Measurement type picometer-scale displacement resolution generation method based on twin double cavities

Abstract

The invention discloses a measurement type picometer-level displacement resolution generation method based on twin double cavities, and the method comprises the steps: employing a group of twin Fabry-Perot cavities with matched parameters, and the twin Fabry-Perot cavities comprise a measurement cavity and a reference cavity; based on the PDH technology, the lasers of the two lasers are locked to harmonic peaks of the measuring cavity and the reference cavity respectively, and then the resonant frequency is measured through an optical frequency comb to represent the displacement amount; a set frequency stepping signal is output through an optical phase-locked loop, the frequency stepping signal is converted into a voltage control signal to be loaded to a PZT of a measurement cavity, the PZT is driven to drive a reflector to move so as to change the cavity length, and a controllable picometer-scale standard displacement step is generated. According to the invention, on the basis of twin Fabry-Perot cavity resonant frequency differential mode detection, a common mode signal caused by Fabry-Perot cavity environment noise can be suppressed, the cavity length displacement is directly traced to an optical frequency standard, and absolute traceability and high-resolution measurement of a picometer-level displacement signal are realized.

Description

Technical Field

[0001] This invention relates to the field of precision displacement measurement and optical metrology, specifically to a metrological picometer-level displacement resolution generation method based on twin cavities. Background Technology

[0002] In high-end technology fields such as precision manufacturing, micro-nano fabrication, and quantum physics experiments, picometer-level (10) -12 Displacement measurement and standard displacement generation at the picometer level are core requirements for ensuring equipment accuracy and improving measurement reliability. They are also key technological bottlenecks in the field of precision metrology. High-resolution displacement generation is not only a prerequisite for picometer-level displacement measurement, but also the foundation for achieving traceable and comparable measurement results. Currently, laser interferometers are the mainstream technology for precision displacement measurement. They utilize the coherence of lasers to achieve optical amplification and detection of displacement. The most advanced laser interferometers can achieve a measurement resolution on the order of tens of picometers. However, due to environmental noise interference and the incompleteness of the traceability link, their actual displacement resolution can only reach the sub-nanometer level (10⁻⁶ picometers). -9 (m), which is insufficient to meet the needs of picometer-level measurement.

[0003] Existing picometer-level displacement generation technologies suffer from the following drawbacks: environmental disturbances such as temperature fluctuations, changes in air refractive index, and mechanical vibrations directly affect the stability of the measurement reference (e.g., cavity length, optical path), resulting in a large amount of noise superimposed on the displacement signal, making it difficult to achieve stable picometer-level resolution; traditional methods often rely on physical structure dimensions or indirect calibration for displacement references, failing to directly trace back to basic units in the International System of Units (SI), leading to insufficient metrological attributes of the measurement results and poor consistency between different devices; existing technologies struggle to generate precise, repeatable picometer-level standard displacement steps and lack corresponding noise control schemes, making them unsuitable as calibration references for high-precision displacement sensors. Therefore, a metrological picometer-level displacement resolution generation method based on twin-cavity systems is needed. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a novel method for generating picometer-level displacement resolution based on twin-cavity measurement, thereby improving the accuracy of picometer-level standard displacement step distance and enhancing the repeatability and stability of the final instrument measurement.

[0005] To achieve the above objectives, the present invention provides the following technical solution: A method for generating metrological picometer-level displacement resolution based on twin-cavity dual-chamber system includes: A set of parameter-matched twin Fabry-Perot cavities is used, including a measurement cavity and a reference cavity; Based on PDH technology, the laser beams of the two lasers are locked onto the resonant peaks of the measurement cavity and the reference cavity, respectively. Then, the resonant frequency is measured by an optical frequency comb to characterize the displacement. An optical phase-locked loop outputs a set frequency step signal, which is then converted into a voltage control signal and applied to the PZT in the measurement cavity. This drives the PZT to move the reflector to change the cavity length, generating a controllable picometer-level standard displacement step.

