JP2019184565A - Displacement measuring method and displacement measuring device - Google Patents

Abstract

To provide a displacement measuring method and a displacement measuring device with which it is possible to suppress a measurement error and accurately measure the displacement of a measurement surface when measuring the displacement of a measurement surface utilizing a phase variation obtained from a 6-port circuit.SOLUTION: With a displacement measuring device 1, since a 6-port circuit 11 is used and a phase delay amount at each frequency in the 6-port circuit 11 is predefined, even when measuring a displacement D using a transmit signal whose frequency is changed in relation to time, it is possible to suppress a measurement error in the 6-port circuit 11 and accurately measure the displacement D of a measurement surface 10. Furthermore, with the displacement measuring device 1, as 2π uncertainty is removable, it is possible to suppress a measurement error and accurately measure the displacement D of the measurement surface 10 to that extent.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a displacement measuring method and a displacement measuring apparatus for measuring the displacement of a measurement surface using a microwave.

  Microwaves have a feature that they are excellent in permeability of particles such as dust and mist, and are used for distance measurement in an iron making process that is a high-temperature dust environment. As distance measurement methods using microwaves, methods using FMCW and pulses are known, but in these methods, distance resolution is limited by the frequency bandwidth.

  For example, when the frequency bandwidth is 1 GHz, the distance resolution is 150 mm. In order to realize a high distance resolution of mm or less, it is necessary to use a very wide frequency bandwidth. However, when microwaves having a wide frequency bandwidth are used, problems such as interference with devices using other radio waves may occur, which is difficult to realize.

  Therefore, as shown in Patent Document 1, a method of obtaining the displacement of an object from a phase change amount generated between a reference signal and a received signal from the object is considered. Patent Document 1 proposes measuring a phase change amount using a 6-port circuit (see Non-Patent Document 1) having two input ports and four output ports.

JP 2007-316066 A

IEEE microwave magazine 11 (7), 35-43, 2010 "The Six-Port in Modern Society"

  However, in the method shown in Patent Document 1, the frequency of the oscillator is fixed to a single value, and the measured phase change amount is limited to the range of 0 to 2π. For this reason, a displacement exceeding the wavelength causes indefiniteness that cannot be distinguished from a displacement that gives the same amount of phase change, and there is a problem that measurement cannot be performed correctly.

  Further, in order to remove the 2π indefiniteness of the phase, there is a method of using a frequency sweep in which the frequency of the transmission signal is changed with respect to time. However, the phase delay amount given by the 6-port circuit differs depending on the frequency. Therefore, there is a problem that a measurement error occurs.

  The present invention has been made in view of the above problems, and in measuring the displacement of the measurement surface using the phase change amount obtained from the 6-port circuit, the measurement error is suppressed and the measurement error is suppressed. An object of the present invention is to provide a displacement measuring method and a displacement measuring apparatus capable of accurately measuring a displacement.

  The displacement measuring method of the present invention is a displacement measuring method for measuring the displacement of a measurement surface using a microwave as a transmission signal, wherein the transmission signal whose frequency is changed with respect to time is transmitted to the measurement surface, and the measurement is performed. A transmission / reception step of receiving a reflected microwave from a surface as a reception signal, and inputting the transmission signal as a reference signal to a 6-port circuit, and receiving the reception signal obtained when measuring the displacement of the measurement surface An actual measurement value input step to be input; power values of four signals output from the 6-port circuit by the actual measurement value input step; and a phase delay amount θ in the 6-port circuit at each frequency of the transmission signal; Based on the phase calculation step of calculating the phase change amount Δφ at each frequency, and the coarse displacement D ′ of the measurement surface is calculated based on the inclination of the phase change amount Δφ with respect to the frequency. Using a displacement calculating step, a phase indeterminacy eliminating step for calculating an integer n that eliminates an indefiniteness of 2π, which is a phase characteristic, using the rough displacement D ′ and the phase change Δφ, the integer n is defined. And a displacement calculating step of calculating the displacement D of the measurement surface using the phase change amount Δφ according to a predetermined arithmetic expression in which the indefiniteness of 2π is eliminated.

  The displacement measuring device of the present invention is a displacement measuring device that measures the displacement of a measurement surface using a microwave as a transmission signal, and transmits the transmission signal whose frequency is changed with respect to time to the measurement surface. A transmitting / receiving unit that receives a reflected microwave from the surface as a received signal; a 6-port circuit in which the transmitted signal is input as a reference signal; and the received signal is input; and four power values output from the 6-port circuit And a phase calculation unit that calculates a phase change amount Δφ at each frequency based on the phase delay amount θ in the 6-port circuit at each frequency of the transmission signal, and the phase change amount Δφ Using the coarse displacement calculation unit for calculating the coarse displacement D ′ of the measurement surface based on the inclination with respect to the frequency, the coarse displacement D ′ and the phase change amount Δφ, the indefiniteness of 2π which is a phase characteristic is obtained. Integer to resolve Displacement calculation for calculating the displacement D of the measurement surface using the phase change amount Δφ by a phase indeterminacy eliminating unit for calculating the phase n and a predetermined arithmetic expression in which the integer n is defined and the indefiniteness of 2π is eliminated A section.

  According to the present invention, a 6-port circuit is used, and even if the displacement D is measured using a transmission signal whose frequency is changed with respect to time, the phase delay amount θ in the 6-port circuit at each frequency is specified in advance. Therefore, it is possible to accurately measure the displacement D of the measurement surface while suppressing measurement errors in the 6-port circuit. In addition, according to the present invention, the indefiniteness of 2π of the phase can be removed, so that a displacement exceeding the wavelength can be accurately measured.

It is the schematic which shows the structure of the displacement measuring apparatus of this invention. It is a block diagram which shows the circuit structure of a computer. It is a flowchart which shows a phase delay amount calculation process. 6 is a graph showing a relationship between a frequency f and a phase change amount Δφ. It is a graph which shows the result of having performed the phase unwrapping process with respect to the frequency and phase variation | change_quantity data shown in FIG. It is a flowchart which shows a displacement calculation process. It is the graph which compared the displacement actually given and the displacement D computed by the displacement measuring apparatus of this invention. It is a graph for demonstrating phase variation amount (DELTA) (phi) containing a nonlinear component. It is a block diagram which shows the circuit structure of the computer in 2nd Embodiment. It is a block diagram which shows the circuit structure of a phase calculating part. 11A is a graph showing the relationship between the frequency f and the amplitude A, FIG. 11B is a graph showing the relationship between the frequency f and the pre-processing phase change Δφ ″, and FIG. 11C shows the amplitude A and the processing. It is the graph which showed the complex signal produced | generated based on front phase variation | change_quantity (DELTA) phi ''. 12A is a graph showing the complex signal of FIG. 11C, FIG. 12B is a graph showing the window function used in the first filter processing, and FIG. 12C shows the complex signal obtained by the first filter processing. It is a graph. 13A is a graph showing the complex signal of FIG. 12C, and FIG. 13B is a graph showing a time-domain waveform obtained by performing inverse Fourier transform on the complex signal of FIG. 13A. 14A is a graph showing the time domain waveform of FIG. 13C, FIG. 14B is a graph showing the window function used in the second filter processing, and FIG. 14C shows the time domain waveform cut out by the window function of FIG. 14B. It is the shown graph. 15A is a graph showing the time domain waveform of FIG. 14C, and FIG. 15B is a graph showing the frequency domain waveform obtained by Fourier transforming the time domain waveform of FIG. 15A. 16A is a graph showing the frequency domain waveform of FIG. 15B, FIG. 16B is a graph showing a window function for reverting the time domain waveform of FIG. 16A, and FIG. 16C is rebated by the window function of FIG. 16B. It is the graph which showed the unnecessary wave suppression signal. 17A is a graph showing the unwanted wave suppression signal of FIG. 16C, FIG. 17B is a graph showing the amplitude A ′ calculated from the unwanted wave suppression signal of FIG. 17A, and FIG. 17C is the unwanted wave suppression signal of FIG. 5 is a graph showing the phase change amount Δφ ″ calculated from It is a flowchart which shows the displacement calculation process in 2nd Embodiment. It is a graph which shows phase change amount (DELTA) phi '' before processing obtained by the verification test. It is the graph which showed the time domain waveform before suppressing an unnecessary wave component. It is the graph which showed the time domain waveform which cut out the desired signal from the time domain waveform of FIG. 20 using the Hanning window. FIG. 22 is a graph showing a phase change amount Δφ calculated from a complex signal obtained by Fourier transforming the time domain waveform of FIG. 21. FIG. 23 is a graph showing the measurement result of the displacement D of the measurement surface calculated based on the phase change amount Δφ in FIG. 22. FIG. 24A is a graph showing the measurement result of the displacement D when the sweep frequency bandwidth is 250 [MHz], and FIG. 24B shows the measurement result of the displacement D when the sweep frequency bandwidth is 500 [MHz]. FIG. 24C is a graph showing a measurement result of the displacement D when the sweep frequency bandwidth is 1 [GHz], and FIG. 24D is a graph when the sweep frequency bandwidth is 2 [GHz]. FIG. 24E is a graph showing the measurement result of the displacement D when the sweep frequency bandwidth is 4 [GHz], and FIG. 24F is a graph showing the measurement result of the displacement D. FIG. It is the graph which showed the measurement result of displacement D at the time of [GHz].

