JP6193644B2 - Displacement measuring device and displacement measuring method - Google Patents

Description

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

  In recent years, higher resolution and higher accuracy of position detection technology regarding displacement sensors and solid scales are progressing. In addition, higher resolution and higher accuracy of drive technology related to actuators and drive stages are also progressing. For this reason, the precision of devices such as semiconductor manufacturing devices, machine tools, and measuring instruments in which these technologies are incorporated is also increasing. For example, a microscope such as an atomic force microscope (AFM) incorporates a displacement sensor for position detection. In this case, a displacement sensor having a picometer resolution has been used in order to realize a fine shape measurement. In addition, solid scales having a resolution on the order of picometers have recently appeared due to the refinement of the scale pitch and the improvement of the number of electrical divisions.

  In order to improve the accuracy and quality of devices such as semiconductor manufacturing equipment, machine tools and measuring instruments, position detection accuracy such as displacement sensors and solid scales, drive accuracy such as actuators and drive stages, or positioning accuracy of devices incorporating these Etc. are required to be evaluated with high accuracy. However, although position detection technology and drive technology in recent years have come to require picometer-order accuracy, evaluation has become increasingly difficult. There are also demands for measuring minute deformations of materials (measurement of thermal expansion coefficient and secular change, etc.) and demands for measuring minute vibrations, but measurement is difficult for the same reason.

  Laser interference length measurement is used to perform highly accurate evaluation as described above. Laser interference length measurement is a highly sensitive measurement method using light interference, and alignment can be freely performed as compared with a solid scale or the like. Laser interferometry is suitable for high-accuracy evaluation because it has the advantage of reducing Abbe error. However, in a minute region where the measurement range is about several μm, the influence of the interpolation correction becomes a size that cannot be ignored, and it is not easy to achieve picometer measurement accuracy.

  In order to improve the measurement accuracy, a technique of shortening the wavelength of the laser used is used. In the industry, visible light is widely used as a laser wavelength in laser interferometry. In order to increase the resolution and reduce the interpolation error, it is advantageous to use a shorter wavelength. However, when light in the ultraviolet or X-ray region, which is shorter than the visible region, is used, there are many practical aspects such as laser wavelength stability, availability of optical components, device dimensions and safety. Will have problems.

  As another method for improving the measurement accuracy, an optical path length multiplication method for increasing the number of round trips of laser light between the laser interferometer and the moving reflecting mirror to be measured is used. If the optical path length is multiplied, the apparent laser wavelength is shortened, so that high-precision measurement can be expected. However, new problems such as complication of the optical system, a decrease in the amount of light due to light reciprocating in the optical element, and generation of stray light and leakage light occur. Moreover, skill is required for attachment and adjustment of the optical system. Therefore, there is a limit to the measurement accuracy improvement effect obtained by multiplying the optical path length.

  In order to overcome the problems of the above-described method, a method is known in which the laser frequency is changed in accordance with the displacement of the measuring reflector and laser length measurement is performed based on the frequency change amount. This method does not require the interpolation correction of the interference signal, so that the influence of the interpolation error does not occur. This method requires beat measurement between the frequency variable laser and the reference laser in order to detect the frequency of the frequency variable laser and the amount of frequency change with high accuracy. When a normal frequency stabilized laser is used as the reference laser, the beat measurement range between the frequency variable laser and the reference laser is limited due to a photo detector for beat measurement and a band limitation of an electronic circuit. In this case, the measurement accuracy and measurement range are also limited.

  Therefore, for the purpose of improving accuracy and expanding the measurement range, a so-called optical frequency comb that can generate laser beams of multiple frequencies at precise frequency intervals instead of a normal frequency stabilized laser is used as a reference laser. A method to be used has been proposed (Non-Patent Document 1). In this method, using the optical frequency comb as a reference laser, the frequency of the frequency variable laser is changed while measuring the beat between the optical frequency comb and the frequency variable laser. At this time, there is a so-called dead zone in which the beat frequency is near zero or the frequency of the frequency variable laser reaches near the center of the longitudinal mode interval of the optical frequency comb. In this dead zone, the beat frequency cannot be measured accurately. Therefore, it is necessary to take measures to prevent the influence of the dead zone region by measuring the frequency of the beat whose frequency is shifted using an acoustooptic device.

Youichi Bitou et al., “Accurate wide-range displacement measurement using tunable diode laser and optical frequency comb generator”, 23 January 2006, OPTICS EXPRESS, vol. 14, No. 2, pp.644-654.

  However, the inventor has found that the method using the above optical frequency comb as a reference laser has the following problems. In this method, it is necessary to measure the absolute frequency of the frequency variable laser. Therefore, the uncertainty of the absolute frequency measurement affects the displacement measurement result, which is a problem in terms of the reliability of the measurement result. In addition, the configuration of the apparatus for performing absolute frequency measurement becomes complicated, leading to an increase in size and cost of the apparatus. Furthermore, in order to avoid a dead zone region in the beat frequency measurement between the optical frequency comb and the frequency variable laser, it is necessary to incorporate an acousto-optic element or the like, which further complicates the apparatus configuration.

  The present invention has been made in view of the above circumstances, and an object of the present invention is to perform displacement measurement using a laser beam without performing frequency measurement of the laser beam.

