JP2022035565A - Displacement measuring device and displacement measuring method - Google Patents

Abstract

To provide a displacement measuring device, etc., with which it is possible to expand a measurement range while maintaining measurement accuracy.SOLUTION: A displacement measurement device comprises: a light generator for generating an intensity-modulated laser beam; an intensity modulator for intensity modulating the return light of the laser beam emitted from the light generator and having been reflected by a measurement object; a first signal generator for outputting a modulation signal to the light generator and the intensity modulator; a phase modulator for phase modulating the modulation signal outputted from the first signal generator to the intensity modulator with a frequency fm; a second signal generator for outputting a modulation signal to the phase modulator; a photodetector for receiving return light having been intensity modulated by the intensity modulator; and a control unit for controlling the first and second signal generators and calculating the distance to the measurement object on the basis of a detection signal from the photodetector. The control unit calculates the distance on the basis of the respective amplitudes of a frequency fm component and a frequency 2 fm component of the detection signal, and corrects the distance in accordance with a combination of signs of respective phases of the frequency fm component and the frequency 2 fm component.SELECTED DRAWING: Figure 1

Description

The present invention relates to a displacement measuring device and a displacement measuring method.

Conventionally, intensity-modulated laser light is emitted toward a measurement target, and the return light reflected by the measurement target is intensity-modulated with a modulation signal having the same modulation frequency as the laser light (and phase-modulated) to intensify the intensity. A method of measuring a distance (displacement) of a measurement target based on a modulated return light detection signal is known (for example, Patent Document 1).

Japanese Unexamined Patent Publication No. 2018-59789

In the above method, there is a trade-off relationship between the measurement range and the measurement accuracy, and there is a problem that the measurement error increases when the measurement range is expanded.

The present invention has been made in view of the above problems, and an object of the present invention is to provide a displacement measuring device or the like capable of expanding a measuring range while maintaining measurement accuracy.

The present invention includes a light generator that generates intensity-modulated laser light, an intensity modulator that modulates the intensity of the return light reflected by the laser beam from the light generator, and the light generator and the intensity. The first signal generator that outputs the modulated signal to the modulator, the phase modulator that phase-modulates the modulated signal output from the first signal generator to the intensity modulator at a frequency _fm , and the phase modulator. A second signal generator that outputs a modulated signal, an optical detector that receives return light that has been intensity-modulated by the intensity modulator, and the light that controls the first signal generator and the second signal generator. The control unit includes a control unit that calculates the distance to the measurement target based on the detection signal from the detector, and the control unit calculates the distance based on the amplitudes of the frequency _fm component and the frequency _2fm component of the detection signal. The present invention relates to a displacement measuring device that corrects the distance according to the combination of the phase codes of the frequency _fm component and the frequency _2fm component.

Further, the present invention has a light generation step in which an intensity-modulated laser beam is generated by a light generation unit, and an intensity modulation in which the return light reflected by the laser light from the light generation unit is intensity-modulated by an intensity modulator. The phase of the step, the first signal generation step of outputting the modulation signal to the light generator and the intensity modulator by the first signal generator, and the modulation signal output from the first signal generator to the intensity modulator. A phase modulation step in which phase modulation is performed at a frequency _fm by a modulator, a second signal generation step in which a modulation signal is output to the phase modulator by a second signal generator, and a return light intensity-modulated by the intensity modulator. A light detection step that receives light from the light detector, and a control step that controls the first signal generator and the second signal generator and calculates the distance to the measurement target based on the detection signal from the light detector. In the control step, the distance is calculated based on the amplitudes of the frequency _fm component and the frequency _2fm component of the detection signal, and the combination of the phase codes of the frequency _fm component and the frequency _2fm component is used. The present invention relates to a displacement measuring method for correcting the distance according to the above.

According to the present invention, the measurement range can be expanded while maintaining the measurement accuracy by correcting the measurement distance according to the combination of the phase codes of the frequency _fm component and the frequency _2fm component of the detection signal.

It is a figure which shows an example of the structure of the displacement measuring apparatus which concerns on this embodiment. It is a figure for demonstrating a zone number. A flowchart showing the processing flow of the control unit. The figure which shows the phase and the measured displacement obtained in the experiment which measured the displacement by the method of this embodiment. The figure which shows the measured displacement after correction obtained in the experiment which measured the displacement by the method of this embodiment.