(1) First Embodiment (1-1) Configuration of Displacement Measuring Device of the Present Invention First, an outline of the displacement measuring device of the present invention will be described. FIG. 1 is a schematic view showing the configuration of a displacement measuring apparatus 1 of the present invention. The displacement measuring apparatus 1 of the present invention measures the displacement D of the measurement surface 10 by changing the position of the measurement surface 10 of the measurement object with respect to the transmission / reception antenna 4 as a transmission / reception unit.

  In the case of this embodiment, the measurement surface 10 moves along the x direction, which is a direction approaching and away from the transmission / reception antenna 4. In the case of this embodiment, the displacement D of the measurement surface 10 is the amount of movement from the reference position O located at a predetermined distance from the transmitting / receiving antenna 4 in the x direction. The displacement measuring apparatus 1 according to the present invention can measure such a displacement D of the measurement surface 10.

  The displacement measuring device 1 sends the transmission signal sent from the oscillator 2 to the transmission / reception antenna 4 via the circulator 3 and irradiates the microwave from the transmission / reception antenna 4 toward the measurement surface 10. The width of the frequency modulation of the microwave applied to the measurement surface 10 and the sweep period of the microwave are set in advance to predetermined values. The frequency of the microwave irradiated from the transmission / reception antenna 4 toward the measurement surface 10 changes with time.

  When the displacement measurement apparatus 1 receives the reflected microwave from the measurement surface 10 by the transmission / reception antenna 4, the displacement measurement apparatus 1 inputs the received signal to the 6-port circuit 11 via the circulator 3. Further, the displacement measuring apparatus 1 inputs the transmission signal of the oscillator 2 to the 6-port circuit 11 as a reference signal.

  The 6-port circuit 11 is a circuit provided with two input ports P1, P2 and four output ports P3, P4, P5, P6. Since the 6-port circuit 11 is a well-known circuit as described in Patent Document 1 and Non-Patent Document 1, detailed description thereof is omitted here.

  The power measuring machine 12 receives signals output from the output ports P3, P4, P5, and P6 of the 6-port circuit 11, measures the power values B3, B4, B5, and B6 for each signal, and converts them to AD. Output to the converter 13. The AD converter 13 performs analog-digital conversion processing on the power values B3, B4, B5, and B6, and outputs the power values B3, B4, B5, and B6 converted into digital signals to the computer 14.

  The computer 14 performs phase delay amount calculation processing and displacement calculation processing using the power values B3, B4, B5, and B6 of the signal obtained from the 6-port circuit, and details thereof will be described later. The display device 16 displays various calculation results of the computer 14 and the displacement D that is a measurement result, and presents various information to the operator. The storage device 15 stores various calculation results of the computer 14.

(1-2) Measurement principle of displacement in the present invention As described above, the present invention can measure the displacement D of the measurement surface 10 in the displacement measuring apparatus 1 including the 6-port circuit 11. The measurement principle of the displacement D will be described below.

  Microwave electromagnetic waves have a feature of high dust permeability because they have longer wavelengths than visible light and infrared light, and are effective means for measurement in adverse environments. On the other hand, since the wavelength is long, for example, when using FMCW, the resolution of distance measurement is low, and if the frequency bandwidth is F [Hz] and the speed of light is c [m / s], the distance resolution is c Limited to / 2F. Therefore, for example, if the frequency bandwidth is 1 [GHz], the resolution is 150 [mm].

  Therefore, in the displacement measuring apparatus 1 of the present invention, as a method for increasing the resolution of the displacement measurement, the phase change amount Δφ obtained from the reference signal and the received signal, not the FMCW that measures the displacement by measuring the frequency value. Is used, and a minute displacement below the wavelength can be obtained with high resolution. However, if the distance to the measurement surface 10 changes by more than one half of the wavelength, the phase characteristic cannot be distinguished between the phase change amount Δφ and the phase change amount (Δφ + 2πn) (n is an integer). That is, an indefiniteness of 2π occurs.

  Therefore, in this embodiment, as one method of removing the indefiniteness of 2π, the frequency of the transmission signal is swept to obtain the coarse displacement D ′ from the slope of the phase change amount Δφ with respect to the frequency, and this coarse displacement D ′ is obtained. It was decided to remove the indefiniteness of 2π by using. The method is described below.

  As shown in FIG. 1, when the reference surface O is set in front of the transmission / reception antenna 4 and the measurement surface 10 is placed, the reflected microwave from the measurement surface 10 returns to the transmission / reception antenna 4 again. When the distance between the tip of the transmitting / receiving antenna 4 and the measurement surface 10 is moved from the reference position O, the phase of the reflected microwave changes with respect to the reference position O. At this time, if the displacement is D [μm], the phase change amount Δφ [rad] can be expressed by the following equation (3).

  Here, f is the frequency [Hz] of the transmission signal (microwave), λ is the wavelength [m] of the transmission signal, and c is the speed of light [m / s]. Therefore, the displacement D can be expressed by the following formula (4).

  However, since the phase change amount Δφ is accompanied by the above-described indefiniteness of 2π, the actual displacement D is expressed by the following equation (5).

  However, n is an arbitrary integer. Therefore, when measuring the displacement D in which the phase change amount Δφ exceeds 2π, it is necessary to uniquely determine the integer n.

  Next, in the above equation (5), both sides are multiplied by f indicating frequency, and then both sides are differentiated by f. At this time, since only the phase change amount Δφ depends on the frequency f, the following equation (6) is obtained.

  Therefore, by sweeping the frequency f and obtaining the slope dΔφ / df of the phase change amount Δφ with respect to the frequency f, a displacement having no indefinite 2π (hereinafter referred to as a coarse displacement D ′) is obtained from the equation (6). ).

  A specific method for obtaining the slope dΔφ / df of the phase change amount Δφ with respect to the frequency f by sweeping the frequency f will be described later with reference to FIGS.

  In addition to this, in this embodiment, in order to obtain the displacement D with higher accuracy, the displacement measurement is performed by combining the equations (5) and (6). That is, after obtaining the coarse displacement D ′ from the equation (6) using the slope dΔφ / df of the phase change amount Δφ when sweeping the frequency f, the coarse displacement D ′, the frequency f, The integer n is determined from the equation (5) using the phase change amount Δφ.

  Furthermore, the phase change amount Δφ itself at the center frequency (the center frequency f of the sweep frequency width, for example, 40 [GHz] if the frequency range to be swept is 38 to 42 [GHz]) is measured, If the integer n is substituted into the determined equation (5), the displacement D below the wavelength can be obtained. In this way, the removal of 2π indefiniteness and the measurement of the phase change amount Δφ can both be achieved, and the displacement D can be measured with a dynamic range that is greater than or equal to the wavelength and high resolution that is less than or equal to the wavelength. .

<About the phase delay of the 6-port circuit>
In the present embodiment, the 6-port circuit 11 is used for calculating the phase change amount Δφ described above. By using the 6-port circuit 11, the phase change amount Δφ can be obtained simply and at high speed only by power measurement and calculation of an arctangent function (atan, arctangent).

Here, first, consider the case of a single frequency. In this case, in the 6-port circuit 11, a reference signal is input to the input port P1, and a reception signal is input to the input port P2. From the output ports P3, P4, P5, and P6, a phase delay amount as shown in Table 1 below is given to the reference signal input to the input port P1 and the received signal input to the input port P2. A signal obtained by adding the received signals is output.

  As shown in Non-Patent Document 1, the 6-port circuit 11 includes a Wilkinson divider and a 90-degree hybrid coupler, and these configurations give a phase delay amount. Measure power values B3, B4, B5, and B6 of signals output from output ports P3, P4, P5, and P6, and obtain a phase change amount Δφ at a single frequency based on the following equation (7). Can do.

  Δφ = atan ((B3-B4) / (B5-B6)) (7)

  In this way, the phase change amount Δφ can be obtained by using only passive elements that are not amplified or rectified and only by simple calculation of the arctangent function. However, a new problem arises in combining the configuration for sweeping the frequency as described above.

  That is, since the phase delay amount by the 90-degree hybrid coupler is given using the physical length of the circuit, the phase given every time it passes through the 90-degree hybrid coupler except for a single operating frequency. The delay amount is a value different from π / 2. Therefore, when a frequency sweep is performed at a frequency other than the predetermined operating frequency, the phase delay amount at this time is not π / 2 even if the phase change amount Δφ is calculated by the above equation (7). The frequency dependence of the desired phase change Δφ cannot be obtained correctly.

Therefore, it is desirable to obtain the phase delay amount θ given by the 90-degree hybrid coupler for each frequency f when performing the frequency sweep. Here, the signals output from the output ports P3, P4, P5, and P6 are added to the input ports P1 and P2 that are given signals having a phase delay amount θ as shown in Table 2 below. Signal.

  Therefore, in order to obtain the phase change amount Δφ from the power values B3, B4, B5, B6 of the signals output from the output ports P3, P4, P5, P6, it is necessary to calculate the following equation (8). is there.

