Data correction device, measurement system and correction method

Abstract

A data correction device 400 includes: an acquisition section 410 that acquires measurement data from a measurement device 100 capable of periodically measuring a distance while moving at least one of (i) a subject 10 to be measured or (ii) at least a part of the measurement device 100, in which first measurement results of the distance are arranged in a time series, and second measurement results obtained by measuring the distance when the subject 10 to be measured and the measurement device 100 are in a stationary state are arranged at a head or a tail of the first measurement results; and a correction section 430 that corrects an error included in the measurement data by applying the measurement data to a recursive formula based on a time derivative of a measurement result of the measurement device.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to a data correction device, a measurement system, a program, and a correction method. BACKGROUND

[0002] A frequency-shifted feedback laser (FSFL) that is provided with a frequency shifter in a cavity (resonator) and outputs a plurality of longitudinal-mode lasers whose oscillation frequencies linearly change with time is known. Further, an optical range finder that uses such a FSFL is known (for example, see Patent Literature 1: Japanese Patent No. 3583906, and Non-Patent Literature 1: “Distance Sensing by FSF Laser and Its Application”, Takefumi HARA, Optonews, Vol. 7, No. 3, 2012, pp. 25-31). SUMMARY

[0003] PROBLEMS TO BE SOLVED BY THE INVENTION

[0004] The optical range finder divides the frequency-shifted feedback laser into reference light and measurement light, and generates a beat signal by mixing the reference light and reflected light that is reflected by irradiating the measurement light onto an object to be measured. Then, the optical range finder measures a distance from the optical range finder to the object to be measured by specifying a frequency of the beat signal. With such an optical range finder, for example, it is possible to measure a three-dimensional geometry of the object to be measured by continuing to measure the distance while moving the object to be measured. However, since light has a wave-like property, and a Doppler shift occurs due to a relative velocity between a light source and the object to be measured, a frequency of the reflected light reflected from the object to be measured can change. Since the frequency of the beat signal changes in this case, there is a problem that a measurement accuracy of the optical range finder decreases.

[0005] The present disclosure is made in view of this, and aims to easily measure a three-dimensional geometry of an object to be measured with an optical range finder while suppressing a decrease in measurement accuracy.

[0006] MEANS FOR SOLVING THE PROBLEMS

[0007] A first aspect of the present disclosure provides a data correction apparatus including: an acquisition part that acquires measurement data from a measurement apparatus that measures a distance from a reference position to an object to be measured using a chirped laser beam and is capable of periodically measuring the distance while at least one of (i) the object to be measured or (ii) at least a part of the measurement apparatus is moving, in the measurement data, a first measurement result of the distance is arranged in a time series, and a second measurement result of the distance obtained by the measurement apparatus when the object to be measured and the measurement apparatus are in a stationary state is arranged at a head or a tail of the first measurement result; and a correction part that corrects an error included in the measurement data based on movement of at least one of the object to be measured or at least a part of the measurement apparatus, by applying the measurement data acquired by the acquisition part to a recursive formula based on a time derivative of a measurement result of the measurement apparatus.

[0008] The correction part can use different recursive formulas according to positive and negative signs of a chirp rate based on a rate of change of a frequency per unit time of the chirped laser beam used by the measurement apparatus.

[0009] When the chirp rate is negative, the acquisition part can acquire measurement data in which the second measurement data is arranged at a head of the first measurement data, and the correction part can use a recursive formula that corrects the measurement data arranged in the time series acquired by the acquisition part in order of the arranged time series.

[0010] The correction part can use, as the recursive formula, a first recursive formula represented by the following equation

[0011]

[0012] or

[0013] a second recursive formula represented by the following equation as the recursive formula

[0014]

[0015] wherein, L n is an nth measurement result including an error caused by a Doppler shift, L n is an nth measurement result corrected for the error caused by the Doppler shift, s = k / Δt, Δt is a time interval at which the measurement apparatus measures the distance, k = 2c0 / λnγ, c0is a speed of light in a vacuum, λ is a wavelength of the chirped laser beam, n is a refractive index of air, and γ is a chirp rate.

[0016] The correction part can use, as the recursive formula, a third recursive formula represented by the following equation

[0017]

[0018] wherein L n is the nth measurement result including an error caused by a Doppler shift, L n is the nth measurement result corrected for the error caused by the Doppler shift, s = k / At, At is a time interval at which the measuring device measures a distance, k = 2c0 / AnY, c0is a speed of light in a vacuum, A is a wavelength of the frequency-modulated laser beam, n is a refractive index of air, Y is a frequency modulation, and the coefficients (a0, a1,..., an) are determined based on the frequency modulation Y. m b) is a coefficient for approximating the time differential data of the measurement data as time differential data using a difference method having an accuracy of the mth order.

[0019] The acquisition part can acquire the measurement data each time the measuring device measures a distance, and the correction part can start correcting the measurement data acquired by the acquisition part to sequentially correct the measurement data while the measuring device continues to measure a distance.

[0020] When the frequency modulation is positive, the acquisition part can acquire measurement data in which the second measurement data is arranged at the tail of the first measurement data, and the correction part can use a recurrence formula that corrects the measurement data acquired by the acquisition part arranged in a time series in a reverse order of the arranged time series.

[0021] The correction part can use a fourth recurrence formula represented by the following equation as the recurrence formula

[0022]

[0023] or a fifth recurrence formula represented by the following equation as the recurrence formula

[0024]

[0025] wherein L n is the nth measurement result including an error caused by a Doppler shift, L n is the nth measurement result corrected for the error caused by the Doppler shift, s = k / At, At is a time interval at which the measuring device measures a distance, k = 2c0 / AnY, c0is a speed of light in a vacuum, A is a wavelength of the frequency-modulated laser beam, n is a refractive index of air, Y is a frequency modulation.

[0026] The correction part can use a sixth recurrence formula represented by the following equation as the recurrence formula

[0027]

[0028] wherein L n ​is the nth measurement result including an error caused by a Doppler shift, L n is the nth measurement result corrected for an error caused by a Doppler shift, s = k / At, At is a time interval at which the measurement device measures a distance, k = 2co / AnY, co is a speed of light in a vacuum, A is a wavelength of a frequency-modulated laser beam, n is a refractive index of air, Y is a frequency modulation, and coefficients (a0, a1,..., an) are coefficients of a polynomial expression of a function of a distance. m , b) is a coefficient for approximating time differential data of the measurement data as time differential data using a difference method having an accuracy of the mth order.

[0029] The acquisition means can acquire measurement data in which second measurement results obtained by measuring the distance while the object under test and the measurement device are in a stationary state are arranged as m pieces of second data from the head or m pieces of second data from the tail, and the correction means can correct errors included in the p pieces of first data by applying measurement data including the m pieces of second data and the p pieces of first data included in the first measurement results to the recursive formula.