  The displacement measuring apparatus according to the first aspect of the present invention includes a frequency variable laser that outputs a first laser beam having a variable frequency, an optical frequency comb that can control a repetition frequency and an offset frequency, the frequency variable laser, Detects interference light between a controller for controlling the optical frequency comb, a Fabry-Perot interferometer on which the first laser light is incident, and the second laser light output from the first laser light and the optical frequency comb. A first light detector, a second light detector for detecting reflected light from the Fabry-Perot interferometer, and a frequency measuring device for detecting a beat frequency from a detection result of the first light detector, The controller uses the beat frequency to lock the frequency of the frequency tunable laser with reference to the spectrum of the second laser beam, and to the first laser beam. The frequency of the frequency variable laser and the repetition frequency are changed so that the reflected light intensity of the Fabry-Perot interferometer and the beat frequency are constant, and the Fabry-Perot is based on the amount of change in the repetition frequency. The displacement of the interferometer length of the interferometer is calculated. This displacement measuring device can calculate the displacement of the interferometer length without measuring the frequency of the frequency variable laser based on the amount of change in the repetition frequency.

  A displacement measuring apparatus according to a second aspect of the present invention is the above-described displacement measuring apparatus, wherein the controller calculates a displacement of the interferometer length of the Fabry-Perot interferometer in proportion to a change amount of the repetition frequency. Is to be calculated. This displacement measuring device can calculate the displacement of the interferometer length without measuring the frequency of the frequency variable laser based on the amount of change in the repetition frequency.

  A displacement measuring apparatus according to a third aspect of the present invention is the above displacement measuring apparatus, wherein the controller is configured to obtain a value obtained by dividing the amount of change of the repetition frequency by a value of the repetition frequency, to the value of the Fabry-Perot interferometer. The displacement of the interferometer length of the Fabry-Perot interferometer is calculated by multiplying the value of the interferometer length. This displacement measuring device can calculate the displacement of the interferometer length without measuring the frequency of the frequency variable laser based on the amount of change in the repetition frequency.

  A displacement measuring apparatus according to a fourth aspect of the present invention is the displacement measuring apparatus described above, wherein the controller is configured to control an atmosphere between the frequency variable laser and the Fabry-Perot interferometer and an atmosphere in the Fabry-Perot interferometer. A value obtained by dividing the amount of change of the refractive index by the value of the refractive index of the atmosphere is further added to calculate the displacement of the interferometer length of the Fabry-Perot interferometer. This displacement measuring device can calculate the displacement of the interferometer length without measuring the frequency of the frequency variable laser based on the amount of change in the repetition frequency.

  A displacement measuring device according to a fifth aspect of the present invention is the displacement measuring device described above, wherein the controller has the offset frequency and the beat frequency so that they have the same value and opposite signs. The optical frequency comb and the frequency variable laser are controlled. This displacement measuring device can calculate the displacement of the interferometer length without measuring the frequency of the frequency variable laser based on the amount of change in the repetition frequency.

  The displacement measuring method according to the sixth aspect of the present invention locks the frequency of the frequency-variable laser with reference to the spectrum of the second laser beam output from the optical frequency comb that can control the repetition frequency and the offset frequency, It is obtained from the reflected light intensity of the Fabry-Perot interferometer with respect to the first laser light output from the variable frequency laser and incident on the Fabry-Perot interferometer, and the interference light between the first laser light and the second laser light. The frequency of the variable frequency laser and the repetition frequency are changed so that the beat frequency is constant, and the displacement of the interferometer length of the Fabry-Perot interferometer is calculated based on the amount of change of the repetition frequency It is.

  According to the present invention, displacement measurement using a laser beam can be performed without measuring the frequency of the laser beam.

  The above and other objects, features and advantages of the present invention will be more fully understood from the following detailed description and the accompanying drawings. The accompanying drawings are presented for purposes of illustration only and are not intended to limit the present invention.

1 is a configuration diagram schematically showing a configuration of a displacement measuring apparatus 100 according to a first embodiment. It is a figure which shows the spectrum of the laser beam which the optical frequency comb 1 outputs. 1 is a configuration diagram illustrating a specific configuration example of a displacement measuring apparatus 100 according to a first embodiment. It is a figure which shows the relationship between the spectrum of the optical frequency comb 1, and beat frequency _fbeat . It is a graph showing the relationship between the reflectivity of the Fabry-Perot interferometer 5 R _N and the phase difference [delta]. 4 is a graph showing the relationship between the reflected light intensity of the Fabry-Perot interferometer 5 and the resonance frequency of the Fabry-Perot interferometer 5. 3 is a flowchart showing a procedure of displacement measurement according to the first embodiment. It is a figure which shows the relationship between the beat frequency before and behind a laser frequency change, and an optical frequency comb. It is a flowchart showing the procedure of step S1 for obtaining the initial value L ₀ interferometer length according to the second embodiment. It is a figure which shows the relationship between the intensity | strength of reflected light _RN , and a laser frequency. It is a figure which shows the relationship between the beat frequency concerning Embodiment 2, and a laser frequency. It is a flowchart showing the procedure of step S1 for obtaining the initial value L ₀ interferometer length according to the third embodiment.

  Embodiments of the present invention will be described below with reference to the drawings. In the drawings, the same elements are denoted by the same reference numerals, and redundant description is omitted as necessary.

Embodiment 1
First, the displacement measuring apparatus 100 according to the first embodiment will be described. FIG. 1 is a configuration diagram schematically illustrating a configuration of a displacement measuring apparatus 100 according to the first embodiment. The displacement measuring apparatus 100 includes an optical frequency comb 1, a frequency variable laser 2, a frequency measuring device 3, a controller 4, a Fabry-Perot interferometer 5, and photodetectors PD1 and PD2.