  In the above equation (8), the phase delay amount θ at each frequency f is an unknown number. Therefore, it is necessary to obtain the phase delay amount θ at each frequency f by prior calibration.

<Outline of calibration of phase delay amount in 6-port circuit>
As described above, since it is necessary to obtain the phase delay amount θ at each frequency f by prior calibration, an outline thereof will be described below. In this case, a signal having a known phase change amount (hereinafter referred to as a known phase change amount) Δφ ′ at a certain frequency f is converted into input ports P1 and P2 of the 6-port circuit 11 for each frequency f. To enter.

  Then, the power values B3, B4, B5, and B6 of the signals output from the output ports P3, P4, P5, and P6 of the 6-port circuit 11 are measured, and Δφ in the above equation (8) is determined as the known phase change amount Δ By setting φ ′, the phase delay amount θ at each frequency f can be calculated.

  However, as is clear from the above equation (8), when obtaining the phase delay amount θ, it is necessary to take the tangent (tan, tangent) of both sides of the equation (8). Taking the tangent of both sides of Equation (8), the following Equation (9) is obtained.

  Further, when the above equation (9) is modified, the following equation (10) is obtained.

  Therefore, as is apparent from the above equation (9), the known phase change amount Δφ ′ given to Δφ at the time of calibration is such that tan Δφ ′ diverges when ± φ ′ = π / 2, 3π / 2 (± ∞), it is necessary to satisfy Δφ ′ ≠ π / 2 and Δφ ′ ≠ 3π / 2. In order to obtain a trivial solution for the phase delay amount θ, it is necessary to satisfy Δφ ′ ≠ 0 and Δφ ′ ≠ π so that tanΔφ ′ ≠ 0 does not occur.

0, [pi / 2, [pi, except 3 [pi] / 2, for example, any two known phase change amount obtained at the same frequency _{f 1 △ φ 1 ', △} φ 2' give. Then, the power values B3 ₁ , B4 ₁ , B5 ₁ , B6 ₁ obtained when the known phase change amount Δφ ₁ ′ is obtained at the predetermined frequency f ₁ are substituted into B3 to B6 of the above equation (10) and known. A first equation is obtained by substituting the phase change amount Δφ ₁ ′ into Δφ in the above equation (10).

Similarly, substituting the same predetermined frequency _{f 1} with a known amount of phase change △ phi ₂ 'power value obtained when the _{B3 2, B4 2, B5 2} , B6 2 to B3~B6 of formula (10) At the same time, the second equation is obtained by substituting the known phase change amount Δφ ₂ ′ into Δφ in the above equation (10).

Then, the phase delay amount θ can be calculated by solving simultaneous equations from the two formulas of the first formula and the second formula obtained from the formula (10) at the same predetermined frequency f ₁ . In this way, the phase delay amount θ is calculated for each frequency f.

In order to calculate the phase delay amount θ, when obtaining the first and second equations for solving the simultaneous equations, for example, the displacement of the measurement surface 10 is changed to D ₁ and D ₂ at the same frequency f ₁ , If the displacements D ₁ and D ₂ of the actually measured values are used, the known phase change amounts Δφ ₁ ′ and Δφ ₂ ′ can be calculated from the above equation (3).

<Outline of displacement measurement using phase delay of 6-port circuit obtained by calibration>
When actually measuring the displacement D of the measurement surface 10, the phase delay amount θ at each frequency f obtained in advance by the calibration as described above is used. Thus, the unknown phase change amount Δφ can be obtained from the above equation (8). Then, the frequency dependency of the unknown phase change amount Δφ (the dependency of the phase change amount Δφ on the frequency f when the frequency f is swept) is obtained, and the above formulas (5) and (6) are used. The displacement D of the measurement surface 10 can be obtained by performing the calculated processing.

<Known and unknown variables at the time of calibration and known and unknown variables at the time of displacement measurement>
Here, with respect to Δφ, B3 to B6, θ in the above formulas (8) to (10), (i) at the time of calibration for obtaining the phase delay amount θ at each frequency f in the 6-port circuit 11, and (ii) Table 3 summarizes which is known or unknown when measuring displacement D after calibration.

  As shown in Table 3, during calibration, Δφ is known because Δφ is given a known phase change amount Δφ ′. At the time of calibration, B3 to B6 are the power values of signals output from the output ports P3, P4, P5, and P6 when the reference signal and the received signal having the known phase change amount Δφ ′ are input to the 6-port circuit 11. Therefore, it becomes a measured amount. At the time of calibration, the phase delay amount θ at each frequency f in the 6-port circuit 11 is unknown.

  On the other hand, at the time of displacement measurement, the phase delay amount θ at each frequency f in the 6-port circuit 11 is known because it is obtained in advance by calibration. At the time of displacement measurement, B3 to B6 are measured values because they are the power values of signals output from the output ports P3, P4, P5, and P6 when the reference signal and the reception signal are input to the 6-port circuit 11. . Further, the phase change amount Δφ is unknown when measuring the displacement.

(1-3) About Computer of Displacement Measuring Device in Present Invention Although the outline of the principle of measuring displacement in the present invention has been described above, next, paying attention to the circuit configuration of the computer 14 in the displacement measuring device 1 of the present invention. The phase delay amount calculation process at the time of calibration and the displacement measurement process at the time of displacement measurement will be described in order.

  As shown in FIG. 2, the calculator 14 includes an input unit 21, a phase delay amount calculation unit 22, a phase calculation unit 23, a phase unwrapping processing unit 24, an inclination calculation unit 25, a coarse displacement calculation unit 26, and a phase ambiguity elimination unit. 27 and a displacement calculator 28. The computer 14 executes a phase delay amount calculation process and a displacement measurement process using these circuits.

<Phase delay amount calculation process during calibration>
Prior to calibration, the phase delay amount θ at each frequency f in the 6-port circuit 11 is unknown. Therefore, prior to the displacement measurement, the computer 14 first needs to calculate the phase delay amount θ at each frequency f when the frequency f is swept by executing the phase delay amount calculation process.

In this case, the phase delay amount calculation unit 22 uses, for example, any two known phase change amounts Δφ ₁ ′ and Δφ ₂ ′ obtained at the same frequency f ₁ other than π / 2, π, and 3π / 2. , Obtained from the storage device 15. Then, the phase delay amount calculation unit 22 inputs the power values B3 ₁ , B4 ₁ , B5 ₁ , B6 ₁ of the signals output from the 6-port circuit 11 at the frequency f ₁ and the known phase change amount Δφ ₁ ′. Acquired from the unit 21 or the storage device 15.

In addition, the phase delay amount calculation unit 22 calculates the power values B3 ₂ , B4 ₂ , B5 ₂ , B6 ₂ of the signals output from the 6-port circuit 11 at the same frequency f ₁ and the known phase change amount Δφ ₂ ′. Obtained from the input unit 21 or the storage device 15.

The phase delay amount calculation unit 22 calculates the known phase change amount Δφ ₁ ′ at the predetermined frequency f ₁ and the power values B3 ₁ , B4 ₁ , B5 ₁ , B6 ₁ at that time from the above equation (10). The first equation assigned to Δφ and B3 to B6, respectively, is calculated. Similarly, the phase delay amount calculation unit 22 calculates the known phase change amount Δφ ₂ ′ at the predetermined frequency f ₁ and the power values B3 ₂ , B4 ₂ , B5 ₂ , and B6 _{2 at} that time using the above formula. The second equation substituted for Δφ of (10) and B3 to B6 is calculated. The phase delay amount calculation unit 22 solves the simultaneous equations for the first and second equations, and calculates the phase delay amount θ at the frequency f ₁ .

  In this manner, the phase delay amount calculation unit 22 solves the simultaneous equations from the two equations for each frequency f at the time of the frequency sweep, and calculates the phase delay amount θ at each frequency f. The phase delay amount calculation unit 22 outputs the phase delay amount θ at each frequency f calculated in this way to the storage device 15 for storage.

Next, a time-series flow of the above-described phase delay amount calculation processing will be briefly described below using the flowchart of FIG. As shown in FIG. 3, in step S <b> ₁ , the calculator 14 determines the known phase change amount Δφ ₁ ′ at the predetermined frequency f ₁ and the power values B3 ₁ and B4 of the signal output from the 6-port circuit 11 at that time. ₁ , B5 ₁ , and B6 ₁ (known phase change amount acquisition step, calibration power value acquisition step), calculate the first equation obtained by substituting them into the above equation (10), and go to the next step S2 Move.

In step S2, the computer 14 calculates another known phase change amount Δφ ₂ ′ at the same frequency f ₁ as in step S1 and the power values B3 ₂ , B4 ₂ , B4 _{2 of} the signal output from the 6-port circuit 11 at that time. B5 ₂ and B62 ₂ are acquired (known phase change amount acquisition step, calibration power value acquisition step), the second equation obtained by substituting them into the above equation (10) is calculated, and the process proceeds to the next step S3.

In step S3, the computer 14 solves the simultaneous equations for the first equation obtained in step S1 and the second equation obtained in step S2, and calculates the phase delay amount θ at the predetermined frequency f ₁ (phase (Delay amount calculation step), the process proceeds to the next step S4.

