A micro-displacement measurement system and method based on a reflecting sphere F-P cavity

Abstract

The application discloses a micro-displacement measurement system and method based on a reflecting sphere F-P cavity, a low-precision F-P cavity is constructed by using a reflecting sphere, so that a response curve of the F-P cavity to a wavelength is close to a sinusoidal curve, and multi-beam reflection in a ranging light path is eliminated. By using the technical scheme, the problem that high reflectivity of two reflecting surfaces of an F-P cavity in the prior art leads to multi-beam interference and causes measurement error can be solved; meanwhile, measurement precision and sensitivity are improved, and high-precision nanometer-level micro-displacement measurement in a large working range can be met.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of sensors, and particularly relates to a micro displacement measurement system and method based on a reflective sphere F-P cavity. BACKGROUND

[0002] Length, as one of the seven basic physical units, with the increasing cognition and exploration of the world by human beings, the accurate measurement and metrology technology thereof plays an important role in many frontier fields such as aerospace technology, nanometer (nm) scale measurement, material science research, ultra-precision manufacturing process, biological exploration and microelectronic industry. In addition, the accurate measurement of length also plays a fundamental supporting role in high-end equipment manufacturing quality and plays a decisive role in the whole manufacturing process. Therefore, the construction of nanometer level measurement standard is a key and basic challenge in the field of metrology science to promote the development of nanotechnology. In the nanometer measurement technology, the resolution of 100 nanometers to 0.1 nanometer can be realized, which provides key technical support for many high-precision and high-resolution requirements and constitutes an important cornerstone of nanotechnology research.

[0003] At present, the method for nanometer level measurement can be divided into non-optical type and optical type. The non-optical type mainly includes capacitive sensor, inductive sensor and scanning probe microscope, etc. This kind of method has the advantages of high resolution, low power consumption, good temperature stability, etc. However, the measurement range of this kind of method is small, only tens of nanometers to micrometers (μm) order of magnitude, which is mainly used for short distance micro displacement measurement. In comparison, the optical method has the advantages of high precision, high resolution, small volume, strong anti-electromagnetic interference ability, non-contact measurement, traceability, etc., and shows more extensive application potential. The optical method mainly includes Michelson interferometer, grating interferometer and Fabry-Perot (F-P) interferometer. The structures of Michelson and grating interferometers both have independent reference arms and measurement arms, and high-precision micro displacement measurement (nm or sub-nm level) is realized by measuring the difference between the two light paths, which requires the stability of the reference optical path to reach nm or sub-nm level. The F-P interferometer cancels the independent reference arm and integrates the reference light path into the measurement system, effectively avoiding the influence of the instability of the reference arm on the measurement result. However, in the existing micro displacement measurement method based on F-P cavity, there is multiple reflection phenomenon in the F-P cavity, forming multiple beam interference, which leads to the introduction of non-linear error in the ranging system. In addition, the F-P cavity is usually composed of two parallel placed reflective film layers, and the parallelism of the two reflective surfaces is required to be high in the actual installation process, which increases the application difficulty. SUMMARY

[0004] The technical problem to be solved by the present application is to provide a micro displacement measurement method and system based on a reflective sphere F-P cavity.

[0005] To achieve the above object, the present application adopts the following technical solutions:

[0006] The present application also provides a micro displacement measurement system based on a reflecting sphere F-P cavity, which uses a reflecting sphere to construct a low-precision F-P cavity, so that the response curve of the F-P cavity to the wavelength is close to a sinusoidal curve, and the multi-beam reflection in the ranging light path is eliminated.

[0007] The present application also provides a micro displacement measurement system based on a reflecting sphere F-P cavity, which comprises a laser, a temperature control module, an optical coupler, an acetylene gas absorption cell, a first photodetector, a demodulator, a radio frequency source, a driving current source, a circulator, a laser collimator, a beam expander, a reflecting sphere, an optical amplifier, an optical filter, a photodetector, a power divider, a first electric amplifier, a second electric amplifier, a first frequency mixer, a second frequency mixer, a first low-pass filter, a second low-pass filter, and a processor.