The optical frequency comb 1 can output a laser beam L1 having a spectrum composed of a plurality of frequency components with equal frequency intervals. The frequency f _N of the _N-th frequency component of the laser light L1 (N is an order indicating the spectrum of the optical frequency comb and is an integer. Hereinafter, N is referred to as the order of the optical frequency comb) is expressed by the following formula ( 1).

In equation (1), f _rep is the repetition frequency. f _ceo is an offset frequency, and is a surplus frequency component when N = 0 in Equation (1). The offset frequency _{f_ceo} is either a positive value or a negative value. FIG. 2 is a diagram illustrating a spectrum of laser light output from the optical frequency comb 1. The optical frequency comb 1 can control the frequencies of a plurality of frequency components to be output with high accuracy by adjusting the repetition frequency f _rep and the offset frequency f _ceo .

  The variable frequency laser 2 can change the wavelength of the laser beam to be output. The laser beam L2 output from the frequency variable laser 2 is branched into a laser beam L21 and a laser beam L22. The laser light L21 interferes with the laser light L1 output from the optical frequency comb 1, and the interference light L10 is generated. The interference light L10 is incident on the photodetector PD1. The laser beam L22 is incident on the Fabry-Perot interferometer 5.

  The Fabry-Perot interferometer 5 includes a reflecting mirror 51, a reflecting mirror 52, an interferometer housing 53, and an actuator 54. The reflecting mirror 51 is a reflecting mirror having a predetermined reflectance, and is disposed at one end of the interferometer housing 53. The reflecting mirror 52 is a reflecting mirror having a high reflectance, and is disposed at the other end of the interferometer housing 53 via an actuator 54. The reflecting mirror 52 is preferably total reflection. In this configuration, the reflecting mirror 51 and the reflecting mirror 52 constitute an optical interferometer. The actuator 54 can displace the position of the reflecting mirror 52 in the resonance direction of the interferometer. That is, the Fabry-Perot interferometer 5 can change the interferometer length by driving the actuator 54. On the surface 55 of the reflecting mirror 52 on the side facing the outside of the interferometer housing 53, an object for displacement measurement is installed.

  The laser beam L22 enters the reflecting mirror 51 and reciprocates between the reflecting mirror 51 and the reflecting mirror 52. A part of the reciprocating laser beam is emitted from the reflecting mirror 51. Here, the emitted laser light is referred to as laser light L23. The laser beam L23 is incident on the photodetector PD2.

  The photodetector PD1 detects the light intensity of the interference light L10 and outputs the detection result as a detection signal DET1. The photodetector PD2 detects the light intensity of the laser light L23 and outputs the detection result as a detection signal DET2.

The frequency measuring device 3 calculates a beat frequency f _beat from the detection signal DET1. The frequency measuring device 3 outputs the calculated beat frequency f _beat to the controller 4. The frequency measuring device 3 can acquire measured values of the repetition frequency f _rep and the offset frequency f _ceo from the optical frequency comb 1, and can output the acquired values to the controller 4. In addition, an electrical signal detected by a photodetector in the optical frequency comb 1 can be output to the controller 4. The controller 4 controls the repetition frequency f _rep and the offset frequency f _ceo based on this electric signal. In order to grasp the repetition frequency f _rep and the offset frequency f _ceo of the optical frequency comb 1, the frequency value actually measured by the frequency measuring device 3 or the set frequency value for controlling the repetition frequency f _rep and the offset frequency f _ceo is set. Can be used.

The controller 4 controls the optical frequency comb 1 and the frequency variable laser 2. Specifically, the controller 4 sets a repetition frequency f _rep and an offset frequency f _ceo in the optical frequency comb 1. Further, the frequency f _laser of the laser beam L2 output from the variable frequency laser 2 is controlled. The controller 4 can control the drive of the actuator 54 of the Fabry-Perot interferometer 5 by the drive signal Sd.

  Subsequently, a specific configuration example of the displacement measuring apparatus 100 will be described. FIG. 3 is a configuration diagram illustrating a specific configuration example of the displacement measuring apparatus 100 according to the first embodiment. In FIG. 3, compared with FIG. 1, a band pass filter BPF, beam splitters BS1 and BS2, a polarizing beam splitter PBS, and a λ / 4 plate 6 are added.

  The laser light L1 is incident on the beam splitter BS1 after unnecessary frequency components are removed by the bandpass filter BPF. A part of the laser beam L1 output from the optical frequency comb 1 passes through the beam splitter BS1.

  The laser beam L2 is branched into a laser beam L21 and a laser beam L22 by the beam splitter BS2. A part of the laser light L21 is reflected by the beam splitter BS1 in the propagation direction of the laser light L1. As a result, the laser light L1 and the laser light L21 interfere with each other to generate interference light L10. The laser beam L22 is incident on the polarization beam splitter PBS. The polarization beam splitter PBS is provided so as to transmit the laser light L22 that is linearly polarized light. The laser light L22 passes through the λ / 4 plate 6 and then enters the Fabry-Perot interferometer 5. The laser light L23 emitted from the Fabry-Perot interferometer 5 passes through the λ / 4 plate 6 and then enters the polarization beam splitter PBS.

  As described above, the laser beam L23 that has reached the polarization beam splitter PBS is obtained after the laser beam L22, which is part of the laser beam L2, has passed through the λ / 4 plate 6 twice. Therefore, the direction of linearly polarized light of the laser beam L23 is orthogonal to the direction of linearly polarized light of the laser beam L22. As a result, the polarization beam splitter PBS can selectively reflect the laser light L23. The reflected laser light L23 is incident on the photodetector PD2. Other configurations are the same as those in FIG.

