A method for traceable uncertainty evaluation of dynamic wavelength calibration

Abstract

This invention provides a traceable uncertainty assessment method for dynamic wavelength calibration. First, it performs uncertainty source analysis based on Taylor series expansion, determining that the time-frequency relationship calibration uncertainty is mainly determined by the uncertainty of the local continuous time-frequency relationship. Then, it assesses the impact of peak location on uncertainty, the uncertainty of the standard interferogram, and the uncertainty of interference intensity under complex tuning conditions, quantifying the standard interferogram uncertainty and the measurement uncertainty generated by local normalized frequency interpolation. These are then combined to obtain the combined uncertainty of the normalized time-frequency relationship. Finally, the combined uncertainty of the normalized time-frequency relationship is multiplied by the free spectral range of the F-P interferometer to obtain the absolute uncertainty of the time-frequency relationship calibration. This invention enables the quantification and propagation analysis of each error component during nonparametric point-by-point calibration, establishing a systematic uncertainty assessment framework and providing a scientific basis for the reliability of the calibration results.

Description

Technical Field

[0001] This invention relates to the field of spectral measurement accuracy assessment technology, specifically to a traceable uncertainty assessment method for dynamic wavelength calibration. Background Technology

[0002] Tunable semiconductor laser absorption spectroscopy (TDLAS) technology, with its advantages of real-time online operation, non-invasiveness, and high sensitivity, has become a core technology in high-precision measurement fields such as combustion diagnostics and hypersonic flow field detection. Accurate calibration of the laser's dynamic wavelength (time-dependent frequency response) is a crucial prerequisite for ensuring the spectral resolution accuracy of the TDLAS system, while scientific uncertainty assessment is the core means of quantifying the reliability of dynamic wavelength calibration results. Only by establishing a full-link uncertainty traceability system covering "hardware error - data processing - dynamic effects" can verifiable accuracy data be provided for measurement results in complex scenarios, meeting the stringent requirements for data reliability in high-precision applications.

[0003] In the field of uncertainty assessment technology for dynamic measurement and spectroscopy, although various patented solutions have been explored, their adaptability to the dynamic wavelength calibration scenario of TDLAS is insufficient, with the following specific limitations:

[0004] Chinese patent CN202411107416.3 discloses a method that calculates the basic uncertainty components using a static model and combines this with time-varying data trends to construct dynamic weighting coefficients to adjust the component proportions. While this improves the real-time performance of general dynamic assessment, it fails to identify core components such as the "standard interferogram construction error" in TDLAS dynamic wavelength calibration, making it impossible to accurately pinpoint key aspects of frequency calibration accuracy. Chinese patent CN202411503913.5 discloses a method that constructs a full-link static error propagation model of "optical system-detector-data processing," identifying error sources such as lens distortion and synthesizing total uncertainty. However, it does not address the time-frequency relationship fluctuations under laser dynamic tuning, which is incompatible with the requirement of quantifying "frequency drift over time" in TDLAS and cannot cover dynamic scanning scenarios. Chinese patent CN202211345623.3 discloses a method for evaluating systematic errors by comparing values ​​before and after calibration using a dual-calibration wavelength meter consisting of an "FP resonant cavity + saturated absorption module." However, it fails to establish an uncertainty propagation relationship based on the core hardware of TDLAS, making it impossible to trace the source from interference signal intensity error to frequency physical dimensions. Another Chinese patent CN202210411685.3 discloses a method for constructing a static spectrometer wavelength reference using low-coherence interference signals and evaluating uncertainty by repeatedly measuring the fluctuation of interference peak positions. However, it does not consider the time-varying characteristics of laser frequency and non-ideal tuning effects under TDLAS dynamic scanning, thus failing to meet the dynamic calibration requirements in harsh environments.

[0005] The common shortcomings of the above-mentioned patents are that none of them specifically identify the core uncertainty components of TDLAS dynamic wavelength calibration, they do not establish a transfer relationship with the core hardware of the system, and most of them are only suitable for static scenarios. They cannot provide scientific and traceable quantitative basis for the uncertainty of TDLAS dynamic wavelength calibration results, which restricts the application expansion of this technology in the field of high-precision measurement.

[0006] Therefore, developing an uncertainty assessment method that is adapted to the dynamic wavelength calibration scenario of TDLAS and covers the entire link error tracing has become a key requirement for improving the reliability of TDLAS measurement results. Summary of the Invention

[0007] To address the technical problems of dynamic wavelength calibration uncertainty assessment methods being unable to adapt to nonparametric point-by-point calibration processes and having poor traceability, this invention proposes a traceable uncertainty assessment method for dynamic wavelength calibration. This method can quantify and transmit the error components during the nonparametric point-by-point calibration process, establish a systematic uncertainty assessment framework, and provide a scientific basis for the reliability of calibration results.

[0008] To address the aforementioned technical problems, this invention provides a traceable uncertainty assessment method for dynamic wavelength calibration, comprising the following steps:

[0009] (1) Uncertainty source analysis

[0010] Uncertainty source analysis was performed based on Taylor series expansion, which determined that the calibration uncertainty of the time-frequency relationship is mainly determined by the uncertainty of the local continuous time-frequency relationship.