  In step S <b> 4, the calculator 14 determines whether or not the phase delay amount θ has been calculated for all frequencies (for example, frequencies obtained at predetermined intervals in the frequency sweep width) f used for the frequency sweep. If a negative result is obtained in step S4, this indicates that the phase delay amount θ has not been calculated for all the frequencies f used for the frequency sweep. At this time, the calculator 14 affirms in step S4. Steps S1 to S4 described above are repeated until a result is obtained.

  On the other hand, if an affirmative result is obtained in step S4, this indicates that the phase delay amount θ has been calculated for all the frequencies f used for the frequency sweep. The delay amount calculation process ends.

<Displacement measurement process during displacement measurement>
When the above-described calibration is completed, the displacement measuring apparatus 1 is in a state where the displacement D of the measurement surface 10 can be measured. At the time of displacement measurement, the displacement measuring apparatus 1 transmits a microwave whose frequency f is changed with respect to time as a transmission signal to the measurement surface 10 and receives a reflected microwave from the measurement surface 10 as a reception signal. The displacement measuring apparatus 1 inputs a transmission signal as a reference signal to the input port P1 of the 6-port circuit 11 and inputs a reception signal obtained from the measurement surface 10 to the input port P2 of the 6-port circuit 11.

  2 acquires the power values B3, B4, B5, and B6 of the signal output from the 6-port circuit 11 for each frequency f, and outputs these to the phase calculation unit 23. . At this time, the phase calculator 23 reads out the phase delay amount θ at each frequency f in the frequency sweep obtained from the calibration from the storage device 15.

  The phase calculation unit 23 uses the power values B3, B4, B5, and B6 of the signal output from the 6-port circuit 11 and the phase delay amount θ based on the above equation (8) for each frequency f. A phase change amount Δφ is calculated.

  Here, the phase change amount Δφ calculated for each frequency f will be described with reference to FIG. FIG. 4 is a graph showing a calculation result when the phase change amount Δφ is calculated for each frequency f by the verification test. In FIG. 4, an aluminum flat plate was used as a measurement object, and microwaves were irradiated toward the aluminum flat plate while sweeping the frequency in the range of 38 to 42 [GHz].

  Further, the phase delay amount θ of the 6-port circuit 11 when the frequency sweep was performed in the range of 38 to 42 [GHz] was obtained in advance by calibration according to the above-described procedure. In FIG. 4, the displacement D from the reference position O is set to 1000 [μm], the power values B3, B4, B5, B6 of the four signals output from the 6-port circuit 11 at that time, and the phase delay obtained in advance. The result of obtaining the phase change amount Δφ for each frequency f from the above equation (8) using the amount θ is shown.

  As shown in FIG. 4, the phase calculation unit 23 calculates the phase change amount Δφ at each frequency f, and uses this as the frequency / phase change amount data as the phase unwrapping processing unit 24 and the storage device 15 (FIG. 1). Output to. The phase unwrapping processing unit 24 performs phase unwrapping processing on the frequency / phase change amount data, and connects the discontinuous points of the phase change amount Δφ along the frequency f as shown in FIG. Then, phase unwrapping data continuously representing the phase change amount Δφ is generated.

  In FIG. 5, among the sawtooth signals shown in FIG. 4, positively increasing signals are connected to generate phase unwrapping data continuously representing the phase change amount Δφ.

  The phase unwrapping processing unit 24 outputs the obtained phase unwrapping data to the inclination calculating unit 25. The slope calculation unit 25 calculates an approximate line from phase unwrapping data that continuously represents the phase change amount Δφ along the frequency f, and calculates the slope dΔφ / df of the approximate line. When the slope calculating unit 25 calculates the slope dΔφ / df of the phase change amount Δφ with respect to the frequency f, the slope calculating unit 25 outputs this to the coarse displacement calculating unit 26.

  The coarse displacement calculator 26 calculates the coarse displacement D ′ from the above equation (6) using the slope dΔφ / df of the phase change amount Δφ when the frequency is swept, and the obtained calculation result is the phase. The result is output to the indeterminacy eliminating unit 27. The phase ambiguity eliminating unit 27 reads out the frequency / phase change amount data from the storage device 15 and obtains the phase change amount Δφ at the center frequency of the frequency range to be swept, for example, and then the absolute value of the phase change amount Δφ. Is calculated. Then, the phase indeterminacy canceling unit 27 uses the center frequency, the absolute value of the phase change amount Δφ, and the coarse displacement D ′ to remove the indefiniteness of 2π from the above equation (5). Is calculated.

  The phase ambiguity elimination unit 27 outputs the calculated integer n information to the displacement calculation unit 28 and the storage device 15. The displacement calculating unit 28 uses the integer n received from the phase indeterminacy eliminating unit 27 to define the integer n in the above equation (5) and remove the indefiniteness of 2π. Further, the displacement calculating unit 28 obtains the phase change amount Δφ at the center frequency of the frequency range to be swept from the frequency / phase change amount data received from the phase calculating unit 23, and then the absolute value of the phase change amount Δφ. Is calculated.

  The displacement calculator 28 uses this absolute value as the phase change amount Δφ in the above equation (5) with the 2π indeterminacy removed, and calculates the displacement D based on the equation (5). As a result, the displacement measuring device 1 can remove the 2π indefiniteness of the phase change Δφ and measure the displacement D, so that the dynamic range during displacement measurement can be expanded and the displacement D can be measured with a high resolution below the wavelength. It becomes possible to do.

  Next, the time-series flow of the displacement measurement process described above will be briefly described below using the flowchart of FIG. In step S11, the computer 14 transmits a microwave whose frequency f is changed with respect to time to the measurement surface 10 as a transmission signal, and receives a reflected microwave from the measurement surface 10 as a reception signal. The power values B3, B4, B5, and B6 of the signal output from the circuit 11 are acquired.

  Next, in step S11, the computer 14 uses the power values B3, B4, B5, and B6 of the signal output from the 6-port circuit 11 at the predetermined frequency f and the phase delay amount θ at the frequency f. From the above equation (8), the phase change amount Δφ at the frequency f is obtained, and the process proceeds to step S12.

  In step S12, the calculator 14 determines whether or not the phase change amount Δφ has been calculated for each frequency f in the frequency range to be swept. Here, if a negative result is obtained, it indicates that the phase change amount Δφ is not calculated at each frequency f. At this time, the computer 14 returns to step S11 and the phase change amount at another frequency f. Δφ is calculated.

  On the other hand, if a positive result is obtained in step S12, this indicates that the phase change amount Δφ has been calculated for all the frequencies f, and at this time, the computer 14 proceeds to step S13. In step S13, the computer 14 performs a phase unwrapping process on the frequency / phase change amount data indicating the relationship between the frequency and the phase change amount Δφ as shown in FIG. 4, and as shown in FIG. Then, phase unwrapping data in which the phase change amount Δφ is continuously connected along the frequency is generated, and the process proceeds to the next step S14.

  In step S14, the computer 14 calculates the slope dΔφ / df of the phase change amount Δφ with respect to the frequency f to be swept from the phase unwrapping data, and proceeds to the next step S15. In step S15, the calculator 14 calculates the coarse displacement D ′ from the above equation (6) using the inclination dΔφ / df, and proceeds to the next step S16.

  In step S16, the computer 14 uses the coarse displacement D ′, the center frequency in the frequency range to be swept, and the absolute value of the phase change amount Δφ at the center frequency, and the indefiniteness of 2π from the above equation (5). Then, an integer n is calculated, and the process proceeds to the next step S17.

  In step S17, the calculator 14 uses the center frequency in the frequency range to be swept and the absolute value of the phase change amount Δφ at the center frequency, and removes the indefiniteness of 2π (ie, the integer n). The displacement D is calculated from the equation (5) defining the above, and the above-described displacement measurement process is terminated.

<Measurement error between the displacement calculated by the displacement measuring apparatus of the present invention and the displacement actually applied>
Next, a verification test for confirming a measurement error between the displacement D calculated by the displacement measuring apparatus 1 according to the present invention and the displacement actually applied was performed. Here, first, the displacement D was calculated using the data shown in FIGS. 4 and 5 obtained by the verification test described above.

  Specifically, an approximate straight line was calculated from the phase unwrapping data of FIG. 5 obtained by the phase unwrapping process from the frequency / phase variation data shown in FIG. Then, the slope dΔφ / df of the phase change amount Δφ with respect to the frequency was calculated from the calculated approximate straight line.

  Using this slope dΔφ / df, the coarse displacement D ′ was calculated from the above equation (6). As a result, the coarse displacement D ′ was 691.8 [μm]. Further, the center frequency when the frequency sweep is performed in the range of 38 to 42 [GHz] is 40 [GHz], and the absolute value of the phase change amount Δφ at this center frequency is specified based on FIG. However, it was 3 [rad].

  Next, using this center frequency, the absolute value of the phase change Δφ at this time, and the coarse displacement D ′, the integer n is obtained from the above equation (5). As a result, n becomes 0. I understood.

  Next, using the center frequency of 40 [GHz] and 3 [rad] which is the absolute value of the phase change amount Δφ at the center frequency specified from FIG. When the displacement D was calculated from (5), the final displacement D was 981.4 [μm].