[0006] Furthermore, by beating the output light from the first and second lasers with an optical frequency comb, respectively, the beat frequency signal and the corresponding comb tooth number are obtained, and then the frequencies of the two lasers are calculated. The displacement of the measuring cavity relative to the reference cavity can then be obtained. The calculation formula is:

[0007] in The repetition frequency of the optical frequency comb; The frequency comb tooth number is used to measure the locking frequency of the cavity; The frequency comb number is the reference cavity locking frequency. To measure the beat frequency of the cavity locking laser and the corresponding comb teeth; The reference cavity lock laser and the beat frequency of the corresponding comb teeth are used to determine the beat frequency. The initial cavity length of the FP cavity, This is the initial resonant frequency.

[0008] Furthermore, the laser frequencies of the two lasers are respectively locked to specific resonant peaks of the twin FP cavity. By detecting the error signal of the reflected light, the laser diode current and PZT voltage of the lasers are adjusted to achieve stable locking. The error signal is obtained by: reflecting the laser light that does not meet the resonant frequency of the twin FP cavity out of the cavity, passing through a quarter wave plate, and then reflecting it to a photodetector in a polarizing beam splitter; the photodetector converts the reflected light signal into an electrical signal, which is the error signal.

[0009] Furthermore, the output light from the two lasers is polarized by a half-wave plate and then reflected by a PBS to the same fiber coupler to achieve beat frequency with an optical frequency comb, which provides a quantitative reference traceable to time and frequency standards.

[0010] Furthermore, the reflected light from the two lasers is spatially combined after its polarization state is adjusted by a half-wave plate, and then beats through a polarizer. The signal is received by a PD and converted into an electrical signal, which is then fed back to the optical phase-locked loop. The optical phase-locked loop converts the phase error signal into a voltage control signal for the PZT through loop filtering.

[0011] Furthermore, the step size of the picometer-level displacement step satisfies: ; in, The initial cavity length of the Fabry-Perot cavity; This is the reference frequency at which the laser locks to the resonant peak of the Fabry-Perot cavity. Step number; This indicates the frequency step value set by the optical phase-locked loop.

[0012] On the other hand, an apparatus for implementing the method includes: A pair of twin Fabry-Perot cavities, including a measurement cavity and a reference cavity; First laser and second laser; The first PDH frequency stabilization system and the second PDH frequency stabilization system are used to lock the frequencies of the first laser and the second laser to the resonant frequencies of the measurement cavity and the reference cavity, respectively. An optical frequency comb system is used to provide a frequency reference; A beat frequency detection system is used to acquire the beat frequency signals of the first laser and the second laser with the optical frequency comb system, respectively. A frequency counter is used to measure the frequency of the beat frequency signal; An optical phase-locked loop is used to control the cavity length variation of the measurement cavity based on the beat frequency signal between the first laser and the second laser and the optical frequency comb system. The output of the first laser is sequentially connected to the first electro-optic modulator, the first polarization beam splitter, and the first quarter-wave plate before being incident on the measurement cavity. The reflected light output of the first polarization beam splitter is connected to the input of the first photodetector. The output of the first photodetector is connected to the first PDH frequency stabilization system. The feedback output of the first PDH frequency stabilization system is connected to the control input of the first laser. The output of the second laser is sequentially connected to the second electro-optic modulator, the second polarization beam splitter, and the second quarter-wave plate before being incident on the reference cavity. The reflected light output of the second polarization beam splitter is connected to the second photodetector. The output of the second photodetector is connected to the second PDH frequency stabilization system. The feedback output of the second PDH frequency stabilization system is connected to the control input of the second laser. After locking, the output terminals of the first and second lasers are respectively connected to the input terminal of the beat frequency detection system. The output terminal of the optical frequency comb system is connected to the reference input terminal of the beat frequency detection system. The output terminal of the beat frequency detection system is connected to the input terminal of the frequency counter. The output terminal of the frequency counter is connected to the input terminal of the optical phase-locked loop. The control output terminal of the optical phase-locked loop is connected to the piezoelectric ceramic driver of the measuring cavity.

