Measurement system and method

Abstract

To measure structure and movement of a measurement object with high frequency and with high resolution.SOLUTION: An optical comb generation device 12 modulates a laser beam with a frequency modulation signal Si of frequency νi, and generates an optical comb including frequency components arranged at frequency νi intervals. An optical device 15 irradiates a measurement object 3 with the optical comb through an interference plate 152 and a 1 / 8λ wavelength plate 154, and makes a reflected optical comb interfere with the optical comb reflected on the interference plate 152. The 1 / 8λ wavelength plate 154 gives a phase difference of π / 2 between S-polarized light and P-polarized light while the optical comb reciprocates between the interference plate 152 and the measurement object 3. An information processing device 17 detects the intensity I of an interference peaks of the p-polarized light and the intensity Q of interference peaks of the s-polarized light, and acquires a distance to a reference surface with μm order on the basis of the frequency νi and interference order. The information processing device 17 acquires deviation to the reflection surface with nm order from a time change in the deviation from the signal intensities I and Q.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a measurement system and a measurement method. [Background technology]

[0002] From the viewpoint of mechanobiology, there is an increasing demand to detect the surface structure, internal structure, and cross-sectional structure of a measurement object such as a biological sample, as well as their high-speed and minute movements in the nanometer-level range, and to elucidate various movements of a living body. For example, vibration of the inner ear sensory epithelium, vibration of the eardrum, bone conduction, and movements of various flagella. The Doppler shift method is known as one method for this purpose. The Doppler shift method is suitable for measuring movements such as vibration of a measurement object. Patent Documents 1 and 2 disclose examples of the Doppler shift method.

[0003] Also, OCT (Optical Coherence Tomograph) is known as a technique for photographing the internal structure of a sample by utilizing the coherence of light. OCT is classified into TD (Time Domain)-OCT, which moves a reference mirror to perform scanning, and FD (Fourier Domain)-OCT, which obtains depth information by Fourier transform instead of sweeping the reference mirror. FD-OCT is further classified into SD (Spectrum Domain)-OCT, which uses a broadband light source and obtains depth information by Fourier transforming the obtained spectrum, and SS (Swept Source)-OCT, which uses a wavelength swept laser and obtains depth information by Fourier transforming the obtained spectrum. Patent Document 3 discloses an example of SD-OCT, and Patent Document 4 discloses an application example of SS-OCT.

[0004] The Doppler shift method and FD-OCT method have a sampling frequency of about 1 kHz because they move a reference mirror, making it difficult to measure high-speed movements. On the other hand, the FD-OCT method can measure movements up to about 3 MHz. However, this method cannot measure the structure of the object being measured. In addition, these methods require fast Fourier transform (FFT) processing for measurement, which places a heavy burden on the calculation processing and is limited by the sensor's response speed and wavelength scanning speed. For this reason, they are mainly specialized for tomographic imaging, and the goal of increasing speed is mainly real-time imaging. For this reason, they are not suitable for detecting movements such as high-speed vibrations of the object being measured. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] JP 2013-061255 A [Patent Document 2] JP 2010-261911 A [Patent Document 3] JP 2015-169650 A [Patent Document 4] JP 2014-228473 A Summary of the Invention [Problem to be solved by the invention]

[0006] The present invention has been made in consideration of the above-mentioned circumstances, and has an object to make it possible to measure the structure and movement of an object to be measured at higher frequencies and with higher resolution. [Means for solving the problem]

[0007] In order to achieve the above object, a measurement system according to a first aspect of the present invention comprises: The distance between the two frequency bands varies depending on whether they are moving toward or away from the center frequency. an optical comb generator for generating an optical comb including a plurality of frequency components corresponding to the an optical device that outputs the optical comb generated by the optical comb generating unit to a measurement object and a reference plane, causes the optical comb reflected by the reflection plane of the measurement object to interfere with the optical comb reflected by the reference plane, and generates an interference signal; a detector for determining the intensity of the envelope of an interference peak contained in the interference signal; a position detection device that determines a distance from a reference position to a reflecting surface of the measurement object based on the intensity detected by the detection device; Equipped with.

[0008] The detection device, for example, includes a separation means for separating an interference signal into a first interference signal and a second interference signal that is shifted in phase by π / 2 from the first interference signal, and a means for calculating the intensity of the first interference signal and the intensity of the second interference signal, and the position detection device calculates the distance from a reference position to the reflecting surface based on, for example, the ratio between the intensity of the first interference signal and the intensity of the second interference signal.

[0009] For example, the detection device includes a means for converting the optical comb into linearly polarized light including a P-polarized component and an S-polarized component, a means for providing a phase difference of π / 2 between one of the P-polarized component and the S-polarized component of the optical comb, and a means for calculating the intensity of an interference signal due to the P-polarized component and the intensity of an interference signal due to the S-polarized component, and the position detection device divides the intensity of the interference signal due to the phase-lagging polarized component of the P-polarized component and the S-polarized component by the intensity of the interference signal due to the phase-leading polarized component, and calculates tangent of the quotient. -1 The phase is obtained by calculating the phase, and the phase of the light constituting the optical comb from the reference position to the reflecting surface is obtained based on the obtained phase.

[0010] For example, the position detection device monitors changes in intensity of the envelope of an interference peak contained in an interference signal, determines the maximum or minimum of the monitored intensities, and determines the position of the reflecting surface based on the maximum or minimum intensity.

[0011] For example, the position detection device detects the position of the reflecting surface a plurality of times while the plurality of frequency components move so as to converge around the center frequency or move so as to move away from the center frequency, The position detection device may comprise means for determining the amplitude and frequency of vibration of the reflecting surface from the determined time series of the position of the reflecting surface.

[0012] An optical path length difference detector may be provided that determines the optical path length difference to the reflecting surface based on the interval frequency of the frequency components of the optical comb and the order of interference for the interference peak contained in the interference signal.

[0013] The optical path length difference detecting apparatus may comprise means for determining a distribution of the positions of the reflecting surface from the optical path length differences obtained at different measurement timings.

[0014] For example, an optical path length difference detection device determines the optical path length difference on the order of μm, and a position detection device determines the distance from a reference position to a reflecting surface on the order of nm.

[0015] In order to achieve the above object, a measurement system according to a second aspect of the present invention comprises: The two frequencies are spaced apart by moving the two frequencies together at the center frequency and then moving away from the center frequency. an optical comb generator that generates an optical comb including a plurality of fluctuating frequency components; an optical device that outputs the optical comb generated by the optical comb generating unit to a measurement object and a reference plane, causes the optical comb reflected by the reflection plane of the measurement object to interfere with the optical comb reflected by the reference plane, and generates an interference signal; an optical path length difference detector that determines an optical path length difference to a reflecting surface based on an interval frequency and an interference order of frequency components of an optical comb for an interference peak included in an interference signal; A means for determining a distribution of positions of a reflecting surface based on the optical path length differences obtained at different times; Equipped with.

[0016] The optical comb generator may be configured to, for example, set the interval (interval frequency) ν i But, ν i =ν a +ν m cos(2πν s t) is generated. a : first frequency, ν m : maximum frequency deviation, ν s : second frequency, t: time.

[0017] The optical comb generating unit includes, for example, a light source device that emits laser light, a device that generates a third signal of a third frequency by frequency-modulating a first signal of a first frequency with a second signal of a second frequency, and an optical modulation device that modulates the laser light from the light source device with the third signal to generate an optical comb including a plurality of frequency components spaced at intervals of the third frequency. picture, the first signal and the second signal are both sinusoidal signals; The first frequency is higher than the second frequency.

[0018] In order to achieve the above object, a measurement method according to a third aspect of the present invention comprises: The spacing between the two frequencies varies depending on whether the frequency is moved toward or away from the center frequency. generating an optical comb having a plurality of frequency components; The generated optical comb is irradiated onto a measurement object, and an interference signal is generated by causing the optical comb reflected by a reflection surface of the measurement object to interfere with a reference light; The distance from the reference position to the reflecting surface is determined based on the intensity of the envelope of the interference peak contained in the interference signal.

[0019] In order to achieve the above object, a measurement method according to a fourth aspect of the present invention comprises: The two frequencies are spaced apart by moving the two frequencies together at the center frequency and then moving away from the center frequency. An optical comb including a plurality of fluctuating frequency components is emitted to a measurement object and a reference surface, and the optical comb reflected by the reflection surface of the measurement object and the optical comb reflected by the reference surface are interfered with each other to generate an interference signal; For the interference peaks included in the interference signal, a difference in optical path length to a reflecting surface of the measurement object is obtained based on the interval frequency of the frequency components of the optical comb and the interference order; The distribution of the positions of the reflecting surface of the measurement object is obtained based on the optical path length differences acquired at different times. Effect of the Invention

[0020] The measurement system and method according to the present invention make it possible to measure the structure and movement of an object at high frequency and with high resolution. [Brief description of the drawings]