  When the frequency / phase variation data shown in FIG. 4 is obtained, the displacement actually applied is 1000 [μm], and therefore the measurement error from the calculated displacement D may be as small as 20 [μm]. It could be confirmed.

  Further, when the actual displacement was changed from 0 [μm] to 8500 [μm] and the displacement D was calculated in the same manner as the above-described calculation processing, the result shown in FIG. 7 was obtained. When a displacement of 3750 [μm] or less is given, the integer n becomes 0, and when a displacement of 3750 [μm] or more and 7500 [μm] or less is given, the integer n becomes 1 and exceeds 7500 [μm]. When the displacement was given, the integer n was 2.

  From FIG. 7, the measurement error is 20 [μm] or less between the displacement of the actually measured value from 0 [μm] to 8500 [μm] and the displacement D calculated by the above-described arithmetic processing, and with high accuracy. It was confirmed that the displacement D of the measurement surface 10 can be measured.

(1-4) Operation and Effect In the above configuration, the displacement measuring apparatus 1 transmits a transmission signal in which the frequency f is changed with respect to time to the measurement surface 10 and receives a reflected microwave from the measurement surface 10 as a reception signal. Is received (transmission / reception process). In addition, a transmission signal is input as a reference signal to the 6-port circuit 11 and a reception signal obtained when measuring the displacement of the measurement surface 10 is input (actual value input step).

  Then, the power values B3, B4, B5, and B6 of the four signals output from the 6-port circuit 11 in the actually measured value input process, and the phase delay amount θ in the 6-port circuit 11 at each frequency f of the transmission signal Based on this, the phase change amount Δφ is calculated at each frequency f (phase calculation step).

  Thereby, the displacement measuring apparatus 1 calculates the rough displacement D ′ of the measurement surface 10 based on the slope dΔφ1 / df of the phase change amount Δφ with respect to the frequency f (coarse displacement calculation step).

  Further, in the displacement measuring apparatus 1, using the coarse displacement D ′, the frequency f, and the phase change amount Δφ at that time, an integer that eliminates the indefiniteness of 2π that is the phase characteristic from the following equation (11): n is calculated (phase ambiguity elimination step).

D ′ = c / 4πf · (Δφ + 2πn) (11)
D ′ is the coarse displacement [μm], c is the speed of light [m / s], f is the frequency [Hz], Δφ is the phase change amount [rad], and n is an integer.

  As a result, the displacement measuring apparatus 1 defines the integer n and eliminates the indefiniteness of 2π from the above equation (5) (ie, D = c / 4πf · (Δφ + 2πn)), and the frequency f and its The displacement D of the measurement surface 10 can be calculated using the phase change amount Δφ at the time (displacement calculating step).

  As described above, the displacement measuring apparatus 1 uses the 6-port circuit 11, and even if the displacement D is measured using a transmission signal in which the frequency f is changed with respect to time, the 6-port circuit 11 at each frequency f Since the phase delay amount θ is defined in advance, the measurement error in the 6-port circuit 11 can be suppressed and the displacement D of the measurement surface 10 can be accurately measured. In addition, since the displacement measuring apparatus 1 can remove the indefiniteness of 2π, the displacement D having a magnitude exceeding the wavelength can be accurately measured.

(1-5) Other Embodiments The present invention is not limited to this embodiment, and various modifications can be made within the scope of the gist of the present invention. For example, although the transmission / reception antenna 4 is applied as the transmission / reception unit, a transmission / reception unit in which a transmission antenna and a reception antenna are provided separately may be applied.

  In the above-described embodiment, when the integer n that removes the indefiniteness of 2π is calculated from the above equation (5), the absolute value of the phase change amount Δφ at the center frequency is calculated as Δφ in the equation (5). However, the present invention is not limited to this. For example, the integer n may be calculated from Expression (5) using an arbitrary frequency f within the frequency range to be swept and the phase change amount Δφ at that time.

  In the above-described embodiment, when the displacement D is calculated from the above equation (5) from which the 2π indeterminacy is removed during the displacement measurement, the absolute value of the phase change amount Δφ at the center frequency is expressed by the equation (5). )), The present invention is not limited to this. For example, the displacement D may be calculated from the equation (5) using an arbitrary frequency f within the frequency range to be swept and the phase change amount Δφ at that time.

(2) Second Embodiment (2-1) Generation of Unwanted Wave Component In the displacement measuring apparatus 1 shown in FIG. 1, by irradiating the microwave from the transmission / reception antenna 4 toward the measurement surface 10, the measurement surface 10 The reflected microwave is received by the transmission / reception antenna 4. At this time, the reflected microwave includes a reflected wave reflected by the end face of the transmission / reception antenna 4 and a portion other than the measurement surface 10 (for example, beyond the measurement surface 10. There may be a multipath wave (hereinafter also referred to as an unnecessary wave) such as a reflected wave that hits an obstacle).

  When such an unnecessary wave exists, the reflected microwave from the measurement surface 10 interferes with the unnecessary wave. As a result, as shown in FIG. 8, when the phase change amount Δφ is obtained by sweeping the frequency, the phase change amount Δφ is distorted and nonlinearly caused by the interference between the reflected microwave and the unnecessary wave as in the region ER1. Will appear. If a non-linear component exists in the phase change amount Δφ, an error occurs in the coarse displacement D ′ when the coarse displacement D ′ of the measurement surface 10 is obtained from the inclination of the phase change amount Δφ with respect to the frequency, and the integer n is set to n. In some cases, it cannot be determined correctly, and the indefiniteness of 2π cannot be removed correctly.

  In such a case, by increasing the bandwidth when sweeping the frequency, if the inclination is obtained in a wide band and the influence of nonlinearity is suppressed (averaged), the integer n can be obtained correctly. Can be removed.

  However, if the frequency is swept in a wide band, it takes time to sweep the frequency, and the measurement cycle of the displacement of the measurement surface 10 becomes longer. In addition, depending on the frequency used, there are restrictions on the frequency width to be swept by the radio wave method, and there is a risk of radio wave interference with other radio equipment, so it is difficult to sweep the frequency in a wide band.

  Therefore, in the second embodiment, at the time of displacement measurement, the power values B3, B4, B5, and B6 of the signals output from the output ports P3, P4, P5, and P6 of the 6-port circuit 11 are measured, and these power values B3 are measured. , B4, B5, B6 and the phase delay amount θ, the unnecessary wave component is removed from the complex signal, and the phase change amount Δφ with the nonlinearity suppressed is calculated. Thereby, in 2nd Embodiment, even if it narrows the bandwidth at the time of sweeping a frequency, the integer n can be calculated | required correctly and the indefiniteness of 2 (pi) can be removed correctly.

(2-2) Computer of Displacement Measuring Device in Second Embodiment Although the second embodiment has the same displacement measurement principle as that of the above-described embodiment (hereinafter referred to as the first embodiment), at the time of displacement measurement The phase change amount based on the power values B3, B4, B5, and B6 of the signals output from the output ports P3, P4, P5, and P6 of the 6-port circuit 11 and the phase delay amount θ obtained by the previous calibration. The configuration of the computer 14 for calculating Δφ is different from that of the first embodiment. Here, description of the same contents as those of the first embodiment described above will be omitted, and the following description will be given focusing on a computer different from that of the first embodiment.

  9 in which the same reference numerals are assigned to the parts corresponding to those in FIG. 2 shows the circuit configuration of the computer 31 provided in the displacement measuring apparatus of the second embodiment. As shown in FIG. 9, the computer 31 is different from the first embodiment only in the configuration of the phase calculation unit 32, the other input unit 21, phase delay amount calculation unit 22, phase unwrapping processing unit 24, inclination The calculation unit 25, the coarse displacement calculation unit 26, the phase ambiguity elimination unit 27, and the displacement calculation unit 28 have the same configuration as that of the first embodiment.

  As shown in FIG. 10, the phase calculation unit 32 includes a first phase change amount calculation unit 33, an amplitude calculation unit 34, a complex signal generation unit 35, an unnecessary wave suppression unit 36, and a second phase change amount calculation unit 37. Yes. The first phase change amount calculation unit 33 and the amplitude calculation unit 34 input the power values B3, B4, B5, and B6 of the four signals output from the 6-port circuit 11 for each frequency f to the input unit 21 (FIG. 9). ) Further, the first phase change amount calculating unit 33 and the amplitude calculating unit 34 read out the phase delay amount θ at each frequency f in the frequency sweep obtained from the calibration from the storage device 15 or the phase delay amount calculating unit 22.

  The first phase change amount calculation unit 33 uses the power values B3, B4, B5, and B6 of the signal output from the 6-port circuit 11 and the phase delay amount θ, for each frequency f, the above equation (8 ) To calculate the phase change amount Δφ as a pre-process phase change amount Δφ ″. When the first phase change amount calculation unit 33 calculates the pre-process phase change amount Δφ ″ at each frequency f, the first phase change amount calculation unit 33 outputs this to the complex signal generation unit 35 as frequency / phase change amount data.