[0013] It should be noted that the "locked output" is the part of the optical path that is drawn from the locked laser and used for subsequent measurements. In the main locked optical path, there is a beam splitter that splits the light into two paths: one path is used to complete the locking, and the other locked output is used to complete the beat frequency.

[0014] Furthermore, the device also includes a polarization control element and an optical fiber coupler to achieve coupling and polarization adjustment of spatial light and optical fiber light.

[0015] This invention provides a metrological picometer-level displacement resolution generation method based on twin-cavity dual-chamber, which has the following beneficial effects: This invention is based on differential mode detection of the resonant frequency of twin Fabry-Perot cavities. It can suppress common-mode signals caused by environmental noise in Fabry-Perot cavities and directly trace the cavity length displacement to the optical frequency standard, realizing absolute traceability and high-resolution measurement of picometer-level displacement signals. It can achieve a resolution of 10 pm within a measurement range of 5 μm. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of a dual-cavity difference frequency phase-locked loop picometer displacement step system for a metrological picometer displacement resolution generation method based on twin cavities according to the present invention. The components are as follows: 1. Optical frequency comb; 2. First polarization-maintaining single-mode fiber; 3. First fiber coupler; 4. First mirror; 5. First PBS; 6. First half-wave plate; 7. First laser; 8. Second half-wave plate; 9. Second PBS; 10. Polarizer; 11. First photodetector; 12. Optical phase-locked loop; 13. Twin FP cavity; 14. Electro-optic modulator; 15. Third PBS; 16. First quarter-wave plate; 17. Second photodetector; 18. PDH frequency stabilization; 19. Second laser; 20. Third half-wave plate; 21. Fourth PBS; 22. Fourth half-wave plate; 23. Fifth PBS; 24. Electro-optic modulator; 25. Sixth PBS; 26. Second quarter-wave plate; 27. Third photodetector; 28. PDH frequency stabilization system; 29. ​​Second mirror; 30. Second fiber coupler; 31. Second polarization-maintaining single-mode fiber. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0018] This invention includes the following steps: A set of parameter-matched twin Fabry-Perot cavities is used, including a measurement cavity and a reference cavity; Based on PDH technology, two lasers are locked onto the resonance peaks of the measurement cavity and the reference cavity, respectively, and then the resonance frequency is measured by an optical frequency comb to characterize the displacement. An optical phase-locked loop outputs a set frequency step signal, which is then converted into a voltage control signal and applied to the PZT in the measurement cavity. This drives the PZT to move the reflector to change the cavity length, generating a controllable picometer-level standard displacement step.

[0019] This invention describes a novel method for generating picometer-level displacement steps using a dual-cavity difference-frequency phase-locked loop (PDH). This method utilizes a PDH to lock the laser frequency to the resonant peak of the FP cavity. Picometer-level displacement changes in the cavity length are detected by an optical frequency comb, and then the picometer-level displacement signal generated by the optical PDH controls the cavity length variation. The basic principle of its implementation is deduced below.

[0020] PDH frequency stabilization lock receives the reflected light from the twin FP cavity through a photoelectric receiver and extracts the error signal. The PDH frequency stabilization module then regulates the laser diode current and PZT voltage of the laser to lock the laser frequencies of the two lasers to the corresponding resonant peaks of the twin FP cavity. The resonant frequency beat frequency measurement involves reflecting the output light from the two locked lasers through a half-wave plate and a PBS to a fiber coupler, which then couples the light to a polarization-maintaining single-mode fiber and beats it with an optical frequency comb. The resonant frequency of a Fabry-Perot cavity is related to the longitudinal mode order, the speed of light in vacuum, the refractive index of the cavity medium, and the cavity length. The change in cavity length is relatively small compared to the cavity length itself. When the change in refractive index is negligible ( The resonant frequency change of the FP cavity can be expressed as:

[0021] The initial cavity length of the FP cavity is Environmental disturbances (temperature, material expansion, etc.) affect the cavity length. In a twin-cavity design, one cavity serves as the measurement cavity, where the PZT drives the cavity length change, while the other cavity serves as the reference cavity, where the PZT remains stationary. Both cavities are affected by the same environmental conditions, thus the environmental impact on the cavity length is the same. However, the displacement to be measured is only superimposed on one of the cavities. Therefore, the value of the displacement to be measured is the difference in cavity length between the two cavities. This is the actual resonant frequency of cavity 1; This is the actual resonant frequency of cavity 2. Common disturbance. exist It's all there, but in the difference It can be eliminated, and at the same time, the difference frequency Only the measured displacement It is directly proportional. This is the principle of common-mode suppression, and its mathematical formula can be expressed as:

[0022]

[0023] In this method, the actual differential is achieved by beating the two laser frequencies with the optical frequency comb. The beat frequency signal value is read by a frequency counter, and the two laser frequencies can be represented by the carrier envelope offset frequency, repetition frequency, and comb tooth number. Then, differential calculation is performed to complete the shift-to-frequency conversion. The specific mathematical formula can be expressed as follows:

[0024] in The repetition frequency (tooth spacing) of the optical frequency comb. The frequency comb tooth number locked for cavity 1; The frequency comb tooth number locked to cavity 2; The laser and the corresponding comb tooth beat frequency are locked in cavity 1; The laser in cavity 2 is locked to the beat frequency of the corresponding comb teeth.

[0025] Then, a standard displacement step is generated using an optical phase-locked loop (OPLL). When the OPLL drives the PZT to actively generate a known displacement signal, it essentially gives a set frequency step to the laser frequency that has been locked to the resonant peak of the FP cavity. Closed-loop automatic adjustment of the PZT length to change the cavity length The new resonance conditions are met. This is to satisfy the frequency set for target locking. The phase error signal is converted into a voltage control signal by the OPLL loop filter and applied to the PZT to make a small step on the frequency setting. The system will automatically change the cavity length to To satisfy the new resonant frequency, perform equal-interval frequency steps. This yields a series of picometer-level standard displacement steps:

[0026] The specific implementation system is as follows: Figure 1 As shown, the output of the first laser is sequentially connected to the first electro-optic modulator, the first polarization beam splitter, and the first quarter-wave plate before being incident on the measurement cavity. The reflected light output of the first polarization beam splitter is connected to the input of the first photodetector. The output of the first photodetector is connected to the first PDH frequency stabilization system. The feedback output of the first PDH frequency stabilization system is connected to the control input of the first laser. The output of the second laser is sequentially connected to the second electro-optic modulator, the second polarization beam splitter, and the second quarter-wave plate before being incident on the reference cavity. The reflected light output of the second polarization beam splitter is connected to the second photodetector. The output of the second photodetector is connected to the second PDH frequency stabilization system. The feedback output of the second PDH frequency stabilization system is connected to the control input of the second laser. After locking, the output terminals of the first and second lasers are respectively connected to the input terminal of the beat frequency detection system. The output terminal of the optical frequency comb system is connected to the reference input terminal of the beat frequency detection system. The output terminal of the beat frequency detection system is connected to the input terminal of the frequency counter. The output terminal of the beat frequency detection system is connected to the input terminal of the optical phase-locked loop. The control output terminal of the optical phase-locked loop is connected to the piezoelectric ceramic driver of the measuring cavity.