[0021] [Figure 1]1 is a diagram showing a configuration of a measurement system according to an embodiment of the present invention; [Diagram 2] 2 is a diagram illustrating an example of a voltage waveform of a scan signal Ss generated by the scan signal generating device shown in FIG. 1. [Diagram 3] 2 is a diagram illustrating an example of the frequency and wavelength of a laser beam outputted by the light source device shown in FIG. [Figure 4] 2 is a diagram illustrating the structure of the optical comb generating device shown in FIG. 1; [Diagram 5] 2A illustrates an example of the configuration of a narrowband optical comb generated by the optical modulation device shown in FIG. 1, and FIG. 2B illustrates an example of its spectral distribution. [Figure 6] FIG. 2A illustrates an example of the configuration of a wideband optical comb output from the highly nonlinear shifted fiber shown in FIG. 1, and FIG. 2B illustrates an example of its spectral distribution. [Figure 7] 13(A) and (B) are diagrams illustrating how the frequency interval of an optical comb changes in accordance with a scan signal. [Figure 8] FIG. 2 is a diagram showing the principle of optical comb interferometry used in the measurement system shown in FIG. 1, where (A) is a diagram showing the envelope of an interference peak generated in an interference signal, and (b) is a diagram showing an example of the relationship between the intensity of the envelope peak and the phase α. [Figure 9] FIG. 13 is a diagram showing an example of an interference signal when distance is a variable. [Figure 10] FIG. 13 is a diagram showing an example of an interference signal when the modulation frequency is a variable. [Figure 11] FIG. 13 is a diagram showing the relationship between the modulation frequency, the interference order, and the optical path length difference. [Figure 12] 13A and 13B are diagrams showing the relationship between the optical path length and the phase of the light that constitutes the optical comb. [Figure 13] FIG. 1A is a diagram showing an example of an object to be measured, FIG. 1B is a diagram showing an example of an envelope of an interference peak of an interference signal, and FIG. 1C is a diagram showing an example of a phase corresponding to the intensity of the envelope. [Figure 14] 1A and 1B are diagrams for explaining a method for determining the amplitude and period of micro-vibrations of a measurement object. [Figure 15]2 is a flowchart of an interference data analysis process executed by the data analysis device shown in FIG. 1. [Figure 16] 2 is a flowchart of a distribution analysis process executed by the data analysis device shown in FIG. 1. [Figure 17] 2 is a flowchart of a microvibration analysis process executed by the data analysis device shown in FIG. 1. [Figure 18] FIG. 2 is a diagram illustrating an experimental system for an operation experiment of the measurement system shown in FIG. [Figure 19] 1A to 1C are waveform diagrams illustrating the first embodiment. [Figure 20] 13(A) to 13(C) are waveform diagrams illustrating the second embodiment. [Figure 21] 13A and 13B are waveform diagrams for explaining the second embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0022] A measurement system and a measurement method according to an embodiment of the present invention will be described with reference to the drawings. In the following embodiments, the same components and values ​​are denoted by the same reference numerals. In the drawings, components that are not necessary for the description may be omitted in order to facilitate understanding.

[0023] The measurement system 1 of this embodiment has the function of simultaneously measuring the vibration and fault of the object to be measured, and as shown in FIG. 1, includes an RF signal generating device 11, an optical comb generating device 12, a polarization controller 13, a circulator 14, an optical device 15, an optical signal processing device 16, and an information processing device 17.

[0024] The RF signal generator 11 includes a carrier signal generator 110, a scan signal generator 112, and a frequency modulator 114, and generates a frequency modulation signal S that modulates the laser light to generate an optical comb. i Generate.

[0025] The optical comb generating device 12 includes a light source device 120, an optical modulator device 122, an optical amplifier device 124, and a highly nonlinear shifted fiber 126, and generates a wideband optical comb.

[0026] The polarization controller 13 converts the light constituting the wideband optical comb generated by the optical comb generator 12 into linearly polarized light.

[0027] The circulator 14 outputs the wideband optical comb output from the polarization controller 13 to the optical device 15 , and also outputs the interference light (interference signal) emitted from the optical device 15 to the optical signal processing device 16 .

[0028] The optical device 15 is composed of an optical interferometer and is equipped with a collimator 150, an interference plate 152, and a 1 / 8λ wavelength plate 154. It generates an interference signal between the reflected light from the object to be measured 3 and the light (reference light) reflected by the interference plate 152, and transmits the interference signal to the circulator 14.

[0029] The optical signal processing device 16 includes a polarizing beam splitter 160, a 1:1 coupler 161 for P polarization, a photodetector 162 for P polarization, a 1:1 coupler 163 for S polarization, a photodetector 164 for S polarization, and a sampling device 165, and processes the interference signal from the circulator 14, separates it into P polarization and S polarization, and samples their intensities.

[0030] The information processing device 17 is composed of a computer device, and includes a storage device 170, a data analysis device 172, and a monitor device 174, processes the signals sampled by the sampling device 165, measures the structure and movement of the measurement object 3 with high resolution, and images the tomographic structure. In other words, the information processing device 17 functions as an optical path length difference detection device that determines the optical path length difference to the reflecting surface and a position detection device that determines the distance from a reference position to the reflecting surface.

[0031] The light source device 120, the optical modulator 122, the optical amplifier 124, the highly nonlinear shift fiber 126, the polarization controller 13, the circulator 14, the optical device 15, the polarized beam splitter 160, the 1:1 coupler for P polarization 161, the photodetector for P polarization 162, the 1:1 coupler for S polarization 163, and the photodetector for S polarization 164 are appropriately connected together via optical transmission paths such as optical fibers.

[0032] In addition, the components of the RF signal generating device 11, the components of the information processing device 17, between the frequency modulation device 114 and the optical modulation device 122, between the sampling device 165 and the memory device 170, and between the scan signal generating device 112, the sampling device 165, and the information processing device 17 are connected by control signal transmission paths such as electric wires.

[0033] The measurement system 1 has an optical path length L op With a precision in the μm range, the minute movement of the measurement object 3 is measured with a precision in the nm range. When the measurement object 3 transmits light, the optical path length L op The reflecting surface is, for example, the interface between materials with different refractive indices.

[0034] In the RF signal generator 11, the carrier signal generator 110 generates a signal of frequency v a = 5GHz~20GHz, preferably 8GHz~12GHz, an electrical sine wave carrier signal S a and outputs it to the frequency modulation device 114.

[0035] Carrier signal S a The voltage waveform is expressed by Equation 1. S a =V am cos(ω a t)...Equation 1 V am is the amplitude value, ω a =2πν a It is.

[0036] The scan signal generating device 112 generates a cosine wave as shown in FIG. 2 at a scan frequency v s , one scan period T s =1 / ν s Scan signal S s Generates a scan signal S s The voltage waveform is expressed by Equation 2. S s =V sm cos(ω s t)...Equation 2 V sm is the amplitude value, ω s =2πν s It is.

[0037] The scan signal generating device 112 also generates a scan signal S s At the timing of phase 0, the synchronizing signal is output to the sampling device 165 and the information processing device 17.

[0038] The frequency modulation device 114 shown in FIG. a The scan signal S s The carrier signal S a By applying a frequency shift to the i and outputs the frequency modulated signal S to the optical modulator 122 of the optical comb generator 12. i The voltage waveform is expressed by Equation 3. S i =V im sin[ω a t+mfsin(ω s t)] ...Equation 3 In Equation 3, V im is the amplitude value, and mf is the modulation index.

[0039] Also, the frequency modulated signal S i The instantaneous frequency of i is expressed by Equation 4. ν i =ν a +ν m cos(ω s t)...Equation 4 In formula 4, vm is the maximum frequency deviation, ν m =mf ν s It is.

[0040] If the modulation index mf=10, the frequency modulated signal S i is expressed by Equation 3', and the frequency modulation signal S i The instantaneous frequency of i is represented by Equation 4'. S i =V im sin[ω a t+10sin(ω s t)] ...Equation 3' ν i =ν a +10ν s cos(ω s t) ...Equation 4'

[0041] Therefore, for example, at a modulation index mf=10, the frequency of the scan signal ν s = 1MHz, the maximum frequency deviation ν m =mf ν s = 10MHz. In this case, the frequency modulation signal S i Frequency ν i would result in one cycle of (10GHz-10MHz)~(10GHz+10MHz)~(10GHz-10MHz) being repeated 1M times per second.

[0042] In addition, the carrier signal S a is an example of the first signal in the claims, frequency v a is an example of the first frequency, the scan signal S s is an example of the second signal, frequency ν s is an example of a second frequency, frequency modulated signal S i is an example of a third signal, frequency ν i is an example of the third frequency.

[0043] The light source device 120 shown in FIG. 1 has a center frequency v c , e.g., 2×10 14 Hz to the optical modulator 122. In this case, the central wavelength λ c =c / νc ≒ 1.49896...μm. c is the speed of light ≒ 299,792,458 m / s.

[0044] The optical modulator 122 shown in FIG. 1 is, for example, a dual drive Mach-Zehnder (DD-MZM) modulator, and outputs a frequency modulation signal S i According to the above, a relatively narrowband optical comb is generated from the laser light emitted from the light source device 120. As shown in FIG. 4, the DD-MZM modulation device 122 includes an amplifier 1221, a phase modulator 1222, an amplifier 1223, an attenuator 1224, a phase controller 1225, and a phase modulator 1226.

[0045] The amplifier 1221 amplifies a signal at one output end of the frequency modulation device 114 of the RF signal generating device 11. The phase modulator 1222 is composed of a lithium niobate phase modulator (LN-PM) or the like, and shifts the phase of the infrared laser input from the light source device 120 according to the output voltage of the amplifier 1221. The amplifier 1223 amplifies a signal at the other output end of the frequency modulation device 114. The attenuator 1224 attenuates the output voltage of the amplifier 1223. The phase controller 1225 controls the phase of the output voltage of the attenuator 1224. The phase modulator 1226 is composed of a lithium niobate phase modulator (LN-PM) or the like, and is connected in parallel to the lithium niobate phase modulator 1222, and shifts the phase of the infrared laser input from the light source device 120 according to the output voltage of the phase controller 1225.