  At this time, the amplitude calculation unit 34 uses the power values B3, B4, B5, and B6 of the signal output from the 6-port circuit 11 and the phase delay amount θ based on the following equation (12), and the 6-port circuit: 11 is calculated for each frequency f. After calculating the amplitude A at each frequency f, the amplitude calculation unit 34 outputs this to the complex signal generation unit 35 as frequency / amplitude data.

  11A shows an example of the waveform of the amplitude A calculated by the amplitude calculator 34, and FIG. 11B shows the pre-processing phase change amount Δφ ″ calculated by the first phase change amount calculator 33. An example of a waveform is shown, and a pre-processing phase change amount Δφ ″ including a non-linear component due to an unnecessary wave component is shown. The complex signal generation unit 35 uses the amplitude A as shown in FIG. 11A acquired along the frequency f and the pre-process phase change amount Δφ ″ as shown in FIG. 11B acquired along the frequency f. While changing the frequency f, the following equation (13) is calculated to generate a complex signal as shown in FIG. 11C. In the following formula (13), i represents an imaginary unit.

  Acos Δφ ″ + iAsin Δφ ″ (13)

  In this way, the complex signal generation unit 35 reconstructs the signal output from the 6-port circuit 11 as a complex signal in which the real part and the imaginary part vibrate sinusoidally with respect to the frequency f. The complex signal is output to the unnecessary wave suppression unit 36 (FIG. 10).

  The unnecessary wave suppression unit 36 includes a first filter processing unit 41, an inverse Fourier transform unit 42, a second filter processing unit 43, a Fourier transform unit 44, and an unnecessary wave suppression signal generation unit 45. When the first filter processing unit 41 receives the complex signal as shown in FIG. 12A from the complex signal generation unit 35, the first filter processing unit 41 performs, for example, a first filter process for multiplying the complex signal by a predetermined window function as shown in FIG. 12B. Thereby, the first filter processing unit 41 generates a complex signal weighted by the window function as shown in FIG. 12C.

  By multiplying the complex signal by a predetermined window function in this way, both ends of the amplitude of the complex signal can be brought close to zero. Therefore, when the complex signal is converted from the frequency domain to the time domain by inverse Fourier transform described later. In addition, unnecessary side lobes can be prevented from occurring in the time domain.

  Here, any window function can be used as the window function, but the center position, full width at half maximum, and finite interval of the window function are determined from the frequency width used for measurement and the amplitude of the complex signal. Can do. That is, when a window function is applied to a complex signal, the amplitude is gently reduced to 0 at both ends of the frequency used for measurement. As the window function used in the first filter processing unit 41, for example, it is desirable to use a Kaiser-Bessel window.

  The first filter processing unit 41 outputs the complex signal multiplied by the window function to the inverse Fourier transform unit 42. The inverse Fourier transform unit 42 performs inverse Fourier transform on a complex signal in a finite interval as shown in FIG. 13A, converts the complex signal in the frequency domain into the time domain, and generates a time domain waveform as shown in FIG. 13B. . The inverse Fourier transform unit 42 outputs the obtained time domain waveform to the second filter processing unit 43.

  Here, in the time domain waveform, the first peak PK1 appearing near time 0 is irradiated from the transmission / reception antenna 4 toward the measurement plane 10 when judged from the positions and distances of the transmission / reception antenna 4 and the measurement plane 10. In this case, the peak appears due to an unnecessary wave generated by the reflection of the microwave on the end face of the transmission / reception antenna 4.

  In the time domain waveform, the second peak PK2 appearing next to the first peak PK1 is a desired signal by the reflected microwave generated by the reflection of the microwave on the measurement surface 10. The unnecessary wave generated by the reflection of the microwave from the obstacle beyond the measurement surface 10 appears as the third peak PK3 delayed from the second peak PK2 in the time domain waveform.

  For example, the second filter processing unit 43 performs a second filter process of multiplying a time domain waveform as shown in FIG. 14A by a predetermined window function as shown in FIG. 14B. Thereby, as shown in FIG. 14C, the second filter processing unit 43 cuts out the second peak PK2 that is a desired signal from the time domain waveform, and suppresses the first peak PK1 and the third peak PK3 that appear due to unnecessary waves. Generate a time domain waveform. The second filter processing unit 43 outputs a time domain waveform obtained by cutting out a region where a desired signal exists from the time domain waveform to the Fourier transform unit 44.

  Here, although an arbitrary window function can be used as the window function, the first peak PK1 and the third peak having an amplitude peak in the vicinity of the second peak PK2 that is a desired signal in the time domain waveform and unnecessary waves are used. A window function whose amplitude is close to zero near the peak PK3 may be used. The center position, full width at half maximum, and finite interval of the amplitude of these window functions can be determined from past operation data. As the window function used in the second filter processing unit 43, for example, a Hanning window can be used.

  As shown in FIG. 15A, the Fourier transform unit 44 performs Fourier transform on a time domain waveform in which a region where a desired signal exists is cut out and suppresses an unnecessary wave component, and the time domain waveform is changed from the time domain to the frequency domain. A frequency domain waveform having a real part and an imaginary part is generated as shown in FIG. 15B. The Fourier transform unit 44 outputs the obtained frequency domain waveform to the unnecessary wave suppression signal generation unit 45.

  The unnecessary wave suppression signal generation unit 45 divides the frequency domain waveform as shown in FIG. 16A by the window function shown in FIG. 16B used in the first filter processing unit 41, and continues along the frequency f as shown in FIG. 16C. An unnecessary wave suppression signal that changes periodically is generated. The unnecessary wave suppression signal thus obtained is a complex signal having a real part and an imaginary part, and the unnecessary wave suppression signal generation unit 45 sends the generated unnecessary wave suppression signal to the second phase change amount calculation unit 37. Output.

  The second phase change amount calculation unit 37 calculates the phase change amount Δφ for each frequency f as shown in FIG. 17C from the unnecessary wave suppression signal as shown in FIG. 17A. After calculating the phase change amount Δφ for each frequency f from the unnecessary wave suppression signal, the second phase change amount calculating unit 37 outputs this to the phase unwrapping processing unit 24 (FIG. 9) as frequency / phase change amount data. To do.

  Here, the unnecessary wave suppression signal shown in FIG. 17A can be expressed by the following equation (14). In Expression (14), i represents an imaginary unit, A ′ represents the amplitude of the unwanted wave suppression signal, and Δφ represents the phase change amount of the unwanted wave suppression signal. FIG. 17B shows a waveform of the amplitude A ′ of the unnecessary wave suppression signal.

  A ′ cos Δφ + iA ′ sin Δφ (14)

  The phase change amount Δφ along the frequency f calculated from the unnecessary wave suppression signal in which the unnecessary wave component is suppressed suppresses a non-linear component generated by interference between the reflected microwave and the unnecessary wave, and the frequency f. It varies linearly along. Therefore, in the second embodiment, when a nonlinear component can be suppressed by the phase change amount Δφ, when the coarse displacement D ′ of the measurement surface 10 is obtained from the inclination of the phase change amount Δφ with respect to the frequency, an error is caused in the coarse displacement D ′. Is less likely to occur, and the integer n can be determined correctly.

  The phase unwrapping processing unit 24 that performs phase unwrapping processing on the frequency / phase variation data, the slope calculating unit 25 that calculates the slope dΔφ / df of the approximate line from the phase unwrapping data, The coarse displacement calculation unit 26 that calculates the coarse displacement D ′ from the equation (6), the phase indeterminacy elimination unit 27 that calculates the integer n that removes the indefiniteness of 2π, and the displacement calculation unit 28 that calculates the displacement D are respectively Since it is the same as that of 1st Embodiment mentioned above, the description is abbreviate | omitted here.

(2-3) Displacement Measurement Processing at the Time of Displacement Measurement in the Second Embodiment Next, the time series flow of the displacement measurement processing in the second embodiment will be briefly described below using the flowchart of FIG. The computer 31 shifts from the start step to step S11 and step S21 during displacement measurement. In step S11, the computer 31 transmits a microwave whose frequency f is changed with time to the measurement surface 10 as a transmission signal, and receives a reflected microwave from the measurement surface 10 as a reception signal, thereby obtaining 6 ports. The power values B3, B4, B5, and B6 of the signal output from the circuit 11 are acquired.

  Next, in step S11, the computer 31 uses the power values B3, B4, B5, B6 of the signal output from the 6-port circuit 11 at the predetermined frequency f and the phase delay amount θ at the frequency f. From the above equation (8), the phase change amount Δφ at the frequency f is calculated as the pre-process phase change amount Δφ ″ (FIG. 11B) (pre-process phase change amount calculating step), and then step S22. Move on.

  At this time, in step S21, the computer 31 uses the power values B3, B4, B5, and B6 of the signal output from the 6-port circuit 11 at the predetermined frequency f and the phase delay amount θ at the frequency f. Thus, the amplitude A (FIG. 11A) at the frequency f is obtained from the above equation (12) (amplitude calculation step), and then the process proceeds to step S22.

  In step S <b> 22, the calculator 31 determines whether or not the pre-processing phase change amount Δφ ″ and the amplitude A are calculated for each frequency f in the frequency range to be swept. Here, if a negative result is obtained, it indicates that the pre-processing phase change Δφ ″ and the amplitude A are not calculated at each frequency f. At this time, the calculator 31 returns to step S11 and step S21. The phase change amount Δφ ″ and the amplitude A before processing at other frequencies f are calculated.