Hereinafter, this embodiment will be described. The embodiments described below do not unreasonably limit the content of the present invention described in the claims. Moreover, not all of the configurations described in the present embodiment are essential constituent requirements of the present invention.

FIG. 1 is a diagram showing an example of the configuration of the displacement measuring device according to the present embodiment. The displacement measuring device 1 includes a laser light source 10 and an intensity modulator 11 that function as a light generator, an intensity modulator 20, a signal generator 30 (first signal generator), a phase modulator 40, and a signal generator. It includes 50 (second signal generator), an optical detector 60, a lock-in amplifier 70, and a control unit 80 having an arithmetic processing unit (processor) and a storage unit.

The intensity modulator 11 intensity-modulates the laser light from the laser light source 10 at the modulation frequency f ₀ to generate the intensity-modulated laser light (probe light) at the modulation frequency f ₀ . Here, the wavelength of the laser light source 10 (single mode laser) is set to 1550 nm. In the example shown in FIG. 1, a case where the light generation unit is composed of a laser light source and an intensity modulator will be described, but a direct modulation method (based on a modulation signal) in which a modulation signal is output to the laser light source 10 to modulate the intensity of the laser light. A method of directly modulating the output intensity of the laser light source by intensifying the drive current) may be adopted.

The probe light emitted from the light generation unit (laser light source 10, intensity modulator 11) becomes parallel light in the lens 12, passes through the polarization beam splitter 13, and becomes circularly polarized in the λ / 4 wave plate 14, and becomes a measurement target. It reaches the reflection point R (mirror such as a corner cube mirror). The return light reflected at the reflection point R (reflected light from the reflection point R) is linearly polarized by the λ / 4 wave plate 14, reflected by the polarizing beam splitter 13, passes through the lens 15, and is incident on the intensity modulator 20. do. Instead of the polarizing beam splitter 13 and the λ / 4 wave plate 14, a half mirror, an optical circulator, or the like may be used.

The signal generator 30 outputs a modulation signal having a modulation frequency f ₀ to the intensity modulator 11 and the intensity modulator 20 based on the control signal from the control unit 80.

The phase modulator 40 phase-modulates the modulated signal output from the signal generator 30 to the intensity modulator 20 at a modulation frequency _fm . The modulation frequency f _m is lower than the modulation frequency f ₀ . Here, the modulation frequency f ₀ is set to 910 MHz, and the modulation frequency f _m is set to 100 kHz.

The intensity modulator 20 intensifies the return light reflected at the reflection point R by the modulated signal having a modulation frequency (basic frequency) _{f 0} from the signal generator 30 and phase-modulated at the modulation frequency fm. Modulate.

The signal generator 50 outputs a modulation signal having a modulation frequency _fm to the phase modulator 40 and outputs a reference signal having a frequency _fm to the lock-in amplifier 70 based on the control signal from the control unit 80.

The photodetector 60 (photodiode) receives the return light intensity-modulated by the intensity modulator 20. The high cutoff frequency _{f c} of the photodetector 60 is higher than the frequency 3 fm (a frequency three times the modulation frequency fm) and lower than the modulation frequency _{f 0} .

The lock-in amplifier 70 detects (synchronous detection) the amplitude and phase of each of the frequency fm component and the frequency _2fm component (frequency component twice the frequency _{fm )} of the detection signal from the optical detector 60. The output signal of the lock-in amplifier 70 is converted into digital data by an AD converter (not shown) and output to the control unit 80.

The control unit 80 controls the signal generators 30 and 50, and calculates the distance to the reflection point R based on the output signal of the lock-in amplifier 70. More specifically, the control unit 80 calculates the distance to the reflection point R based on the ratio of the amplitudes of the frequency _fm component and the frequency _2fm component detected by the lock-in amplifier 70, and uses the frequency _fm component. The distance is corrected according to the combination of the sign (positive or negative) of the phase of each of the frequency _2fm components.

Here, the intensity _Ip of the probe light emitted from the light generating unit (intensity modulator 11) is expressed by the following equation (1).