[0046] The optical modulator 122 converts the infrared laser light into a frequency modulated signal S i As shown in Fig. 5(A), the center frequency is ν c The optical comb is generated by distributing j frequency components on each side of the frequency comb. Each frequency component corresponds to a tooth of the optical comb. The central frequency of the frequency component is ν c-j ~ν c ~ν c+j The interval of the frequency modulated signal S i Frequency ν iThe bandwidth BW of this optical comb is relatively narrow, for example, about 1.1 nm, as shown in FIG. 5B. As shown in FIG. 1 and FIG. 4, the optical modulation device 122 outputs the generated optical comb to the optical amplification device 124.

[0047] The optical amplifier 124 shown in FIG. 1 is composed of, for example, a high-power erbium-doped optical fiber amplifier (EDFA), amplifies the optical comb output from the optical modulator 122 by about 30 dB to 35 dB, and outputs it to the highly nonlinear shifted fiber 126.

[0048] The highly nonlinear shift fiber 126 has a length of, for example, about 200 m, and outputs the optical comb optically amplified by the optical amplifier 124 to the polarization controller 13. The highly nonlinear shift fiber 126 increases the interference order of the optical comb, thereby broadening the bandwidth of the optical comb.

[0049] As shown in Fig. 6(A), the broadband optical comb has a center frequency of ν c On either side of the interval frequency ν i The frequency components are arranged in a sequence of n, totaling 2n+1. Each frequency component has a center frequency ν c-n ~ν c ~ν c+n The interval is the modulation frequency ν i Here, n is a natural number, and n>j. At this stage, the bandwidth BW of the optical comb is wider than the bandwidth of the optical comb generated by the optical modulation device 122, that is, the bandwidth is widened, as shown in FIG. 6(B). In FIG. 6(A), G(ν-ν c ) represents the envelope of the entire intensity distribution, and the central frequency ν c Distance from (ν-ν c ) where F(ν) is the intensity of the longitudinal mode waveform at frequency ν.

[0050] The interval between the center frequencies of the frequency components that make up the broadband optical comb is ν i The instantaneous value of is expressed by the above-mentioned formula 4. Therefore, the frequency components that make up the optical comb have a center frequency v cThe action of moving to converge at the center and the center frequency ν c The operation of moving away from the target, i.e., the operation of periodically varying the interval, is called the scan signal S s Frequency ν s Repeat with:

[0051] 1, the wideband optical comb generated by the highly nonlinear shifted fiber 126 is output to the polarization controller 13. The polarization controller 13 converts the light constituting the wideband optical comb generated by the optical comb generator 12 into linearly polarized light (hereinafter, polarized light) and outputs it to the circulator 14.

[0052] The circulator 14 outputs an optical comb formed from the linearly polarized light output from the polarization controller 13 to the optical device 15 .

[0053] Optical device 15 is composed of an optical device such as a common path interferometer, and collimates the broadband optical comb from circulator 14 with collimator 150 and emits the parallel light toward measurement target 3 via interference plate 152. A part of the optical comb is reflected by the reflecting surface of interference plate 152 and becomes reference light. The reflecting surface of interference plate 152 serves as a reference for distance measurement and is an example of a reference surface.

[0054] On the other hand, the light that has passed through the interference plate 152 passes through the 1 / 8 λ wavelength plate 154, reaches the measurement object 3, and has an optical path length L op The optical comb is reflected by a reflecting surface separated by 2 / 8λ (π / 2) from the P-polarized light. The reflecting surface is, for example, a boundary between regions with different refractive indexes, such as the outer surface of the object to be measured 3 or an internal reflecting surface. A part of the optical comb reflected by the object to be measured 3 passes through the 1 / 8λ wave plate 154 again and enters the interference plate 152. The 1 / 8λ wave plate 154 provides a phase difference of π / 2 between the P-polarized light and the S-polarized light while the optical comb travels back and forth between the interference plate 152 and the object to be measured 3. In the following explanation, it is assumed that the S-polarized light is delayed by 2 / 8λ (π / 2) compared to the P-polarized light.

[0055] The light reflected from the measurement object 3 and the light reflected by the interference plate 152 (reference light) interfere with each other, generating an interference signal (interference light) as shown in FIG. 8A. Fringes (interference fringes) do not appear in the interference signal, and only the envelope B of the interference peak is observed. Note that FIG. 8A shows that the optical comb is reflected at four points on the measurement object 3, generating four peak frequencies ν 11 ~ν 14 This shows an example where an interference peak occurs.

[0056] The interference signal will now be explained in more detail. If the optical comb shown in FIG. 6A, that is, the optical comb input to the optical device 15, is ideal, the center frequency of the optical comb is ν c mth frequency component (center frequency = ν c +m ν i ) caused by interference signal I m (ν i ) is shown in Equation 5. m is an integer, including positive and negative numbers. Here, m is different from m of the interference order described later.

[0057] I m (ν i )=a m cos[2π(ν c +m ν i )L / c]...Equation 5 a m : amplitude, ν c : center frequency of optical comb, L: optical path length difference = 2 L op , Optical path length L op Distance between the reflecting surface of the interference plate 152 and the reflecting surface of the measurement object 3

[0058] The entire optical comb is the sum of interference from all frequency components, so the interference signal I(ν i ) is as shown in Equation 6.

number

[0059] In Equation 6, the part in [ ] is the periodic even function B Τ (ν i) is equivalent to the Fourier series expansion of Equation 6. Therefore, Equation 6 can be transformed into Equation 7. I(ν i )=cos[2πν c L / c]B Τ (ν i )...Equation 7

[0060] Even function B Τ (ν i The period of the interference is c / L. The interference order is p, and the frequency of the interference peak is ν p =P(c / L), even function B Τ (ν i ) function for one period of B(ν i ), then the interference signal I(ν i ) is expressed by Equation 8.

number

[0061] Therefore, the interference signal I p (ν i ) is expressed by Equation 9. I p (ν i )=cos(α)B(ν i -ν p )...Equation 9

[0062] The interference signal I shown in Equation 9 p (ν i ) is the center frequency (peak frequency) v p (i.e., ν 11 ,ν 12 ,ν 13 ,ν 14 ) and modulation frequency ν i The difference between (ν i -ν p ) The envelope B is a function of B(0), that is, ν i =ν p The envelope B(νi -ν p ) is amplitude modulated by cos(α) to produce the interference signal I p (ν i ) varies depending on the phase α, as illustrated in FIG. 8(B).

[0063] Next, the envelope B(ν i -ν p ) will be considered in more detail. The power spectrum (power spectral density) S(ν) of the optical comb shown in FIG. 6(A) is expressed by Equation 10.

number

[0064] The interference signal is expressed by the autocorrelation function of the time waveform of the optical comb, and is equal to the real part of the inverse Fourier transform F of the power spectrum according to the "Wiener-Kindzin theorem." Therefore, the interference signal I(τ) is expressed by Equation 11.

number

[0065] Here, g(τ) is the result of the inverse Fillier transform of G(ν), and f(τ) is the result of the inverse Fillier transform of F(ν). The observed interference signal has a real part, and since f(τ) ≈ 1, Equation 12 holds.

number

[0066] When the variables are changed to L=cτ, Equation 13 holds.

number

[0067] From Equation 13, the envelope of the interference peak B(ν i ), Equation 14 holds. B(ν i )=1 / ν i g(L-mc / ν i )...Equation 14

[0068] From Equation 14, the envelope of the interference peak B(ν i ) is the power spectrum envelope G(ν-ν c ) inverse Fourier transform g(ν i ) That is, according to the measurement system 1 of this embodiment, the envelope B of the interference peak can be obtained without performing high-load data processing such as inverse Fourier transform.

[0069] When the optical path difference L is a variable, the interference peak is expressed as c / ν i More specifically, the shortest optical path length L1 at which an interference peak appears is L1=c / ν i Therefore, the m-th order interference peak appears when formula 15 holds. Moreover, by differentiating formula 15, formula 15' holds. L=mL1=mc / ν i ...Formula 15 δL=mc / (ν i 2 )δν i ...Formula 15' m: interference order

[0070] Therefore, interference occurs at an appropriate interference order m according to the optical path length difference L of the reflecting surfaces, and an interference peak I p (L) is generated. Modulation frequency ν i Since varies periodically, the optical path length difference L at which the interference peak occurs changes. If Δν=c / L, the FWHM (half width) of the envelope B of each interference peak is approximately proportional to 1 / Δν.

[0071] Furthermore, from equations 9 and 14, equation 16 holds for the intensity of the m-th order interference peak. I p (L)=cos(α)·(1 / ν i )·B(ν i ) =cos(2πν c L / c)·(1 / ν i )·g(L-mc / ν i ) ...Formula 16

[0072] Also, the interval frequency ν i When is used as a variable, Equation 17 holds true.

number

[0073] From Equation 17, the interference peak I p As shown in Figure 10, occurs at intervals of Δν=c / L up to p=infinity. However, except for p=1, the frequency becomes high and the energy becomes small, so it can be ignored. Therefore, if we only consider p=1, we can rewrite Equation 9 as Equation 9'. I1(ν i )=cos(α)·B(ν i -ν1)...Equation 9'

[0074] According to Equation 9', when an interference peak occurs in the interference signal, the modulation frequency ν i If we calculate the interference order m, we can calculate the optical path difference L.

