Tunable optical frequency comb spectrum calibration method

Abstract

The invention belongs to the technical field of spectrum calibration, and discloses a tunable optical frequency comb spectrum calibration method, which adopts a repetition frequency adjustable optical frequency comb as a calibration source, realizes flexible adjustment of comb tooth intervals by adjusting repetition frequency, and can accurately meet the requirements of spectrometers with different resolutions. The method mainly comprises the following steps: generating an offset frequency locking repetition frequency adjustable optical frequency comb, recording pixel positions of comb teeth of the optical frequency comb on a spectrometer CCD, establishing a wavelength-position mapping relation, optimizing a calibration model by applying machine learning, and carrying out error analysis and correction. Compared with a traditional spectrum calibration method, the method has the advantages of high-precision calibration, wide spectrum coverage range, flexible comb tooth intervals and adaptive optimization, is suitable for the fields of high-resolution spectrum analysis, scientific research and the like, and is particularly suitable for spectrum application scenes needing accurate wavelength calibration.

Description

Technical Field

[0001] This invention belongs to the field of spectral calibration technology, specifically a method for calibrating the wavelength of a spectrometer using a repetition-rate-tunable optical frequency comb. This method is applicable to fields requiring precise wavelength calibration, such as high-precision scientific instrumentation, spectral analysis, optical communications, quantum optics, and spectral imaging. It can significantly improve the measurement accuracy and reliability of spectrometers. Background Art

[0002] Spectroscopic instrument calibration involves both spectral and radiometric calibration. Spectral calibration is the foundation of high-precision radiometric calibration. Its primary task is to determine the wavelength center position and response characteristics of each detector pixel, establishing a pixel-wavelength function and spectral responsivity calibration. Accurate spectral calibration is crucial for improving spectrometer measurement accuracy, particularly in areas such as high-resolution spectral measurement, precision optical metrology, and scientific research.

[0003] At present, common spectral calibration methods mainly include atomic spectral lamp spectral calibration, monochromator spectral calibration and tunable laser spectral calibration. These methods have their own advantages and disadvantages:

[0004] Atomic spectrometer lamp calibration utilizes the characteristic spectral lines emitted by mercury or sodium lamps. Using a known discrete line spectrum, the relationship between scanning steps and wavelength is determined at a limited number of discrete points. The entire spectral range is then interpolated from these discrete points. A major limitation of this method is that the wavelength of light emitted by atomic spectrometer lamps is fixed, so calibration can only be performed on the center wavelength of a specific spectral channel, and comprehensive calibration of all spectral channels and the spectral response bandwidth is not possible.

[0005] The monochromator spectral calibration method uses a monochromator as a light source to produce a continuous monochromatic beam output, allowing the spectral response distribution function (SDR) of the spectrometer to be obtained across the entire wavelength range. However, this method has a low error tolerance, as factors such as the stability of the light source, the monochromator's optical system, and the dispersion coefficient of the dispersive element all affect the calibration accuracy. Furthermore, the monochromator's output spectrum has a wide linewidth, making it difficult to accurately calibrate high-resolution spectrometers.

[0006] The tunable laser spectral calibration method uses the output of a wavelength-tunable laser as the calibration light source. This method provides narrow-linewidth monochromatic light, which improves calibration accuracy. However, it can only calibrate a single wavelength at a time. Calibration at multiple wavelengths is cumbersome and introduces measurement errors with each operation, reducing overall calibration efficiency and accuracy.

[0007] In recent years, optical frequency comb technology has attracted widespread attention due to its unique spectral characteristics. An optical frequency comb is a light source composed of tens of thousands of equally spaced, narrow-linewidth spectral lines. The frequency of each comb tooth can be determined by the formula f n =n·f rep +fceo Exact calculation, where n is an integer, f rep is the repetition frequency, f ceo The carrier envelope offset frequency. The optical frequency comb is locked to an atomic clock, and the frequency stability can reach 10 -16 It provides an ideal reference source for high-precision spectral calibration.

