Dynamic relaxation stack imaging reconstruction method and system for femtosecond pulse phase characterization

Abstract

The present application relates to the technical field of ultrafast optical measurement and computational imaging reconstruction, in particular to a dynamic relaxation stack imaging reconstruction method and system for femtosecond pulse phase characterization, first, the femtosecond pulse to be measured is measured in trajectory, and a two-dimensional FROG trace diagram corresponding to the femtosecond pulse to be measured is obtained; secondly, the two-dimensional FROG trace diagram is processed to generate a standardized FROG trace diagram; then, the initial complex electric field is constructed based on the standardized FROG trace diagram; finally, the dynamic relaxation update regulation mechanism is adopted, the initial complex electric field and the standardized FROG trace diagram are used for complex electric field iterative update processing, and the reconstruction parameters corresponding to the femtosecond pulse to be measured are output. The static or random update mode in the traditional iterative process is converted into the dynamic relaxation update regulation mechanism evolving with the reconstruction process, so that the pulse complex electric field recovery process can be smoothly transitioned from the effective search in the early stage to the stable convergence in the later stage, which not only improves the FROG trace reconstruction efficiency, but also enhances the complex electric field recovery stability under the noise condition.

Description

Technical Field

[0001] This invention relates to the field of ultrafast optical measurement and computational imaging reconstruction technology, and in particular to a dynamic relaxation stacked imaging reconstruction method and system for femtosecond pulse temporal characterization. Background Technology

[0002] Currently, femtosecond lasers are widely used in ultrafast optics, precision machining, nonlinear optics, fiber optic communication, biomedical imaging, and strong-field physics. In these applications, the pulse width, temporal envelope, spectral distribution, and phase characteristics of the femtosecond pulse directly affect the output quality and experimental results of the laser system. Especially in pulse compression, dispersion compensation, and diagnosis of complex ultrafast processes, if the complete complex electric field information of the pulse cannot be accurately obtained, it is difficult to determine whether the pulse is approaching the transformation limit, and it is also difficult to effectively correct the residual dispersion and phase distortion of the system. Therefore, achieving rapid, accurate, and stable reconstruction of the complex electric field of a femtosecond pulse is a key technical problem in ultrafast optical measurement and femtosecond laser diagnostics.

[0003] Currently, commonly used reconstruction algorithms for femtosecond pulses include generalized projection algorithms and principal component generalized projection algorithms. These methods can achieve pulse recovery under ideal traces and high signal-to-noise ratio conditions. However, under complex pulses, noisy traces, or traces acquired in actual experiments, they are still prone to problems such as slow convergence speed, long computation time, sensitivity to initial conditions, and unstable reconstruction results.

[0004] Extended layered imaging engines utilize redundant information at different delay positions to progressively update the complex electric field of the pulse under test. They offer advantages such as simple structure, high computational efficiency, and ease of implementation, and have been used in femtosecond pulse reconstruction in recent years. However, during femtosecond pulse reconstruction, the update coefficients typically employ fixed values ​​or random values ​​within a certain range, making it difficult to simultaneously balance search speed and convergence. Therefore, how to construct a femtosecond pulse reconstruction method that simultaneously meets the demodulation requirements of speed and high stability based on complex femtosecond pulses remains a key technical challenge for this field. Summary of the Invention

[0005] The purpose of this invention is to provide a dynamic relaxation stacked imaging reconstruction method and system for femtosecond pulse phase characterization, so as to achieve high reconstruction efficiency and high stability.

[0006] To achieve the above objectives, this invention provides a dynamic relaxation stacked imaging reconstruction method for femtosecond pulse temporal characterization, the method comprising:

[0007] The trajectory of the femtosecond pulse to be tested is measured to obtain a two-dimensional FROG trace map corresponding to the femtosecond pulse to be tested.

[0008] The two-dimensional FROG trace map is processed to generate a standardized FROG trace map;

[0009] Construct the initial complex electric field based on the standardized FROG trace plot;

[0010] A dynamic relaxation update control mechanism is adopted to perform iterative update processing of the complex electric field based on the initial complex electric field and the standardized FROG trace map, and output the reconstruction parameters corresponding to the femtosecond pulse to be measured.

[0011] Optionally, the process of processing the two-dimensional FROG trace map to generate a standardized FROG trace map specifically includes:

[0012] Determine whether the two-dimensional FROG trace map originates from experimental measurements; if the two-dimensional FROG trace map originates from experimental measurements, then standardize the two-dimensional FROG trace information to generate the standardized FROG trace map; if the two-dimensional FROG trace map originates from simulation processing, then directly use the two-dimensional FROG trace map as the standardized FROG trace map after unifying the intensity scale.