[0075] The relationship that satisfies Equation 15 is illustrated in FIG. 11. As an example, i = 10GHz, then c / ν i=0.03m. Therefore, for example, when the interference order m=1, L≈0.03m can be obtained, and when m=2, L≈0.06m can be obtained. In this way, the interference order m is estimated from the known approximate optical path length difference of the interferometer constituting the optical device 15, and the optical path length difference L can be obtained from Equation 15 based on the estimated interference order m. However, when the modulation frequency ν i fluctuates, with a precision on the order of μm.

[0076] The method for calculating the interference order m is not limited to the above example. The interference order m may be calculated by other methods. For example, the small fluctuation Δν of the interference peak frequency with respect to the small fluctuation ΔL of the measurement object 3 shown in Equation 15′ is i Alternatively, any other method may be used.

[0077] When an interference peak occurs in the interference signal, the optical path length difference L is ideally set to λ 1 / λ 2 , as shown in FIG. 12(A). c However, in reality, as shown in FIG. 12(B), the optical path length difference L and the central wavelength λ of the light constituting the optical comb are c There is a "deviation" (distance) ΔL = LN λ between the natural number (N) times c exists.

[0078] As mentioned above, the interference signal I1(ν i ) is amplitude modulated by cos(α), and the envelope B of the interference peak has a phase α=2πν c It changes depending on L / c. Here, the central wavelength of the optical comb, λ c Using the above-mentioned deviation ΔL, the optical path difference L is expressed by Equation 18. L=Nλ c +ΔL=N(c / ν c )+ΔL...Equation 18 L=2 L op ΔL=2 ΔL op N=natural number

[0079] Using equation 18, cos(α) can be transformed as follows: cos(α) = cos(2πν c L / C) =cos[2πν c (N c +ΔL) / c)] =cos(2πN+2πΔL / λ c ) =cos[2π(ΔL / λ c )] =cos(2πν c ΔL / c)...Equation 19 Hereafter, the phase α=2πν c This is expressed as (ΔL / c).

[0080] From Equation 19, it can be seen that there is a correlation between the amplitude of the envelope B of the interference peak and the shift ΔL. Therefore, it is possible to obtain the phase α based on the amplitude of the envelope B of the interference peak, and to obtain the shift ΔL of the optical path length difference from the phase α.

[0081] A specific method for determining the phase α and the shift ΔL based on the amplitude of the envelope B will be described below.

[0082] As described above, of the linearly polarized light constituting the optical comb output from the circulator 14, the optical comb that passes through the interference plate 152 passes through the 1 / 8λ wave plate 154 and reaches the measurement object 3. Furthermore, a part of the optical comb reflected by the measurement object 3 passes through the 1 / 8λ wave plate 154 again.

[0083] The 1 / 8λ wavelength plate 154 is disposed at a position and orientation where the S-polarized light component of the optical comb passes through its slow axis. Therefore, the S-polarized light that has passed through the interference plate 152 is delayed by 1 / 8λ relative to the P-polarized light by passing through the 1 / 8λ wavelength plate 154, and is further delayed by 1 / 8λ by being reflected by the measurement object 3 and passing through the 1 / 8λ wavelength plate 154 again. On the other hand, the P-polarized light is incident on the interference plate 152 without being delayed. Therefore, the S-polarized light reflected by the measurement object 3 is delayed by 2 / 8λ, i.e., π / 2, relative to the P-polarized light.

[0084] Therefore, the P-polarized component and the S-polarized component are out of phase with each other by π / 2, resulting in an IQ orthogonal modulation relationship. Specifically, for the P-polarized optical comb, there is no phase shift in the reflected light from the measurement target 3, and there is also no phase shift in the reflected light from the reflecting surface of the interference plate 152. Therefore, the phase of the interference light, α=2πν c ΔL / c, and the interference signal remains as in Equation 9.

[0085] In contrast, for an S-polarized optical comb, the reflected light from the object to be measured 3 is delayed by λ / 4=π / 2 during the round trip. Therefore, the phase of the interference signal due to interference of S-polarized light becomes α-π / 2. Note that one of the interference signal due to the P-polarized component and the interference signal due to the S-polarized component is an example of the first interference signal in the claims, and the other is an example of the second interference signal.

[0086] Due to this phase difference, the signal intensity I(ν i -Δν i ) and the signal intensity Q(ν i -Δν i ) is expressed by Equation 20 and Equation 21. As mentioned above, the interference order p can be limited to 1. If p=1, Δν i is equal to the frequency ν1 of the first-order interference peak shown in FIG. 10, i.e., Δν i =ν1. Note that I(ν i -ν1) and Q(ν i -ν1) are assumed to be equal in energy.

[0087] I(ν i -ν1)=cos(α)B(ν i -ν1)...Equation 20 Q(ν i -ν1)=cos(α-π / 2)B(ν i -ν1) =sin(α)B(ν i -ν1)...Equation 21

[0088] Equation 22 is derived from equations 20 and 21. α=tan -1 [Q(ν i-ν1) / I(ν i -ν1)]...Equation 22 In addition, in Equation 22, Q(ν i -ν1) and I(ν i -ν1) is the envelope B(ν i -ν1) total energy or ν i The peak value when =ν1 may be used.

[0089] Therefore, i) the signal intensity I(ν i -ν1) and the signal intensity Q(ν i -ν1), and ii) apply it to Equation 22 to obtain the signal strength I(ν i -ν1) with signal strength Q(ν i -ν1) and take the quotient (ratio value) [Q(ν i -ν1) / I(ν i -ν1)] tan -1 iii) the integer multiple N λ of the wavelength of the light that constitutes the optical comb c The phase α of the light that constitutes the optical comb up to the reflecting surface can be calculated by using the position determined by the reference position. Furthermore, the deviation ΔL = α2πν c / c, and then ΔL op =ΔL / 2. Note that the phase α, the shift ΔL, and the distance ΔL op are mutually convertible, and it is up to the user to decide which one is the final solution.

[0090] Returning to FIG. 1, the P-polarized interference signal and the S-polarized interference signal outputted from the optical device 15 are each incident on the circulator 14.

[0091] The circulator 14 outputs the P-polarized interference signal and the S-polarized interference signal to the polarized beam splitter 160 of the optical signal processing device 16. The polarized beam splitter 160 functions as a separation means that separates and outputs the P-polarized interference signal (I interference signal) to a 1:1 coupler 161 for P polarization and the S-polarized interference signal (Q interference signal) to a 1:1 coupler 163 for S polarization.

[0092] The 1:1 coupler 161 for P polarized light divides the supplied interference signal of P polarized light into two equal parts, and outputs the two to the photodetector 162 for P polarized light. The 1:1 coupler 163 for S polarized light divides the supplied interference signal of S polarized light into two equal parts, and outputs the two to the photodetector 164 for S polarized light.

[0093] The P polarized light photodetector 162 is composed of, for example, a balanced detector, and disperses one of the supplied P polarized interference signals (first P polarized input) to obtain the intensity for each frequency band corresponding to the frequency components of the optical comb to obtain the spectrum of the interference signal, i.e., the distribution of the signal intensity. At this time, the spectrum intensity is normalized based on the total energy of the other supplied P polarized interference signal (second P polarized input) to obtain the distribution of the signal intensity, and output it to the sampling device 165.

[0094] The S-polarized light detection device 164 is composed of, for example, a balanced detector, and disperses one of the supplied S-polarized interference signals (first S-polarized input) to obtain the intensity for each frequency band corresponding to the frequency components of the optical comb to obtain the signal intensity distribution of the interference signal. At this time, the spectrum intensity is normalized to obtain the distribution based on the total energy of the other supplied S-polarized interference signal (second S-polarized input), and the distribution is output to the sampling device 165.

[0095] The output of the P polarized light photodetector 162 indicates the normalized signal intensity I(ν) of the interference signal due to P polarized light, and the output of the S polarized light photodetector 164 indicates the normalized signal intensity Q(ν) of the interference signal due to S polarized light.

[0096] The sampling device 165 includes an analog / digital (A / D) converter, a high-speed digitizer, and the like. In synchronization with a synchronization signal from the scan signal generator 112, the sampling device 165 samples the analog interference signals supplied from the P-polarized light detection device 162 and the S-polarized light detection device 164 for each frequency band, and converts them into digital interference data ID(ν) and QD(ν). The sampling device 165 attaches a time stamp to the obtained interference data ID(ν) and QD(ν) and stores them in the storage device 170. The sampling period of the sampling device 165 is, for example, a scan frequency ν s It is set to a natural number multiple of 2 or more, for example, 10 times.

[0097] The storage device 170 of the information processing device 17 sequentially stores the P polarized interference data ID(ν) and the S polarized interference data QD(ν) supplied from the sampling device 165. The storage device 170 also stores optical path length data indicating the optical path length difference L determined by the data analysis device 172, and outputs the data to the data analysis device 172 upon request.

[0098] The data analyzer 172 processes the interference data ID(ν) and QD(ν) stored in the storage device 170 and acquired at the same timing, and detects an interference peak on the frequency ν axis as shown in Fig. 8(A). In addition, the data analyzer 172 processes the interference data ID(ν) and QD(ν) acquired at the same timing, and detects the modulation frequency ν i Identify.

[0099] The data analyzer 172 calculates the envelope B and the peak frequency v p For example, in FIG. 8(A), envelope B 11 ~B 14 and the peak (center) frequency ν 11 ~ν 14 Identify.