Subsequently, the principle of displacement measurement of the displacement measuring apparatus 100 will be described. The frequency f _laser of the laser light L2 output from the frequency variable laser 2 is expressed by the following formula (2) using the repetition frequency f _{rep, the} offset frequency f _ceo , the beat frequency f _beat, and the order N.

FIG. 4 is a diagram showing the relationship between the spectrum of the optical frequency comb 1 and the beat frequency f _beat . As will be described later, in this embodiment, the offset frequency f _ceo is set as a value having the opposite sign as large as the beat frequency f _beat.

As described above, the laser light L22 incident on the Fabry-Perot interferometer 5 reciprocates many times in the interferometer, and a part of the light is emitted as the laser light L23 out of the Fabry-Perot interferometer 5. The laser beam L23 is incident on the photodetector PD2. The photodetector PD2 measures the light intensity of the laser beam L23 and outputs it as a detection signal DET2. The controller 4 controls the frequency f _laser of the frequency variable laser 2 and the displacement amount of the actuator 54 so that the light intensity of the laser light L23 becomes maximum (or minimum) while monitoring the detection signal DET2. The displacement of the reflecting mirror 52 of the Perot interferometer 5 can be measured.

ファブリペロー干渉計５にレーザ光が入射した場合のファブリペロー干渉計５の透過率Ｔ_Ｎは、以下の式（４）で表される。

Ｆは、以下の式（５）で表される。

式（５）における変数の定義は次の通りである。ｒは、反射鏡の振幅反射係数である。Ｒは、反射鏡５１及び５２の反射率である。
δは位相差であり、以下の式（６）で表される。

式（６）における変数の定義は次の通りである。ｎは、空気の屈折率である。Ｌは、ファブリペロー干渉計の対向する反射鏡間の距離（幾何学的距離）、すなわち干渉計長である。λ_０は、真空中のレーザ光の波長である。 Fabry-Perot interferometer 5 of reflectance R _N when the Fabry-Perot interferometer 5 is incident laser light is expressed by the following equation (3).

The transmittance _TN of the Fabry-Perot interferometer 5 when laser light is incident on the Fabry-Perot interferometer 5 is expressed by the following equation (4).

F is represented by the following formula (5).

The definition of the variable in Formula (5) is as follows. r is the amplitude reflection coefficient of the reflecting mirror. R is the reflectance of the reflecting mirrors 51 and 52.
δ is a phase difference and is expressed by the following equation (6).

The definition of the variable in Formula (6) is as follows. n is the refractive index of air. L is the distance (geometric distance) between the reflecting mirrors of the Fabry-Perot interferometer, that is, the interferometer length. λ ₀ is the wavelength of the laser light in vacuum.

When using a reflector having high reflectance as a reflecting mirror of the Fabry-Perot interferometer, the reflectivity R _N and transmittance T _N shows a sharp change when the phase difference δ is an integer multiple of [pi. The phase difference δ at this time is expressed by the following equation (7) using an integer k.

Figure 5 is a graph showing the relationship between the reflectance of the Fabry-Perot interferometer 5 R _N and the phase difference [delta]. Reflectivity R _N, the phase difference δ is minimized when integer multiples of [pi. FIG. 6 is a graph showing the relationship between the reflected light intensity of the Fabry-Perot interferometer 5 and the resonance frequency of the Fabry-Perot interferometer 5. The reflected light intensity becomes minimum for each interval (free spectral interval) f _FSR between adjacent resonance frequencies.

Here, when the resonance frequency f of the Fabry-Perot interferometer 5 and the speed of light c in vacuum are used, Equation (7) can be transformed into Equation (8).

When the equation (8) is transformed, the resonance frequency f is expressed by the following equation (9).

From the equation (9), the interval between adjacent resonance frequencies (free spectral interval) f _FSR in which the value of the integer k is different by 1 is expressed by the following equation (10).

式（１１）では、周波数を一般化したので、以下では、ｆを周波数可変レーザ２から出力されてファブリペロー干渉計５に入射するレーザ光の周波数として取り扱う。以下では、ｆをレーザ周波数と称する。 If equation (8) is generalized in consideration of frequencies other than the resonance frequency, the interferometer length L can be expressed by the following equation (11) using the order M (M is a real number).

Since the frequency is generalized in Equation (11), f is treated as the frequency of the laser light that is output from the frequency variable laser 2 and incident on the Fabry-Perot interferometer 5 below. Hereinafter, f is referred to as a laser frequency.

Here, the influence of the laser frequency f, the refractive index n of the measurement atmosphere, and the order M on the interferometer length L of the Fabry-Perot interferometer 5 will be examined. The atmosphere here refers to the atmosphere through which the optical path of laser light output from the frequency variable laser 2 and incident on the Fabry-Perot interferometer 5 and the optical path of laser light reciprocating in the Fabry-Perot interferometer 5 pass. means. By fully differentiating the equation (11), the displacement dL of the interferometer length L is expressed by the following equation (12).

In the present embodiment, the laser frequency f is controlled so as to cancel the change in the order M in Expression (12), that is, dM = 0. In this case, it is possible to measure the displacement of the reflecting mirror with high accuracy without being affected by the interpolation error without requiring the interpolation correction for the interference signal which is a problem in the measurement of the normal interferometer length. Since dM = 0, Expression (12) is rewritten to Expression (13).