[0008] However, the repetition rate of conventional optical frequency combs is typically fixed, and the inter-comb spacing cannot be adjusted to accommodate the resolution requirements of different spectrometers. For example, when the spectrometer's resolution is lower than the inter-comb spacing, some of the comb information cannot be resolved by the detector. Conversely, when the spectrometer's resolution is much higher than the inter-comb spacing, information redundancy and computational burden will result. Therefore, developing a method for calibrating optical frequency comb spectra with an adjustable repetition rate to flexibly match the requirements of spectrometers with different resolutions has important theoretical and practical value.

[0009] To address these challenges, the present invention proposes a tunable optical frequency comb spectral calibration method. This method achieves flexible control of the comb tooth spacing by adjusting the repetition frequency. Combined with machine learning algorithms to optimize the calibration model, it significantly improves the accuracy, efficiency, and adaptability of spectral calibration. This method not only overcomes the limitations of traditional calibration methods but also provides a new technical approach for high-precision spectral measurement. Summary of the Invention

[0010] The purpose of the present invention is to provide a tunable optical frequency comb spectrum calibration method, aiming to solve the technical problems of existing spectrum calibration methods such as insufficient accuracy, limited wavelength coverage, and poor adaptability, and to achieve high-precision, wide-band, and flexible spectrum calibration.

[0011] The technical solutions of the present invention are as follows:

[0012] A method for calibrating a tunable optical frequency comb spectrum comprises the following steps:

[0013] Step S1, generating a bias-frequency locked repetition-rate adjustable optical frequency comb: using a bias-frequency locked repetition-rate adjustable optical frequency comb system to generate an optical frequency comb locked to the frequency reference of a hydrogen atomic clock, wherein each comb tooth frequency of the optical frequency comb satisfies f n =n·f rep +f ceo , where n is an integer, f rep is the repetition frequency, f ceo is the carrier envelope offset frequency;

[0014] Step S2, recording the comb teeth information of the optical frequency comb: input the optical frequency comb into the spectrometer to be calibrated, and use the CCD detector to record the pixel position and intensity of each comb tooth;

[0015] Step S3: Establish wavelength-position mapping relationship: Use the comb teeth of known frequency to Establish a mapping model between pixel position and wavelength;

[0016] Step S4, machine learning optimization: Use BP neural network to process optical frequency comb data, take pixel position, temperature, air pressure and other parameters as input, and absolute wavelength as output to build an adaptive calibration model;

[0017] Step S5, error analysis and correction: calculate the comb center wavelength fitting residual, remove abnormal points, and optimize the calibration model;

[0018] Step S6, repetition frequency adjustment verification: adjust the repetition frequency of the optical frequency comb to generate different comb tooth intervals, and verify the repeatability and accuracy of the calibration.

[0019] Furthermore, the bias-locked, repetition-rate-adjustable optical frequency comb system in step S1 employs a grating + biconvex lens comb filter beat signal detection method with a signal-to-noise ratio of no less than 40 dB. This design ensures a sufficient signal-to-noise ratio for the beat signal, providing a foundation for subsequent precise locking.

[0020] Furthermore, in step S1, the phase error of the beat signal is determined using a lock-in amplifier-based frequency and phase detection method. The tunable laser frequency is then adjusted using a proportional-integral closed-loop control system to achieve offset frequency lock. This design enables precise control of the optical frequency comb offset frequency, ensuring its frequency stability and accuracy.

[0021] Furthermore, in step S1, dual-wavelength continuous light with different repetition rates is used for spectral pre-broadening, and time-domain pulse compression is performed using a single-mode fiber to generate ultrashort laser pulses with different repetition rates. By adjusting the length ratio of the single-mode fiber, ultrashort pulses with different repetition rates can be obtained, laying the foundation for the generation of optical frequency combs with adjustable repetition rates.

[0022] Furthermore, in step S1, digital frequency control technology is used to pre-control the beat frequency, a digital frequency control circuit is used to improve frequency stability, and an acousto-optic frequency shifter (AOFS) feedforward control system is combined for precise control. This multi-level control structure improves the stability and accuracy of the optical frequency comb frequency.