[0008] The temperature control module is connected with a temperature control pin of the laser; the output of the laser is connected with the input of the optical coupler; the first output end of the optical coupler is connected with the input end of the acetylene gas absorption cell; the second output end of the optical coupler is connected with the first port of the circulator; the output end of the acetylene gas absorption cell is connected with the input end of the first photodetector; the output end of the first photodetector is connected with the input end of the demodulator; the output end of the demodulator is connected with the output end of the driving current source; the output end of the driving current source is connected with the current driving of the laser; the first output end of the radio frequency source is connected with the radio frequency input end of the demodulator; the second port of the circulator is connected with the input end of the laser collimator; the output end of the laser collimator is connected with the input end of the beam expander, and the output end of the beam expander serves as a transmitting end and is incident to the reflecting sphere surface of the measured target; the third port of the circulator is connected with the input end of the optical amplifier; the output end of the optical amplifier is connected with the input end of the optical filter; the output end of the optical filter is connected with the input end of the second photodetector; the output end of the second photodetector is connected with the input end of the power divider; the first output end of the power divider is connected with the input end of the first electric amplifier; the second output end of the power divider is connected with the input end of the second electric amplifier; the output end of the first electric amplifier is connected with the radio frequency input end of the first frequency mixer; the output end of the second electric amplifier is connected with the radio frequency input end of the second frequency mixer; the second output end of the radio frequency source is connected with the local oscillator input end of the first frequency mixer; the third output end of the radio frequency source is connected with the local oscillator input end of the second frequency mixer; the output end of the first frequency mixer is connected with the input end of the first low-pass filter; the output end of the second frequency mixer is connected with the input end of the second low-pass filter; the output end of the first low-pass filter is connected with the first input end of the processor; and the output end of the second low-pass filter is connected with the second input end of the processor.

[0009] Preferably, the input end of the laser collimator is an optical fiber and the output end is free space light.

[0010] The application also provides a micro displacement measurement method based on the reflective sphere F-P cavity.

[0011] The application also provides a micro displacement measurement method based on the reflective sphere F-P cavity, which comprises the following steps.

[0012] A radio frequency source is turned on to output a modulation signal with a frequency of f0;

[0013] Laser output with a wavelength of λ0 is converted into free space light by a laser collimator, and about 4% of the end reflection exists on the exit end face of the laser collimator. The reflected light returns to the optical fiber of the laser collimator, and returns to the second port of the circulator. This part of the light field is recorded as a reference light field.

[0014] About 96% of the spatial transmission light of the laser collimator is reflected by the expansion lens and then the reflective sphere. The reflective sphere is placed on a piezoelectric nanometer positioning table, and then the light field returns to the end face of the laser collimator. This part of the light field is recorded as a measurement light field. The reference light field and the measurement light field interfere with each other at the end face of the laser collimator, and the light field after the interference returns to the second port of the circulator and is output from the third port of the circulator.

[0015] The photoelectric detector converts the optical signal into an electrical signal, and the frequency components of the electrical signal are f0 and 2f0.

[0016] The second frequency f0 signal output by the radio frequency source is used as the local oscillator input signal of the first mixer, and the third frequency 2f0 signal output by the radio frequency source is used as the local oscillator input signal of the second mixer.

[0017] The moving parameters of the piezoelectric nanometer positioning table are set so that the reflective sphere vibrates in a square wave with a peak-to-peak value of 50 nm.

[0018] Only the signal with the same frequency as the local oscillator signal f0 can be mixed to a direct current signal in the first mixer. The direct current signal is transmitted to the first low-pass filter, and after filtering out the sum frequency signal, the signal is recorded as A0.

[0019] Only the signal with the same frequency as the local oscillator signal 2f0 can be mixed to a direct current signal in the second mixer. The direct current signal is transmitted to the second low-pass filter, and after filtering out the sum frequency signal, the signal is recorded as B0.

[0020] The amplitude of the modulation signal output by the radio frequency source is adjusted so that A0=B0.

[0021] The processor brings the two-way direct current signals A0 and B0 into the formula Wherein, φ1 is the initial phase of the light field when the reflecting sphere is not moved, and arccos is the inverse trigonometric function of the cosine function.

[0022] The reflecting sphere is set to move a fixed distance, and the moving distance is denoted as ΔL.

[0023] After the reflecting sphere moves, the output signal of the first low-pass filter is denoted as A1, and the output signal of the second low-pass filter is denoted as B2.

[0024] The processor brings the two-way direct current signals A1 and B2 after the reflecting sphere moves into the formula Wherein, φ1 is the phase of the light field after the reflecting sphere moves.

[0025] The processor takes the difference between φ0 and φ1 to obtain Δφ L = φ1- φ0, wherein Δφ L is the change amount of the phase of the light field before and after the reflecting sphere moves.

[0026] The processor brings Δφ L into the formula to obtain the to-be-measured micro-displacement parameter ΔL.