When the atmosphere is evacuated, the influence of the refractive index of the atmosphere can be ignored, and dn = 0. Since dn = 0, Expression (13) can be rewritten to Expression (14).

この場合、干渉計長の変位ｄＬの不確かさｄＬ_ｅ（Ｌ_ｅ＝ｄＬ）は、式（１５）を全微分して、以下の式（１６）で表される。

Here, when the displacement dL of the interferometer length is set to L _e and the change amount df of the frequency is set to _fe , Equation (14) becomes the following Equation (15).

In this case, the uncertainty dL _e (L _e = dL) of the displacement dL of the interferometer length is expressed by the following equation (16) by fully differentiating the equation (15).

The first term on the right side of Equation (16) indicates the influence of df (df = f _e ), which is a differential amount indicating the uncertainty of the laser frequency f. Therefore, in order to reduce the influence of the uncertainty of the laser frequency f, it is necessary to obtain the laser frequency f with high accuracy.

The second term on the right side of Equation (16) shows the influence of df _e which is a differential amount indicating the uncertainty of the change amount of the laser frequency f. Therefore, in order to reduce the influence of the uncertainty df _e of the change amount of the laser frequency f, it is necessary to accurately obtain the change df of the laser frequency.

The third term on the right side of Expression (16) indicates the influence of dL (dL = L _e ), which is a differential amount indicating the uncertainty of the interferometer length L. Therefore, in order to reduce the uncertainty of the interferometer length L, it is necessary to obtain the interferometer length L with high accuracy.

In the present embodiment, the interferometer length L is obtained with high accuracy without measuring the laser frequency by the method described later. As a result, it is possible to reduce the uncertainty dL _e displacement of the measurement target interferometer length L. In the present embodiment, an optical frequency comb is used to obtain the interferometer length L with high accuracy.

Next, a method for measuring the displacement of the interferometer length will be described. In the equation (2), when the beat frequency f _beat is constant and the repetition frequency f _rep is changed by Δf _rep , that is, when the frequency of the frequency variable laser is controlled so that the value of f _beat is constant, The change amount df of the laser frequency f is expressed by the following equation (17).

但し、αは、以下の式（１９）で表される。

By substituting equation (17) into equation (13), the following equation (18) is obtained. In Equation (18), the initial value of the frequency of the variable frequency laser 2 before changing the repetition frequency f _rep is f ₀ , the initial value of the interferometer length L of the Fabry-Perot interferometer 5 is L ₀ , and the refraction of the atmosphere _Assume that the initial value of the rate is n ₀ and the initial value of the repetition frequency is f _rep0 .

However, (alpha) is represented by the following formula | equation (19).

In this embodiment, the controller 4, alpha = 0, i.e. so that the _f ceo _{= -f beat,} controls the offset frequency _{f ceo} and the beat frequency _{f beat.} As a result, Expression (19) becomes Expression (20).

よって、式（２１）より、本実施の形態では、ファブリペロー干渉計５の干渉計長の初期値Ｌ_０、繰り返し周波数の初期値ｆ_ｒｅｐ０、繰り返し周波数の変化量Δｆ_ｒｅｐのみで、ファブリペロー干渉計５の干渉計長の変位ｄＬを測定することができる。 Furthermore, by making the atmosphere a vacuum, the contribution of the refractive index of the atmosphere can be ignored. Therefore, Expression (20) is rewritten to Expression (21).

Therefore, from the equation (21), in the present embodiment, only the initial value L ₀ of the interferometer length of the Fabry-Perot interferometer 5, the initial value f _{rep0 of} the repetition frequency, and the change amount Δf _rep of the repetition frequency are used. The displacement dL of the interferometer length of a total of 5 can be measured.

Specifically, when the interferometer length of the Fabry-Perot interferometer 5 is changed, so that the reflectance R _N of the Fabry-Perot interferometer 5 is minimized, the controller 4 changes the repetition frequency. Then, the displacement dL of the interferometer length of the Fabry-Perot interferometer 5 is substituted by substituting the change amount Δf _rep of the repetition frequency when the change of the interferometer length of the Fabry-Perot interferometer 5 stops into the equation (21). Can be calculated.

  Next, a procedure for measuring the displacement will be described. FIG. 7 is a flowchart of a displacement measurement procedure according to the first embodiment.

Step S1
First, in order to obtain the displacement dL of the interferometer length of the Fabry-Perot interferometer 5 shown in Expression (12), an initial value L ₀ of the interferometer length of the Fabry-Perot interferometer 5 is obtained.

Step S2
The laser frequency f is locked to the optical frequency comb 1.

Step S3
Controller 4, while measuring the beat frequency _{f beat,} so that the f ceo _{= -f beat,} and controls the optical frequency comb 1.

Step S4
Next, the frequency of the variable frequency laser 2 is matched with the resonance frequency of the Fabry-Perot interferometer 5. Specifically, the controller 4 changes the repetition frequency f _rep of the optical frequency comb 1 while monitoring the detection signal DET2, and the intensity of the reflected light (laser light L23) detected by the photodetector PD2 is minimized. Control.

Step S5
The controller 4 is held as the initial value _{f Rep0} repetition frequency _{f rep} the repetition rate at which the reflectance _{R N} is minimized.