[0023] Furthermore, in step S3, for the virtual imaging phased array spectrometer, the transmission peak of a single comb tooth is fitted using the following Lorentz function: Where x is the position within one of the VIPA orders on the detector, a1, a2, and a3 represent coefficients, μ represents the expected position of the line center, and a3 is a parameter related to the full width at half maximum of the comb teeth. Using the Lorentzian function better aligns with the physical properties of the comb peaks, improving the accuracy of line center location.

[0024] Furthermore, the BP neural network architecture in step S4 includes an input layer, two hidden layers, and an output layer, wherein: (a) the input layer includes environmental parameters such as pixel position x, temperature T, and air pressure P; (b) the output layer is the absolute wavelength λ; (c) the output value calculation formula of the neuron node is: where x i is the input variable, w i is the input weight, s is the bias value, and f(x) is the activation function. This neural network structure can adaptively learn complex nonlinear mapping relationships and improve the accuracy and robustness of the calibration model.

[0025] Furthermore, the calculation method of the error correction in step S5 is: Δλ x =λ 实际,x -λ 拟合,x When |Δλ|>3σ (σ is the standard deviation), it is identified as an outlier and removed before refitting. This statistical method effectively identifies and removes outliers and improves the reliability of the calibration model.

[0026] Furthermore, in step S6, by adjusting the repetition frequency f of the optical frequency comb rep , monitor the wavelength deviation of the fixed comb teeth, and verify the comb frequency f by linear regression analysis n With f rep This verification method ensures the physical correctness and consistency of the calibration results.

[0027] Furthermore, this method achieves a wavelength calibration accuracy of ±0.002nm, suitable for high-resolution spectral analysis applications in the 500Hz to 8kHz frequency range. This accuracy meets the requirements of most high-precision spectral analysis applications.

[0028] The tunable optical frequency comb spectrum calibration method of the present invention has the following significant advantages over the prior art:

[0029] 1) High-precision calibration: The frequency of each tooth of the optical frequency comb can be accurately calculated by a formula, and by locking to an atomic clock, the frequency stability can reach 10 -16 The wavelength calibration accuracy is up to ±0.002nm.

[0030] 2) Wide spectral coverage: The optical frequency comb spectrum consists of tens of thousands of equally spaced comb teeth, which can cover the spectral range from hundreds of nanometers to several microns. It is suitable for high-precision calibration of wide-band spectrometers.

[0031] 3) Flexible comb spacing: By adjusting the repetition frequency (f rep ) and carrier envelope offset frequency (f ceo ), which can flexibly match the free spectral range or specific wavelength requirements of different spectrometers.

[0032] 4) Adaptive Optimization: Combines machine learning technology to process optical frequency comb data and automatically optimizes the wavelength-position mapping model to adapt to complex spectral characteristics and environmental changes.

[0033] 5) Efficient integration: A single measurement can complete the calibration of the entire band, greatly improving efficiency and reducing human errors compared to traditional methods.

[0034] The tunable optical frequency comb spectrum calibration method of the present invention can be widely used in fields such as high-precision spectral measurement, spectral imaging, quantum optics, optical communication, and scientific research, and is particularly suitable for high-resolution spectral application scenarios that require precise wavelength calibration. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. Those skilled in the art can also derive other drawings based on these drawings without inventive work, among which:

[0036] Figure 1 Schematic diagram of the optical frequency comb output. The left figure shows the optical frequency comb in the time domain, and the right figure shows the optical frequency comb in the frequency domain.

[0037] Figure 2 This is a diagram of the offset frequency locking scheme for tunable laser wavelengths over a wide range of optical frequency combs;

[0038] Figure 3 Mid-infrared frequency comb spectra and pulse diagrams generated by lasers with different repetition rates;

[0039] Figure 4 This is a diagram of the experimental setup, showing the system structure for spectral calibration based on a repetition rate-tunable optical frequency comb;

[0040] Figure 5 The left image shows a partial view of the spectrometer output, and the right image shows the identification of the comb pattern number.