[0027] As preferred, the temperature control module is connected with the temperature control pin of the laser; the output of the laser is connected with the input of the optical coupler; the first output end of the optical coupler is connected with the input end of the acetylene gas absorption cell; the second output end of the optical coupler is connected with the first port of the circulator; the output end of the acetylene gas absorption cell is connected with the input end of the first photodetector; the output end of the first photodetector is connected with the input end of the demodulator; the output end of the demodulator is connected with the output end of the driving current source; the output end of the driving current source is connected with the current driving of the laser; the first output end of the radio frequency source is connected with the radio frequency input end of the demodulator; the second port of the circulator is connected with the input end of the laser collimator; the output end of the laser collimator is connected with the input end of the beam expander lens, and the output end of the beam expander lens is taken as the emission end and is incident to the measured target reflecting sphere surface; the third port of the circulator is connected with the input end of the optical amplifier; the output end of the optical amplifier is connected with the input end of the optical filter; the output end of the optical filter is connected with the input end of the second photodetector; the output end of the second photodetector is connected with the input end of the power divider; the first output end of the power divider is connected with the input end of the first electric amplifier; the second output end of the power divider is connected with the input end of the second electric amplifier; the output end of the first electric amplifier is connected with the radio frequency input end of the first frequency mixer; the output end of the second electric amplifier is connected with the radio frequency input end of the second frequency mixer; the second output end of the radio frequency source is connected with the local oscillator input end of the first frequency mixer; the third output end of the radio frequency source is connected with the local oscillator input end of the second frequency mixer; the output end of the first frequency mixer is connected with the input end of the first low pass filter; the output end of the second frequency mixer is connected with the input end of the second low pass filter; the output end of the first low pass filter is connected with the first input end of the processor; and the output end of the second low pass filter is connected with the second input end of the processor.

[0028] The present application utilizes the reflecting sphere to construct a low-fineness F-P cavity, so that the response curve of the F-P cavity to the wavelength should be close to a sinusoidal curve, which can effectively eliminate the multi-beam reflection in the ranging light path and reduce the nonlinear error of the system. In addition, due to the symmetry structure of the reflecting sphere itself, the construction of the system light path has the characteristic of being insensitive to installation deviation. BRIEF DESCRIPTION OF DRAWINGS

[0029] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description only are the embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor based on the provided drawings.

[0030] Figure 1A structure schematic diagram of a micro displacement measurement system based on a reflecting sphere F-P cavity according to an embodiment of the present application;

[0031] Figure 2 A flow chart of a micro displacement measurement method according to an embodiment of the present application.

[0032] Figure 3 The demodulation signal when the center wavelength of the laser output is at different positions of the acetylene gas absorption peak; wherein, Figure 3 (a) of the present application is that the center wavelength of the laser output is aligned with the acetylene gas absorption peak, Figure 3 (b) of the present application is that the center wavelength of the laser output is at the left side of the acetylene gas absorption peak, Figure 3 (c) of the present application is that the center wavelength of the laser output is at the right side of the acetylene gas absorption peak.

[0033] Figure 4 The experimental results when the reflecting sphere moves with a peak-to-peak value of 50 nm in the form of a square wave; wherein, (a) is the f and 2f terms, (b) is the displacement curve, and (c) is 18 groups of micro displacement values. DETAILED DESCRIPTION

[0034] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative efforts belong to the scope of protection of the present application.

[0035] In order to make the above objectives, characteristics and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0036] As shown in Figure 1 the present application provides a micro displacement measurement system based on a reflecting sphere F-P cavity, which comprises a laser 1, a temperature control module 2, an optical coupler 3, an acetylene gas absorption cell 4, a first photodetector 5, a demodulator 6, a radio frequency source 7, a driving current source 8, a circulator 9, a laser collimator 10, a beam expander 11, a reflecting sphere 12, an optical amplifier 13, an optical filter 14, a photodetector 15, a power divider 16, a first electric amplifier 17, a second electric amplifier 18, a first frequency mixer 19, a second frequency mixer 20, a first low pass filter 21, a second low pass filter 22, and a processor 23.