Step S6
The controller 4 changes the repetition frequency f _rep of the optical frequency comb 1 so as to match the resonance frequency of the Fabry-Perot interferometer 5 while changing the interferometer length by displacing the reflecting mirror 52 with the actuator 54. At this time, the controller 4 changes the repetition frequency f _rep of the optical frequency comb 1 so that the reflectance _RN is minimum and the beat frequency f _beat is constant.

Step S7
When the driving of the actuator 54 is finished, the controller 4 calculates a change amount Δf _rep of the repetition frequency.

Step S8
The controller 4 substitutes L ₀ , Δf _{rep, and} f _rep0 into Equation (21), and calculates the displacement dL of the interferometer length of the Fabry-Perot interferometer 5.

In the present embodiment, only the initial value L ₀ of the interferometer length of the Fabry-Perot interferometer 5, the initial value f _{rep0 of} the repetition frequency, and the change amount Δf _rep of the repetition frequency are used to change the displacement of the interferometer length of the Fabry-Perot interferometer 5. dL can be measured. Therefore, according to this configuration, the displacement of the interferometer length of the Fabry-Perot interferometer can be measured without measuring the laser frequency. Thereby, the interferometer length can be measured with high accuracy with a simple configuration.

  Note that although FIG. 7 illustrates the case where the atmosphere is a vacuum, the equation (20) may be used when the atmosphere is not a vacuum. That is, a refractive index measuring means is separately provided to measure the refractive index of the atmosphere before and after the laser frequency change, and is substituted into equation (20).

Embodiment 2
Next, a second embodiment will be described. In this embodiment, the measurement of the initial value L ₀ length of the Fabry-Perot interferometer 5 in the step S1 shown in FIG. 7, a specific example. First, the measurement principle of the initial length L ₀ of the Fabry-Perot interferometer 5 in the second embodiment will be described.

よって、式（２２）より、干渉計長の初期値Ｌ_０は、以下の式（２３）で表される。

In the present embodiment, by changing the laser frequency in a state that the interferometer length is fixed at L _0, measuring an initial value L ₀ of the interferometer length. At this time, the influence of the laser frequency is expressed by the following equation (22).

Therefore, from the equation (22), the initial value L ₀ of the interferometer length is represented by the following equation (23).

That is, if the frequency change amount Δf and the resonance order change amount ΔM generated by the change of the laser frequency are known, the initial value L ₀ of the interferometer length can be obtained using the equation (23).

よって、周波数変化量Δｆ_１２は、以下の式（２６）で表される。

Here, the initial value of the laser frequency is f ₁ , and the changed laser frequency is f ₂ . Also, let N _{1 be} the initial value of the order of the optical frequency comb, and N ₂ be the order of the optical frequency comb after the change. The initial value f ₁ of the laser frequency is expressed by the following formula (24) from the formula (2). The laser frequency f ₂ after the change is expressed by the following formula (25) from the formula (2).

Therefore, the frequency change amount Δf ₁₂ is expressed by the following equation (26).

FIG. 8 is a diagram showing the relationship between the beat frequency before and after the laser frequency change and the optical frequency comb. In the example of FIG. 8, there is a difference of 2f _FSR between the beat frequency f _beat1 and the beat frequency f _beat2 , so the resonance order change amount is 2.

Substituting equation (26) into equation (23), the initial value L ₀ of the interferometer length is expressed by the following equation (27). ΔM ₁₂ is a change amount of the resonance order M in the Fabry-Perot interferometer 5.

Subsequently, a method for obtaining the initial value L ₀ of the interferometer length using Expression (27) will be specifically described. Figure 9 is a flowchart showing the procedure of step S1 for obtaining the initial value L ₀ of the interferometer length. In the present embodiment, step S1 includes steps S11 to S16.

Step S11
First, an interferometer length _{L 0,} to fix the offset frequency _{f ceo0.}

Step S12
The beat frequency f _beat1 is measured.

Step S13
The controller 4 obtains the resonance order change ΔM ₁₂ and the optical frequency comb order change (N ₂ −N ₁ ) while changing the frequency of the frequency variable laser 2.

A method for obtaining the resonance order change ΔM ₁₂ will be described. In this case, as seen from equation (7), the phase δ is changed, the reflectivity R _N of the Fabry-Perot interferometer 5 is changed accordingly. With the reflectance R _N, also changes the reflected light intensity. Figure 10 is a graph showing the relationship between the intensity and the laser frequency of the reflected light R _N. As shown in FIG. 10, the resonance order change ΔM can be known by counting the number of times the light intensity passes through the zero cross point Pz.

A method of obtaining the optical frequency comb order change (N ₂ −N ₁ ) will be described. FIG. 11 is a diagram showing the relationship between the beat frequency and the laser frequency. The beat frequency changes in the form of a triangular wave with a period f _{rep as} the laser frequency changes. That is, the controller 4 can easily obtain the optical frequency comb order change (N ₂ −N ₁ ) by counting the number of times that the beat frequency changes from increasing to decreasing. When the laser frequency is locked to the resonance frequency, if the optical frequency comb and the laser frequency are near the minimum value or the maximum value (f _rep / 2), it is difficult to accurately measure the beat frequency. In this case, for example, the offset frequency _fceo may be shifted to a position where the beat frequency can be measured.

Step S14
The beat frequency f _beat2 is measured.

Step S15
Next, the refractive index n of air is obtained.

Step S16
The initial value L ₀ of the length of the Fabry-Perot interferometer 5 is calculated using the equation (27).

The following describes the reliability of the measurement of the initial value L ₀ of the interferometer length according to the second embodiment. First, in order to examine the measurement uncertainty of the initial value L ₀ of the interferometer length, the equation (23) is fully differentiated to obtain the following equation (28).