[0011] (2) Evaluation of uncertainty components

[0012] The impact of peak location on uncertainty, standard interferogram uncertainty, and interference intensity uncertainty under complex tuning conditions were evaluated, and the standard interferogram uncertainty was quantified respectively. Measurement uncertainty arising from local normalized frequency interpolation ;

[0013] (3) Calculation of combined uncertainty

[0014] uncertainty of standard interferogram and measurement uncertainty The combined uncertainty of the normalized time-frequency relationship is obtained by combining the results. Then, the combined uncertainty of the normalized time-frequency relationship is multiplied by the free spectral range of the FP interferometer to obtain the absolute uncertainty of the time-frequency relationship calibration.

[0015] As a preferred embodiment of the present invention, the specific process of the uncertainty source analysis is as follows:

[0016] Mathematical model based on nonparametric point-by-point calibration method:

[0017] ;

[0018] Time-frequency relationship calibration results uncertainty Source tracing analysis can be performed using Taylor series expansion. The free spectral range of the FP interferometer The step function is an extension of the normalized discrete time-frequency relation calibrated by discrete interference peaks. For the locally normalized continuous time-frequency relationship defined by the standard interferogram, since these three components are independent, the total uncertainty is... The transitive relationship is as follows:

[0019] ;

[0020] In practical measurements for dynamic wavelength calibration, the FP interferometer, with its high precision, is essential. By limiting The fitting range ensures its uncertainty. Neglecting this, the above formula simplifies to:

[0021] ;

[0022] The derivative is zero in the non-endpoint region, and the uncertainty of the time-frequency relationship calibration. The uncertainty mainly consists of the local continuous time-frequency relationship. Decide:

[0023] .

[0024] As a preferred embodiment of the present invention, the specific process of peak location impact assessment in step (2) is as follows:

[0025] Considering the indirect impact of peak localization error on the construction of standard interferograms, the standardization of measured signals, and the establishment of time-domain references, peak region data is included in the uncertainty assessment of standard interferograms, and peak standardization error is considered in complex tuning analysis. Specifically, the steps include:

[0026] (2.1.1) Standard Interferogram Construction Stage

[0027] When constructing a standard interferogram, multi-period interferometric signals are superimposed and averaged, with peak region data retained and included in the statistics; for each normalized frequency point... Interference intensity The standard deviation is calculated using the Bessel formula:

[0028] ;

[0029] In the above formula, The number of interference periods. For the same normalized frequency point in multi-period measurements The corresponding standard deviation of the interference intensity;

[0030] Will As input, the standard interference intensity after range normalization is calculated using the following formula for uncertainty propagation. uncertainty :

[0031] ;

[0032] Based on the frequency-intensity mapping relationship in the standard interferogram, the local normalized frequency is obtained. Uncertainty:

[0033] ;

[0034] For the extreme regions where the intensity-frequency mapping sensitivity of the interferogram approaches zero at the crests and troughs, the uncertainty is limited by the peak positioning accuracy. Therefore, the upper limit of the uncertainty is set to the width of this region. A uniform conservative estimate is taken across all frequency positions in all interferometry cycles, and three times the maximum uncertainty in the non-extreme regions is taken as the overall estimate of the standard interferogram uncertainty. ;

[0035] (2.1.2) Standardization stage of measured signal

[0036] For the measured interferometric signals acquired under complex tuning conditions, the peak intensity of all interferometric peaks was statistically analyzed. ;calculate Standard deviation As the interference intensity coefficient Uncertainty:

[0037] ;

[0038] Interference intensity coefficient uncertainty The interference intensity is transmitted to the measured standard through a standardized processing procedure. Interference intensity coefficient The fluctuations cause an overall scaling of the interference intensity within each interference cycle. After smoothing the signal within a single interference cycle using spline fitting, the interference intensity is linearly mapped to the [0,1] interval according to the left and right monotonic intervals. This fluctuation is included in the total uncertainty of the interference intensity and is ultimately transmitted to the measurement uncertainty. ;

[0039] (2.1.3) Time-domain reference establishment stage

[0040] The positioning error at the peak moment will cause the normalized discrete time-frequency relationship to be affected. The time base is shifted, which manifests as a translation of the step function on the time axis; due to Since the derivative is zero in the non-endpoint region, the direct impact of this time base offset on frequency measurement is limited to the peak neighborhood, and therefore its contribution to the frequency uncertainty of most measurement points is negligible.