[0030] The acquisition means can further acquire information on m' from the measurement device, m' being the number of pieces of data of the second measurement results included in the measurement data, and the correction means can correct errors of the measurement data only after m - m' times of duplication of the data of the second measurement results, m' being the number of pieces of data of the second measurement results included in the measurement data.

[0031] A second aspect of the present disclosure provides a measurement system including: a measurement device; and the data correction device according to the first aspect, the measurement device measuring a distance from a reference position to an object under test, and including: a laser device outputting a frequency-modulated laser beam; a branching means branching the frequency-modulated laser beam output from the laser device into (i) reference light and (ii) measurement light, the reference light being a portion of the frequency-modulated laser beam, the measurement light being at least some of the remaining portion of the frequency-modulated laser beam; a beat signal generation means generating a beat signal by mixing the reference light and reflected light reflected by irradiating the measurement light onto the object under test; a frequency analysis means frequency-analyzing the beat signal; and a calculation means calculating the distance between the reference position and the object under test based on a result of the frequency analysis of the beat signal by the frequency analysis means, wherein the measurement device generates measurement data in which first measurement results of measurement results of the distance measured periodically while at least one of (i) the object under test or (ii) at least a portion of the measurement device is moving is arranged in a time series, and second measurement results obtained by measuring the distance while the object under test and the measurement device are in a stationary state are arranged at a head or a tail of the first measurement results.

[0032] A third aspect of the present disclosure provides a correction method including the following steps performed by a computer: acquiring measurement data from a measurement device that measures a distance from a reference position to an object to be measured using a frequency-modulated laser beam, in which measurement data, a first measurement result of a measurement result of the distance measured periodically while at least one of (i) the object to be measured or (ii) at least a part of the measurement device is moving is arranged in a time series, and a second measurement result obtained by measuring the distance when the object to be measured and the measurement device are in a stationary state is arranged at a head or a tail of the first measurement result; and correcting an error included in the measurement data based on movement of at least one of the object to be measured or at least a part of the measurement device, by applying the measurement data to a recursive formula based on a time derivative of a measurement result of the measurement device.

[0033] Effects of Invention

[0034] According to the present disclosure, it is possible to easily measure a three-dimensional geometry of an object to be measured with an optical range finder while suppressing a decrease in measurement accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 A configuration example of a measurement system 1000 and an object to be measured 10 according to the present embodiment is shown.

[0036] Figure 2 A configuration example of a measurement device 100 and a data correction device 400 according to the present embodiment is shown.

[0037] Figure 3 A configuration example of a laser device 110 according to the present embodiment is shown.

[0038] Figure 4 An example of a laser beam output from the laser device 110 according to the present embodiment is shown. DETAILED DESCRIPTION

[0039] [Configuration example of measurement system 1000]

[0040] Figure 1 A configuration example of a measurement system 1000 and an object to be measured 10 according to the present embodiment is shown. The measurement system 1000 measures a three-dimensional geometry of the object to be measured 10 while suppressing a decrease in measurement accuracy due to Doppler shift. The measurement system 1000 includes a measurement device 100 and a data correction device 400.

[0041] The measurement device 100 optically measures a distance from a reference position to the object to be measured 10. The measurement device 100 is a device capable of measuring a three-dimensional geometry of the object to be measured 10 by periodically measuring the distance while moving at least one of (i) the object to be measured 10 or (ii) at least a part of the measurement device 100. Here, the reference position is, for example, a position inside the measurement device 100. As an example, the reference position is a laser beam exit end of an optical head member 140 that irradiates a laser beam onto the object to be measured 10 to measure the distance.

[0042] For example, the measurement device 100 moves the optical head member 140 so that the optical head member 140 scans a position of the surface of the object to be measured 10 irradiated with the laser beam. In this case, it is preferable that the optical head member 140 be disposed so that it is movable in parallel with the object to be measured 10.

[0043] The optical head member 140 is, for example, movable in an X direction, a Y direction, and a Z direction orthogonal to each other. Further, the optical head member 140 is rotatably disposed so as to be rotatable around at least one of the X direction, the Y direction, and the Z direction as an axis. Alternatively or additionally, the optical head member 140 can scan a position of the object to be measured 10 irradiated with the laser beam by moving optical components such as a mirror, a lens, and the like.

[0044] Alternatively or additionally, the measurement device 100 can be configured to be movable. In this case, the measurement device 100 further includes a device stage on which the measurement device 100 is mounted, and a position of the object to be measured 10 irradiated with the laser beam is scanned by moving the device stage. The device stage moves the measurement device 100, for example, in the X direction, the Y direction, and the Z direction. Further, the device stage can rotate the measurement device 100 around at least one of the X direction, the Y direction, and the Z direction as an axis.

[0045] Alternatively or additionally, the object to be measured 10 can be movable. In this case, the measurement device 100 further includes a stage on which the object to be measured 10 is mounted, and a position of the object to be measured 10 irradiated with the laser beam is scanned by moving the stage. The stage moves the object to be measured 10, for example, in the X direction, the Y direction, and the Z direction. Further, the stage can rotate around at least one of the X direction, the Y direction, and the Z direction as an axis.

[0046] As described above, the measurement device 100 measures a three-dimensional geometry of the object to be measured 10 by moving at least one of (i) the object to be measured 10 or (ii) at least a part of the measurement device 100 and continuing to measure the distance while scanning a position of the object to be measured 10 irradiated with the laser beam. Then, the data correction device 400 corrects the measurement result of the measurement device 100. Next, the measurement device 100 and the data correction device 400 are described in detail.

[0047] [Configuration example of measurement device 100]

[0048] Figure 2 A configuration example of a measurement device 100 and a data correction device 400 according to the present embodiment is shown. The measurement device 100 includes a laser device 110, a branching member 120, an optical circulator 130, an optical head member 140, a beat signal generating member 150, a frequency analysis member 160, a calculation member 170, a display member 180, and a control member 190.

[0049] The laser device 110 has an optical cavity (laser resonator) and outputs a frequency-modulated laser beam having a plurality of modes. The laser device 110 is provided with a frequency shifter in the cavity (resonator) and outputs a plurality of longitudinal mode lasers whose oscillation frequencies linearly change over time. The laser device 110 is, for example, a frequency-shifted feedback laser (FSFL). The FSFL will be described later.

[0050] The branching member 120 divides the frequency-modulated laser beam output from the laser device 110 into (i) reference light, which is a portion of the frequency-modulated laser beam, and (ii) measurement light, which is at least some of the remaining portion of the frequency-modulated laser beam. The branching member 120 is, for example, an in-out optical fiber coupler. In Figure 2 In the example, the branching member 120 supplies the measurement light to the optical circulator 130 and supplies the reference light to the beat signal generating member 150.