[0027] Two identical 780nm semiconductor lasers output spatial light, which, after passing through an electro-optic modulator, generates a modulation frequency sideband of approximately 20MHz. This light then passes through a PBS (Polymerizable Surface Photonics) and a quarter-wave plate before entering separate FP (Fractional Photonic) cavities. Each cavity length has a specific resonant frequency. Laser light that does not meet this resonant frequency is reflected out of the cavity, passes through the quarter-wave plate again, and is reflected in the PBS. This reflection is then received by a PD (Polymerization Device) for error signal processing. A PDH (Polymerization Device) stabilizes the laser diode current and PZT (Polymerization Z-T) voltage of the two ECDLs (Electronic Laser Diodes), thereby controlling the laser frequency to lock to the resonant frequency of the specific cavity length of the FP cavity. The two FP cavities are strictly parameter-matched "twin cavities," made of the same material, and located in the same environment. Environmental disturbances such as temperature, refractive index, and mechanical drift are treated as common modes and significantly eliminated in the difference frequency modulation. After locking the laser frequency to the FP cavity resonant frequency, the lasers from the two ECDLs pass through a half-wave plate and are reflected by a PBS to an optical fiber coupler. This couples the spatial light into the fiber to achieve beat frequency with the optical frequency comb. Utilizing the high-precision frequency comb teeth of the femtosecond optical frequency comb, the dual-cavity resonant frequency is traced back to a time reference, achieving high-precision measurement of the laser frequency and direct frequency-to-displacement tracing. The PZT drives the intracavity mirror to move, thereby changing the cavity length and generating displacement. The laser frequencies from both lasers are reflected in the same direction after passing through the half-wave plate and PBS. One reflected beam passes through the half-wave plate again to change its polarization state and spatially combines with the other laser beam. After passing through a polarizer, the beam beats and is received by a PD and converted into an electrical signal. This signal is then controlled by an optical phase-locked loop (PLL), which acts as the displacement "driving core." Frequency tuning precisely controls the cavity length change, and combined with PZT driving, achieves controllable and repeatable picometer-level standard displacement steps.

[0028] In a specific embodiment, two 780nm wavelength ECDLs generate a 20MHz modulation sideband via an electro-optic modulator, which is then fed into a twin-cavity system with a cavity length of 100mm, an FSR of 1.5GHz, and a precision of 312.8. PDH frequency stabilization successfully locks the laser frequency to the resonant peak of the twin-cavity system. One of the FP cavities is driven to change its cavity length via PZT. The two lasers, now locked to their resonant peaks, are then subjected to beat frequency detection with an optical frequency comb to obtain two beat frequency signals and two comb tooth sequence numbers. The difference in the frequencies of the two lasers at this point can be calculated, representing the difference in the cavity lengths of the twin cavities and thus the magnitude of the displacement to be measured. Furthermore, controlling the beat frequency of the two lasers to 38kHz via an optical phase-locked loop allows for a 10pm change in the FP cavity length.

[0029] Picometer-level displacement resolution is generated by precisely controlling the difference frequency of the dual-cavity resonant frequencies using an optical phase-locked loop (PLL). Specifically, this involves locking the frequencies of two 780nm ECDL lasers to the dual-cavity resonant peaks using PDH technology, measuring the dual-cavity resonant frequencies with high precision using an optical frequency comb, and characterizing the cavity length using frequency via Fabry-Perot cavity resonant frequency detection. Picometer-level displacement changes in cavity length are then translated into minute frequency changes. Finally, the PZT is moved by controlling the standard picometer-level displacement signal through the optical PLL, causing a change in cavity length and thus generating picometer-level displacement resolution.

[0030] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A metrology picometer displacement resolution generation method based on twin-cavity twin, characterized in that, The method comprises the following steps: A set of twin Fabry-Perot cavities matched with a set of parameters are used, including a measurement cavity and a reference cavity; Based on the PDH technology, the laser of two lasers is locked to the resonance peak of the measurement cavity and the reference cavity respectively, and then the resonance frequency is measured by an optical frequency comb to characterize the displacement amount; A set frequency step signal is output by an optical phase-locked loop, the frequency step signal is converted into a voltage control signal, and the voltage control signal is loaded to the PZT of the measurement cavity to drive the PZT to move the mirror to change the cavity length, thereby generating a controllable picometer standard displacement step.

2. The twin-cavity based metrology picometer displacement resolution generation method of claim 1, wherein: By beating the output light of the first laser and the second laser with the optical frequency comb respectively, beat signals and corresponding comb tooth numbers are obtained, and then the frequencies of the two lasers are calculated. The displacement amount of the measurement cavity relative to the reference cavity can be obtained , and the calculation formula is: ； wherein is the repetition frequency of the optical frequency comb; is the frequency comb tooth number of the measurement cavity locked laser; is the frequency comb tooth number of the reference cavity locked laser; is the beat frequency of the measurement cavity locked laser and the corresponding comb tooth, is the beat frequency of the reference cavity locked laser and the corresponding comb tooth, is the initial cavity length of the FP cavity, is the initial resonance frequency.