ここで、Ｉ_ｉｎはレーザー光源１０から出射したレーザー光の強度であり、ｍ_１は強度変調器１１の変調度であり、ｔは時間であり、θは初期位相である。プローブ光が強度変調器１１から出射してから強度変調器２０に至るまでの光路長（反射点Ｒまでの往復距離に屈折率を乗じた値）をΔＬ~（ΔＬ~＞０）とすると、強度変調器２０の入射端でのプローブ光の強度Ｉ_ｐ’は、以下の式（２）で表される。

Here, I _in is the intensity of the laser light emitted from the laser light source 10, m ₁ is the degree of modulation of the intensity modulator 11, t is the time, and θ is the initial phase. Let ΔL ~ (ΔL ~> 0) be the optical path length (value obtained by multiplying the round-trip distance to the reflection point R by the refractive index) from the time when the probe light is emitted from the intensity modulator 11 to the intensity modulator 20. The intensity I _p'of the probe light at the incident end of the intensity modulator 20 is expressed by the following equation (2).

ここで、ｃは光速である。強度変調器２０を出射したプローブ光の強度Ｉ_Ｓは、以下の式（３）で表される。

Here, c is the speed of light. The intensity _IS of the probe light emitted from the intensity modulator 20 is represented by the following equation (3).

ここで、ｍ_２は強度変調器２０の変調度であり、Φ_ｍは位相変調器４０の変調度である。高域カットオフ周波数ｆ_ｃの光検出器６０からの出力電流ｉは、以下の式（４）で表される。

Here, m ₂ is the degree of modulation of the intensity modulator 20, and Φ _m is the degree of modulation of the phase modulator 40. The output current _i from the photodetector 60 having a high cutoff frequency fc is expressed by the following equation (4).

ここで、Ｊは第一種ベッセル関数である。ロックインアンプ７０からの出力信号（Ｓ_１、Ｓ_２、Ｓ_３）は、以下の式（５）～（７）で表される。

Here, J is a first-class Bessel function. The output signals (S ₁ , S ₂ , S ₃ ) from the lock-in amplifier 70 are represented by the following equations (5) to (7).

ここで、Ｓ_１はロックインアンプ７０で検出された周波数ｆ_ｍ成分の振幅であり、Ｓ_２は周波数２ｆ_ｍ成分の振幅であり、Ｓ_３は周波数３ｆ_ｍ成分の振幅である。位相変調に用いる変調信号の位相θを調節して、Ｓ_１が０になるようにする。ここで、ΔＬ~をあらためて、基準点から反射点Ｒまでの光路長（反射点Ｒまでの距離に屈折率を乗じた値）として再定義すると、Ｓ_１、Ｓ_２、Ｓ_３は、以下の式（８）～式（１０）で表される。

Here, S ₁ is the amplitude of the frequency _fm component detected by the lock-in amplifier 70, S ₂ is the amplitude of the frequency 2 _fm component, and S ₃ is the amplitude of the frequency 3 _fm component. Adjust the phase θ of the modulation signal used for phase modulation so that S ₁ becomes 0. Here, if ΔL ~ is redefined as the optical path length from the reference point to the reflection point R (the value obtained by multiplying the distance to the reflection point R by the refractive index), S ₁ , S ₂ , and S ₃ are as follows. It is represented by the formulas (8) to (10).

変調度Φ_ｍは、以下の式（１１）から求められる。Ｒ_１は周波数ｆ_ｍ成分の振幅Ｓ_１と周波数３ｆ_ｍ成分の振幅Ｓ_３の比である。この計算は測定前に一回だけ行えばよい。

The modulation degree Φ _m is obtained from the following equation (11). R ₁ is the ratio of the amplitude S ₁ of the frequency _fm component to the amplitude S ₃ of the frequency 3 _fm component. This calculation only needs to be done once before the measurement.

周波数ｆ_ｍ成分の振幅Ｓ_１と周波数２ｆ_ｍ成分の振幅Ｓ_２の比をＲ_２とすると、Ｒ_２は、以下の式（１２）で表され、基準点から反射点Ｒまでの光路長ΔＬ~は、以下の式（１３）で表される。

Assuming that the _ratio of the amplitude S1 of the frequency _fm component and the amplitude S2 of the frequency _2fm component is _R2 , _R2 is expressed by the following equation ( ₁₂ ), and the optical path length ΔL from the reference point to the reflection point R. ~ Is expressed by the following equation (13).