[0051] The optical circulator 130 has a plurality of input / output ports. For example, the optical circulator 130 outputs light input from one port to the next port and also outputs light input from the next port to the next-but-one port. Figure 2 An example in which the optical circulator 130 has three input / output ports is shown. In this case, the optical circulator 130 outputs the measurement light supplied from the branching member 120 to the optical head member 140. In addition, the optical circulator 130 outputs light input from the optical head member 140 to the beat signal generating member 150.

[0052] The optical head member 140 irradiates light input from the optical circulator 130 toward the object 10 to be measured. The optical head member 140 includes, for example, a collimator lens. In this case, the optical head member 140 first adjusts the light input from the optical circulator 130 via an optical fiber into a beam shape using the collimator lens and then outputs the light.

[0053] Further, the optical head member 140 receives reflected light of the measurement light that is irradiated onto the object 10 to be measured. The optical head member 140 focuses the received reflected light on the optical fiber with a collimator lens and supplies it to the optical circulator 130. In this case, the optical head member 140 can include one common collimator lens, and the collimator lens can irradiate the object 10 to be measured with the measurement light and receive the reflected light from the object 10 to be measured. The distance between the optical head member 140 and the object 10 to be measured is defined as L.

[0054] Alternatively, the optical head member 140 can include a focusing lens. In this case, the optical head member 140 focuses the light input from the optical circulator 130 via the optical fiber on the surface of the object 10 to be measured. The optical head member 140 receives at least a part of the reflected light that is reflected on the surface of the object 10 to be measured. The optical head member 140 focuses the received reflected light on the optical fiber with the focusing lens and supplies it to the optical circulator 130. Also in this case, the optical head member 140 can include one common focusing lens, and the focusing lens can irradiate the object 10 to be measured with the measurement light and receive the reflected light from the object 10 to be measured.

[0055] The beat signal generating member 150 receives the reflected light that is reflected by irradiating the measurement light onto the object 10 to be measured from the optical circulator 130. Further, the beat signal generating member 150 receives the reference light from the branching member 120. The beat signal generating member 150 includes an optical coupler or the like and mixes the reflected light and the reference light to generate a beat signal. For example, the beat signal generating member 150 includes a photoelectric conversion element, converts the beat signal into an electric signal, and outputs the electric signal. The beat signal generating member 150 can also perform quadrature detection on the reflected light and the reference light.

[0056] Here, since the reflected light travels back and forth over the distance from the optical head member 140 to the object 10 to be measured, a difference in the propagation distance corresponding to at least the distance 2L occurs compared to the reference light. Since the oscillation frequency of the light output from the laser device 110 changes linearly over time, a frequency difference depending on the propagation delay corresponding to the difference in the propagation distance occurs between the oscillation frequency of the reference light and the oscillation frequency of the reflected light. The beat signal generating member 150 generates a beat signal corresponding to such a frequency difference.

[0057] The frequency analysis section 160 performs frequency analysis on the beat signal generated by the beat signal generation section 150. For example, the frequency analysis section 160 converts the beat signal into a digital signal, and converts the converted digital signal into a frequency signal. Then, the frequency analysis section 160 detects the frequency of the beat signal by analyzing the frequency signal generated by converting the beat signal into a frequency domain signal. For example, the frequency analysis section 160 detects the peak frequency of the beat signal. Here, the frequency of the beat signal is defined as v B .

[0058] The calculation section 170 calculates the difference in the propagation distance between the reference light and the measurement light, based on the result of the frequency analysis performed by the frequency analysis section 160 on the beat signal. The calculation section 170 calculates the distance L from the optical head section 140 to the object 10 to be measured, based on the frequency v B of the beat signal.

[0059] The display section 180 displays the result of the calculation by the calculation section 170. The display section 180 can include a display or the like, and display the calculation result. In addition, the display section 180 can store the calculation result in a storage section or the like. The display section 180 can provide the calculation result to an external device via a network or the like.

[0060] The control section 190 controls each section of the measurement device 100. For example, the control section 190 controls the laser device 110 to output the frequency-modulated laser beam. In addition, the control section 190 controls the frequency analysis section 160 and the calculation section 170 to calculate the distance L from the optical head section 140 to the object 10 to be measured. The control section 190 can control the display section 180 to display the calculation result of the distance L. The control section 190 can transmit the measurement data to the data correction device 400 and receive the measurement data from the data correction device 400. For example, the control section 190 provides the measurement data to the data correction device 400. The control section 190 also receives the measurement data corrected by the data correction device 400.

[0061] Preferably, at least a part of the frequency analysis section 160, the calculation section 170, and the control section 190 is formed of an integrated circuit or the like. At least a part of the frequency analysis section 160, the calculation section 170, and the control section 190 includes, for example, a field programmable gate array (FPGA), a digital signal processor (DSP), and / or a central processing unit (CPU). In addition, the frequency analysis section 160, the calculation section 170, and the control section 190 can be integrally formed. Such a control section 190 has a storage section.

[0062] The storage section can store intermediate data, calculation results, setting values, threshold values, parameters, and the like generated or used in the operation of the frequency analysis section 160, the calculation section 170, and the control section 190. The storage section can provide the stored data to the request source in response to a request from each section of the measurement device 100.

[0063] When a CPU or the like operates as at least a part of the frequency analysis section 160, the calculation section 170, and the control section 190, the storage section can store an operating system (OS) and various information, such as a program that functions as the frequency analysis section 160, the calculation section 170, and the control section 190. Further, the storage section can store various types of information, including a database to be referred to when a program is executed. For example, a computer functions as the frequency analysis section 160, the calculation section 170, and the control section 190 by executing a program stored in the storage section.

[0064] The storage section includes, for example, a read only memory (ROM) that stores a basic input output system (BIOS) of a computer or the like, and a random access memory (RAM) that functions as a work area. The storage section can include a large capacity storage device such as a hard disk drive (HDD) and / or a solid state drive (SSD). Further, the computer can also include a graphics processing unit (GPU) or the like.

[0065] The measurement device 100 described above can measure the distance L between the measurement device 100 and the object 10 to be measured by analyzing a frequency difference between reflected light and reference light of measurement light irradiated onto the object 10 to be measured. That is, the measurement device 100 can form a non-contact and non-destructive optical range finder.

[0066] [Configuration example of laser device 110]

[0067] Figure 3 A configuration example of the laser device 110 according to the present embodiment is shown. Figure 3 The laser device 110 of FIG. 1 shows an example of an FSFL. The laser device 110 includes an optical cavity, and oscillates a laser beam in the optical cavity. The optical cavity of the laser device 110 includes a frequency shifter 112, a gain medium 114, a WDM coupler 116, a pump light source 117, and an output coupler 118.

[0068] The frequency shifter 112 shifts the frequency of the input light by an approximately constant frequency. The frequency shifter 112 is, for example, an acousto-optic frequency shifter (AOFS) having an acousto-optic element. Here, the frequency shift amount of the frequency shifter 112 is defined as +v s . That is, the frequency shifter 112 shifts the frequency of the light circulating around the cavity so that the frequency increases v s for each round.