[0041] Figure 6 To fit the line center diagram of the CCD, the frequencies of the observed comb modes are shown in relation to their line center positions on the CCD;

[0042] Figure 7 This is a diagram of the BP neural network architecture, showing the neural network structure used to optimize the calibration model. DETAILED DESCRIPTION

[0043] The following, in conjunction with specific embodiments, describes in detail the specific steps and operating procedures of a tunable optical frequency comb spectrum calibration method of the present invention so that ordinary technicians in the relevant technical field can implement the present invention. Through the following specific embodiments, technicians can fully understand and implement the technical solutions of the present invention.

[0044] See also Figure 1-7 As shown, this embodiment provides a specific implementation of a tunable optical frequency comb spectrum calibration method:

[0045] 1. Spectral Calibration Principle

[0046] Spectral instrument calibration includes spectral calibration and radiometric calibration. Spectral calibration is the basis for high-precision radiometric calibration of spectral instruments. Its main task is to determine the center position and response characteristics of each detector pixel corresponding to each wavelength, that is, to establish the pixel-wavelength function and spectral responsivity calibration.

[0047] Typically, the core of absolute wavelength calibration for a spectrometer lies in determining the wavelength-position relationship of each spectral fringe, which requires precise calibration of the fringe's centerline. Traditional methods, such as atomic spectral lamp calibration and monochromator calibration, have their limitations: atomic spectral lamps can only provide fixed discrete wavelength points, monochromator output spectral linewidths are wide, and calibration accuracy is limited by the accuracy of the monochromator itself. Tunable laser calibration is inefficient and suffers from large cumulative errors.

[0048] The present invention uses an optical frequency comb with offset frequency locking and adjustable repetition frequency for spectrum calibration. The basic principle is that the frequency of each tooth of the optical frequency comb can be calculated by the formula f n =n·f rep +f ceo Precise calculation, by locking to the atomic clock, the frequency stability can reach 10 -16 An optical frequency comb of known precise frequency is introduced into the spectrometer, and the position of the comb teeth on the detector is recorded using a CCD. A pixel-wavelength mapping relationship is established to achieve high-precision calibration.

[0049] 2. Principle of Optical Frequency Comb and Implementation of Adjustable Repetition Rate

[0050] 2.1 Principle of Optical Frequency Comb

[0051] like Figure 1 As shown, an optical frequency comb is an ultra-precise optical frequency measurement tool. Its spectrum consists of a series of equally spaced, narrow-linewidth frequency components, resembling a "comb," hence its name. The optical frequency comb's time domain output is a sequence of periodic laser pulses with a duration on the order of femtoseconds. Through Fourier transform, it is represented in the frequency domain as millions of equally spaced frequency components f. rep The laser longitudinal mode.

[0052] In the frequency domain, the nth comb tooth frequency f of the optical frequency comb isn Mathematically expressed as: f n =n·f rep +f ceo

[0053] Where n is an integer, f rep is the repetition frequency, f ceo is the carrier envelope offset frequency. By precisely controlling f rep and f ceo , the frequencies of all laser longitudinal modes can be determined.

[0054] 2.2 Bias frequency locking and re-frequency adjustable structure

[0055] like Figure 2 As shown, the present invention employs a beat signal detection method based on grating and biconvex lens comb filtering, achieving a signal-to-noise ratio (SNR) exceeding 40dB. Furthermore, a frequency and phase detection method based on the lock-in amplifier principle is used to obtain the phase error of the beat signal. The tunable laser frequency is then adjusted through a proportional-integral closed-loop control, ultimately locking its offset frequency to the target comb tooth. This achieves offset frequency locking of a tunable wide-range optical frequency comb traceable to a hydrogen atomic clock frequency reference.