The first term on the right side of the equation (28) shows the influence of ΔM _e (ΔM = M _e ), which is a differential amount indicating the uncertainty of the change in resonance order ΔM. The uncertainty ΔM _e of the change in the resonance order is caused by factors such as incomplete locking of the frequency tunable laser 5 to the Fabry-Perot interferometer 5. The influence of the uncertainty ΔM of the resonance order M can be reduced by increasing the finesse of the Fabry-Perot interferometer 5 or increasing the frequency change amount.

The second term on the right side of Equation (28) shows the influence of Δf _e (Δf = f _e ), which is a differential amount indicating the uncertainty of the frequency change amount Δf of the laser frequency. The uncertainty Δf _e of the frequency change amount of the laser frequency can be reduced by increasing the frequency change amount or making the frequency change amount accurate. Increasing the frequency change amount is also related to increasing the order change amount ΔM of the first term on the right side.

Third term on the right side of equation (28) shows the effect of [Delta] n ([Delta] n = n _e) is a differential amount indicating the uncertainty of the air refractive index n. The uncertainty Δn of the air refractive index n can be reduced by stabilizing the measurement environment. Further, by making the measurement environment a vacuum, it is possible to remove the uncertainty Δn of the air refractive index n.

In the present embodiment, as shown in FIG. 9, even if the laser frequency is largely changed, Fabry-Perot interference is obtained by measuring each parameter appearing on the right side of the equation (27) without measuring the laser frequency itself. An initial value L ₀ of a total length of 5 can be measured. Since the repetition frequency f _rep , beat frequencies f _beat1 and f _beat2 are values in a certain range, they can be easily measured even when the laser frequency is greatly varied.

Therefore, according to the above method, by increasing the frequency variation of the laser frequency, and .DELTA.M _e is a differential amount indicating the uncertainty of the resonant order M, the uncertainty Delta] f _e of the frequency variation of the laser frequency, the Can be small. As a result, it is possible to measure the initial value L ₀ of the interferometer length with high accuracy.

Embodiment 3
Next, Embodiment 3 will be described. In this embodiment, the measurement of the initial value L ₀ of the interferometer length at step S1 shown in FIG. 7, illustrating another embodiment. First, description will be given of a measurement principle of the initial value L ₀ of the interferometer length in the third embodiment.

As in the second embodiment, the laser frequency is changed. The interval (free spectrum interval) f _FSR between adjacent resonance frequencies at this time is expressed by the following equation (29) by _modifying equation (27).

In this embodiment, without measuring the degree N of the comb of optical frequencies, measuring an initial value L ₀ of the interferometer length. Therefore, in order to calculate the initial value L ₀ of the interferometer length, it is necessary to estimate the amount of change in the order N of the optical frequency comb.

Here, in Equation (29), when the estimate of the order change amount (N ₂ −N ₁ ) of the optical frequency comb is larger by 1 than the actual order change amount, the resonance frequency interval (free spectral interval) is As shown in Expression (30), the deviation is caused by δf _FSR .

In this case, the measurement value of the interferometer length is deviated from the actual value L ₀ by L _d. The amount of deviation Ld of the measured value of the interferometer length is expressed by the following equation (31).

Here, a range of L ₀ ± L _d (that is, the order change of the optical frequency comb is (N2−N1) ± 1) is assumed with reference to the true value (N2−N1) of the order change amount of the optical frequency comb. . Since the range L _{min to} L _max that can be taken by the initial value L ₀ of the interferometer is found from the design information of the interferometer, etc., if the range L _{min to} L _max is located within L ₀ ± L _d The order change amount (N2-N1) of the optical frequency comb can be determined so that the right side of the following equation (32) satisfies the range L _{min to} L _max .

Therefore, the initial value L ₀ of the length of the Fabry-Perot interferometer 5 can be determined from the equation (32).

Next, a method for obtaining the initial value L ₀ of the interferometer length according to the third embodiment will be specifically described. Figure 12 is a flowchart showing the procedure of step S1 for obtaining the initial value L ₀ interferometer length according to the third embodiment. In the present embodiment, step S1 includes steps S21 to S27.

Step S21
First, an interferometer length _{L 0,} to fix the offset frequency _{f ceo0.}

Step S22
The beat frequency f _beat1 is measured.

Step S23
The resonance order change ΔM is obtained while changing the frequency of the frequency variable laser 2.

Step S24
The beat frequency f _beat2 is measured.

Step S25
Next, the refractive index n of air is obtained.

Step S26
The order change amount (N2-N1) of the optical frequency comb is determined so as to satisfy the range L _{min to} L _max .

Step S27
The initial value L ₀ of the interferometer length is calculated using Equation (32).

Thus, according to this method, without measuring the degree change in the optical frequency comb can determine the initial value L ₀ of the interferometer length. Therefore, it is possible to prevent the influence due to the counting error of the order change of the optical frequency comb, and to calculate the initial value L ₀ of the interferometer length with high accuracy.

Further, in this method, by increasing the order change of the optical frequency comb can calculate the initial value L ₀ of the interferometer length more accurately.

Steps S22 to S24 can be performed a plurality of times. The first resonance frequency is f _1, the resonant frequency after the change corresponding thereto and f _2. In this case, L ₀ is represented by the same expression as Expression (32).

Then, starting from the resonance frequency f _2, to change the laser frequency. The resonance frequency after change corresponding to the first resonance frequency f ₂ and f _3. In this case, L ₀ is represented by the following formula (33).