すなわち、周波数ｆ_ｍ成分の振幅Ｓ_１と周波数２ｆ_ｍ成分の振幅Ｓ_２の比Ｒ_２に基づいて反射点Ｒまでの距離を算出することができる。但し、以下の式（１４）の条件を満たすときのみ、式（１３）が正しい距離を与える。すなわち、測定レンジはｃ／８ｆ_０で与えられる。プローブ光の変調周波数ｆ_０を低くすることで測定レンジは拡大するが、測定誤差も拡大する。

That is, the distance to the reflection point R can be calculated based _on the _{ratio R2} of the amplitude S1 of the frequency _fm component and the amplitude S2 of the frequency _2fm component. However, the equation (13) gives the correct distance only when the condition of the following equation (14) is satisfied. That is, the measurement range is given at c / 8f ₀ . By lowering the modulation frequency f ₀ of the probe light, the measurement range is expanded, but the measurement error is also expanded.

本実施形態の手法では、周波数ｆ_ｍ成分の振幅Ｓ_１の式がｓｉｎ波であり周波数２ｆ_ｍ成分の振幅Ｓ_２の式がｃｏｓ波であることに着目して、周波数ｆ_ｍ成分の位相符号と周波数２ｆ_ｍ成分の位相符号の組み合わせを用いて測定レンジを拡大する（式（１３）により算出した距離を補正する）。

In the method of the present embodiment, focusing on the fact that the equation of the amplitude S1 of the frequency _fm component is a sine wave and the equation of the _amplitude S2 of the frequency _2fm component is _a cos wave, the phase code of the frequency _fm component is The measurement range is expanded by using the combination of the phase code of the frequency _2fm component and the frequency code (correcting the distance calculated by the equation (13)).

When the reference point is determined and the phase in the initial state is determined, the relationship between the combination of the phase code of the frequency _fm component and the phase code of the frequency _2fm component and the distance is determined. As shown in FIG. 2, the distance range every c / 8f ₀ corresponds to the zone number N. Since the change of the phase sign has periodicity, the distance is not uniquely determined from the combination of the phase codes, but by sequentially tracking the combination of the phase codes and the change, the distance displacement exceeding ΔL ~ can be found.

A reference point is set, and then the distance obtained from the _amplitudes S1 and S2 by Eq. ( ₁₃ ) is set to ΔL'. However, it is assumed that the zone number is "1" at first. Further, the zone number obtained from the sequential measurement of the phase code is N, and the width of each zone is L ₀ (L ₀ = c / 8f ₀ ). At this time, the distance ΔL (N, T) from the reference point to the reflection point R at the zone number N and the time T is given by the following equation (15) when N> 0, and the following equation when N <0. Given in (16).

ここで、Ｆｏｏｒ［ｘ］は、実数ｘに対してｘを超えない最大の整数を与える関数である。

Here, Floor [x] is a function that gives the maximum integer that does not exceed x for the real number x.

FIG. 3 is a flowchart showing a flow of processing for measuring the distance ΔL (N, T) by obtaining the zone number N one by one. The processes of steps S10 to S13 are processes in the preparatory stage before measurement, and the processes after step S14 are processes during measurement.

First, the control unit 80 acquires the amplitude S ₁ and the phase θ ₁ of the frequency _fm component detected by the lock-in amplifier 70, and the amplitude S ₂ and the phase θ ₂ of the frequency 2 _fm component (step S10). Next, the signal generator 50 is controlled to adjust the initial phase θ of the phase modulator 40 so that the amplitude S1 of the frequency _fm component becomes ₀ (step S11). The initial phase θ at this time is set to θ ₀ , and further adjustment is made so that the initial phase θ has a positive value θ ₊ = θ ₀ + δ θ (δ θ> 0) (step S12). When the initial phase θ = θ ₊ , it is equivalent to the reflection point R being virtually moved away. Set θ ₊ in the range where the distance ΔL (N, T) calculated at this time is smaller than c / 8f ₀ (zone number N = 1 does not exceed), and this is used as the initial value. If the initial value is started from 0, it becomes impossible to distinguish whether the reflection point R is approaching or far away, but by moving the initial value to the positive value θ ₊ , is the reflection point R approaching? You can tell if you are far away. The initial value may be moved to a negative value θ ₋ = θ ₀ − δθ.