[0041] As a preferred embodiment of the present invention, the specific process for evaluating the uncertainty of the standard interferogram is as follows:

[0042] (2.2.1) Analyze the sources of error, including interpolation method, detection system response deviation, system electrical noise, optical path noise, and interference peak positioning deviation:

[0043] (2.2.2) By superimposing and averaging multiple interferometric periodic signals to suppress random errors, the measurement uncertainty of the interferometric intensity is calculated using Bessel's formula:

[0044] ;

[0045] (2.2.3) Obtain the uncertainty of the standard interferogram through uncertainty propagation. :

[0046] ;

[0047] Finally, the uncertainty of the locally normalized frequency is obtained through the mapping relationship:

[0048] ;

[0049] For extreme regions such as peaks and troughs, the sensitivity of the interference intensity-frequency mapping approaches zero, and direct calculation will lead to uncertainty divergence. Therefore, the upper limit of uncertainty is set to the width of this region. For extreme regions such as peaks and troughs where point-by-point calculation diverges due to sensitivity approaching zero, three times the maximum uncertainty of non-extreme regions is used as the overall estimate of the uncertainty of the standard interferogram to replace the unobtainable point-by-point uncertainty value.

[0050] As a preferred embodiment of the present invention, the specific process for evaluating the uncertainty of interference intensity under complex tuning conditions is as follows:

[0051] (2.3.1) Obtaining the standard deviation of the interference intensity coefficient

[0052] ① Under complex tuning conditions, peak detection is performed on the measured interference signal, and the peak intensity of all interference peaks is extracted. According to the FP interference principle, the peak intensity of each interference peak should theoretically be equal to the interference intensity coefficient. ,Right now ;

[0053] ② Due to the influence of detection system response deviation, optical path disturbance, and noise, the peak intensity detected in different interference periods fluctuates; therefore, the peak intensity of all interference peaks is statistically analyzed, and their standard deviation is calculated. As the interference intensity coefficient Measurement uncertainty:

[0054] ;

[0055] In the above formula, The total number of interference peaks detected. The peak intensity of the i-th interference peak, The arithmetic mean of all peak intensities;

[0056] ③ Interference intensity coefficient uncertainty The interference intensity is transmitted to the measured standard after a standardization process. ; The fluctuations cause an overall scaling of the interference intensity within each interference cycle. After smoothing the signal within a single interference cycle using spline fitting, the interference intensity is linearly mapped to the [0,1] interval according to the left and right monotonic intervals, and the uncertainty is propagated using the following formula:

[0057] ;

[0058] Calculate the uncertainty of standard interference intensity This fluctuation is incorporated into the total uncertainty of the interference intensity and ultimately propagates to the measurement uncertainty. ;

[0059] (2.3.2) Quantization of residuals from smooth spline fitting

[0060] Smooth spline fitting is performed on the interference signal within a single interference period to obtain the fitting residual. If the residuals follow a zero-mean normal distribution and are uniform in the time domain, then:

[0061] ;

[0062] If the residuals exhibit asymmetric distribution or time-varying characteristics, then:

[0063] ;

[0064] (2.3.3) Combination of total uncertainty of interference intensity

[0065] The detection system response deviation and the fitting residual components are synthesized using the following formula:

[0066] ;

[0067] (2.3.4) Measurement uncertainty propagated to the local normalized frequency

[0068] Through standardization, Transmission to standard interference intensity The uncertainty is then obtained by interpolation mapping to obtain the uncertainty of the locally normalized frequency:

[0069] ;

[0070] For the extreme value region, the globally unified estimate is taken as... The upper limit estimate.

[0071] As a preferred embodiment of the present invention, the specific process of the synthesis uncertainty of the normalized time-frequency relationship is as follows:

[0072] The uncertainty of the standard interferogram Measurement uncertainty caused by interpolation of local normalized frequencies According to the formula The synthesis yields the synthesis uncertainty of the normalized time-frequency relationship. ;Will Free spectral range of FP interferometer Multiply them to obtain the absolute uncertainty of the time-frequency relationship calibration.

[0073] By adopting the above technical solution, the present invention has the following beneficial effects:

[0074] The present invention presents a well-conceived method for assessing traceable uncertainty in dynamic wavelength calibration. It constructs an uncertainty assessment framework adapted to the non-parametric point-by-point calibration process, enabling end-to-end traceability analysis from interference signal intensity error to final frequency uncertainty. Compared with existing technologies, this invention solves the technical problem of the difficulty in quantifying and assessing uncertainty using non-parametric methods, providing a scientific quantitative basis for the reliability of TDLAS dynamic wavelength calibration results.

[0075] This invention systematically identifies and quantifies multi-source errors in the dynamic wavelength calibration process, including interpolation method errors, detection system response deviations, system electrical noise, optical path noise, and interference peak positioning deviations. By independently evaluating and synthesizing each error component, this invention achieves a refined characterization of calibration uncertainty, which is more scientific and complete than traditional methods that rely solely on the standard deviation of fitted residuals.

[0076] This invention establishes a full-process impact assessment mechanism for peak positioning error, which incorporates the impact of peak positioning error into three stages: standard interferogram construction, measured signal standardization, and time domain benchmark establishment for systematic evaluation. This ensures that the peak positioning error is fully reflected in the final composite uncertainty, avoiding the problem of this error being ignored or underestimated in traditional methods.