[0069] The gain medium 114 is provided with pump light, and the gain medium 114 amplifies the input light. The gain medium 114 is, for example, an optical fiber doped with impurities. The impurities are, for example, rare earth elements such as erbium, neodymium, ytterbium, terbium, thulium, or the like. The pump light is provided to the gain medium 114 from a pump light source 117 via a WDM coupler 116. An output coupler 118 outputs a part of the light that has been laser oscillated in the cavity to an external device.

[0070] That is, Figure 3 The laser device 110 shown includes a fiber ring laser having the frequency shifter 112 in the cavity. The laser device 110 preferably further includes an isolator in the cavity. Also, the laser device 110 can have an optical bandpass filter that passes light of a predetermined wavelength band in the cavity. The frequency characteristics of the laser beam output from the laser device 110 are described below.

[0071] Figure 4 An example of the laser beam output from the laser device 110 according to the present embodiment is shown. Figure 4 The spectrum of the laser beam output from the laser device 110 at time t0is shown on the left. In this spectrum, the horizontal axis represents the light intensity, and the vertical axis represents the frequency of the light. Also, a plurality of longitudinal modes of the spectrum are represented by the number q. The frequencies of the plurality of longitudinal modes are arranged at an approximately constant frequency interval. Assuming that τ RT (=1 / v C ) represents the time for the light to travel around the cavity once, the plurality of longitudinal modes are arranged at an interval of 1 / τ RT (=v C ), as shown in the following equation. Note that v0is the initial frequency of the spectrum at time t0. Also, v C is the cavity frequency (resonator frequency) v C of the optical cavity.

[0072] [Equation 1]

[0073]

[0074] Figure 4 The frequency change of the multiple longitudinal modes output from the laser device 110 over time is shown on the right side. In Figure 4 the right side, the horizontal axis represents time, and the vertical axis represents frequency. That is, Figure 4 The frequency change of the laser beam output from the laser device 110 over time is shown on the right side, and the instantaneous frequency of the laser beam at time t0 is shown on the left side.

[0075] In the laser device 110, the frequency of the light traveling around the cavity is increased by v s by the frequency shifter 112 each time the light in the cavity propagates around the cavity. RT Since the frequency of each mode is increased by v s every time t s passes, the rate of change of the frequency dν / dt (i.e., the frequency modulation rate) becomes approximately equal to v RT / t q' . Therefore, the multiple longitudinal modes represented by Equation 1 change over time t to be as shown in the following equation.

[0076] [Equation 2]

[0077]

[0078] [Details of the distance measurement process]

[0079] The measurement device 100 according to the present embodiment measures the distance L between the optical head member 140 and the object to be measured 10 by using the laser device 110 that outputs the frequency element represented by Equation 2. It is assumed that the optical path difference between the reference light and the reflected light is only the distance 2L, i.e., the distance L to and fro, and the propagation delay corresponding to the distance 2L is At. That is, when the measurement light is reflected and returned from the object to be measured 10 at time t, the frequency of the returned reflected light approximately matches the past frequency at time t - At, and thus can be represented by the following equation.

[0080] [Equation 3]

[0081]

[0082] On the other hand, the reference light at time t, which is v q' (t), can be represented by the following equation in a similar manner to Equation 2.

[0083] [Equation 4]

[0084]

[0085] Because the beat signal generating part 150 superimposes the reflected light and the reference light, a plurality of beat signals is generated between the plurality of longitudinal modes represented by Equation 3 and the plurality of longitudinal modes represented by Equation 4. Assuming that the frequency of such a beat signal is v B , v B can be represented by the following equation according to Equation 3 and Equation 4. Note that M is the difference of the number of longitudinal modes (= q - q'), At = 2L / c, c = c0 / n, and 1 / τ ＲＴ = v C . Incidentally, γ (= v S• v C ) is a parameter based on the rate of change of the frequency per unit time of the frequency-modulated laser beam, and is called the frequency modulation rate. Furthermore, n is the refractive index of air, and c0is the speed of light in vacuum. For simplicity, the case where M = 0 is described below.

[0086] [Equation 5]

[0087]

[0088] According to Equation 5, the distance L is represented by the following equation.

[0089] [Equation 6]

[0090]

[0091] As is clear from Equation 6, the distance L can be calculated from the observation of the frequency v of the beat signal. When the difference M is not 0, when the amount of frequency shift v s of the laser device 110 is changed, the value of M can be identified by detecting the change in the beat signal, thereby calculating the distance L. Because such a method of determining the difference M is known as described in Patent Literature 1 and the like, detailed description thereof is omitted.

[0092] As described above, the measurement device 100 can measure the distance L from the optical head part 140 to the object to be measured 10. Furthermore, the measurement device 100 can calculate and output the distance from the reference position to the object to be measured 10 by adding the offset value corresponding to the reference position to the distance L.

[0093] The three-dimensional geometry of the object to be measured 10 can be measured using such a measurement device as described above. However, because the laser beam has a wave-like property, the Doppler shift occurs due to the relative velocity between the optical head part 140 and the object to be measured 10, and the frequency of the reflected light reflected from the object to be measured 10 can change. In this case, when the frequency of the reflected light changes, a decrease in measurement accuracy occurs because, as described above, the measurement device 100 measures the distance based on the frequency difference between the reference light and the reflected light.

[0094] In general, the Doppler shift amount v of the light frequency D is represented by the following equation, where V is the relative speed between the light source and the observer, and the direction in which the light source and the observer move toward each other is positive. λ is the wavelength of the light.

[0095] [Equation 7]

[0096]

[0097] Because the measurement device 100 reciprocally moves FSFL between the optical head member 140 and the object 10 to be measured, the Doppler shift amount v of the frequency of the reflected light D is represented by the following equation.

[0098] [Equation 8]

[0099]

[0100] Assuming that the beat frequency v when the Doppler shift occurs is B , then v B is represented by the following equation.

[0101] [Equation 9]

[0102]

[0103] Here, by substituting Equation 6 and Equation 8 into Equation 9, the following equation is obtained by simplification. Here, L' shows the measurement result when the measurement device 100 is affected by the Doppler shift, and k = 2c0 / λnγ.

[0104] [Equation 10]

[0105]

[0106] As described above, when the distance measurement by the measurement device 100 is performed by moving at least one of (i) the object 10 to be measured or (ii) at least a part of the measurement device 100, it can be seen that the measurement result includes an error based on the Doppler shift. In order to reduce such an error, it can be conceivable to detect the moving speed of the object 10 to be measured, at least a part of the measurement device 100, or the like, and calculate and correct the Doppler shift amount based on the detection result. However, further installation of a speed meter or the like in the measurement device 100 can cause an increase in cost and an increase in the size of the device.