Next, when the initial value is a positive value θ ₊ = θ ₀ + δθ, “1” is set in the zone number N. When the initial value is a negative value θ ₋ = θ ₀ − δθ, “-1” is set in the zone number N. Further, " ₀ " is set at the time T, and the distance ΔL (1,0) calculated by the equations ( ₁₂ ), (13), and (15) based on the amplitudes S1 and S2 acquired after the adjustment is set. It is recorded as the initial value ΔL _ini of the distance (step S13). Further, in step S13, the combination (sgn (θ ₁ ), sgn (θ ₂ )) of the sign sgn (θ ₁ ) of the phase θ ₁ and the sign sgn (θ ₂ ) of the phase θ ₂ acquired after the adjustment is recorded. deep. sgn (x) is a function that gives a sign (positive or negative) of a real number x. The combination of the symbols changes every time ΔL ~ changes by c / 8f ₀ . When ΔL ~ continues to increase monotonically from 0, the sign combination is (sgn (θ ₁ ), sgn (θ ₂ )) → (sgn (θ ₁ ), −sgn (θ ₂ )) → (−sgn (θ)). ₁ ), -sgn (θ ₂ )) → (-sgn (θ ₁ ), sgn (θ ₂ )) → Repeatedly, and so on (changes alternately from the sign of phase θ ₂ ). When ΔL ~ continues to decrease monotonically from 0, the sign combination is (sgn (θ ₁ ), sgn (θ ₂ )) → (-sgn (θ ₁ ), sgn (θ ₂ )) → (-sgn (θ)). ₁ ), -sgn (θ ₂ )) → (sgn (θ ₁ ), -sgn (θ ₂ )) → Repeatedly, and so on (changes alternately from the sign of phase θ ₁ ). Therefore, by recording the combination of the phase codes in the initial state and tracking the change of the combination of the phase codes after that, whether the zone number has increased (the reflection point R has moved away) or the zone number has decreased (the zone number has decreased). Whether the reflection point R is approaching) can be determined.

Next, the control unit 80 determines whether or not the time ΔT has elapsed (the time T has increased by the time ΔT) (step S14). Here, it is assumed that the reflection point R moves only a distance sufficiently smaller than c / 8f ₀ during the time ΔT. When the time ΔT has elapsed (Y in step S14), the amplitudes S ₁ and S ₂ and the phases θ ₁ and θ ₂ detected by the lock-in amplifier 70 are acquired, and the phase codes sgn (θ ₁ ) and sgn ( θ ₂ ) is calculated (step S15). The combination of phase codes is recorded as a history in association with the time T. Next, it is determined whether or not the combination of phase codes (sgn (θ ₁ ), sgn (θ ₂ )) has changed from the previous combination (step S16). If the combination of phase codes has not changed (N in step S16), the zone number N is not updated and the process proceeds to step S21. When the combination of phase codes changes (Y in step S16), it is determined whether or not _one of the _amplitudes S1 and S2 is "0" (step S17). _When any _one of the amplitudes S1 and S2 is "0" (Y in step S17), the _amplitudes S1, S2, the _phase θ1, θ2, and the zone _{number N} before the time ΔT elapses. Is maintained, and the process proceeds to step S14. _When neither of the amplitudes S1 and S2 is " ₀ " (N in step S17), it is determined from the change (history) of the combination of phase codes whether the zone number N has increased or decreased (step S18). .. When the zone number N increases (Y in step S18), the zone number N is increased by 1 (step S19), and when the zone number N decreases (N in step S18), the zone number N is increased by 1. (Step S20).

Next, the distance ΔL (N, T) is calculated by the equations (12), (13), (15), and (16) based on the amplitudes S1 and S2 and the zone _{number N} (step S21). Next, the value obtained by subtracting ΔL _ini from the calculated distance ΔL (N, T) is output as the measurement result of the distance at time T (step S22), the process proceeds to step S14, and the processing after step S14 is measured. Repeat until you finish.