[0037] The temperature control module 2 is connected to the temperature control pin of the laser 1; the output of the laser 1 is connected to the input of the optical coupler 3; the first output terminal of the optical coupler 3 is connected to the input terminal of the acetylene gas absorption cell 4; the second output terminal of the optical coupler 3 is connected to the first port of the circulator 9; the output terminal of the acetylene gas absorption cell 4 is connected to the input terminal of the first photodetector 5; the output terminal of the first photodetector 5 is connected to the input terminal of the demodulator 6; the output terminal of the demodulator 6 is connected to the output terminal of the drive current source 8; The output of the driving current source 8 is connected to the current drive of the laser 1; the first output of the radio frequency source 7 is connected to the radio frequency input of the demodulator 6; the second port of the circulator 9 is connected to the input of the laser collimator 10; the output of the laser collimator 10 is connected to the input of the beam expander lens 11, and the output of the beam expander lens 11 serves as the emitting end of this device, incident on the surface of the target reflector sphere 12; the third port of the circulator 9 is connected to the input of the optical amplifier 13; the output of the optical amplifier 13 is connected to the optical filter. The input terminal of optical filter 14 is connected to the input terminal of second photodetector 15; the output terminal of second photodetector 15 is connected to the input terminal of power divider 16; the first output terminal of power divider 16 is connected to the input terminal of first amplifier 17; the second output terminal of power divider 16 is connected to the input terminal of second amplifier 18; the output terminal of first amplifier 17 is connected to the RF input terminal of first mixer 19; the output terminal of second amplifier 18 is connected to the RF input terminal of second mixer 20; the second output terminal of RF source 7 is connected to the local oscillator input terminal of first mixer 19; the third output terminal of RF source 7 is connected to the local oscillator input terminal of second mixer 20; the output terminal of first mixer 19 is connected to the input terminal of first low-pass filter 21; the output terminal of second mixer 20 is connected to the input terminal of second low-pass filter 22; the output terminal of first low-pass filter 21 is connected to the first input terminal of processor 23; the output terminal of second low-pass filter 22 is connected to the second input terminal of processor 23.

[0038] The laser collimator 10 has an optical fiber input and free-space light output. The beam expander 11 expands the laser beam, improving its propagation performance. The optical amplifier 13 amplifies the power of the optical signal. The optical filter 14 filters out noise and improves signal quality.

[0039] like Figure 2 As shown, this embodiment of the invention also provides a method for measuring micro-displacement using a micro-displacement measurement system based on a reflective sphere FP cavity, comprising:

[0040] Step 1: open the radio frequency source 7, output frequency modulation signal f0, when the laser 1 output wavelength is located at different positions of acetylene gas absorption cell absorption peak, the phase of feedback signal is 180°, as shown in Figure 3 , demodulator 6 by judging the phase of the feedback signal to identify the output wavelength of the laser 1, thereby controlling the output current of the driving current source 8, and then feedback control the output wavelength of the laser 1, finally the stability of the wavelength is accurately controlled, so that it can be stabilized output;

[0041] Step 2: record the center wavelength of the laser 1 output laser as λ0, due to the influence of wavelength modulation, the phase change caused by the change of wavelength is sinusoidal, which is expressed as: Δφ(t) = φ0+ ΔφsinΩt, wherein, φ0 = 2nΔL·2π / λ0, φ0 represents the additional phase introduced by the center wavelength. ΔL is the moving distance of the reflecting ball, that is, the micro displacement to be measured, Δλ is the maximum change of wavelength, and Δφ is the maximum value of the additional phase change.

[0042] Step 3: the laser 1 output wavelength λ0 laser through the laser collimator 10 becomes free space light, there is about 4% end face reflection at the exit end face of the laser collimator 10, this part of the reflected light returns to the optical fiber of the laser collimator 10, returns to the second port of the circulator 9, this part of the light field is recorded as reference light field;

[0043] Step 4: about 96% of the space transmission light emitted by the laser collimator 10 is incident on the surface of the reflecting ball 12 through the beam expander lens 11, the reflecting ball 12 is placed on the piezoelectric nanometer positioning table, and then the light field returns to the end face of the laser collimator 10, this part of the light field is recorded as measurement light field, the reference light field and the measurement light field interfere at the end face of the laser collimator 10, and the interference light field returns to the second port of the circulator 9 and is output from the third port of the circulator 9;

[0044] Step 5: the photoelectric detector 15 converts the optical signal into an electrical signal, and the frequency components of the electrical signal are f0 and 2f0;

[0045] Step 6: the second frequency f0 signal output by the radio frequency source 7 is used as the local oscillator input signal of the first frequency mixer 19, and the third frequency 2f0 signal output by the radio frequency source 7 is used as the local oscillator input signal of the second frequency mixer 20;