3. The twin-cavity based metrology picometer displacement resolution generation method of claim 1, wherein: The laser frequency of two lasers is locked to the specific resonance peak of the twin FP cavity, and the laser diode current and PZT voltage of the laser are adjusted to achieve stable locking by detecting the error signal of the reflected light, and the error signal is obtained by: the laser that does not satisfy the resonance frequency of the twin FP cavity is reflected out of the cavity, passes through a 1 / 4 wave plate, is reflected to a photodetector in a polarization beam splitter prism, and the reflected light signal is converted into an electrical signal by the photodetector, which is the error signal.

4. The twin-cavity based metrology picometer displacement resolution generation method of claim 1, wherein: The output light of the two lasers is adjusted in polarization state by a half-wave plate, reflected to a fiber coupler through a PBS, and beat with an optical frequency comb, which provides a traceable value reference to the time frequency standard.

5. The twin-cavity based metrology picometer displacement resolution generation method of claim 1, wherein: The reflected light of the two lasers is adjusted in polarization state by a half-wave plate to achieve spatial beam combination, and then beat through a polarizer, and the beat signal is received by a PD and converted into an electrical signal and fed back to an optical phase-locked loop, which converts the phase error signal into a voltage control signal of the PZT through loop filtering.

6. The twin-cavity based metrology picometer displacement resolution generation method of claim 1, wherein: The step amount of the picometer displacement step satisfies: ； wherein, is the initial cavity length of the Fabry-Perot cavity; is the reference frequency at which the laser is locked to the Fabry-Perot cavity resonance peak, is the step number of the step, represents the frequency step value set by the optical phase-locked loop.

7. A twin-cavity based metrology picometer displacement resolution generating device for implementing the method of any one of claims 1-6, characterized in that, It comprises: A pair of twin Fabry-Perot cavities, including a measurement cavity and a reference cavity; A first laser and a second laser; A first PDH frequency stabilization system and a second PDH frequency stabilization system for locking the frequencies of the first laser and the second laser to the resonance frequencies of the measurement cavity and the reference cavity respectively; An optical frequency comb system for providing a frequency reference; A beat detection system for obtaining beat signals of the first laser and the second laser with the optical frequency comb system respectively; A frequency counter for measuring the frequency of the beat signal; An optical phase-locked loop for controlling the change of the cavity length of the measurement cavity according to the output of the frequency counter; The output end of the first laser is connected to a first electro-optic modulator, a first polarization beam splitter, and a first quarter-wave plate in sequence, and then incident to the measurement cavity, the reflected light output end of the first polarization beam splitter is connected with the input end of a first photodetector, the output end of the first photodetector is connected with the first PDH frequency stabilization system, and the feedback output end of the first PDH frequency stabilization system is connected with the control input end of the first laser. The output end of the second laser is connected to a second electro-optic modulator, a second polarization beam splitter, a second quarter-wave plate in sequence and then incident to the reference cavity, the reflected light output end of the second polarization beam splitter is connected to a second photodetector, the output end of the second photodetector is connected to the second PDH frequency stabilization system, and the feedback output end of the second PDH frequency stabilization system is connected to the control input end of the second laser; The locked output ends of the first laser and the second laser are respectively connected to the input end of the beat frequency detection system, the output end of the optical frequency comb system is connected to the reference input end of the beat frequency detection system, the output end of the beat frequency detection system is connected to the input end of the frequency counter, the output end of the beat frequency detection system is connected to the input end of the optical phase-locked loop, and the control output end of the optical phase-locked loop is connected to the piezoelectric ceramic driver of the measurement cavity.

8. The apparatus of claim 7, wherein, The device further comprises a polarization control element and a fiber coupler to realize the coupling of spatial light and fiber light and polarization adjustment.

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