[0013] Optionally, constructing the initial complex electric field based on the standardized FROG trace plot specifically includes:

[0014] The sampling range required for complex electric field reconstruction is determined based on the frequency axis and delay axis of the standardized FROG trace plot;

[0015] The initial spectral intensity of the femtosecond pulse to be measured is estimated within the sampling range based on the intensity distribution of the standardized FROG trace plot.

[0016] The initial spectral intensity is normalized and square-rooted to obtain the initial spectral amplitude;

[0017] The initial spectral amplitude is combined with a preset initial phase to construct a frequency domain complex electric field;

[0018] The frequency domain complex electric field is transformed by inverse Fourier transform to obtain the time domain complex electric field;

[0019] The time-domain complex electric field is used as the initial complex electric field.

[0020] Optionally, the dynamic relaxation update control mechanism is adopted to perform iterative update processing of the complex electric field based on the initial complex electric field and the standardized FROG trace map, and output the reconstruction parameters corresponding to the femtosecond pulse to be measured, specifically including:

[0021] Step S41: Based on the extended stacked imaging engine, amplitude constraints are performed according to the initial complex electric field and the delay position in the normalized FROG trace map to obtain the amplitude-constrained time-domain nonlinear signal;

[0022] Step S42: Based on the dynamic relaxation update control mechanism, generate dynamic relaxation update coefficients according to the current iteration number;

[0023] Step S43: Update the complex electric field of the femtosecond pulse to be reconstructed based on the difference between the time-domain nonlinear signals before and after amplitude constraint, and in conjunction with the dynamic relaxation update coefficients.

[0024] Step S44: Determine whether the preset conditions are met based on the updated complex electric field corresponding to the last delay position under the current iteration number; if the preset conditions are met, stop reconstruction and output the reconstruction parameters corresponding to the femtosecond pulse to be measured; if the preset conditions are not met, use the updated complex electric field corresponding to the last delay position under the current iteration number as the initial complex electric field and return to step S41.

[0025] Optionally, the step of using an extended layered imaging engine to perform amplitude constraints based on the initial complex electric field and the delay position in the normalized FROG trace map to obtain an amplitude-constrained time-domain nonlinear signal specifically includes:

[0026] Based on the extended stacked imaging engine, the time-domain nonlinear signal at different delay positions is calculated according to the initial complex electric field and the delay position in the normalized FROG trace map;

[0027] The amplitude of the time-domain nonlinear signal at different delay positions is constrained using the measured amplitude information in the standardized FROG trace plot to obtain the amplitude-constrained frequency-domain nonlinear signal.

[0028] The amplitude-constrained frequency-domain nonlinear signal is subjected to an inverse Fourier transform to obtain the amplitude-constrained time-domain nonlinear signal.

[0029] Optionally, the dynamic relaxation update control mechanism generates dynamic relaxation update coefficients based on the current iteration number, with the specific formula as follows:

[0030] ;

[0031] in, These are the dynamic relaxation update coefficients during the k-th iteration. For the initial update strength, For the amplitude of random disturbance, This refers to the random perturbation term during the k-th iteration update process. As the attenuation factor, The maximum number of iterations, This represents the minimum update intensity.

[0032] The present invention also provides a dynamic relaxation stacked imaging reconstruction system for femtosecond pulse temporal characterization, the system comprising:

[0033] The FROG measurement module is used to measure the trajectory of the femtosecond pulse to be measured and obtain the two-dimensional FROG trace map corresponding to the femtosecond pulse to be measured.

[0034] The data preprocessing module is used to process the two-dimensional FROG trace map to generate a standardized FROG trace map.

[0035] An initial complex electric field generation module is used to construct an initial complex electric field based on the standardized FROG trace diagram;

[0036] The dynamic relaxation update reconstruction module is used to perform iterative update processing of the complex electric field based on the initial complex electric field and the standardized FROG trace map using a dynamic relaxation update control mechanism, and output the reconstruction parameters corresponding to the femtosecond pulse to be measured.

[0037] Optionally, the dynamic relaxation update reconstruction module includes:

[0038] The frequency domain amplitude constraint unit is used to perform amplitude constraint based on the extended stacked imaging engine, according to the initial complex electric field and the delay position in the normalized FROG trace map, to obtain the amplitude-constrained time-domain nonlinear signal.

[0039] The dynamic relaxation coefficient update unit is used to generate dynamic relaxation update coefficients based on the current iteration number, according to the dynamic relaxation update control mechanism.

[0040] The complex electric field update unit is used to update the complex electric field of the femtosecond pulse to be reconstructed based on the difference between the time-domain nonlinear signals before and after amplitude constraint, and in combination with the dynamic relaxation update coefficients.