[0056] The present invention realizes adjustable repetition frequency through the following steps:

[0057] The spectrum of dual-wavelength continuous light with fixed central wavelength and different repetition frequencies is pre-broadened, and the time domain pulse is compressed using single-mode optical fiber. By appropriately adjusting its length ratio, ultrashort pulse lasers with different repetition frequencies are obtained.

[0058] The digital frequency control technology is used to pre-control the beat frequency, and the digital frequency control circuit is used to improve the frequency stability.

[0059] A digital control module consisting of a microcontroller and a high-precision digital-to-analog converter is used to obtain PID control parameters through system identification.

[0060] A feedforward control system based on acousto-optic frequency shifter (AOFS) is used for precise control, and the relationship between the phase noise suppression effect and the delay time of AOFS is analyzed.

[0061] The semiconductor laser frequency is coarsely controlled and finely controlled respectively through digital frequency pre-control technology and AOFS-based feedforward control technology to achieve the same frequency stability as the reference frequency.

[0062] With AOFS as an optical voltage-controlled oscillator (OVCO), an optical phase-locked loop system is built and a mathematical model of the system is constructed to establish the relationship between the laser linewidth, loop gain and loop delay that meets the phase-locking conditions.

[0063] like Figure 3As shown in the figure, by using ultrashort pulses with different repetition rates as pump light, optical frequency combs with different comb tooth spacings can be generated. Under certain conditions of pump light pulse width and average power, a low repetition rate corresponds to a high peak power, and the lower the repetition rate, the wider the spectrum of the generated mid-infrared optical frequency comb.

[0064] 3. Spectral Calibration Method Based on Repetition-Rate Tunable Optical Frequency Comb

[0065] 3.1 Experimental setup

[0066] like Figure 4 As shown, the experimental setup of the present invention primarily comprises a repetition-rate-tunable optical frequency comb generator, a spectrometer, a CCD detector, and a data processing system. The frequency comb signal generated by the repetition-rate-tunable optical frequency comb generator is transmitted via optical fiber to the spectrometer to be calibrated. The spectrometer disperses the comb teeth of different frequencies to different positions. The CCD detector records the position and intensity of each comb tooth. Finally, the data processing system performs analysis and calculations to establish a pixel-to-wavelength mapping relationship.

[0067] 3.2 Calibration process and algorithm

[0068] Taking a virtual imaging phased array spectrometer as an example, the calibration process of the present invention is as follows:

[0069] 1. Comb frequency determination: The absolute frequency of the comb lines observed on the CCD can be expressed as f n =n·f rep +f ceo Since the laser diode frequency is known, the modulus n can be determined by combining the repetition frequency and offset frequency of the optical frequency comb. Figure 5 As shown, the left figure is a partial view of the spectrometer output, and the white solid line with arrows indicates the direction of indexing and counting continuous modes; the right figure shows the identification of the comb mode number, and the mode number n of the comb line at the position indicated by the dotted line is derived from the known wavelength of the diode frequency.

[0070] 2. Comb center positioning: According to the spectral dispersion law of the virtual imaging phased array spectrometer, the transmission peak of a single comb tooth is a Lorentz line shape. The comb signal recorded on the CCD is fitted using the Lorentz function, which is expressed as: Where x is the position within one of the VIPA steps on the detector, a1, a2, and a3 represent coefficients, μ represents the expected position of the line center, and a3 is a parameter related to the full width at half maximum of the comb teeth. The pixel center position of each comb tooth is determined by fitting.

[0071] 3. Establishment of wavelength-position mapping relationship: Figure 6As shown, the frequency of the comb pattern observed on the CCD is related to the position of the line center on the CCD. Using the comb teeth of the optical frequency comb with known frequencies, a pixel position-wavelength mapping relationship is established. The comb tooth frequency is converted to wavelength: where c is the speed of light in vacuum.