[0077] This invention proposes an upper limit setting method based on region width constraints for extreme regions such as peaks and troughs in interferograms, solving the technical problem of uncertainty calculation divergence caused by the "intensity-frequency mapping sensitivity approaching zero" in extreme regions. A conservative estimation strategy of three times the maximum uncertainty of non-extreme regions is adopted in the global unified estimation, balancing the reliability of the evaluation results with the convenience of practical application.

[0078] Experimental verification shows that, using the uncertainty assessment method proposed in this invention, with FSR=0.0172 cm⁻¹, -1 Under conditions of a silicon-based FP interferometer, the absolute uncertainty of the time-frequency relationship calibration can be as low as 0.00053 cm⁻¹. -1 The accuracy is approximately 15 MHz, close to the physical limit of the intrinsic linewidth (~10 MHz) of a DFB laser. This level of accuracy is significantly better than traditional parameterization methods, providing a reliable optical frequency reference for high-precision spectral measurements.

[0079] The method of this invention can effectively adapt to complex modulation strategies such as sinusoidal scanning, sinusoidal modulation, and square wave modulation, and can capture dynamic fluctuations in laser frequency. Comparative experiments show that the method of this invention, while maintaining system accuracy comparable to the parameterization method (deviation <3.1%), reduces random error to 1 / 3 of the latter, demonstrating excellent anti-interference ability and measurement repeatability.

[0080] The uncertainty assessment method established in this invention can be extended to high-precision measurement scenarios such as combustion diagnostics, hypersonic flow field detection, and engine combustion monitoring. It provides key input parameters for the reliability assessment of TDLAS measurement results and has significant theoretical value and engineering application prospects. Attached Figure Description

[0081] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0082] Figure 1 This is a flowchart for assessing the uncertainty of time-frequency relationships.

[0083] Figure 2 This is an example diagram of standard interferogram uncertainty estimation involved in the present invention;

[0084] Figure 2 Figure (a) shows the result of multi-period interferogram overlay; Figure (b) shows the result of average interferometry and normalization; Figure (c) shows... The standard deviation is calculated using the Bessel formula. Then calculate using the uncertainty propagation formula. Figure (d) is The uncertainty is represented by the red dashed line, which indicates the upper limit estimate of the uncertainty.

[0085] Figure 3 The invention relates to Example of uncertainty assessment;

[0086] Figure 3 Figure (a) shows the statistical distribution of the interference intensity factor; Figure (b) shows the interferogram (white dots), the interferogram after smoothing spline fitting (black solid line), the standardized interferogram (red solid line), and the locally normalized time-frequency relationship (blue solid line); Figure (c) shows the residuals of the smoothing spline fitting (absolute value, white dots); Figure (d) shows... Uncertainty (white dot) and Uncertainty (red dot); Figure (e) Single measurement uncertainty, the red dashed line represents the upper limit estimate of the uncertainty;

[0087] Figure 4 This invention relates to a schematic diagram of the FP interferometer and a diagram showing the periodic variation of interference intensity;

[0088] Figure 4 Figure (a) shows a schematic diagram of an FP interferometer, and Figure (b) shows the... At that time, the interference intensity changes periodically with the optical frequency;

[0089] Figure 5 This invention relates to an example of a point-by-point measurement of a normalized time-frequency relationship;

[0090] Figure 5 Figure (a) shows the interference signal measured under complex tuning conditions and the normalized discrete time-frequency relationship obtained by peak finding; Figure (b) shows the step function expanded from the normalized discrete time-frequency relationship; Figure (c) shows the comparison between the reference interference intensity (black) and the standard interference intensity (red) (the red dashed line is the boundary between the two monotonic intervals); Figure (d) shows the local normalized time-frequency relationship; Figure (e) shows the global normalized time-frequency relationship. Detailed Implementation

[0091] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0092] The present invention will be further explained below with reference to specific embodiments.

[0093] like Figure 1 As shown in the figure, this embodiment provides a traceable uncertainty assessment method for dynamic wavelength calibration, which includes the following steps:

[0094] S100 Uncertainty Source Analysis

[0095] Based on the Taylor series expansion method, the sources of dynamic wavelength calibration uncertainty are analyzed. Since the FSR uncertainty of the FP interferometer is negligible, the calibration uncertainty of determining the time-frequency relationship is mainly determined by the uncertainty of the local continuous time-frequency relationship.

[0096] The specific process of uncertainty source analysis is as follows:

[0097] Mathematical model based on nonparametric point-by-point calibration method: Time-frequency relationship calibration results uncertainty Source tracing analysis can be performed using Taylor series expansion. Among other things, The free spectral range of the FP interferometer The step function is an extension of the normalized discrete time-frequency relation calibrated by discrete interference peaks. This represents the locally normalized continuous time-frequency relationship as defined by the standard interferogram (“L scale”). Since these three components are independent, the total uncertainty is... The transitive relationship is as follows: In practical measurements for dynamic wavelength calibration, the FP interferometer, with its high precision, is crucial. By limiting The fitting range ensures its uncertainty. This can be ignored. Therefore, the above formula can be simplified to: Normalized discrete time-frequency relationship The derivative is zero in the non-endpoint region, and the uncertainty of the time-frequency relationship calibration. The uncertainty mainly consists of the local continuous time-frequency relationship. Decide: .