[0046] Step 7: set the moving parameters of the piezoelectric nanometer positioning table, so that the reflecting ball 12 vibrates with a peak-to-peak value of 50 nm;

[0047] Step 8: Only the signal with the same frequency as the local oscillator signal f0 can be mixed to a direct current signal in the first mixer 19, and the direct current signal is transmitted to the first low pass filter 21. After filtering the sum frequency signal, the signal is recorded as A0;

[0048] Step 9: Only the signal with the same frequency as the local oscillator signal 2f0 can be mixed to a direct current signal in the second mixer 20, and the direct current signal is transmitted to the second low pass filter 22. After filtering the sum frequency signal, the signal is recorded as B0;

[0049] Step 10: Adjust the amplitude of the output modulation signal of the radio frequency source 7 so that A0=B0, so as to satisfy the following relationship: J1(Δφ)=J2(Δφ), where J1 is the first order Bessel function value. This step completes the optical path calibration process of the system, ensuring that the amplitudes of the two orthogonal item signals measured vary completely equally with the distance;

[0050] Step 11: The processor 23 brings the two direct current signals A0 and B0 into the following formula Where φ1 is the initial phase of the optical field when the reflecting sphere is not moved, and arccos is the inverse trigonometric function of the cosine function;

[0051] Step 12: Set the reflecting sphere 12 to move a fixed distance, and the moving distance is recorded as ΔL;

[0052] Step 13: After the reflecting sphere 12 moves, the output signal of the first low pass filter 21 is recorded as A1, and the output signal of the second low pass filter 22 is recorded as B2;

[0053] Step 14: The processor 23 brings the two direct current signals A1 and B2 after the reflecting sphere 12 moves into the following formula Where φ1 is the phase of the optical field after the reflecting sphere moves;

[0054] Step 15: The processor 23 takes the difference between φ0 and φ1 to obtain Δφ L = φ1-φ0, where Δφ L is the change amount of the optical field phase before and after the reflecting sphere 12 moves;

[0055] Step 16: The processor 23 brings Δφ L into the following formula to obtain the measured micro displacement parameter ΔL, and the result is shown in Figure 3 (a). The high and low steps of each complete square wave are averaged with the same number of steps to obtain the result shown by the white dots in Figure 3 (b). The difference between adjacent values is obtained to obtain 18 groups of displacement values, as shown in Figure 3 (c). The average of the 18 groups of values is taken to obtain the final micro displacement value measured by the system as 53 nm.

[0056] The present application has the following technical effects:

[0057] 1. Only one radio frequency source is needed, which simplifies the structure and reduces the cost of practical application;

[0058] 2. The F-P cavity is constructed by the end surface of the laser collimator and the surface of the reflecting sphere, and the precision can be flexibly adjusted;

[0059] 3. The F-P cavity greatly simplifies the optical alignment process, and the angle of the reflecting surface does not need to be adjusted, thereby reducing the difficulty of application;

[0060] 4. The spatial distance is measured by the laser collimator and the reflecting sphere, and the device is simple and flexible, easy to realize and integrate;

[0061] 5. The low-precision F-P cavity realized by the reflecting sphere makes the wavelength response curve close to a sinusoidal curve, which can effectively eliminate the multi-beam reflection in the distance measuring optical path and reduce the measurement error of the system.

[0062] 6. Since the low-precision F-P cavity avoids the influence of nonlinear error, the device has the characteristics of high measurement precision and high sensitivity;

[0063] 7. In the quadrature demodulation algorithm, the amplitudes of the two quadrature signals change completely equally with the distance, which can meet the measurement precision in a large working range.

[0064] 8. Through monitoring the output quadrature signals of the system, real-time display and real-time measurement can be realized.

[0065] The present application can solve the problem of multi-beam interference caused by the high reflectivity of the two reflecting surfaces of the F-P cavity in the prior art, which causes measurement error. The technical solution provided by the present application improves the measurement precision and sensitivity by using the design of the reflecting sphere, and can meet the high-precision nanometer-level micro-displacement measurement in a large working range.

[0066] The above-described embodiments are only descriptions of the preferred modes of the present application, and do not limit the scope of the present application. Without departing from the design spirit of the present application, various modifications and improvements to the technical solutions of the present application made by those skilled in the art shall fall within the protection scope determined by the claims of the present application.