[0100] The data analyzer 172 analyzes each of the identified peak frequencies v pThe data analysis device 172 further determines the order of interference m for each envelope B based on the modulation frequency v i The value of is applied to Equation 15 to obtain the optical path length difference L to each reflecting surface with an accuracy of μm. Then, by dividing it by 2, the optical path length L to the reflecting surface is obtained. op Request.

[0101] When multiple interference peaks are detected, the data analyzer 172 executes a process for calculating the optical path length difference L and a process for calculating the intensity distribution of the envelope B for each peak, and stores the obtained data in the storage device 170 with a time stamp indicating the time when the interference signal that is the basis of the calculation was obtained. Therefore, in the example of FIG. 8(A), each peak frequency v 11 ~ν 14 Based on envelope B 11 ~B 14 For each, the interference order m 11 ~m 14 Identify the optical path difference L 11 ~L 14 is calculated with an accuracy of μm, and the optical path length L op11 ~L op14 Request.

[0102] The data analyzer 172 executes processing to obtain the distribution of a series of optical path length differences L stored in the memory device 170, their respective time changes (movements), and their derivatives (velocities). i Since the modulation frequency varies periodically and multiple interference data ID(ν) and QD(ν) are sampled during one period of the modulation frequency, the interference conditions are different at each sampling timing. Therefore, for example, it is possible to detect a reflecting surface that could not be detected or could not be clearly detected at other sampling timings. Or, the reflecting surface may move on the order of μm. In addition, if the reflecting surface has a thickness, it may be possible to detect the reflecting surface at multiple consecutive sampling timings. The data analysis device 172 processes these data on the time axis to obtain a more detailed tomographic structure including the distribution of the reflecting surface of the measurement object 3.

[0103] The data analyzer 172 further calculates the envelope B(ν) of each interference peak based on the interference data ID(ν). i -ν1) signal intensity I(ν i Similarly, based on the interference data QI(ν), the envelopes B(ν i -ν1) signal strength Q(ν i -ν1) is calculated. That is, the envelope B(ν i -ν1) signal intensity I(ν i -ν1) and the envelope B(ν i -ν1) signal strength Q(ν i -ν1).

[0104] The data analysis device 172 calculates the ratio or quotient Q(ν i -ν1) / I(ν i -ν1). In other words, the ratio between the magnitude of the second interference signal and the magnitude of the first interference signal, or the value of the ratio, is calculated. Next, the calculated value is applied to Equation 22 to obtain the phase α (=tan -1 [Q(ν i -ν1) / I(ν i In the example of FIG. 8(A), the phase α 11 =tan -1 [Q(ν i -ν 11 ) / I(ν i -ν 11 )], phase α 12 =tan -1 [Q(ν i -ν 12 ) / I(ν i -ν 12 )], phase α 13 =tan -1 [Q(ν i -ν 13 ) / I(ν i -ν 13 )], phase α 14 =tan -1 [Q(ν i -ν 14 ) / I(ν i -ν 14 )] is calculated.

[0105] The data analysis device 172 further calculates ΔL=αc / 2πν according to equation 19. c By calculating the phase α, the phase shift ΔL in the nm domain is converted. As mentioned above, the shift ΔL is the central wavelength λ of the light that constitutes the optical comb. c This corresponds to the optical path length difference between the reference position, which is determined by the optical path length L' that is an integer (N) times the position of each reflecting surface. In the example of FIG. 8(A), the data analyzer 172 calculates ΔL 11 = α 11 c / 2πν c , ΔL 12 = α 12 c / 2πν c , ΔL 13 = α 13 c / 2πν c , ΔL 14 = α 14 c / 2πν c By finding the phase α 11 , α 12 , α 13 , α 14 nm range shift ΔL 11 , ΔL 12 , ΔL 13 , ΔL 14 Convert to.

[0106] The data analyzer 172 stores the obtained phase α, shift ΔL, etc. in the storage device 170 together with a time stamp indicating the time when the interference signal on which the calculations were based was obtained.

[0107] The data analysis device 172 obtains the time change of the series of shifts ΔL stored in the storage device 170, obtains the waveform of the shifts ΔL using curve approximation or the like, and obtains the period, frequency, and amplitude. If the position of the optical device 15 is fixed, this waveform represents the period and amplitude of the fluctuation in the position of the light reflecting surface of the measurement object 3.

[0108] The monitor device 174 includes a display section and an input section, and displays information input from the data analysis device 172. The monitor device 174 also supplies instructions from a user to the data analysis device 172.

[0109] The information processing device 17 is composed of a computer. The data analysis device 172 is composed of components required for high-speed arithmetic processing, such as a computer's CPU (Central Processing Unit), DSP (Digital Signal Processor), and memory. The storage device 170 is composed of, for example, an auxiliary storage device of the computer.

[0110] Next, a measurement operation by the measurement system 1 having the above configuration will be described. The carrier signal generator 110 generates a carrier signal having a frequency v a A sine wave carrier signal S a In the following description, the frequency v a = 10 GHz. The scan signal generating device 112 generates a frequency v s Cosine wave scan signal S s In the following description, the frequency v s is set to 1MHz.

[0111] The frequency modulation device 114 generates a carrier signal S a The scan signal S s The frequency modulation signal S i Output. In the following description, the modulation index mf=10. Therefore, the frequency modulated signal S i is expressed by Equation 3', and the modulation frequency ν i is expressed by Equation 4'.

[0112] On the other hand, the light source device 120 emits light at a frequency v c , wavelength λ c In the following explanation, the laser beam having a frequency of v c =2×10 14 Hz, λ c ≒ 1.5 μm.

[0113] The optical modulation device 122 shown in FIG. 4 modulates the laser light emitted from the light source device 120 into a frequency modulation signal S iAs shown in FIG. 5(A), the frequency is c The spectrum is discrete with frequencies ν i The frequency modulation signal S i Modulation frequency ν i As shown in Equation 4', the frequency components constituting the optical comb vary periodically with a center frequency v c It repeats continuous back and forth motion around the center.

[0114] The optical comb generated by the optical modulation device 122 shown in FIG. 1 is broadened by the optical amplifier 124 and the highly nonlinear shift fiber 126 shown in FIG. 4. However, the center frequency is ν c , the frequency component interval is ν i Therefore, the frequency components that make up the broadband optical comb are the frequency v i As the temperature changes, the distance between them fluctuates periodically, as shown in Figures 7(a) and 7(b), and the reciprocating motion is continuously repeated.

[0115] The wideband optical comb thus generated is converted by the polarization controller 13 into linearly polarized light including a P-polarized component and an S-polarized component, and is supplied to the circulator 14 .

[0116] The circulator 14 outputs the supplied optical comb to the optical device 15 .

[0117] The optical device 15 emits the optical comb output from the circulator 14 toward the measurement target 3 via the collimator 150 and the interference plate 152. A part of the emitted optical comb is reflected by the reflecting surface of the interference plate 152.

[0118] On the other hand, a part of the light constituting the optical comb passes through the 1 / 8λ wave plate 154 and is irradiated onto the measurement target 3. Of the light passing through the 1 / 8λ wave plate 154, the S-polarized component passes through the slow axis of the 1 / 8λ wave plate 154 and is delayed by 1 / 8λ relative to the P-polarized component.

[0119] Here, it is assumed that the measurement object 3 is a living tissue having the configuration shown in FIG. 13(A). The frequency band of the optical comb is 2×10 14 Because the optical comb is 100 Hz, it is not only reflected by the surface of the measurement object 3, but also penetrates 50 μm to 1 mm into the interior. After penetrating the living body, the optical comb is reflected by reflection surfaces that correspond to the interfaces of layers with different refractive indexes, such as the interface between tissues. In FIG. 13(A), attention is focused on four reflection surfaces 1 to 4 that exist in the living tissue.

[0120] The optical comb reflected by reflecting surfaces 1 to 4 enters circulator 14 via ⅛ λ wave plate 154 , interference plate 152 , and collimator 150 .

[0121] Of the reflected light that passes through 1 / 8λ waveplate 154, the S-polarized component passes through the slow axis of 1 / 8λ waveplate 154 and is further delayed by 1 / 8λ relative to the P-polarized component. As a result, the S-polarized component is delayed by 1 / 4λ=π / 2 relative to the P-polarized component.

[0122] The optical comb reflected by the interference plate 152 and the optical comb reflected by the measurement target 3 interfere with each other. However, P-polarized light interferes with S-polarized light. Therefore, the optical path length difference L from the reflecting surface 1 to the reflecting surface 4 is calculated for each of the P-polarized interference signal and the S-polarized interference signal, as shown in FIG. 13B. 21 ~L 24 Frequency ν according to 21 ~ν 24 The envelope of the interference peak B 21 ~B 24 appears.

[0123] The interference signal generated by the optical device 15 enters the circulator 14 and is transmitted to the polarizing beam splitter 160 of the optical signal processing device 16 .

[0124] The circulator 14 outputs the P polarized interference signal and the S polarized interference signal to the polarizing beam splitter 160 of the optical signal processing device 16. The polarizing beam splitter 160 outputs the P polarized interference signal to a 1:1 coupler 161 for P polarized light and outputs the S polarized interference signal to a 1:1 coupler 163 for S polarized light.

[0125] P polarized light 1:1 coupler 161 divides the supplied P polarized light interference signal into two equal parts, and outputs the two to P polarized light photodetector 162. S polarized light 1:1 coupler 163 divides the supplied S polarized light interference signal into two equal parts, and outputs the two to S polarized light photodetector 164.