[0098] S200, Evaluation of each uncertainty component

[0099] S201, Peak Location Impact Assessment

[0100] Considering the indirect impact of peak location error on the construction of standard interferograms, standardization of measured signals, and establishment of time-domain references, peak region data is included in the uncertainty assessment of standard interferograms, and peak standardization error is considered in complex tuning analysis.

[0101] The specific process for the above-mentioned peak location impact assessment is as follows:

[0102] Considering the indirect impact of peak localization error on the construction of standard interferograms, the standardization of measured signals, and the establishment of time-domain references, peak region data is included in the uncertainty assessment of standard interferograms, and peak standardization error is considered in complex tuning analysis. Specifically, the steps include:

[0103] S2011, Standard Interferogram Construction Stage: During the construction of the standard interferogram, multi-period interference signals are superimposed and averaged, with peak region data retained and included in the statistics; for each normalized frequency point... Interference intensity The standard deviation is calculated using the Bessel formula: ,in The number of interference periods. For the same normalized frequency point in multi-period measurements The corresponding standard deviation of the interference intensity; As input, the standard interference intensity after range normalization is calculated using the uncertainty propagation relationship shown in the following formula. uncertainty : Based on the mapping relationship between frequency and intensity in the standard interferogram, the local normalized frequency is obtained. Uncertainty: For extreme regions such as peaks and troughs where the sensitivity of the interference intensity-frequency mapping approaches zero, the uncertainty is limited by the peak positioning accuracy. Therefore, the upper limit of the uncertainty is set to the width of this region. A uniform conservative estimate is taken across all frequency positions in all interference cycles, and three times the maximum uncertainty in non-extreme regions is taken as the overall estimate of the standard interferogram uncertainty. .

[0104] S2012, Standardization stage of measured signal: For the measured interference signal acquired under complex tuning conditions, the peak intensity of all interference peaks is statistically analyzed. ;calculate Standard deviation As the interference intensity coefficient Uncertainty: Interference intensity coefficient uncertainty The interference intensity is transmitted to the measured standard through a standardized processing procedure. Interference intensity coefficient The fluctuations cause an overall scaling of the interference intensity within each interference cycle. After smoothing the signal within a single interference cycle using spline fitting, the interference intensity is linearly mapped to the [0,1] interval according to the left and right monotonic intervals. This fluctuation is included in the total uncertainty of the interference intensity and is ultimately transmitted to the measurement uncertainty. .

[0105] S2013, Time-Domain Reference Establishment Stage: The positioning error at the peak moment will cause the normalized discrete time-frequency relationship to be affected. The time base is shifted, which manifests as a translation of the step function on the time axis. Because Since the derivative is zero in the non-endpoint region, the direct impact of this time base offset on frequency measurement is limited to the peak neighborhood, and therefore its contribution to the frequency uncertainty of most measurement points is negligible.

[0106] S202, Standard Interferogram Uncertainty Assessment

[0107] S2021. Analyze the sources of error, including interpolation methods, detection system response deviation, system electrical noise, optical path noise, and interference peak positioning deviation; the specific process is as follows:

[0108] ① Uncertainty analysis introduced by interpolation method: Under simple tuning conditions, through the normalized discrete time-frequency relationship... Perform cubic spline interpolation to obtain the normalized continuous time-frequency relationship. In sinusoidal scanning mode, the upper limit of interpolation error can be expressed as: ,in The laser frequency scanning amplitude, The interferometric sampling rate is used. By selecting an interferometer with a specific FSR, it is ensured that at least 40 interference peaks are included within a half-cycle of scanning, and the interpolation error can be controlled within 0.5%.

[0109] ② Detection system response deviation: A dual-detector synchronous measurement scheme is adopted, which involves synchronously monitoring the reference light intensity. With transmitted light intensity This is to eliminate the influence of laser source fluctuations. Differences in detector response manifest as interference intensity coefficients. The measurement error is a systematic error in a single period, and is considered a random error in multi-period measurements.

[0110] ③ System electrical noise: This mainly includes modulation timing errors caused by signal generator jitter, frequency modulation noise caused by laser controller current fluctuations, detector dark current and conversion noise, and oscilloscope quantization errors. These factors collectively cause random fluctuations in the interference signal, affecting measurement repeatability.

[0111] ④ Optical path noise: This includes mode coupling effects caused by fiber bending, optical path changes caused by interferometer mechanical vibration, and thermal drift caused by ambient temperature fluctuations. These disturbances mainly manifest as random noise in the short term, but may exhibit systematic drift characteristics over long time scales.

[0112] ⑤ Interference peak positioning deviation: It is introduced by both signal noise and peak detection algorithm, and has random distribution characteristics. In multi-period measurement, it manifests as random error in interference intensity.

[0113] S2022. By superimposing and averaging multiple interferometric periodic signals to suppress random errors, the measurement uncertainty of the interferometric intensity is calculated using Bessel's formula: .

