wavelength bands where the accuracy of the coupler is not strictly guaranteed, the distribution ratio and phase difference of the coupler change with time. This point is compensated for by including it in the photoelectric efficiency of the photodetector.

[0035] Figure 5 shows a graph obtained by Hilbert transforming three interference signals to extract factors related to amplitude change and photoelectric efficiency due to the optical coupler. This allows the amplitude components of each interference signal to be derived. The difference in amplitude of the three interference signals is due to the time dependence of the photoelectric efficiency of each photodetector and the coupler's distribution ratio. The time change of this amplitude component is related to the photoelectric efficiency r of each photodetector. １ (t), r ２ (t), r ３ It can be substituted as (t).

[0036] Figure 6 shows a graph of the phase shift of each interference signal calculated to extract the factors related to the phase change caused by the optical coupler. In other words, each interference signal should have a phase difference of 120° (±2π / 3), but if the difference is greater than that, it is not the designed phase difference, but rather a phase shift. Here, using interference signal 2 as the reference, φ ２ When (t) = 0, the phase difference between interference signal 2 and interference signal 1, and the phase difference between the phase of interference signal 2 and interference signal 3, as shown in Figure 6, are given by φ, respectively. １ (t), φ ３ It can be substituted as (t).

[0037] Based on the above, the time-varying correction matrix shown in Figure 4 can be obtained from the three interference signals. Below, we will summarize the method for measuring the coherence distance using this correction matrix.

[0038] Figure 7 is a flowchart showing the processing flow of the coherence distance measurement method of this disclosure.

[0039] First, in step S101, the light source 100 outputs wavelength-swept light as the light to be measured.

[0040] Next, in step S102, the light to be measured is split into signal light and reference light by the first optical coupler 110.

[0041] Next, in step S103, the signal light and the reference light are combined by the second optical coupler 140 and output as a first interference signal, a second interference signal, and a third interference signal, each with a phase difference of 120°.

[0042] Next, in step S104, the three interference signals are detected and acquired by the photodetectors 150A, 150B, and 150C, respectively.

[0043] Next, in step S105, the analysis unit 160 uses the first interference signal, the second interference signal, and the third interference signal to calculate a correction matrix that corrects the first interference signal, the second interference signal, and the third interference signal, in which factors related to the amplitude change due to the first optical coupler 110 and the second optical coupler 140, the photoelectric efficiency of the photodetectors 150A, 150B, and 150C, and the phase change due to the second optical coupler 140 change over time.

[0044] Next, in step S106, the analysis unit 160 calculates the phase difference between the signal light and the reference light using the first interference signal, the second interference signal, the third interference signal, and the correction matrix.

[0045] Next, in step S107, the analysis unit 160 calculates the spectral width of the wavelength-swept light source using the phase difference. First, an unwrapping process is performed on the phase difference. The time derivative of the instantaneous phase of the light is reconstructed from the phase difference of the unwrapped interference signal. The reconstructed instantaneous phase is differentiated with respect to time and divided by 2π. This gives the instantaneous frequency.

[0046] Furthermore, a quasi-linear function for the frequency sweep is obtained using polynomial fitting. The residual frequency error is then obtained by subtracting the quasi-linear function from the instantaneous frequency. The power spectral density (PSD) of the frequency variation within a specific observation time window is then estimated using the residual frequency error. Here, the PSD is not treated as the absolute value of the spectrum, but rather as information representing the frequency fluctuation (shift) centered on the sweep frequency. The spectral width is calculated using the obtained PSD.

[0047] Figure 8 shows an intermediate processing result that provides a visually easy-to-understand comparison between calculations using a static correction matrix and calculations using a time-varying correction matrix. In this figure, the electric field, the SFFT (Short-time Fourier Transform) of the electric field, and the PSD are shown for each of the two cases described above. It can be visually understood that the oscillation spectral width is more uniform over the entire wavelength sweep time, i.e., the entire wavelength sweep range, when calculated using the time-varying correction matrix, and that the measurement accuracy is improved. Furthermore, it can be seen that the PSD is close to the shape of an ideal Lorentz laser.

[0048] Figure 9 is a table comparing the spectral widths measured and calculated for a coherence light source swept at sweep frequencies of 100 to 400 kHz, using a static correction matrix, a time-varying correction matrix, and the noise floor method, which is also introduced as an invention described in Patent Document 1. In this table, assuming that the accuracy of the spectral width calculation values ​​using the noise floor method is high, it can be seen that, at all sweep frequencies, the values ​​calculated using the time-varying correction matrix have higher measurement accuracy than the values ​​calculated using the static correction matrix.

[0049] Next, in step S108, the coherence distance is calculated from the spectral width.

[0050] As described above, the coherence distance measurement method of this disclosure can be used to measure the coherence distance of a light source. This makes it possible to measure the coherence distance of a coherence light source operating in a very high frequency band.

[0051] This concludes the explanation provided in this disclosure. However, the new technologies described herein can be realized in various other forms, and parts of the content may be omitted, modified, or replaced without departing from the spirit of this disclosure. The embodiments and variations thereof shown in this disclosure are also included in the scope and spirit of this disclosure and shall be treated as equivalent and comparable to the technologies protected under the claims.

[0052] 1. Measuring device 10 Wavelength sweep light source 11a-i Light guide path 20 Light branching section 30 Measuring section 32 Optical element 40 Interference section 41 Optical coupling section 50 Photodetector section 60 Analysis section 70 Reference section 71 Optical circulator 72 Optical element 73 Reference mirror M Moving mirror 2. Coherence distance measuring device 100 Light source 110 First optical coupler 120 Signal coil 130 Reference coil 140 Second optical coupler 150A, 150B, 150C Photodetector 160 Analysis section

Claims

1. A coherence distance measurement method comprising: outputting light to be measured from a coherence wavelength sweep light source; separating the light to be measured into signal light and reference light using a first optical coupler; combining the signal light and the reference light using a second optical coupler and outputting them as a first interference signal, a second interference signal, and a third interference signal, each with a phase difference of 120°, respectively, and detecting each of them with a photodetector; calculating a correction matrix using the first interference signal, the second interference signal, and the third interference signal, in which factors related to amplitude changes due to the first and second optical couplers, the photoelectric efficiency of the photodetector, and the phase change due to the second optical coupler change with time; calculating the phase difference between the signal light and the reference light using the first interference signal, the second interference signal, the third interference signal, and the correction matrix; and calculating the spectral width of the light using the phase difference. A method for measuring coherence distance, which calculates the coherence distance of the light using the spectral width.

2. A coherent distance measuring device comprising: a coherence wavelength sweep light source that outputs light to be measured; a first optical coupler that separates the light to be measured into signal light and reference light; a second optical coupler that, after combining the signal light and the reference light, outputs a first interference signal, a second interference signal, and a third interference signal, each with a phase difference of 120°; and a photodetector that detects the first interference signal, the second interference signal, and the third interference signal, respectively, wherein the analysis unit calculates a correction matrix that corrects the first interference signal, the second interference signal, and the third interference signal using the first interference signal, the second interference signal, and the third interference signal, the correction matrix being calculated in which factors related to amplitude changes due to the first optical coupler and the second optical coupler, the photoelectric efficiency of the photodetector, and the phase change due to the second optical coupler change over time, A coherence distance measuring device that calculates the phase difference between the signal light and the reference light using the first interference signal, the second interference signal, the third interference signal, and the correction matrix; calculates the spectral width of the light using the phase difference; and calculates the coherence distance of the light using the spectral width.

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