In the example shown in FIG. 1, an experiment was conducted in which the displacement of the reflection point R was measured under the conditions that the modulation frequency f ₀ was 910 MHz and the measurement range (c / 8f ₀ ) was about 40 mm. In FIG. 4, when the stage (fine movement table) to which the reflection point R (mirror) is attached is moved by 80 mm by 2 _mm , the phase θ ₁ of the frequency fm component, the phase θ ₂ of the frequency 2 _fm component, and the displacement (before correction). The measured value of the distance ΔL ~) is shown. Here, the measured displacement is biased by 20 mm. From FIG. 4, it can be confirmed that the combination of the signs of the phases θ ₁ and θ ₂ changes before and after the measurement range. In the example of FIG. 4, when the measured displacement exceeds about 40 mm, the combination of the signs of the phases θ ₁ and θ ₂ changes from “negative, positive” to “negative, negative”, and when the measured displacement is further displaced by about 40 mm, it becomes “positive, negative”. Has changed to. FIG. 5 shows the measured displacement (distance ΔL (N, T)) corrected based on the change in the combination of phase codes. From FIG. 5, it can be confirmed that the displacement can be measured beyond the measurement range of c / 8f ₀ by the method of the present embodiment.

As described above, according to the method of the present embodiment, the amplitude S ₁ and the phase θ ₁ of the frequency _fm component of the output signal of the optical detector 60 and the amplitude S ₂ and the phase θ ₂ of the frequency 2 _fm component are detected. The distance ΔL ~ is calculated based on the ratio of the detected amplitudes S ₁ and S ₂ , and the zone number N is updated according to the change in the combination of the codes of the detected phases θ ₁ and θ ₂ , and based on this zone number N. By correcting the distance ΔL ~ (calculating the distance ΔL (N, T)), the measurement range can be expanded while maintaining the measurement accuracy. Further, in the method of the present embodiment, since it is sufficient that the sign of the phase can be measured, the measurement accuracy for the phase value is not required, and there is an advantage that an expensive device is not required as a device for detecting the phase.

The present invention is not limited to the above-described embodiment, and various modifications can be made. The present invention includes substantially the same configurations as those described in the embodiments (eg, configurations with the same function, method and result, or configurations with the same purpose and effect). The present invention also includes a configuration in which a non-essential part of the configuration described in the embodiment is replaced. Further, the present invention includes a configuration having the same action and effect as the configuration described in the embodiment or a configuration capable of achieving the same object. Further, the present invention includes a configuration in which a known technique is added to the configuration described in the embodiment.

1 ... displacement measuring device, 10 ... laser light source, 11 ... intensity modulator, 12 ... lens, 13 ... polarized beam splitter, 14 ... λ / 4 wave plate, 15 ... lens, 20 ... intensity modulator, 30 ... signal generator , 40 ... phase modulator, 50 ... signal generator, 60 ... optical detector, 70 ... lock-in amplifier, 80 ... control unit, R ... reflection point

Claims (2)

A light generator that generates intensity-modulated laser light,
An intensity modulator that modulates the intensity of the return light reflected by the laser beam from the light generating unit on the measurement target.
A first signal generator that outputs a modulated signal to the light generator and the intensity modulator,
A phase modulator that phase-modulates a modulated signal output from the first signal generator to the intensity modulator at a frequency _fm , and
A second signal generator that outputs a modulated signal to the phase modulator,
A photodetector that receives the intensity-modulated return light with the intensity modulator,
It includes a control unit that controls the first signal generator and the second signal generator and calculates the distance to the measurement target based on the detection signal from the photodetector.
The control unit
The distance is calculated based on the amplitudes of the frequency _fm component and the frequency _2fm component of the detection signal, and the distance is corrected according to the combination of the phase codes of the frequency _fm component and the frequency _2fm component. , Displacement measuring device. A light generation step in which an intensity-modulated laser beam is generated by a light generator,
An intensity modulation step in which the return light reflected by the laser beam from the light generating unit is intensity-modulated by an intensity modulator, and
A first signal generation step of outputting a modulated signal to the light generator and the intensity modulator by the first signal generator, and
A phase modulation step in which a modulation signal output from the first signal generator to the intensity modulator is phase-modulated by a phase modulator at a frequency _fm , and
A second signal generation step of outputting a modulated signal to the phase modulator by the second signal generator, and
A photodetection step in which the photodetector receives the return light intensity-modulated by the intensity modulator,
A control step of controlling the first signal generator and the second signal generator and calculating the distance to the measurement target based on the detection signal from the photodetector is included.
In the control step,
The distance is calculated based on the amplitudes of the frequency _fm component and the frequency _2fm component of the detection signal, and the distance is corrected according to the combination of the phase codes of the frequency _fm component and the frequency _2fm component. , Displacement measurement method.

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