  On the other hand, if an affirmative result is obtained in step S22, this means that the calculation of the pre-processing phase change amount Δφ ″ and the amplitude A has been completed for all the frequencies f. The process moves to S23. In step S23, the computer 31 generates a complex signal in the frequency domain as shown in FIG. 11C based on the above equation (13) (complex signal generation step), and proceeds to the next step S24.

  In step S24, the computer 31 performs a first filter process that multiplies the complex signal by a window function (FIG. 12B), and generates a complex signal (FIG. 12C) with both ends gently approaching 0 (first filter processing step). Then, the process proceeds to the next step S25. In step S25, the computer 31 converts the complex signal from the frequency domain to the time domain by inverse Fourier transform to generate a time domain waveform (FIG. 13B) (time domain conversion step), and proceeds to the next step S26.

  In step S26, the computer 31 performs a second filter process that multiplies the time domain waveform by a window function (FIG. 14B), generates a time domain waveform (FIG. 14C) in which a desired signal is cut out and unnecessary wave components are suppressed (first waveform). 2 filter processing step), the process proceeds to the next step S27. In step S27, the calculator 31 converts the time domain waveform from the time domain to the frequency domain by Fourier transform to generate a frequency domain waveform (FIG. 15B) (frequency domain conversion process), and proceeds to the next step S28.

  In step S28, the computer 31 divides the frequency domain waveform by the window function (FIG. 16B) used in the first filter processing in step S24, and generates an unnecessary wave suppression signal (FIG. 16C) having a real part and an imaginary part. Then (unnecessary wave suppression signal generation step), the process proceeds to the next step S29. In step S29, the computer 31 calculates the phase change amount Δφ from the unnecessary wave suppression signal expressed by the above formula (14) (phase change amount calculating step), and the step of FIG. 6 described in the first embodiment. The process proceeds to S13.

  Thereafter, also in the second embodiment, the steps S13 to S17 shown in FIG. 6 are executed in order as in the first embodiment described above. In addition, since step S13-step S17 after step S29 are the same as that of 1st Embodiment, the description is abbreviate | omitted.

(2-4) Verification Test Next, the verification test will be described. FIG. 19 is a graph showing a calculation result when the pre-processing phase change amount Δφ ″ is calculated for each frequency f by the verification test. In FIG. 19, an aluminum flat plate (also referred to as an aluminum plate) is used as an object to be measured, and microwaves are applied to the aluminum plate while sweeping the frequency in the range of 48 to 52 [GHz] (sweep frequency bandwidth is 4 [GHz]). Irradiated towards. In this verification test, an unnecessary wave is generated when the reflected microwave from the aluminum plate is received.

  The phase delay amount θ of the 6-port circuit 11 when the frequency sweep was performed in the range of 48 to 52 [GHz] was obtained in advance by calibration according to the above-described procedure. In FIG. 19, the displacement D from the reference position O is set to 1000 [μm], and the power values B3, B4, B5, B6 of the four signals output from the 6-port circuit 11 at that time, and the phase delay obtained in advance. Using the amount θ, the phase change amount Δφ obtained for each frequency f from the above equation (8) is shown as a pre-processing phase change amount Δφ ″. In FIG. 19, it was confirmed that the signal that should have a linear sawtooth shape is distorted by the influence of unnecessary waves.

  Next, the power values B3, B4, B5, B6 of the four signals output from the 6-port circuit 11 and the phase delay amount θ obtained in advance are used for each frequency f from the above equation (12). The amplitude A was obtained. Then, using the amplitude A acquired along the frequency f and the pre-processing phase change Δφ ″ acquired along the frequency f, the above equation (13) is calculated while changing the frequency f. To generate a complex signal.

  Next, as the first filter processing, a complex signal is multiplied by a Kaiser-Bessel window with β = 6 as a window function, and the obtained complex signal is subjected to inverse Fourier transform to convert the complex signal from the frequency domain to the time domain. A time domain waveform was generated. As a result, a result as shown in FIG. 20 was obtained. The signal originally necessary from the position of the measurement surface 10 is a signal in the vicinity of 2 [ns], but from FIG. 20, other locations (for example, in the vicinity of 0.5 [ns] and 4 [ns]) It was confirmed that there was a peak due to unnecessary waves.

  Next, as a second filter process, a Hanning window having a center of 2 [ns] and a full width at half maximum of 1.5 [ns] is used as a window function, and the vicinity of 2 [ns] in the time domain waveform shown in FIG. The signal was cut out as a desired signal. As a result, a time domain waveform as shown in FIG. 21 was obtained. Then, the time domain waveform shown in FIG. 21 was Fourier transformed, and the time domain waveform was converted from the time domain to the frequency domain to generate a frequency domain waveform.

  Next, this frequency domain waveform was divided back by a Kaiser-Bessel window with β = 6 used as a window function in the first filter processing to generate an unnecessary wave suppression signal. The unnecessary wave suppression signal obtained in this way has a real part and an imaginary part, and is represented by the above equation (14). Next, when the amount of phase change Δφ was calculated along each frequency f from this unnecessary wave suppression signal, the result shown in FIG. 22 was obtained. From the result of FIG. 22, it was confirmed that the nonlinear component existing in the pre-processing phase change amount Δφ ″ was suppressed and a linear sawtooth signal was obtained.

  Next, FIG. 23 shows the result of calculating the displacement D using the pre-processing phase change amount Δφ ″ shown in FIG. 19 and the phase change amount Δφ shown in FIG. When the treatment for suppressing the unwanted wave component was not performed, the displacement was not correctly measured when the displacement applied to the aluminum plate was 3000 [μm]. However, when the process for suppressing the unwanted wave component is performed, the displacement D can be correctly obtained over the entire measurement range.

  Next, the center frequency is 50 [GHz], and the sweep frequency bandwidth (bandwidth) is 250 [MHz], 500 [MHz], 1 [GHz], 2 [GHz], 4 [GHz], and 8 [GHz]. In other words, the process of suppressing the unwanted wave component was performed, and the displacement D was measured. And the measurement result of the obtained displacement D is shown in FIG. The processing for suppressing unnecessary wave components is performed by performing a series of processes such as the first filter process and the second filter process in the same manner as in the verification test described above, and the window function used at that time is also the same Kaiser as in the verification test described above.・ Bessel window and Hanning window were used.

  24A shows the measurement result of the displacement D when the sweep frequency bandwidth is 250 [MHz], FIG. 24B shows the measurement result of the displacement D when the sweep frequency bandwidth is 500 [MHz], and FIG. Indicates a measurement result of the displacement D when the sweep frequency bandwidth is 1 [GHz]. FIG. 24D shows the measurement result of the displacement D when the sweep frequency bandwidth is 2 [GHz], and FIG. 24E shows the measurement result of the displacement D when the sweep frequency bandwidth is 4 [GHz]. FIG. 24F shows the measurement result of the displacement D when the sweep frequency bandwidth is 8 [GHz].

  It was confirmed that the displacement D was correctly measured when the sweep frequency bandwidth was 1 [GHz] to 8 [GHz]. On the other hand, when the sweep frequency bandwidth is 250 [MHz] and 500 [MHz], as shown in FIGS. 24A and 24B, the movement amount of the aluminum plate is 1 [μm], 5 [μm] and 9. At 5 [μm], the measured value greatly deviated from the actual movement amount. These are errors that occur because the integer n cannot be obtained correctly when determining the integer n from the slope of the phase change amount Δφ.

  Therefore, when the phase change amount Δφ in which the nonlinear component is suppressed by the processing for suppressing the unnecessary wave component, the sweep frequency bandwidth necessary for obtaining the displacement D can be narrowed to 1 [GHz]. . From the above, it was confirmed that even when the sweep frequency bandwidth when measuring the displacement D of the measurement surface 10 is narrowed, the measurement error can be suppressed and the displacement of the measurement surface 10 can be measured accurately.

(2-5) Operation and effect In the above configuration, the displacement measuring apparatus according to the second embodiment is similar to the first embodiment described above, in the transmission / reception process, the actual value input process, the phase calculation process, the coarse displacement calculation process, By executing the phase ambiguity elimination step and the displacement calculation step, the measurement error in the 6-port circuit 11 can be suppressed and the displacement D of the measurement surface 10 can be accurately measured. In addition, since this displacement measuring apparatus can remove the indefiniteness of 2π, the displacement D exceeding the wavelength can be accurately measured.

  In addition, in the displacement measuring apparatus of the second embodiment, when the phase calculation process is executed, the power values B3, B4, B5, B6 of each signal output from the 6-port circuit 11 and the frequency obtained during calibration are obtained. The phase change amount Δφ ″ and the amplitude A before processing are calculated using the phase delay amount θ at each frequency f in the sweep, and a complex signal is calculated based on the phase amount Δφ ″ and amplitude A before the processing. It was made to generate (complex signal generation process). Next, in this displacement measuring apparatus, a desired signal included in the complex signal is cut out to generate an unnecessary wave suppression signal in which the unnecessary wave component is suppressed (unnecessary wave suppression step), and the phase at each frequency f is generated from this unnecessary wave suppression signal. The amount of change Δφ was calculated (phase change amount calculating step).