[0107] [Configuration example of data correction device 400]

[0108] Accordingly, the data correction device 400 according to the present embodiment corrects the error based on the Doppler shift included in the measurement result of the measurement device 100 without using the measurement result of the speed system. The data correction device 400 is, for example, incorporated into the measurement device 100 and formed integrally with the measurement device 100. In this case, preferably, the data correction device 400 is formed of an integrated circuit or the like in a similar manner to the control means 190 or the like. Further, the data correction device 400 can be formed integrally with the control means 190 or the like. In this case, for example, the measurement device 100 functions as the calculation means 170, the control means 190, and the data correction device 400 by executing a program stored in a storage means of the measurement device 100.

[0109] Alternatively, the data correction device 400 can be a device independent of the measurement device 100. In this case, preferably, the data correction device 400 is formed of a computer having a processor. As shown in FIG. 6, the data correction device 400 includes an acquisition means 410, a storage means 420, and a correction means 430. Figure 1

[0110] The acquisition means 410 acquires measurement data obtained by the measurement device 100 by periodically measuring a distance from a reference position to the object to be measured 10 while moving at least one of (i) the object to be measured 10 or (ii) at least a part of the measurement device 100. It should be noted that the time interval at which the measurement device 100 measures the distance is Δt. Further, the measurement result of the distance output by the measurement device 100 should be a first measurement result during a measurement time period including a time period in which the measurement device 100 has moved the relative position of the measurement device 100 and the object to be measured 10.

[0111] Here, at least one of (i) the data of the head of the measurement data or (ii) the data of the tail of the measurement data acquired by the acquisition means 410 is data indicating the result of measuring the distance when the object to be measured 10 and the measurement device 100 are in a stationary state. The result of the measurement device 100 measuring the distance when the object to be measured 10 and the measurement device 100 are in the stationary state should be a second measurement result. Then, the acquisition means 410 acquires the measurement data in which the first measurement result is arranged in a time series and the second measurement result is arranged at the head or the tail of the first measurement result.

[0112] ​In other words, the measurement device 100 generates measurement data in which first measurement results obtained by measuring the distance periodically while moving at least one of (i) the object 10 to be measured or (ii) the measurement device 100 are arranged in a time series, and second measurement results obtained by measuring the distance when the object 10 to be measured and the measurement device 100 are in a stationary state are arranged at the head or tail of the first measurement results. The acquisition section 410 can acquire such measurement data from the measurement device 100, or alternatively, from an external database or the like. The acquisition section 410 is preferably connected to the database via a network.

[0113] The storage section 420 stores at least some of intermediate data, calculation results, set values, threshold values, parameters, and the like generated or used in the operation process of the data correction device 400. The storage section 420 stores, for example, the measurement data acquired by the acquisition section 410. The storage section 420 can provide the stored data to the source of the request in response to a request from each section of the data correction device 400.

[0114] When a CPU or the like operates as at least a part of the acquisition section 410 and the correction section 430, the storage section 420 can store an operating system (OS) and various information, such as a program that functions as the acquisition section 410 and the correction section 430. The storage section 420 can also store various types of information, including a database to be referred to when executing a program. For example, a computer functions as the acquisition section 410 and the correction section 430 by executing a program stored in the storage section 420.

[0115] The storage section 420 includes, for example, a read-only memory (ROM) that stores a basic input / output system (BIOS) of a computer or the like, and a random access memory (RAM) that functions as a work area. The storage section 420 can include a large-capacity storage device, such as a hard disk drive (HDD) and / or a solid state drive (SSD). Furthermore, the computer can also include a graphics processing unit (GPU) or the like. The storage section 420 can have at least a part of the functions of the storage section of the measurement device 100. For example, when the measurement device 100 and the data correction device 400 are integrally formed, preferably, the storage section 420 operates as the storage section of the measurement device 100.

[0116] [Examples of error correction by the correction section 430]

[0117] The correction section 430 applies the measurement data acquired by the acquisition section 410 to a recursive formula to correct an error included in the measurement data, which is based on movement of at least one of (i) the object 10 to be measured or (ii) at least a part of the measurement device 100. The predetermined recursive formula used by the correction section 430 is described below. In general, a derivative of a function f(x) with respect to x can be approximated by a forward difference method as in the following equation.

[0118] [Equation 11]

[0119]

[0120] A derivative of the function f(x) with respect to x can also be approximated by a backward difference method as in the following equation.

[0121] [Equation 12]

[0122]

[0123] By using Equation 11, the time differential data dL n / dΔt, i.e., the measurement data L n is represented by the following equation.

[0124] [Equation 13]

[0125]

[0126] Similarly, by using Equation 12, the time differential data dL n / dΔt is represented by the following equation.

[0127] [Equation 14]

[0128]

[0129] By substituting Equation 13 into Equation 10 and substituting Equation 14 into Equation 10, the following equation is obtained.

[0130] [Equation 15]

[0131]

[0132] [Equation 16]

[0133]

[0134] Here, when the frequency modulation γ > 0, the following equation is obtained by simplifying Equations 15 and 16 because s = k / Δt. It should be noted that Equation 18 shows a result of using a substitution of n → n+1.

[0135] [Equation 17]

[0136]

[0137] [Equation 18]

[0138]

[0139] The correction section 430 corrects the error included in the measurement data using a recursive formula as shown in Equations 17 and 18 based on the time derivative of the measurement result of the measurement device 100. The recursive formula shown in Equations 17 and 18 is an equation for correcting the measurement data L n+1 n of the nth distance using the measurement data Lof the n+1th distance. In order to correct a certain piece of measurement data, the next piece of measurement data is used, and therefore, preferably, at least the last piece of measurement data among the measurement data is a second measurement result obtained by measuring the distance when the object to be measured 10 and the measurement device 100 are in a stationary state.

[0140] In other words, when the frequency modulation rate γ is positive, the acquisition section 410 acquires measurement data in which the second measurement result is arranged at the tail of the first measurement result, and the correction section 430 corrects the measurement data arranged in the time series acquired by the acquisition section 410 using a recursive formula that corrects the measurement data in the reverse order of the arrangement in the time series. In this case, the data correction device 400 corrects the measurement data after the measurement device 100 generates all of the measurement data.

[0141] The following equation shows a more specific example when the correction section 430 corrects the measurement data by using Equation 17 as a recursive formula. L n ' of the following equation shows an example of the second measurement result.

[0142] [Equation 19]

[0143]

[0144] As described above, the data correction device 400 according to the present embodiment can reduce the error based on the Doppler shift by applying the measurement data to a predetermined recursive formula. Therefore, the data correction device 400 can easily reduce the error without using a speedometer or the like. Needless to say, the first measurement result can include a measurement result of measuring the distance when the object to be measured 10 and the measurement device 100 are in a stationary state, a measurement result when the direction of the relative velocity of the object to be measured 10 and the measurement device 100 changes, or the like.