[0072] 4. Machine learning optimization calibration model: Use CCD detector to record the pixel position and intensity of the optical frequency comb teeth, use machine learning algorithm to process the optical frequency comb data, and automatically optimize the wavelength-position mapping model. Figure 7 As shown in the figure, a BP neural network architecture is used to process data. The input is parameters such as pixel position x, temperature T, and air pressure P, and the output label is the absolute wavelength λ. The output value calculation formula of each artificial neural node in the neural network is: Where x i is the input variable, w i is the input weight, s is the bias value, f(x) is the activation function, and y is the output value, i.e., the absolute wavelength λ. The hidden layer is set to 2 layers to form the final calibration model.

[0073] 5. Error correction: Calculate the fitting residual of all comb center wavelengths: Δλ x =λ 实际,x -λ 拟合,x If the residual error of a comb tooth exceeds three times the standard deviation (|Δλ|>3σ), it is judged as an outlier and removed and refitted to obtain the optimized model.

[0074] 6. Repetition frequency adjustment verification: Use a continuous optical input with fixed step lengths and different repetition frequencies to offset lock the repetition frequency adjustable optical frequency comb system, repeat the above calibration process, and monitor whether a fixed comb tooth changes with f rep Tune away from the absorption line center. Generate a wavelength-position mapping model for each repetition frequency to verify the repeatability of the wavelength calibration. n and f rep Perform linear regression analysis to verify that the slope is an integer n.

[0075] IV. Experimental Verification

[0076] To verify the effectiveness of the method of the present invention, an experimental test was conducted. The spectral line 1550.120nm was selected, and the experimental conditions were temperature T = 25°C and air pressure P = 1atm. The wavelength was calculated based on the pixel position and Gaussian fitting was performed to obtain the following data:

[0077]

[0078] Elimination condition: |Δλ|>0.003nm.

[0079] Further verification of dynamic repetition frequency adjustment was performed by adjusting the repetition frequency of the optical frequency comb and monitoring the wavelength shift of one of the comb teeth (original frequency 193.300 THz):

[0080]

[0081] This series of experiments verified that the wavelength calibration accuracy of the method of the present invention can reach ±0.002nm, which meets the needs of high-resolution spectral analysis, and can be flexibly adapted to the free spectral range of different spectrometers through repetition frequency adjustment.

[0082] V. Conclusion

[0083] The tunable optical frequency comb spectrum calibration method proposed in this invention has the following advantages:

[0084] 1) High-precision calibration: An optical frequency comb locked to an atomic clock provides an absolute frequency reference, achieving a wavelength calibration accuracy of ±0.002nm;

[0085] 2) Wide spectral coverage: The optical frequency comb spectrum consists of tens of thousands of equally spaced comb teeth, covering the spectral range from hundreds of nanometers to several microns;

[0086] 3) Flexible comb spacing: By adjusting the repetition frequency and carrier envelope offset frequency, it can flexibly match the resolution requirements of different spectrometers;

[0087] 4) Adaptive Optimization: Combines machine learning techniques to process optical frequency comb data, automatically optimizing the wavelength-position mapping model to adapt to complex spectral characteristics;

[0088] 5) Efficient integration: A single measurement can complete the calibration of the entire band, greatly improving efficiency and reducing human errors.

[0089] This method can be widely used in high-precision spectral measurement, spectral imaging, quantum optics, optical communications, scientific research and other fields, and is particularly suitable for high-resolution spectral application scenarios that require precise wavelength calibration.

[0090] Although specific embodiments of the present invention have been described above, those skilled in the art will appreciate that these specific embodiments are merely illustrative, and that those skilled in the art may omit, substitute, and modify the details of the methods and systems described above without departing from the principles and spirit of the present invention. For example, combining the above method steps to perform substantially the same functions in substantially the same manner to achieve substantially the same results falls within the scope of the present invention. Accordingly, the scope of the present invention is limited solely by the appended claims.