[0114] S2023, Then, the uncertainty of the standard interferogram is obtained through uncertainty propagation. : Finally, the uncertainty of the locally normalized frequency is obtained through the mapping relationship: .

[0115] For extreme regions such as peaks and troughs, the sensitivity of the interference intensity-frequency mapping approaches zero, and direct calculation will lead to uncertainty divergence. Therefore, the upper limit of uncertainty is set to the width of this region. For extreme regions such as peaks and troughs where point-by-point calculation diverges due to sensitivity approaching zero, three times the maximum uncertainty of non-extreme regions is used as the overall estimate of the uncertainty of the standard interferogram to replace the unobtainable point-by-point uncertainty value.

[0116] S203. Evaluation of Interference Intensity Uncertainty under Complex Tuning Conditions

[0117] Considering the detection system response deviation, system electrical noise, and uncertainties introduced by standardization, the standard deviation of the interference intensity coefficient is obtained by statistically analyzing the peak-to-peak intensity of the interference. The effects of electrical noise and laser frequency jitter are quantified by fitting the residuals of smoothed splines, and the total uncertainty of the interference intensity is synthesized. This uncertainty is then transferred to the measurement uncertainty generated by interpolation at the locally normalized frequency. The specific process is as follows:

[0118] S2031. Obtaining the standard deviation of the interference intensity coefficient

[0119] ① Under complex tuning conditions, peak detection is performed on the measured interference signal, and the peak intensity of all interference peaks is extracted. According to the FP interference principle, the peak intensity of each interference peak should theoretically be equal to the interference intensity coefficient. ,Right now .

[0120] ② Due to detection system response deviations, optical path disturbances, and noise, the peak intensities detected within different interference periods fluctuate. Therefore, the peak intensities of all interference peaks are statistically analyzed, and their standard deviations are calculated. As the interference intensity coefficient Measurement uncertainty: ,in The total number of interference peaks detected. The peak intensity of the i-th interference peak, This is the arithmetic mean of all peak intensities.

[0121] ③ Interference intensity coefficient uncertainty The standardization process transmits the measured standard interference intensity. . The fluctuations cause an overall scaling of the interference intensity within each interference cycle. After smoothing the signal within a single interference cycle using spline fitting, the interference intensity is linearly mapped to the [0,1] interval according to the left and right monotonic intervals, and the uncertainty is propagated using the following formula:

[0122] ;

[0123] Calculate the uncertainty of standard interference intensity This fluctuation is incorporated into the total uncertainty of the interference intensity and ultimately propagates to the measurement uncertainty. .

[0124] S2032, Smoothing spline fitting residual quantization

[0125] Smooth spline fitting is performed on the interference signal within a single interference period to obtain the fitting residual. If the residuals follow a zero-mean normal distribution and are uniform in the time domain, then: If the residuals exhibit asymmetric distribution or time-varying characteristics, then: .

[0126] S2033, Combined total uncertainty of interference intensity

[0127] The detection system response deviation and the fitting residual components are synthesized using the following formula: .

[0128] S2034. Measurement uncertainty transferred to the local normalized frequency

[0129] Through standardization, Transmission to standard interference intensity The uncertainty is then obtained by interpolation mapping to obtain the uncertainty of the locally normalized frequency: For the extreme value region, a globally uniform estimate (e.g., 0.03) is taken as the baseline. The upper limit estimate.

[0130] Based on the quantitative assessments conducted through the three methods described above, the impact of peak positioning error has been factored into the uncertainty of the standard interferogram. (Through path a) and measurement uncertainty (Through approach b), this is reflected in the calculation of combined uncertainty.

[0131] S300, Calculation of combined uncertainty: Calculate the uncertainty of the standard interferogram. Measurement uncertainty caused by interpolation of local normalized frequencies According to the formula The synthesis yields the synthesis uncertainty of the normalized time-frequency relationship. ;Will Multiplying by FSR yields the absolute uncertainty of the time-frequency relationship calibration.

[0132] The present invention will be further described below with reference to specific embodiments:

[0133] (I) Experimental System Setup

[0134] The experimental system uses a DFB tunable semiconductor laser (NLK1E5EAAA, NTT) with a center wavelength of 1391 nm. The laser output is split by optical fiber, and one path passes through a silicon-based FP interferometer (FSR=0.0172 cm⁻¹). -1 One beam (with a reflectivity R=0.3) passes through a gas cell filled with high-purity nitrogen, while the other beam serves as a reference beam. A quartz pillar is installed in the optical window, and the air in the optical path is replaced with high-purity nitrogen to suppress interference from ambient moisture. Reference signal With transmitted signal Data was simultaneously acquired by two photodiode detectors (PDA20CS2, Thorlabs) and recorded by a digital oscilloscope (SDS5000X, Siglent) with a sampling rate of 50 MHz. The oscilloscope clock was strictly synchronized with a 10 MHz reference clock.