  As described above, in the displacement measuring apparatus according to the second embodiment, the phase change amount Δφ along the frequency f is calculated from the unnecessary wave suppression signal in which the unnecessary wave component is suppressed. It is possible to obtain a phase change amount Δφ in which non-linear components are suppressed without interference with unnecessary waves. Therefore, when the coarse displacement D ′ of the measurement surface 10 is obtained from the inclination of the phase change amount Δφ with respect to the frequency, an error hardly occurs in the coarse displacement D ′, and the integer n can be correctly determined. Can be removed correctly.

  Further, in the displacement measuring apparatus, when the coarse displacement D ′ of the measurement surface 10 is obtained from the inclination of the phase change amount Δφ with respect to the frequency, the phase change amount Δφ that linearly changes while suppressing the unnecessary wave component is used. As a result, even if the sweep frequency bandwidth is narrowed, the integer n can be determined correctly. Therefore, even if the sweep frequency bandwidth is narrowed, the 2π indefiniteness can be correctly removed, and the displacement D of the measurement surface 10 can be accurately measured.

(2-6) Other Embodiments in Second Embodiment In the second embodiment described above, as shown in FIG. 14B, the second filter used in the second filter processing step is directed from the peak toward both ends. Although a sinusoidal window function having a gradually decreasing amplitude and having an amplitude of 0 at the end is applied, the present invention is not limited to this. For example, a pulse-like signal having steep rising and falling edges may be applied as the second filter used in the second filter processing step. Even in the case of using a pulsed signal, a rising region is present in the vicinity of the second peak PK2, which is a desired signal in the time domain waveform, and the amplitude is 0 in the vicinity of the first peak PK1 and the third peak PK3 due to unnecessary waves. What is necessary is just to have a falling area.

  Further, in the second embodiment described above, a sine wave window function is used as the second filter used in the second filter processing step, unnecessary waves generated by reflection of microwaves at the end face of the transmission / reception antenna 4, and measurement surface Although the case where both the unwanted wave generated by the reflection of the microwave by the obstacle of 10 or more is suppressed has been described, the present invention is not limited to this.

  For example, when the influence of unnecessary waves generated beyond the measurement surface 10 is small, as the second filter, only the first peak PK1 due to unnecessary waves caused by the reflection of microwaves at the end face of the transmission / reception antenna 4 is suppressed. You may make it use the 2nd filter which leaves 3 peak PK3 as it is. Specifically, at the time of the second filter processing, a stepped signal having an amplitude of 0 when the delay time is around 0 to 0.5 [ns] and an amplitude of 1 in other regions may be used as the second filter. Good. The step-like signal may be a signal that rises steeply, or may be a signal that rises gently.

  In addition, when the influence of the unnecessary wave generated at the end face of the transmission / reception antenna 4 is small, only the unnecessary wave component in the time domain waveform that is generated at a position located beyond the measurement plane 10 is suppressed by the second filter. May be. In this case, as the second filter, a second filter having an amplitude of 0 only near the third peak PK3 due to an unnecessary wave generated by reflection beyond the measurement surface 10 and an amplitude of 1 at other locations may be used. .

1 Displacement measuring device 4 Transmission / reception antenna (transmission / reception unit)
11 6-port circuit 23, 32 Phase calculation unit 26 Coarse displacement calculation unit 27 Phase indefiniteness cancellation unit 28 Displacement calculation unit 35 Complex signal generation unit 36 Unwanted wave suppression unit 37 Second phase change amount calculation unit 41 First filter processing unit 42 Inverse Fourier transform unit 43 Second filter processing unit 44 Fourier transform unit 45 Unwanted wave suppression signal generation unit

Claims (11)

In a displacement measurement method for measuring the displacement of a measurement surface using a microwave as a transmission signal,
A transmission / reception step of transmitting the transmission signal whose frequency is changed with respect to time to the measurement surface, and receiving a reflected microwave from the measurement surface as a reception signal;
An actual value input step of inputting the transmission signal as a reference signal to the 6-port circuit and inputting the reception signal obtained when measuring the displacement of the measurement surface;
Based on the power values of the four signals output from the 6-port circuit in the measured value input step and the phase delay amount θ in the 6-port circuit at each frequency of the transmission signal, at each frequency. A phase calculation step of calculating a phase change amount Δφ;
A coarse displacement calculating step of calculating a coarse displacement D ′ of the measurement surface based on an inclination of the phase change amount Δφ with respect to the frequency;
A phase ambiguity eliminating step of calculating an integer n that eliminates the indefiniteness of 2π, which is a phase characteristic, using the coarse displacement D ′ and the phase change amount Δφ;
A displacement calculating step of calculating a displacement D of the measurement surface using the phase change amount Δφ by a predetermined arithmetic expression in which the integer n is defined and the indefiniteness of 2π is eliminated. A calibration step is provided before the actual value input step,
The calibration step includes
A known phase change amount obtaining step for obtaining a known phase change amount Δφ ′ that changes according to the displacement of the measurement surface for each of the frequencies of the transmission signal;
A calibration power value acquisition step of acquiring power values of four signals output from the 6-port circuit when the known phase change amount Δφ ′;
Based on the known phase change amount Δφ ′ and the power value obtained in the calibration power value obtaining step, the phase delay amount θ in the 6-port circuit at each frequency of the transmission signal is calculated. The displacement measuring method according to claim 1, further comprising: a phase delay amount calculating step.   The displacement measuring method according to claim 2, wherein the known phase change amount Δφ ′ is other than 0, π / 2, π, and 3π / 2. The displacement according to any one of claims 1 to 3, wherein an arithmetic expression for calculating the integer n that eliminates 2π indefiniteness in the phase indefiniteness elimination step is the following expression (1). Measuring method.
D ′ = c / 4πf · (Δφ + 2πn) (1)
D ′ is the coarse displacement [μm], c is the speed of light [m / s], f is the frequency [Hz], Δφ is the phase change amount [rad], and n is the integer. The displacement measuring method according to any one of claims 1 to 4, wherein an arithmetic expression for calculating the displacement D in the displacement calculating step is the following expression (2).
D = c / 4πf · (Δφ + 2πn) (2)
D is the displacement [μm], c is the speed of light [m / s], f is the frequency [Hz], Δφ is the phase change [rad], and n is the integer. The phase calculation step includes
A complex signal is generated based on the pre-processing phase change amount Δφ ″ and the amplitude A calculated using the power values of the four signals output from the 6-port circuit and the phase delay amount θ. Complex signal generation process;
An unnecessary wave suppression step of generating an unnecessary wave suppression signal by cutting out a desired signal included in the complex signal and suppressing an unnecessary wave component;
The displacement measurement method according to claim 1, further comprising: a phase change amount calculation step of calculating the phase change amount Δφ at each frequency from the unnecessary wave suppression signal. The unnecessary wave suppressing step includes
A first filter processing step of performing a first filter process on the complex signal and generating a complex signal of a finite interval in which both ends gently approach 0;
A time domain conversion step of converting the complex signal generated in the first filter processing step from a frequency domain to a time domain to generate a time domain waveform;
Performing a second filter process on the time domain waveform to generate a time domain waveform in which the predetermined unnecessary wave component is suppressed; and
A frequency domain conversion step of generating a frequency domain waveform by converting the time domain waveform suppressing the unnecessary wave component from the time domain to the frequency domain;
Reducing the frequency domain waveform by the first filter used in the first filter processing step, and generating the unnecessary wave suppression signal,
The displacement measuring method according to claim 6, comprising: The second filter processing step includes
The unnecessary signal component in the time-domain waveform generated at a location located in a transmission / reception unit that transmits the transmission signal to the measurement surface and receives the reflected microwave as the reception signal is suppressed by a second filter. The displacement measuring method according to claim 7. The second filter processing step includes
The displacement measurement method according to claim 7, wherein the unnecessary wave component in the time-domain waveform generated at a location located farther from the measurement surface is suppressed by a second filter.   The displacement measuring method according to claim 8 or 9, wherein the second filter is a Hanning window. In a displacement measuring device that measures the displacement of a measurement surface using a microwave as a transmission signal,
A transmission / reception unit that transmits the transmission signal having a frequency changed with respect to time to the measurement surface, and receives a reflected microwave from the measurement surface as a reception signal;
A 6-port circuit to which the transmission signal is input as a reference signal and the reception signal is input;
Based on the four power values output from the 6-port circuit and the phase delay amount θ in the 6-port circuit at each frequency of the transmission signal, the phase change amount Δφ is calculated at each frequency. A phase calculation unit;
A coarse displacement calculator for calculating a coarse displacement D ′ of the measurement surface based on an inclination of the phase change amount Δφ with respect to the frequency;
A phase indeterminacy eliminating unit that calculates an integer n that eliminates the indeterminacy of 2π, which is a phase characteristic, using the coarse displacement D ′ and the phase change amount Δφ;
A displacement measuring device comprising: a displacement calculating unit that calculates the displacement D of the measurement surface using the phase change amount Δφ by a predetermined arithmetic expression that defines the integer n and eliminates the indefiniteness of 2π.

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