Claims

1. A method for calibrating a tunable optical frequency comb spectrum, characterized in that: The following steps are involved: Step S1, generating a bias-frequency locked repetition-rate adjustable optical frequency comb: using a bias-frequency locked repetition-rate adjustable optical frequency comb system to generate an optical frequency comb locked to the frequency reference of a hydrogen atomic clock, wherein each comb tooth frequency of the optical frequency comb satisfies f n =n·f rep +f ceo , where n is an integer, f rep is the repetition frequency, f ceo is the carrier envelope offset frequency; Step S2, recording the comb teeth information of the optical frequency comb: input the optical frequency comb into the spectrometer to be calibrated, and use the CCD detector to record the pixel position and intensity of each comb tooth; Step S3: Establish wavelength-position mapping relationship: Use the comb teeth of known frequency to Establish a mapping model between pixel position and wavelength; Step S4, machine learning optimization: Use BP neural network to process optical frequency comb data, take pixel position, temperature, air pressure and other parameters as input, and absolute wavelength as output to build an adaptive calibration model; Step S5, error analysis and correction: calculate the comb center wavelength fitting residual, remove abnormal points, and optimize the calibration model; Step S6, repetition frequency adjustment verification: adjust the repetition frequency of the optical frequency comb to generate different comb tooth intervals, and verify the repeatability and accuracy of the calibration.

2. The method for calibrating a tunable optical frequency comb spectrum according to claim 1, wherein: The bias-frequency locked repetition-frequency adjustable optical frequency comb system in step S1 adopts a grating + biconvex lens comb filter beat frequency signal detection method, and the signal-to-noise ratio is not less than 40dB.

3. The method for calibrating a tunable optical frequency comb spectrum according to claim 1, wherein: In step S1, the phase error of the beat signal is obtained by the frequency and phase detection method based on the lock-in amplifier principle, and the frequency of the tunable laser is adjusted through a proportional integral control closed loop to achieve offset frequency locking.

4. The method for calibrating a tunable optical frequency comb spectrum according to claim 1, wherein: In step S1, dual-wavelength continuous light with different repetition frequencies is selected for spectrum pre-broadening, and time-domain pulses are compressed using single-mode optical fiber to obtain ultrashort pulse lasers with different repetition frequencies.

5. The method for calibrating a tunable optical frequency comb spectrum according to claim 1, wherein: In step S1, the beat frequency is pre-controlled by using digital frequency control technology, the frequency stability is improved by using a digital frequency control circuit, and precise control is performed in combination with an acousto-optic frequency shifter (AOFS) feedforward control system.

6. The method for calibrating a tunable optical frequency comb spectrum according to claim 1, wherein: In step S3, for the virtual imaging phased array spectrometer, the transmission peak of a single comb tooth is fitted using the following Lorentz function: where x is the position within one of the VIPA orders on the detector, a1, a2, and a3 represent coefficients, μ represents the expected position of the line center, and a3 is a parameter related to the full width at half maximum of the comb teeth.

7. The method for calibrating a tunable optical frequency comb spectrum according to claim 1, wherein: The BP neural network architecture in step S4 includes an input layer, two hidden layers, and an output layer, wherein: (a) the input layer includes environmental parameters such as pixel position x, temperature T, and air pressure P; (b) the output layer is the absolute wavelength λ; (c) the output value calculation formula of the neuron node is: where x i is the input variable, w i is the input weight, s is the bias value, and f(x) is the activation function.

8. The method for calibrating a tunable optical frequency comb spectrum according to claim 1, wherein: The calculation method of the error correction in step S5 is: Δλ x =λ 实际,x -λ 拟合,x ,xWhen |Δλ|>3σ (σ is the standard deviation), it is determined to be an abnormal point and is removed and refitted.

9. The method for calibrating a tunable optical frequency comb spectrum according to claim 1, wherein: In step S6, the repetition frequency f of the optical frequency comb is adjusted rep , monitor the wavelength deviation of the fixed comb teeth, and verify the comb frequency f by linear regression analysis n With f rep Whether the slope of is an integer n.

10. The method for calibrating a tunable optical frequency comb spectrum according to claim 1, wherein: The wavelength calibration accuracy achieved by this method can reach ±0.002nm, which is suitable for high-resolution spectral analysis applications in the frequency range of 500Hz to 8kHz.

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