[0135] (ii) Uncertainty assessment of standard interferograms

[0136] Based on the constructed experimental system, multi-period interference signals under simple tuning mode were acquired. After superposition and averaging, the standard deviation of the interference intensity corresponding to each local normalized frequency was calculated. The measurement uncertainty of the interference intensity was calculated using Bessel's formula. The uncertainty of the standard interferogram was calculated using the uncertainty propagation formula. Reasonable constraints were imposed on the uncertainty in extreme regions such as peaks and troughs, and a globally unified uncertainty estimate was adopted. .

[0137] (III) Evaluation of uncertainty in interference intensity under complex tuning conditions

[0138] Interference signals under complex tuning modes were acquired, and the peak intensities of all interference peaks were statistically analyzed, yielding a standard deviation of 0.009 for the interference intensity coefficient. Residuals were extracted through smooth spline fitting. Based on the non-normal time-varying characteristics of the residuals, the uncertainty component introduced by dynamic effects and random noise was calculated to be approximately 0.01. The total uncertainty of the interference intensity was obtained by synthesizing these components. After standardization and propagation, the measurement uncertainty caused by interpolation at the locally normalized frequency was obtained, and a globally unified estimate was taken. .

[0139] (iv) The calculation of combined uncertainty is based on the formula. Calculate the combined uncertainty of the normalized time-frequency relationship. Combine this with the FP interferometer. The absolute uncertainty of the time-frequency relationship calibration is obtained as follows: (Approximately 15 MHz) to achieve the source tracing and quantification of uncertainty.

[0140] This invention enables the quantification and transmission analysis of each error component during nonparametric point-by-point calibration, establishes a framework for evaluating the uncertainty of the system, and provides a scientific basis for the reliability of the calibration results.

[0141] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A traceable uncertainty assessment method for dynamic wavelength calibration, characterized in that, Includes the following steps: (1) Uncertainty source analysis Uncertainty source analysis was performed based on Taylor series expansion, which determined that the calibration uncertainty of the time-frequency relationship is mainly determined by the uncertainty of the local continuous time-frequency relationship. (2) Evaluation of uncertainty components The impact of peak location on uncertainty, standard interferogram uncertainty, and interference intensity uncertainty under complex tuning conditions were evaluated, and the standard interferogram uncertainty was quantified respectively. Measurement uncertainty arising from local normalized frequency interpolation ; (3) Calculation of combined uncertainty uncertainty of standard interferogram and measurement uncertainty The combined uncertainty of the normalized time-frequency relationship is obtained by combining the results. Then, the combined uncertainty of the normalized time-frequency relationship is multiplied by the free spectral range of the FP interferometer to obtain the absolute uncertainty of the time-frequency relationship calibration.

2. The traceable uncertainty assessment method for dynamic wavelength calibration as described in claim 1, characterized in that, The specific process of the uncertainty source analysis is as follows: Mathematical model based on nonparametric point-by-point calibration method: ； Time-frequency relationship calibration results uncertainty Source tracing analysis can be performed using Taylor series expansion. The free spectral range of the FP interferometer. The step function is an extension of the normalized discrete time-frequency relation calibrated by discrete interference peaks. For the locally normalized continuous time-frequency relationship defined by the standard interferogram, since these three components are independent, the total uncertainty is... The transitive relationship is as follows: ； In practical measurements for dynamic wavelength calibration, the FP interferometer, with its high precision, is essential. By limiting The fitting range ensures its uncertainty. Neglecting this, the above formula simplifies to: ； The derivative is zero in the non-endpoint region, and the uncertainty of the time-frequency relationship calibration. The uncertainty mainly consists of the local continuous time-frequency relationship. Decide: 。 3. The traceable uncertainty assessment method for dynamic wavelength calibration as described in claim 1, characterized in that, The specific process for assessing the peak location impact in step (2) is as follows: Considering the indirect impact of peak localization error on the construction of standard interferograms, the standardization of measured signals, and the establishment of time-domain references, peak region data is included in the uncertainty assessment of standard interferograms, and peak standardization error is considered in complex tuning analysis. Specifically, the steps include: (2.1.1) Standard Interferogram Construction Stage When constructing a standard interferogram, multi-period interferometric signals are superimposed and averaged, with peak region data retained and included in the statistics; for each normalized frequency point... Interference intensity The standard deviation is calculated using the Bessel formula: ； In the above formula, The number of interference periods. For the same normalized frequency point in multi-period measurements The corresponding standard deviation of interference intensity; Will As input, the standard interference intensity after range normalization is calculated using the following formula for uncertainty propagation. uncertainty : ； Based on the frequency-intensity mapping relationship in the standard interferogram, the local normalized frequency is obtained. Uncertainty: ； For the extreme regions where the intensity-frequency mapping sensitivity of the interferogram approaches zero at the crests and troughs, the uncertainty is limited by the peak positioning accuracy. Therefore, the upper limit of the uncertainty is set to the width of this region. A uniform conservative estimate is taken across all frequency positions in all interferometry cycles, and three times the maximum uncertainty in the non-extreme regions is taken as the overall estimate of the standard interferogram uncertainty. ; (2.1.2) Standardization stage of measured signal For the measured interferometric signals acquired under complex tuning conditions, the peak intensity of all interferometric peaks was statistically analyzed. ;calculate Standard deviation As the interference intensity coefficient Uncertainty: ； Interference intensity coefficient uncertainty The interference intensity is transmitted to the measured standard through a standardized processing procedure. Interference intensity coefficient The fluctuations cause an overall scaling of the interference intensity within each interference cycle. After smoothing the signal within a single interference cycle using spline fitting, the interference intensity is linearly mapped to the [0,1] interval according to the left and right monotonic intervals. This fluctuation is included in the total uncertainty of the interference intensity and is ultimately transmitted to the measurement uncertainty. ; (2.1.3) Time-domain reference establishment stage The positioning error at the peak moment will cause the normalized discrete time-frequency relationship to be affected. The time base is shifted, which manifests as a translation of the step function on the time axis; due to The derivative is zero in the non-endpoint region, and the direct impact of this time base offset on frequency measurement is limited to the peak neighborhood. Therefore, its contribution to the frequency uncertainty of most measurement points is negligible.