[0145] In the above-described data correction device, an example in which the frequency modulation γ is positive has been described, but the present embodiment is not limited thereto. For example, when the frequency modulation γ is negative (γ < 0), by simplifying each of Equations 15 and 16, the following Equations can be obtained, because s = -k / Δt. It should be noted that Equation 20 shows a result of using a substitution of n → n-1.

[0146] [Equation 20]

[0147]

[0148] [Equation 21]

[0149]

[0150] The correction section 430 corrects the error included in the measurement data using the recursive formula as in Equations 20 and 21 based on the time derivative of the measurement result of the measurement device 100. In this way, the correction section 430 uses different recursive formulas according to the positive or negative sign of the frequency modulation of the frequency-modulated laser beam used by the measurement device 100. The recursive formulas shown in Equations 20 and 21 are equations for correcting the measurement data Ln at the nth distance using the measurement data Ln-1 at the n-1th distance. n-1 n To correct a certain piece of measurement data, the previous measurement data is used, and therefore, it is preferable that at least the first piece of measurement data among the measurement data is a second measurement result obtained by measuring the distance when the object to be measured 10 and the measurement device 100 are in a stationary state.

[0151] In other words, when the frequency modulation γ is negative, the acquisition section 410 acquires measurement data in which the second measurement result is arranged at the head of the first measurement result, and the correction section 430 uses a recursive formula that corrects the measurement data arranged in the time series acquired by the acquisition section 410 in order of the arrangement of the time series. In this case, for example, the data correction device 400 corrects the measurement data after the measurement device 100 generates all of the measurement data.

[0152] Alternatively, the measurement device 100 can generate the measurement result while measuring the distance, and the data correction device 400 can acquire and sequentially correct the measurement result generated by the measurement device 100. In this way, since the data correction device 400 can sequentially correct the measurement result while the measurement device 100 performs distance measurement multiple times, it is possible to reduce the time between the start of measurement and the output of the corrected result.

[0153] The following Equations show a more specific example when the correction section 430 corrects the measurement data using Equation 21 as the recursive formula. L1' of the following Equations shows an example of the second measurement result.​

[0154] [Equation 22]

[0155]

[0156] The data correction apparatus 400 according to this embodiment has been described using time-differential data dL. n An example of the recursive formula for / dΔt (as shown in Equations 13 and 14) is provided, but this embodiment is not limited thereto. The data correction device 400 can use a difference method with m-th order accuracy to improve the accuracy of the time differential data dL. n The accuracy of the approximation of / dΔt. The difference method with the m-th order accuracy approximates the derivative of the function f(x) with respect to x as follows.

[0157] [Equation 23]

[0158]

[0159] or

[0160] [Equation 24]

[0161]

[0162] coefficients (a0, a1, …, a m , The combination of (b) is well known; for example, when m = 2, it is (-3, 4, -1, 2). The correction component 430 can more accurately correct the error caused by the Doppler frequency shift by using recursive formulas based on Equations 23 and 24. As mentioned above, the recursive formulas based on Equation 23 and Equation 24 are different recursive formulas based on the positive and negative signs of the modulation frequency γ.

[0163] For example, when the modulation frequency γ is positive, the corresponding recursive formula is expressed as the following equation obtained by simplifying equation 23 into equation 10. Here, s = k / Δt.

[0164] [Equation 25]

[0165]

[0166] Furthermore, when the modulation frequency γ is negative, the corresponding recursive formula is expressed as the following equation obtained by simplifying equation 24 into equation 10. Here, s = k / Δt.

[0167] [Equation 26]

[0168]

[0169] When the differential method with the mth order accuracy is used, the acquisition part 410 acquires measurement data in which the second measurement result is shown as the second data, which is m pieces of data from the head of the measurement data or m pieces of data from the tail of the measurement data. For example, when the object to be measured 10 and the measurement device 100 are in a stationary state, the measurement device 100 measures the distance m times to generate measurement data in which m pieces of second data are arranged at the head or the tail of the first measurement result. Then, the acquisition part 410 acquires such measurement data.

[0170] More specifically, when the frequency modulation γ is positive, the acquisition part 410 acquires measurement data in which m pieces of second data are arranged at the tail of the first measurement result, and the correction part 430 uses a recurrence formula that corrects the measurement data arranged in the time series acquired by the acquisition part 410 in the reverse order of the arranged time series. Further, when the frequency modulation γ is negative, the acquisition part 410 acquires measurement data in which m pieces of second data are arranged at the head of the first measurement result, and the correction part 430 uses a recurrence formula that corrects the measurement data arranged in the time series acquired by the acquisition part 410 in the order of the arranged time series.

[0171] The following equation shows a more specific example when the correction part 430 corrects the measurement data using Equation 25 as the recurrence formula. It should be noted that, in the following equation, m = 2, and L1' and L2' of the following equation each show an example of the second measurement result. n ' and L n-1 ' each show an example of the second measurement result.

[0172] [Equation 27]

[0173]

[0174] The following equation shows a more specific example when the correction part 430 corrects the measurement data using Equation 26 as the recurrence formula. It should be noted that, in the following equation, m = 2, and L1' and L2' of the following equation each show an example of the second measurement result.

[0175] [Equation 28]

[0176]

[0177] By the way, when the object 10 and the measurement device 100 are in a stationary state, the measurement device 100 can generate measurement data including m' pieces of second data by measuring the distance m' times (m' is smaller than m (0 < m' < m)). In this case, the acquisition section 410 only copies the data included in the m' pieces of second data m - m' times, and generates measurement data in which, for example, a total of m pieces of data are arranged at the head or the tail of the first measurement result.

[0178] Here, an example in which the measurement device 100 generates measurement data in which one piece of second data is arranged at the tail of the first measurement result including p pieces of first data will be described. In this case, the control section 190 can notify the acquisition section 410 that one piece of second data is arranged at the tail of the measurement data. The acquisition section 410 acquires measurement data including 1 + p pieces of data from the measurement device 100, only copies one piece of second data at the tail four times, and generates measurement data including 5 + p pieces of data in which a total of five pieces of second data are arranged at the tail of the first measurement result.

[0179] By so doing, when m = 5, the correction section 430 can correct the error included in the p pieces of first data by applying the measurement data including (i) m (=5) pieces of second data and (ii) p pieces of first data in the first measurement result to the recursive formula represented by Equation 25. In other words, even if the measurement device 100 does not increase the number of pieces of second data included in the second measurement result to two or more, by copying the second data, the data correction device 400 can further increase the accuracy of the correction using the differential method with the mth order accuracy.

[0180] The correction section 430 supplies the corrected measurement data to the measurement device 100. The measurement device 100 displays the corrected measurement data on the display section 180. Further, the data correction device 400 can also include a display device to display the corrected measurement data.