[0126] The P polarized light photodetector 162 separates one P polarized interference signal (first P polarized input) and obtains the intensity for each frequency band corresponding to the frequency components of the optical comb to obtain the signal intensity distribution I(ν) of the interference signal. At this time, the total energy of the other P polarized interference signal (second P polarized input) supplied is used as a reference to normalize the spectral intensity to obtain the signal intensity distribution I(ν) and output it to the sampling device 165.

[0127] The S-polarized light detection device 164 separates one of the supplied S-polarized interference signals (first S-polarized input) and obtains the intensity for each frequency band corresponding to the frequency components of the optical comb to obtain the signal intensity distribution Q(ν) of the interference signal. At this time, the total energy of the other supplied S-polarized interference signal (second S-polarized input) is used as a reference to normalize the spectral intensity to obtain the signal intensity distribution Q(ν) and output it to the sampling device 165.

[0128] The sampling device 165 samples the analog interference signals supplied from the P-polarized light detection device 162 and the S-polarized light detection device 164 for each frequency band in synchronization with the synchronization signal from the scan signal generation device 112, and converts them into digital interference data ID(ν) and QD(ν). In the following description, the sampling frequency is the same as the scan signal S s Frequency ν s = 10 MHz, which is 10 times 1 MHz. The sampling device 165 attaches a time stamp to the obtained interference data, and stores the data in the storage device 170.

[0129] The storage device 170 sequentially stores the interference data of P polarized light and the interference data of S polarized light supplied from the sampling device 165 .

[0130] The data analyzer 172 processes the interference data of the P polarized light and the S polarized light stored in the storage device 170, and detects the envelope B of the interference peak and the frequency indicating the peak value. In this example, the envelope B shown in FIG. 21 ~B 24 and its peak P 21 ~P 24 Frequency ν 21 ~ν 24 Detect.

[0131] The data analyzer 172 identifies the timing at which the original interference signal was obtained from the time stamp attached to the interference data to be processed. s This phase determines the modulation frequency v i is calculated according to Equation 4'.

[0132] Next, the data analyzer 172 calculates the envelope B 21 For the modulation frequency ν i and the interference order m 21 Based on envelope B 21 The optical path difference L from the reflecting surface 1 that generated the reflected light 21 =m 21 c / ν i is calculated with an accuracy of μm. For example, at a certain sampling timing, i = 10.01GHz, then L 21 =m 21 c / (10.01 10 9 ) as the optical path length difference. Similarly, the data analysis device 172 calculates the modulation frequency v i and the interference order m 22 ~m 24 Based on envelope B 22 ~B 24 The optical path difference L from the reflecting surface 2 to the reflecting surface 4 that generated the reflected light 22 =m 22 c / ν i ~L 24 , L 23 =m 23 c / νi , m 24 c / ν i If necessary, for example, the optical path difference L 21 ~L 24 By dividing it by 2, the optical path length L op21 ~L op24 may be converted to

[0133] In the above description, the interference peaks are clearly obtained by the reflected light from the reflecting surfaces 1 to 4. However, depending on the position and characteristics of the reflecting surfaces, there are cases where a clear interference peak is not obtained. i Therefore, even for a reflecting surface where a clear interference peak was not obtained at a certain timing, the scan signal S s As the measurement of a half period is repeated, the frequency at which the interference peak occurs may vary, and a peak may be detected, as shown in Fig. 10. This allows a more accurate peak distribution in the depth direction on the order of μm.

[0134] The data analyzer 172 further analyzes the envelopes B in the P-polarized interference data ID and the S-polarized interference data QD. 21 Frequency ν 21 Signal strength I(ν 21 ) and Q(ν 21 ) according to Eq. 22, the phase α 21 =tan -1 [Q(ν 21 ) / I(ν 21 )] is calculated. Furthermore, ΔL 21 = α 21 c / (2πν c ) from the difference in optical path length L, ΔL 21 In other words, the position at a distance of N times the wavelength of the light that constitutes the optical comb is used as the reference position, and the minute deviation ΔL 11 If necessary, calculate the difference in optical path length L 11 By dividing it by 2, the optical path length L op21 The deviation ΔL op may be converted to

[0135] Similarly, the data analyzer 172 calculates the envelope B of the P-polarized interference data and the S-polarized interference data. 22 , B 23 , B 24 Peak P 22 , P 23 , P 24 Frequency ν 22 , v 23 , v 24 The signal strength I(ν 22 ) and Q(ν 22 ), I(ν 23 ) and Q(ν 23 ), I(ν 24 ) and Q(ν 24 ) based on the phase α 22 , α 23 , α 24 Then, the phase α 22 , α 23 , α 24 The difference in optical path length ΔL 22 , ΔL 23 , ΔL 24 If necessary, calculate the difference in optical path length ΔL 22 , ΔL 23 , ΔL 24 By dividing it by 2, the distance ΔL op22 , ΔL op23 , ΔL op24 Convert it into a deviation of .

[0136] The data analyzer 172 calculates the optical path difference L 21 ~L 24 , phase α 21 ~α 24 , deviation ΔL 21 ~ΔL 24 The interference data on which the calculation is based is stored in the storage device 170 with a time stamp indicating the time at which it was obtained. s Data is accumulated every 0.1 μs.

[0137] After the measurement is completed, the data analyzer 172 analyzes the series of optical path length differences L 21 ~L 24 The data analyzer 172 reads out the optical path difference L 21The distribution of the modulation frequency v i changes periodically, and by analyzing the positions of the reflecting surfaces detected during one period of the modulation frequency, the tomographic structure including the distribution of the reflecting surfaces of the measurement object 3 can be obtained in more detail.

[0138] In addition, the data analyzer 172 may, for example, analyze the deviation ΔL stored in the memory device 170 after the measurement is completed. 21 ~ΔL 24 is read out and plotted in time series as shown in Figure 14. Note that Figure 14 shows the difference ΔL 21 and ΔL 22 Only the time series is shown.

[0139] The data analysis device 172 calculates the plotted deviation ΔL 21 ~ΔL 24 The amplitude A of the curve that approximates m21 ~A m24 and period T 21 ~T 24 , frequency 1 / T 21 ~1 / T 24 The amplitude, period, and frequency of the micro vibrations of reflecting surfaces 1 to 4 are calculated as follows: m21 ~A m24 and period T 21 ~T 24 and frequency ν 21 ~ν 24 Shows.

[0140] The data analyzer 172 also calculates the optical path lengths L op21~ L op24 By visualizing the intensity distribution of the intensities I(ν) and Q(ν), it is possible to obtain the imaging of the fault distribution of the internal structure of the measurement object 3, and the displacement and vibration between the faults.

[0141] The monitor device 174 receives information input from the data analyzer 172, such as a tomographic image of the internal structure of the measurement object 3, a displacement ΔL 21 ~ΔL 24 The amplitude of vibration A m21 ~A m24 and period T 21 ~T24 , frequency 1 / T 21 ~1 / T 24 The monitor device 174 also displays the image of the fault distribution generated by the data analysis device 172, the displacement between faults, vibration, and the like.

[0142] Next, details of the data processing executed by data analysis device 172 will be described with reference to the flowcharts of FIGS.

[0143] When one set of interference data ID and QD is stored in the storage device 170, the data analysis device 172 starts the interference data analysis process shown in FIG.

[0144] When the data analyzer 172 starts the process, it first analyzes the newly stored P-polarized interference data ID and S-polarized interference data QD, respectively, and determines whether or not an interference peak exists, and if so, the frequency ν p Then, the modulation frequency ν i For example, in the case of the interference data shown in FIG. 13B, the envelope B of the interference peak is identified. 21 ,B 22 ,B 23 ,B 24 Detect the peak P 21 ,P 22 ,P 23 ,P 24 Frequency ν 21 ,ν 22 ,ν 23 ,ν 24 Also, the modulation frequency ν i Identify.

[0145] The data analyzer 172 detects the modulation frequency v i From the interference order m previously obtained, the optical path difference L corresponding to the round trip optical path length from the reflection surface of the interference plate 152 to the reflection surface of the measurement object 3 is calculated as L=mc / ν i In the example of FIG. 13, the data analyzer 172 calculates the modulation frequency v iand the interference order m 21 The optical path difference L corresponding to the round trip optical path length from the reflecting surface of the interference plate 152 to the reflecting surface 1 of the measurement object 3 is calculated from the 21 =m 21 c / ν i Similarly, the optical path difference L from reflecting surface 2 to reflecting surface 4 is calculated. 22 =m 22 c / ν i ~Optical path length difference L 24 =m 24 c / ν i Request.

[0146] The data analyzer 172 then obtains the intensities I(ν) and Q(ν) of the peaks P of the envelopes B for the P-polarized interference data ID and the S-polarized interference data QD (step S113). In the example of FIG. 13, the data analyzer 172 obtains the intensities I(ν) and Q(ν) of the peaks P of the envelopes B of the interference peaks of the P-polarized and S-polarized light. 21 ~B 24 Peak P 21 ~P 24 The intensity I(ν 21 )~I(ν 24 ) and Q(ν 21 )~Q(ν 24 ) is required.

[0147] Next, the data analyzer 172 calculates the phase α as α=tan -1 (Q / I), and then calculate the phase shift ΔL from the phase α by ΔL=αc / 2πν c In the example of FIG. 13, the data analysis device 172 calculates α 21 =tan -1 (Q(ν 21 ) / I(ν 21 ), ~, α 24 =tan -1 (Q(ν 24 ) / I(ν 24 ) is calculated as shown in FIG. 13(C). 21 ~α 24 From the deviation ΔL 21 = α 21 c / 2πν c , ~, ΔL 24 = α 24c / 2πν c Request.