4. The traceable uncertainty assessment method for dynamic wavelength calibration as described in claim 1, characterized in that, The specific process for evaluating the uncertainty of the standard interferogram is as follows: (2.2.1) Analyze the sources of error, including interpolation method, detection system response deviation, system electrical noise, optical path noise, and interference peak positioning deviation: (2.2.2) By superimposing and averaging multiple interferometric periodic signals to suppress random errors, the measurement uncertainty of the interferometric intensity is calculated using Bessel's formula: ； (2.2.3) Obtain the uncertainty of the standard interferogram through uncertainty propagation. : ； Finally, the uncertainty of the locally normalized frequency is obtained through the mapping relationship: ； For the extreme regions of the crests and troughs, the sensitivity of the interference intensity-frequency mapping approaches zero. Direct calculation will lead to uncertainty divergence. Therefore, the upper limit of uncertainty is set to the width of this region. For extreme regions where point-by-point calculations diverge due to sensitivity approaching zero in the peak and trough regions, three times the maximum uncertainty of the non-extreme region is used as the overall estimate of the uncertainty of the standard interferogram to replace the unobtainable point-by-point uncertainty value.

5. The traceable uncertainty assessment method for dynamic wavelength calibration as described in claim 1, characterized in that, The specific process for evaluating the uncertainty of interference intensity under complex tuning conditions is as follows: (2.3.1) Obtaining the standard deviation of the interference intensity coefficient ① Under complex tuning conditions, peak detection is performed on the measured interference signal, and the peak intensity of all interference peaks is extracted. ; According to the FP interference principle, the peak intensity of each interference peak should theoretically be equal to the interference intensity coefficient. ,Right now ; ② Due to the influence of detection system response deviation, optical path disturbance, and noise, the peak intensity detected in different interference periods fluctuates; therefore, the peak intensity of all interference peaks is statistically analyzed, and their standard deviation is calculated. As the interference intensity coefficient Measurement uncertainty: ； In the above formula, The total number of interference peaks detected. The peak intensity of the i-th interference peak, The arithmetic mean of all peak intensities; ③ Interference intensity coefficient uncertainty The interference intensity is transmitted to the measured standard after a standardization process. ; The fluctuations cause an overall scaling of the interference intensity within each interference cycle. After smoothing the signal within a single interference cycle using spline fitting, the interference intensity is linearly mapped to the [0,1] interval according to the left and right monotonic intervals, and the uncertainty is propagated using the following formula: ； Calculate the uncertainty of standard interference intensity This fluctuation is incorporated into the total uncertainty of the interference intensity and ultimately propagates to the measurement uncertainty. ; (2.3.2) Quantization of residuals from smooth spline fitting Smooth spline fitting is performed on the interference signal within a single interference period to obtain the fitting residual. If the residuals follow a zero-mean normal distribution and are uniform in the time domain, then: ； If the residuals exhibit asymmetric distribution or time-varying characteristics, then: ； (2.3.3) Combination of total uncertainty of interference intensity The detection system response deviation and the fitting residual components are synthesized using the following formula: ； (2.3.4) Measurement uncertainty propagated to the local normalized frequency Through standardization, Transmission to standard interference intensity The uncertainty is then obtained by interpolation mapping to obtain the uncertainty of the locally normalized frequency: ； For the extreme value region, the globally unified estimate is taken as... The upper limit estimate.

6. The traceable uncertainty assessment method for dynamic wavelength calibration as described in claim 1, characterized in that, The specific process of the synthesis uncertainty of the normalized time-frequency relationship is as follows: The uncertainty of the standard interferogram Measurement uncertainty caused by interpolation of local normalized frequencies According to the formula The synthesis yields the synthesis uncertainty of the normalized time-frequency relationship. ;Will Free spectral range of FP interferometer Multiplying them together yields the absolute uncertainty of the time-frequency relationship calibration.

Images