[0181] The present disclosure is explained based on exemplary embodiments. The technical scope of the present disclosure is not limited to the scope explained in the above-described embodiments, and various changes and modifications can be made within the scope of the present invention. For example, all or a part of the apparatuses can be configured with any functionally or physically distributed or integrated units. Further, new exemplary embodiments generated by any combination thereof are included in the exemplary embodiments of the present disclosure. Further, the effects of the new embodiments brought by the combination also have the effects of the original exemplary embodiments together.

[0182] [Description of reference numerals]

[0183] 10 object

[0184] 100 measurement device

[0185] 110 laser device

[0186] 112 frequency shifter

[0187] 114 gain medium

[0188] 116 WDM coupler

[0189] 117 pump light source

[0190] 118 output coupler

[0191] 120 branching member

[0192] 130 optical circulator

[0193] 140 optical head member

[0194] 150 beat signal generating member

[0195] 160 frequency analyzing member

[0196] 170 calculating member

[0197] 180 display member

[0198] 190 control member

[0199] 400 data correction device

[0200] 410 acquisition member

[0201] 420 storage member

[0202] 430 correction member

[0203] 1000 measurement system

Claims

1. A data correction apparatus comprising: an acquisition section that acquires measurement data from a measurement apparatus that measures a distance from a reference position to an object to be measured using a frequency-modulated laser beam and is capable of periodically measuring the distance while at least one of moving the object to be measured or at least a part of the measurement apparatus, in the measurement data, first measurement results of the distance are arranged in a time series, and second measurement results obtained by the measurement apparatus measuring the distance while the object to be measured and the measurement apparatus are in a stationary state are arranged at a head or a tail of the first measurement results; and a correction section that corrects an error included in the measurement data acquired by the acquisition section, the error being based on the movement of at least one of the object to be measured or at least a part of the measurement apparatus, by applying the measurement data to a recurrence formula based on a time derivative of a measurement result of the measurement apparatus, wherein the correction section uses different recurrence formulas according to positive and negative signs of a frequency modulation rate based on a rate of change of a frequency per unit time of the frequency-modulated laser beam used by the measurement apparatus, wherein when the frequency modulation rate is negative, the acquisition section acquires measurement data in which the second measurement results are arranged at a head of the first measurement results, and the correction section uses a recurrence formula that corrects the measurement data arranged in the time series acquired by the acquisition section, the correction being performed in order of the arranged time series, wherein the correction section uses, as the recurrence formula, a first recurrence formula represented by an equation or a second recurrence formula represented by an equation , wherein L n is the n-th measurement including an error caused by Doppler shift, L n is the n-th measurement corrected for said error caused by Doppler shift, L n-1 is the n-1 -th measurement including an error caused by Doppler shift, L n-1 is the n-1 -th measurement corrected for said error caused by Doppler shift, s = k / At, At is the time interval in which said measuring device measures said distance, k = 2co / A N y, co is the speed of light in vacuum, A is the wavelength of said frequency-modulated laser beam, N is the refractive index of air, and y is said frequency modulation.

2. The data correction apparatus according to claim 1, wherein each time the measurement apparatus measures the distance, the acquisition section acquires the measurement data, and the correction section starts correcting the measurement data acquired by the acquisition section to sequentially correct the measurement data while the measurement apparatus continues measuring the distance.

3. A data correction apparatus comprising: an acquisition section that acquires measurement data from a measurement apparatus that measures a distance from a reference position to an object to be measured using a frequency-modulated laser beam and is capable of periodically measuring the distance while at least one of moving the object to be measured or at least a part of the measurement apparatus, in the measurement data, first measurement results of the distance are arranged in a time series, and second measurement results obtained by the measurement apparatus measuring the distance while the object to be measured and the measurement apparatus are in a stationary state are arranged at a head or a tail of the first measurement results; and a correction section that corrects an error included in the measurement data acquired by the acquisition section, the error being based on the movement of at least one of the object to be measured or at least a part of the measurement apparatus, by applying the measurement data to a recurrence formula based on a time derivative of a measurement result of the measurement apparatus, wherein the correction section uses different recursive formulas according to positive and negative signs of a frequency modulation rate based on a rate of change of frequency per unit time of the frequency-modulated laser beam used by the measurement device, wherein when the frequency modulation rate is negative, the acquisition section acquires measurement data in which the second measurement result is arranged at a head of the first measurement result, and the correction section uses a recursive formula that corrects measurement data acquired by the acquisition section arranged in a time series, the correction being performed in an order of the arranged time series, wherein the correction section uses a third recursive formula represented by the following equation as the recursive formula wherein L n is the nth measurement including an error caused by a Doppler shift, L n is the nth measurement corrected for the error caused by the Doppler shift, L n-i is the nth-i measurement corrected for the error caused by the Doppler shift, s = k / At, At is a time interval in which the measuring device measures the distance, k = 2co / A N y, co is the speed of light in a vacuum, A is a wavelength of the frequency-modulated laser beam, N is a refractive index of air, y is the frequency modulation, and the coefficients a0, a i , b are coefficients for approximating the time differential data of the measurement data as time differential data using a difference method having an accuracy of the mth order.

4. The data correction device according to claim 3, wherein each time the measurement device measures the distance, the acquisition section acquires the measurement data, and the correction section starts correcting the measurement data acquired by the acquisition section while the measurement device continues measuring the distance, to sequentially correct the measurement data.

5. A data correction device comprising: an acquisition section that acquires measurement data from a measurement device that measures a distance from a reference position to an object to be measured using a frequency-modulated laser beam and is capable of periodically measuring the distance while at least one of moving the object to be measured or at least a part of the measurement device, in the measurement data, a first measurement result of the distance is arranged in a time series, and a second measurement result obtained by the measurement device measuring the distance while the object to be measured and the measurement device are in a stationary state is arranged at a head or a tail of the first measurement result; and a correction section that corrects an error included in the measurement data acquired by the acquisition section, the error being based on movement of at least one of the object to be measured or at least a part of the measurement device, by applying the measurement data to a recursive formula based on a time derivative of a measurement result of the measurement device, wherein the correction section uses different recursive formulas according to positive and negative signs of a frequency modulation rate based on a rate of change of frequency per unit time of the frequency-modulated laser beam used by the measurement device, wherein when the frequency modulation rate is positive, the acquisition section acquires measurement data in which the second measurement result is arranged at a tail of the first measurement result, and the correction section uses a recursive formula that corrects the measurement data acquired by the acquisition section arranged in a time series, the correction being performed in a reverse order of the arranged time series, wherein the correction section uses a fourth recursive formula represented by the following equation as the recursive formula or a fifth recursive formula represented by the following equation as the recursive formula where L n is the n-th measurement including the error caused by the Doppler shift, L n is the n-th measurement corrected for the error caused by the Doppler shift, L n+1 is the n+1 -th measurement including the error caused by the Doppler shift, L n+1 is the n+1 -th measurement corrected for the error caused by the Doppler shift, s = k / At, At is the time interval in which the measuring device measures the distance, k = 2co / A N y, co is the speed of light in vacuum, A is the wavelength of the frequency-modulated laser beam, N is the refractive index of air, and y is the frequency modulation.