Then, N ₂ and f ₂ are deleted using Expression (32) and Expression (33), and the expression indicating L ₀ is updated as shown in Expression (34) below.

When the above update is repeated k−1 times, L ₀ is expressed by the following equation (35).

If this method is adopted, the value of N _k -N ₁ of the optical frequency comb can be increased, so that L ₀ can be obtained with higher accuracy.

Other Embodiments The present invention is not limited to the above-described embodiments, and can be appropriately changed without departing from the spirit of the present invention. The origin signal generation circuit described above is merely an example. The arrangement of the bandpass filter BPF, the beam splitters BS1 and BS2, the polarization beam splitter PBS, and the λ / 4 plate 6 shown in FIG. 3 is merely an example. That is, the configuration of FIG. 3 is not limited as long as the laser beam can be branched and interfered in the same manner.

The measurement of the initial value L ₀ interferometer length according to the second embodiment, the measurement of the initial value L ₀ of the interferometer length according to the third embodiment, can also be carried out simultaneously.

The measurement of the initial value L ₀ of the interferometer length according to the second embodiment, the measurement of the initial value L ₀ of the interferometer length according to the third embodiment, both, performed using two variable frequency laser Also good. Specifically, first, two frequency variable lasers are locked to the same resonance frequency point (first position) of the Fabry-Perot interferometer 5. Thereafter, one frequency tunable laser (referred to as frequency tunable laser A) is kept locked, and the other frequency tunable laser (referred to as frequency tunable laser B) is laser as described in the second and third embodiments. Change the frequency. At this time, the beat frequency of the frequency variable laser A and the optical frequency comb 1 is used as the beat frequency f _beat1 . In the second embodiment, the beat frequency of the frequency variable laser B and the optical frequency comb 1 is used as the beat frequency f _beat2 . In the third embodiment, the beat frequency of the frequency variable laser B and the optical frequency comb 1 is used as the beat frequency f _beat2 , and the change in the resonance order is measured on the frequency variable laser B side. Thus, the initial value L ₀ of the interferometer length can be determined as well. According to this method, since the beat frequencies applied to the two frequency variable lasers are simultaneously measured, the interferometer length can be obtained with higher accuracy without being affected by the drift of the interferometer length.

DESCRIPTION OF SYMBOLS 1 Optical frequency comb 2 Frequency variable laser 3 Frequency measuring device 4 Controller 5 Fabry-Perot interferometer 6 λ / 4 board 51, 52 Reflector 53 Interferometer housing 54 Actuator 55 Surface 100 Displacement measuring device BPF Band pass filter BS1, BS2 Beam Splitter DET1, DET2 Detection signal L1, L2, L21-L23 Laser light L10 Interference light PBS Polarization beam splitter PD1, PD2 Photodetector Sd Drive signal

Claims (6)

A variable frequency laser that outputs a first laser beam having a variable frequency;
An optical frequency comb with controllable repetition frequency and offset frequency;
A controller for controlling the frequency variable laser and the optical frequency comb;
A Fabry-Perot interferometer on which the first laser beam is incident;
A first photodetector for detecting interference light between the first laser beam and the second laser beam output from the optical frequency comb;
A second photodetector for detecting reflected light from the Fabry-Perot interferometer;
A frequency measuring device for detecting a beat frequency from the detection result of the first photodetector,
Wherein the controller,
The frequency before Symbol frequency tunable laser to lock the spectrum of the second laser beam as a reference,
The frequency of the variable frequency laser and the repetition frequency are changed so that the reflected light intensity of the Fabry-Perot interferometer with respect to the first laser light and the beat frequency are constant.
Based on the amount of change in the repetition frequency, the displacement of the interferometer length of the Fabry-Perot interferometer is calculated.
Displacement measuring device. The controller is
In proportion to the amount of change in the repetition frequency, the displacement of the interferometer length of the Fabry-Perot interferometer is calculated.
The displacement measuring apparatus according to claim 1. The controller is
The value obtained by dividing the amount of change of the repetition frequency by the value of the repetition frequency is multiplied by the value of the interferometer length of the Fabry-Perot interferometer to calculate the displacement of the interferometer length of the Fabry-Perot interferometer.
The displacement measuring device according to claim 2. The controller is
A value obtained by dividing the amount of change of the repetition frequency of value in the repetition frequency, the value obtained by dividing the amount of change in refractive index of the atmosphere of the Fabry-Perot interferometer in the value of the refractive index of the atmosphere, by adding a value Multiplying the value of the interferometer length of the Fabry-Perot interferometer to calculate the displacement of the interferometer length of the Fabry-Perot interferometer,
The displacement measuring device according to claim 2 . The controller is
Controlling the optical frequency comb and the frequency tunable laser such that the offset frequency and the beat frequency have the same value and opposite signs.
The displacement measuring device according to any one of claims 1 to 4. Locking the frequency of the frequency tunable laser with reference to the spectrum of the second laser beam output by the optical frequency comb that can control the repetition frequency and offset frequency;
Obtained from the reflected light intensity of the Fabry-Perot interferometer with respect to the first laser light output from the frequency-variable laser and incident on the Fabry-Perot interferometer, and interference light between the first laser light and the second laser light. And changing the frequency of the frequency variable laser and the repetition frequency so that the beat frequency is constant,
Based on the amount of change in the repetition frequency, the displacement of the interferometer length of the Fabry-Perot interferometer is calculated.
Displacement measurement method.

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