Claims

1. A micro-displacement measurement system based on a reflective spherical FP cavity, characterized in that, include: Laser, temperature control module, optical coupler, acetylene gas absorption cell, first photodetector, demodulator, radio frequency source, drive current source, circulator, laser collimator, beam expander lens, reflector sphere, optical amplifier, optical filter, photodetector, power divider, first electrical amplifier, second electrical amplifier, first mixer, second mixer, first low-pass filter, second low-pass filter, processor; The temperature control module is connected to the temperature control pin of the laser; the output of the laser is connected to the input of the optical coupler; the first output of the optical coupler is connected to the input of the acetylene gas absorption cell; the second output of the optical coupler is connected to the first port of the circulator; the output of the acetylene gas absorption cell is connected to the input of the first photodetector; the output of the first photodetector is connected to the input of the demodulator; the output of the demodulator is connected to the output of the driving current source; the output of the driving current source is connected to the current drive of the laser; the first output of the radio frequency source is connected to the radio frequency input of the demodulator; the second port of the circulator is connected to the input of the laser collimator; the output of the laser collimator is connected to the input of the beam expander lens, and the output of the beam expander lens serves as the emitting end, incident on the surface of the reflective sphere of the target being measured; the third port of the circulator is connected to the input of the optical amplifier; the output of the optical amplifier... The following components are connected to the input of an optical filter: the output of the optical filter is connected to the input of a second photodetector; the output of the second photodetector is connected to the input of a power divider; the first output of the power divider is connected to the input of a first electrical amplifier; the second output of the power divider is connected to the input of a second electrical amplifier; the output of the first electrical amplifier is connected to the RF input of a first mixer; the output of the second electrical amplifier is connected to the RF input of the second mixer; the second output of the RF source is connected to the local oscillator input of the first mixer; the third output of the RF source is connected to the local oscillator input of the second mixer; the output of the first mixer is connected to the input of a first low-pass filter; the output of the second mixer is connected to the input of a second low-pass filter; the output of the first low-pass filter is connected to the first input of a processor; and the output of the second low-pass filter is connected to the second input of the processor. The input of the laser collimator is an optical fiber, and the output is free space light. The micro-displacement measurement method based on a reflective spherical FP cavity implemented by the system includes: Turn on the RF source, the output frequency is The modulated signal; The laser output wavelength is The laser light is converted into free space light through the laser collimator. There is about 4% end-face reflection at the output end face of the laser collimator. This part of the reflected light returns to the optical fiber of the laser collimator along the original path and returns to the second port of the circulator. This part of the optical field is called the reference optical field. Approximately 96% of the spatially transmitted light emitted from the laser collimator is incident on the surface of the reflecting sphere through a beam expander lens and reflected. The reflecting sphere is placed on a piezoelectric nanopositioning stage, and then the light field returns to the end face of the laser collimator along the original path. This part of the light field is denoted as the measurement light field. At the end face of the laser collimator, the reference light field and the measurement light field interfere with each other. The light field after interference returns to the second port of the circulator and is output from the third port of the circulator. Photodetectors convert optical signals into electrical signals, and the frequency components of the electrical signals are: and ; The second frequency output from the RF source is The signal is used as the local oscillator input signal of the first mixer, and the third frequency output from the RF source is... The signal is used as the local oscillator input signal of the second mixer; Set the movement parameters of the piezoelectric nano-positioning stage to make the reflective sphere vibrate with a square wave with a peak-to-peak value of 50nm; The first mixer only contains the local oscillator signal. Only signals with the same frequency can be mixed to form a DC signal. This DC signal is then transmitted to the first low-pass filter. After filtering out the sum-frequency signal, the resulting signal is denoted as... ; The second mixer contains only the local oscillator signal. Only signals with the same frequency can be mixed to form a DC signal. This DC signal is then transmitted to a second low-pass filter. After filtering out the sum-frequency signal, the resulting signal is denoted as... ; Adjust the amplitude of the modulation signal output by the radio frequency source so that ; The processor will convert two DC signals and Substitute into the formula ,in, The initial phase of the light field when the reflecting sphere is not moving. It is the inverse trigonometric function of the cosine function; The reflector ball is set to move a fixed distance, denoted as . ; After the reflecting ball moves, the output signal of the first low-pass filter is denoted as: The output signal of the second low-pass filter is denoted as ; The processor moves the two DC signals. and Substitute into the formula ,in, The phase of the light field after the reflecting sphere moves; The processor will and Doing bad things, getting... ,in, This represents the change in the phase of the light field before and after the reflecting sphere moves; The processor will Substitute into the formula Obtain the micro-displacement parameters to be measured .

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