[0148] The data analyzer 172 adds a time stamp to the obtained optical path length difference L, phase α, and shift ΔL, and records them in the storage device 170 (step S115).

[0149] In this way, one sampling period 1 / (10ν s Each time 100 m 2 passes, the optical path length L is calculated on the order of μm, and further, the deviation ΔL between the reference position and the position of the reflecting surface is calculated on the order of nm and stored in the storage device 170 .

[0150] The data analysis device 172 executes a distribution analysis process shown in FIG. 16 at the end of measurement or the like in order to obtain the distribution of the reflecting surface and specify the three-dimensional cross-sectional structure of the measurement object 3 in more detail.

[0151] When the process starts, the data analysis device 172 analyzes the positions of the reflecting surfaces obtained in a series of measurements, and identifies the distribution of the reflecting surfaces in the depth direction (step S211).

[0152] More specifically, the scan signal S s While the phase of varies, for example, from 0 to π, the modulation frequency ν i is the maximum value (ν a +10ν s ) to the minimum value (ν a -10ν s ), that is, from (10G+10M)Hz to (10G-10M)Hz. For this reason, a reflecting surface that is not detected at one measurement timing may be detected at another measurement timing, or a reflecting surface that is detected at one measurement timing may not be detected at another measurement timing. Furthermore, when the reflecting surface has thickness and distribution, interference peaks are detected consecutively. Therefore, the distribution of the reflecting surface in the depth direction is obtained from the positions of the reflecting surface obtained at multiple consecutive timings.

[0153] Next, the data analysis device 172 images the obtained distribution of the reflection surface in the depth direction, and synthesizes a tomographic image (step S212).

[0154] The data analysis device 172 assigns a time stamp to the obtained tomographic image and stores it in the storage device 170 (step S213).

[0155] In addition, the scan signal S s Period T s Even if the reflection surface obtained over a period of more than half of the phase (a period of more than phase π) is processed, the modulation frequency ν i Therefore, in the process of step S211, the scan signal S s It is desirable to perform the scan in half cycles of T. The tomographic image obtained in this way corresponds to a tomographic image in the depth direction of a specific point where the optical comb is irradiated. s For example, a distance of one dot may be scanned every 1 / 2.

[0156] Furthermore, the data analyzer 172 starts a micro-vibration analysis process shown in FIG. 17 to identify the micro-vibrations of each reflecting surface periodically or at the end of measurement.

[0157] When the data analysis device 172 starts the process, it reads out a series of deviations ΔL stored in the storage device 170 and plots them in time series (step S311). In the example of FIG. 13, the data analysis device 172 reads out the deviations ΔL stored in the storage device 170 and plots them in time series (step S312). 21 A series of data, ΔL 22 A series of data, ΔL 23 A series of data, ΔL 24 The series of data is read out and plotted in time series as shown in Fig. 14. Note that if the series of deviations ΔL can be processed, there is no need to actually plot them.

[0158] The data analysis device 172 obtains a curve that approximates the plotted deviation ΔL (step S312). The data analysis device 172 calculates the amplitude A of the obtained approximation curve. mThe amplitude, period, and frequency are calculated based on the amplitude A of the minute vibration of the reflecting surface of the measurement object 3 (step S313). m , period T and frequency 1 / T. In the example of FIG. 14, the data analysis device 172 calculates the plotted deviation ΔL 21 and ΔL 22 The amplitude A of the approximate curve is calculated. m21 , A m22 and period T 21 , T 22 and frequency 1 / T 21 , 1 / T 22 The amplitude, period, and frequency of the minute vibrations of reflecting surfaces 1 and 2 are calculated as follows: m21 , A m22 and period T 21 , T 22 and frequency 1 / T 21 , 1 / T 22 Shows.

[0159] The data analyzer 172 calculates the amplitude A m The period T and frequency 1 / T are stored in the storage device 170 (step S314), and the process ends.

[0160] As described above, the measurement system 1 according to the present embodiment has a scanning frequency v s At a high speed of 10 MHz, which is 10 times faster than the op In addition, the deviation ΔL of the reflecting surface from the reference position can be measured in the order of nm. Furthermore, if the measurement object 3 is made of a material into which light can penetrate, the internal structure and cross-sectional structure can be measured.

[0161] Although the embodiment of the present invention has been described above, the present invention is not limited to the above embodiment. For example, in the above embodiment, an example was shown in which the S-polarized light constituting the optical comb is delayed by π / 2 from the P-polarized light by the 1 / 8 λ wavelength plate 154 in order to obtain the shift ΔL, but the P-polarized light constituting the optical comb may be configured to be delayed by π / 2 from the S-polarized light by the 1 / 8 λ wavelength plate 154. Any method may be used as long as a phase difference of π / 2 can be applied between the P-polarized light and the S-polarized light to generate an orthogonal signal.

[0162] It is also possible to observe the intensity of each envelope during a scan period without using polarized light, determine the maximum or minimum value (negative maximum value), and determine the phase α by setting the phase α = 0 or 2π at the maximum value and the phase α = π at the minimum value. For example, cos(α) changes between the maximum value (+1) and the minimum value (-1) between the first half π and the second half π of the scan period 2π. Therefore, when the scan period T s The first half of T s / 2 or second half T s / 2, the envelope intensity is observed, and the timing when it reaches a maximum value is regarded as the timing when the phase α is 0 or 2π, and the timing when it reaches a minimum value is regarded as the timing when the phase α is π. This processing may be performed in real time, or may be performed collectively after multiple envelope intensities are obtained.

[0163] In the above description, for ease of understanding, the optical device 15 has a reference optical path length L r = 0, but the reference optical path length L r may be present. In this case, 2(L op -L r ) is the optical path difference.

[0164] In the above description, the carrier signal S a Frequency ν a 10GHz, scan signal S s Frequency ν s is 1MHz, modulation index mf is 10, sampling frequency is 10MH, and wavelength of laser light λ c Although an example in which the wavelength is 1500 nm has been shown, these values ​​can be changed arbitrarily.

[0165] In addition, the RF signal generating device 11 may have any circuit configuration as long as it can generate a frequency modulated signal. i According to the above, the interval between the frequency components constituting the optical comb is set to the modulation frequency ν i Furthermore, as long as an optical comb including multiple frequency components whose intervals vary periodically can be generated, the configuration of the optical comb generator itself is not limited to the RF signal generator 11 and the optical comb generator 12, and may be any configuration.

[0166] In the above embodiment, the frequency modulated signal S i In order to synchronize the sampling timing with the scan signal S s A synchronous signal synchronized with the scan signal S is supplied to the sampling device 165 and the storage device 170. However, the present invention is not limited to this, and any method for synchronizing the circuit operations may be used. Also, a time stamp is added to the sampling data, but the present invention is not limited to this. For example, instead of the time stamp, a scan signal S s A phase value may be added.

[0167] In the above embodiment, the data sampled by the sampling device 165 is stored in the storage device 170, and the data is processed by the data analysis device 172. The data analysis device 172 may process the output data of the sampling device 165 directly.

[0168] In the above embodiment, the data sampled by the sampling device 165 is stored in the storage device 170, and the data is processed by the data analysis device 172. The data analysis device 172 may process the output data of the sampling device 165 directly.

[0169] When the measurement object 3 is a light-transmitting material and there is a large distance between the light reflecting surfaces, a difference occurs in the timing of measuring the optical path length difference L. In this case, the optical path length difference L can be measured accurately by correcting the timing according to the time required for light propagation. For example, if the distance between the first reflecting surface and the second reflecting surface of the measurement object 3 is L, p Assume that the first reflecting surface is located on the optical comb input side. In this case, it takes 2·L p Therefore, the data analyzer 172 obtains a sampled value from the first reflecting surface at a timing t and a sampled value from the second reflecting surface at a timing t+2·L p The sampling values ​​at the timings of / c and / c are processed as signals generated by the same optical comb. By using such time correction, the tomographic structure in the measurement object 3 can be accurately measured.

[0170] In addition, the optical path difference L and the optical path length (distance) L op are mutually convertible and are substantially equivalent. In addition, the phase α and the optical path length difference deviation ΔL and the optical path length deviation ΔL op are mutually convertible and substantially equivalent. Therefore, either one may be used as the final solution. EXAMPLES

[0171] An embodiment of the measurement system 1 will now be described. Example 1 Fig. 18 is a diagram illustrating an experimental system 30 for an operation experiment of the measurement system 1 shown in Fig. 1. As shown in Fig. 18, the experimental system 30 is fixed to the floor of a building or the like by a fixing device 34. The measurement object 3 is attached to a piezoelectric element and vibration is applied thereto.

[0172] A plane mirror that totally reflects and returns light was used as the measurement object 3. The measurement system 1 and the measurement object 3 were aligned so that the optical comb was emitted from the measurement system 1 at a right angle to the plane of the measurement object 3, and the reflected light was returned to the optical device 15 of the measurement system 1. In addition, a 1 / 8 λ wave plate was placed in the path of the optical comb so that the phase of the S-polarized light was delayed by π / 2 in the round trip with respect to the P-polarized light. Note that in the experimental system 30, the optical path length Lop was approximately 620 mm, and corresponded to approximately 33rd order interference.