6. The data correction device according to claim 5, wherein the acquisition section acquires measurement data in which the second measurement result obtained by measuring the distance while the object to be measured and the measurement device are in a stationary state is arranged as m pieces of second data from a head or m pieces of second data from a tail, and The correction section corrects errors included in p pieces of first data by applying the measurement data to the recursive formula, the measurement data including m pieces of second data and the p pieces of first data included in the first measurement result.

7. The data correction apparatus according to claim 6, wherein the acquisition section further acquires information on m' from the measurement apparatus, the m' being the number of pieces of data of the second measurement result included in the measurement data, and the correction section corrects errors of the measurement data only m - m' times of copying of data of the second measurement result, and then when m' is smaller than the order m of a difference method having an accuracy of the m-th order, m' being the number of pieces of data of the second measurement result included in the measurement data.

8. A data correction apparatus comprising: an acquisition section that acquires measurement data from a measurement apparatus that measures a distance from a reference position to an object to be measured using a frequency-modulated laser beam and is capable of periodically measuring the distance while at least one of moving the object to be measured or at least a part of the measurement apparatus, in the measurement data, a first measurement result of the distance is arranged in a time series, and a second measurement result obtained by measuring the distance while the object to be measured and the measurement apparatus are in a stationary state is arranged at a head or a tail of the first measurement result; and a correction section that corrects errors included in the measurement data by applying the measurement data acquired by the acquisition section to a recursive formula based on a time derivative of a measurement result of the measurement apparatus, the errors being based on movement of at least one of the object to be measured or at least a part of the measurement apparatus, wherein the correction section uses different recursive formulas according to positive and negative signs of a frequency modulation rate based on a rate of change of a frequency per unit time of the frequency-modulated laser beam used by the measurement apparatus, wherein when the frequency modulation rate is positive, the acquisition section acquires measurement data in which the second measurement result is arranged at a tail of the first measurement result, and the correction section uses a recursive formula that corrects the measurement data arranged in a time series acquired by the acquisition section in a reverse order of the arranged time series, wherein the correction section uses a sixth recursive formula represented by the following equation as the recursive formula wherein L n is the nth measurement including an error caused by a Doppler shift, L n is the nth measurement corrected for the error caused by the Doppler shift, L n+i is the nth+i measurement corrected for the error caused by the Doppler shift, s = k / At, At is a time interval in which the measuring device measures the distance, k = 2co / A N y, co is the speed of light in a vacuum, A is a wavelength of the frequency-modulated laser beam, N is a refractive index of air, y is the frequency modulation, and the coefficients a0, a i , b are coefficients for approximating the time differential data of the measurement data as time differential data using a difference method having an accuracy of the mth order.

9. The data correction apparatus according to claim 8, wherein the acquisition section acquires measurement data in which a second measurement result obtained by measuring the distance while the object to be measured and the measurement apparatus are in a stationary state is arranged as m pieces of second data from a head or m pieces of second data from a tail, and the correction section corrects errors included in p pieces of first data by applying the measurement data to the recursive formula, the measurement data including m pieces of second data and the p pieces of first data included in the first measurement result.

10. The data correction apparatus according to claim 9, wherein the acquisition means further acquires information on m' from the measurement apparatus, the m' being the number of pieces of data of the second measurement result included in the measurement data, and the correction means corrects an error of the measurement data only m - m' times the data of the second measurement result is copied, and then when m' is smaller than the order m of the difference method having the mth order accuracy, m' being the number of pieces of data of the second measurement result included in the measurement data.

11. A measurement system comprising: a measurement apparatus that measures a distance from a reference position to an object to be measured, and including a laser apparatus that outputs a frequency-modulated laser beam, a branching means that branches the frequency-modulated laser beam output from the laser apparatus into a reference light that is a part of the frequency-modulated laser beam and a measurement light that is at least some of the rest of the frequency-modulated laser beam, a beat signal generation means that generates a beat signal by mixing the reference light and a reflection light that is reflected by irradiating the measurement light onto the object to be measured, a frequency analysis means that performs frequency analysis on the beat signal, and a calculation means that calculates the distance between the reference position and the object to be measured based on a result of the frequency analysis performed on the beat signal by the frequency analysis means; and a data correction apparatus, wherein the data correction apparatus includes: an acquisition means that acquires measurement data from a measurement apparatus that measures a distance from a reference position to an object to be measured using a frequency-modulated laser beam and is capable of periodically measuring the distance while at least one of moving the object to be measured or at least a part of the measurement apparatus, in which first measurement results of the distance are arranged in a time series in the measurement data, and a second measurement result obtained by measuring the distance while the object to be measured and the measurement apparatus are in a stationary state is arranged at a head or a tail of the first measurement results; and a correction means that corrects an error included in the measurement data acquired by the acquisition means based on movement of at least one of the object to be measured or at least a part of the measurement apparatus, by applying the measurement data to a recursive formula based on a time derivative of a measurement result of the measurement apparatus.

12. A correction method including the following steps performed by a computer: acquiring measurement data from a measurement apparatus that measures a distance from a reference position to an object to be measured using a frequency-modulated laser beam, in which first measurement results of measurement results of the distance measured periodically while at least one of moving the object to be measured or at least a part of the measurement apparatus are arranged in a time series in the measurement data, and a second measurement result obtained by measuring the distance while the object to be measured and the measurement apparatus are in a stationary state is arranged at a head or a tail of the first measurement results, and correcting an error included in the measurement data based on movement of at least one of the object to be measured or at least a part of the measurement device by applying the measurement data to a recursive formula based on a time derivative of a measurement result of the measurement device, wherein in the step of correcting the error, different recursive formulas are used according to a positive sign and a negative sign of a frequency modulation rate based on a rate of change of a frequency per unit time of the frequency-modulated laser beam used by the measurement device, wherein when the frequency modulation rate is negative, in the step of acquiring, measurement data in which the second measurement result is arranged at a head of the first measurement result is acquired, and in the step of correcting the error, a recursive formula that corrects the acquired measurement data arranged in a time series is used, the correction being performed in order of the arranged time series, in the correction step, a first recursive formula represented by the following equation is used as the recursive formula or a second recursive formula represented by the following equation is used as the recursive formula , wherein L n is the n-th measurement including an error due to Doppler shift, L n is the n-th measurement corrected for said error due to Doppler shift, L n-1 is the n-1 -th measurement including an error due to Doppler shift, L n-1 is the n-1 -th measurement corrected for said error due to Doppler shift, s = k / At, At is the time interval in which said measuring device measures said distance, k = 2co / A N y, co is the speed of light in vacuum, A is the wavelength of said frequency-modulated laser beam, N is the refractive index of air, y is said frequency modulation.

Images