[0173] Carrier signal S of measurement system 1 a Frequency ν a 10GHz, scan signal S s Frequency ν s is 1MHz, the modulation index mf is 10, and the wavelength λ of the infrared laser is c was set to 1500 μm. The sampling frequency of the sampling device 165 was set to 10 MHz.

[0174] An AC voltage with a frequency of 30 kHz was applied to the piezoelectric element, causing the reflector to vibrate at 30 kHz.

[0175] 19(A) and (B) show signal waveform diagrams of the I interference signal and the Q interference signal obtained by the experiment. The horizontal axis is time, and the waveforms are shown for 0.4 ms. The vertical axis of Figure 19(C) represents the phase α calculated from the ratio of the signal strength of the interference peaks of the I interference signal and the Q interference signal, and the horizontal axis represents time, with two 0.2 ms waveforms, which correspond to one vibration period of the piezoelectric element, being superimposed.

[0176] As shown in Figure 19(C), it was confirmed that the phase α [rad] changes in a sine wave shape in response to the vibration of the reflector by the piezoelectric element, and that the phase α obtained in the first and second round trips of the reflector are almost the same, demonstrating excellent reproducibility.

[0177] Example 2 A glass plate with a thickness of 120 μm was fixed as a measurement object to the fixing device 34 of the experimental system 30 shown in Fig. 18. The glass plate was vibrated by placing a speaker that could emit a pure tone with a frequency of 10 kHz close to the glass plate without using a piezoelectric element.

[0178] 20(A) and (B) show signal waveform diagrams of the obtained I and Q signals. The horizontal axis is time, and the waveforms are shown from 0 to 4.5 ms. FIG. 20(C) shows the waveforms of one period of the I and Q signals, with the horizontal axis being time, and the waveforms are shown at 1.632×10-4 ~1.644×10 -4 The signal waveform for a period of 100 s is shown enlarged.

[0179] FIG. 21(A) shows the intensity of the interference signal, with the horizontal axis representing time, and is the same as FIG. 20(C), 1.632×10 -4 ~1.644×10 -4 The signal waveform for 100 s is shown in Fig. 1. As shown in the figure, four interference peaks were observed, and two reflections were confirmed on the front and back of the glass.

[0180] Furthermore, FIG. 21(B) shows the phase α obtained from the I and Q signals of FIG. 20(C). It was confirmed that the phases of the front and back surfaces of the glass plate fluctuated with the same tendency in response to the vibration of the glass plate, and the phase could be measured correctly at high speed.

[0181] According to the optical comb interferometry realized by the measurement system 1 described above, the optical path length L op With the measurement system 1, the structure and the movement of the object 3 can be measured simultaneously. -n ~ν n The frequency ν of the interval i is a frequency-modulated periodic variation frequency, and an optical comb with a FWHM (full width at half maximum) of 50 μs can be generated. Furthermore, since measurement system 1 does not require FFT processing and the calculation required for analysis processing in data analyzer 172 is light, vibrations of object 3 to be measured in a 100 kHz band can be measured in real time.

[0182] Although the embodiment of the present invention has been described, this embodiment is presented as an example and is not intended to limit the scope of the invention. This novel embodiment can be embodied in various other forms, and various omissions, substitutions, and modifications can be made without departing from the gist of the invention. This embodiment and its modifications are included in the scope and gist of the invention, and are included in the scope of the invention and its equivalents described in the claims. [Explanation of symbols]

[0183] 1 Measurement system, 3 Measurement object, 11 RF signal generator, 12 Optical comb generator, 13 Polarization controller, 14 Circulator, 15 Optical device, 16 Optical signal processing device, 17 Information processing device, 30 Experimental system, 34 Fixed device, 110 Carrier signal generator, 112 Scan signal generator, 114 Frequency modulation device 120 Light source device, 122 Optical modulation device, 124 Optical amplifier, 126 Highly nonlinear shift fiber, 150 Collimator, 152 Interference plate, 154 1 / 8 λ wave plate, 160 Polarizing beam splitter, 161 1:1 coupler for P polarization, 162 Photodetector for P polarization, 163 1:1 coupler for S polarization, 164 Photodetector for S polarization, 165 Sampling device, 170 Storage device, 172 Data analysis device, 174 Monitor device

Claims

1. An optical comb generator that generates an optical comb including a plurality of frequency components arranged on both sides of a center frequency and whose intervals vary by moving so as to converge on the center frequency and by moving so as to move away from the center frequency; an optical device that outputs the optical comb generated by the optical comb generating unit to a measurement object and a reference plane, causes the optical comb reflected by the reflection plane of the measurement object to interfere with the optical comb reflected by the reference plane, and generates an interference signal; a detector for determining the intensity of the envelope of an interference peak contained in the interference signal; a position detection device that determines a distance from a reference position to a reflecting surface of a measurement object based on the intensity detected by the detection device; A measurement system comprising:

2. the detection device comprises: a separation means for separating an interference signal into a first interference signal and a second interference signal having a phase shift of π / 2 from the first interference signal; and a means for determining an intensity of the first interference signal and an intensity of the second interference signal; the position detection device determines a distance from a reference position to the reflecting surface based on a ratio between an intensity of the first interference signal and an intensity of the second interference signal; The measurement system of claim 1 .

3. The detection device includes: a means for converting the optical frequency comb into linearly polarized light including a P-polarized component and an S-polarized component; a means for providing a phase difference of π / 2 between one of the P-polarized component and the S-polarized component of the optical frequency comb; and a means for determining the intensity of an interference signal due to the P-polarized component and the intensity of an interference signal due to the S-polarized component; The position detection device divides the intensity of the interference signal due to the polarized component with a delayed phase by the intensity of the interference signal due to the polarized component with a leading phase out of the P polarized component and the S polarized component, and calculates tangent of the quotient. －１ The phase is calculated by calculating the phase of the light constituting the optical comb from the reference position to the reflecting surface based on the calculated phase.

3. A measuring system according to claim 1 or 2.

4. the position detection device monitors changes in intensity of an envelope of an interference peak contained in the interference signal, determines a maximum or minimum of the monitored intensities, and determines the position of the reflecting surface based on the maximum or minimum intensity; The measurement system of claim 1 .

5. The position detection device detects a position of a reflective surface a plurality of times while the plurality of frequency components move to converge on the center frequency or move away from the center frequency, The position detection device includes a means for determining an amplitude and a frequency of vibration of the reflecting surface from a time series of the determined position of the reflecting surface. A measuring system according to any one of claims 1 to 4.

6. an optical path length difference detector that determines an optical path length difference to a reflecting surface based on an interval frequency of frequency components of an optical comb and an order of interference for an interference peak included in an interference signal; The measurement system according to claim 1 , further comprising:

7. the optical path length difference detection device includes a means for determining a distribution of positions of a reflecting surface from optical path length differences obtained at different measurement timings; The measurement system of claim 6.

8. the optical path length difference detection device determines an optical path length difference on the order of μm, and the position detection device determines a distance from a reference position to a reflecting surface on the order of nm.

8. A measuring system according to claim 6 or 7.

9. An optical comb generator that generates an optical comb including a plurality of frequency components arranged on both sides of a center frequency and whose intervals vary by moving so as to converge on the center frequency and by moving so as to move away from the center frequency; an optical device that outputs the optical comb generated by the optical comb generating unit to a measurement object and a reference plane, causes the optical comb reflected by the reflection plane of the measurement object to interfere with the optical comb reflected by the reference plane, and generates an interference signal; an optical path length difference detector that determines an optical path length difference to a reflecting surface based on an interval frequency and an interference order of frequency components of an optical comb for an interference peak included in an interference signal; A means for determining a distribution of positions of a reflecting surface based on the optical path length differences obtained at different times; A measurement system comprising:

10. The optical comb generating unit generates an optical comb in which the interval frequency ν between the center frequencies of two adjacent frequency components is expressed as ν = ν + ν cos (2πν); νa: first frequency νm: maximum frequency deviation νs: second frequency t: time A measurement system according to any one of claims 1 to 9.

11. The optical comb generator includes: A light source device that emits laser light; a device for generating a third signal at a third frequency by frequency modulating a first signal at a first frequency with a second signal at a second frequency; an optical modulation device that modulates the laser light from the light source device with a third signal to generate an optical comb including a plurality of frequency components spaced at intervals of the third frequency on both sides of a center frequency; Equipped with the first signal and the second signal are both sinusoidal signals; the first frequency is higher than the second frequency; A measurement system according to any one of claims 1 to 10.

12. An optical comb is generated having a plurality of frequency components arranged on either side of a center frequency, the frequency components being spaced apart by an operation of moving the frequency components so as to converge on the center frequency and an operation of moving the frequency components so as to move away from the center frequency; The generated optical comb is irradiated onto a measurement object, and an interference signal is generated by causing the optical comb reflected by a reflection surface of the measurement object to interfere with a reference light; determining a distance from a reference position to a reflecting surface based on the intensity of an envelope of an interference peak contained in the interference signal; Measurement method.

13. An optical comb including a plurality of frequency components arranged on both sides of a center frequency and having intervals that vary by moving so as to converge on the center frequency and by moving so as to move away from the center frequency is emitted to a measurement object and a reference plane, the optical comb reflected by the reflection plane of the measurement object and the optical comb reflected by the reference plane are made to interfere with each other to generate an interference signal, For the interference peaks included in the interference signal, a difference in optical path length to a reflecting surface of the measurement object is obtained based on the interval frequency of the frequency components of the optical comb and the interference order; A distribution of positions of a reflecting surface of the measurement object is obtained based on the optical path length differences acquired at different times. Measurement method.

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