[0041] The judgment unit is used to determine whether the updated complex electric field corresponding to the last delay position under the current iteration number meets the preset conditions. If the preset conditions are met, the reconstruction is stopped and the reconstruction parameters corresponding to the femtosecond pulse to be measured are output. If the preset conditions are not met, the updated complex electric field corresponding to the last delay position under the current iteration number is used as the initial complex electric field and the result is returned to the frequency domain amplitude constraint unit.

[0042] The present invention also provides a computer-storable medium storing a computer program, which, when executed by a processor, implements the steps of the dynamic relaxation stacked imaging reconstruction method for femtosecond pulse phase characterization as described above.

[0043] The present invention also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the above-described dynamic relaxation stacked imaging reconstruction method for femtosecond pulse phase characterization.

[0044] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0045] This invention discloses a dynamic relaxation stacked imaging reconstruction method and system for femtosecond pulse temporal characterization. First, the trajectory of the femtosecond pulse to be measured is measured to obtain a two-dimensional FROG trace map corresponding to the pulse. Second, the two-dimensional FROG trace map is processed to generate a standardized FROG trace map. Then, an initial complex electric field is constructed based on the standardized FROG trace map. Finally, a dynamic relaxation update control mechanism is employed to iteratively update the complex electric field based on the initial complex electric field and the standardized FROG trace map, outputting the reconstruction parameters corresponding to the femtosecond pulse to be measured. This invention transforms the static or random update method in the traditional iterative process into a dynamic relaxation update control mechanism that evolves with the reconstruction process. This allows the pulse complex electric field recovery process to smoothly transition from an effective search in the early stage to stable convergence in the later stage, improving not only the FROG trace reconstruction efficiency but also enhancing the stability of complex electric field recovery under noisy conditions. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 This is a flowchart of the dynamic relaxation stacked imaging reconstruction method for femtosecond pulse phase characterization according to an embodiment of the present invention;

[0048] Figure 2 A schematic diagram of a dynamic relaxation stacked imaging reconstruction system for femtosecond pulse temporal characterization;

[0049] Figure 3 is a schematic diagram of the femtosecond pulse reconstruction results;

[0050] Figure 4 This is a schematic diagram of the femtosecond laser processing light source status monitoring and feedback structure. Detailed Implementation

[0051] 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 skilled in the art without creative effort are within the scope of protection of the present invention.

[0052] The purpose of this invention is to provide a dynamic relaxation stacked imaging reconstruction method and system for femtosecond pulse phase characterization, so as to achieve high reconstruction efficiency and high stability.

[0053] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0054] Existing frequency-resolved optical gating (FROG) systems can acquire two-dimensional time-frequency traces of femtosecond pulses, but these traces do not directly provide the temporal intensity and phase of the pulse under test; phase retrieval algorithms are required for inversion. Current extended layered imaging engines typically use fixed or random-range update coefficients in femtosecond pulse reconstruction. While this approach is simple to implement, the update intensity lacks phased control throughout the iteration process: if the update intensity is too high, the algorithm is prone to oscillations, leading to instability and amplifying noise disturbances; if the update intensity is too low, the search capability is insufficient, resulting in slow error reduction and an increase in the number of iterations. Existing methods struggle to simultaneously achieve both fast search speeds and stable reconstruction quality. Therefore, based on frequency-resolved optical switch femtosecond pulse measurement technology and an extended stacked imaging engine reconstruction framework, a dynamic relaxation iterative reconstruction mechanism for the pulse complex electric field recovery process is established. By coordinating the global search capability in the early stages of reconstruction with the stable convergence capability in the later stages, the impact of noise disturbances, local stagnation, and overcorrection on the reconstruction results is reduced, achieving fast, high-precision, and high-stability reconstruction of complex femtosecond pulse FROG traces. The specific steps are as follows:

[0055] like Figure 1 As shown, this invention discloses a dynamic relaxation stacked imaging reconstruction method for femtosecond pulse temporal characterization, the method comprising:

[0056] Step S1: Perform trajectory measurement on the femtosecond pulse to be measured to obtain the two-dimensional FROG trace map corresponding to the femtosecond pulse to be measured.

[0057] Step S2: Process the two-dimensional FROG trace map to generate a standardized FROG trace map.

[0058] Step S3: Construct the initial complex electric field based on the standardized FROG trace plot.

[0059] Step S4: Employ a dynamic relaxation update control mechanism to iteratively update the complex electric field based on the initial complex electric field and the standardized FROG trace map, and output the reconstruction parameters corresponding to the femtosecond pulse to be measured.

[0060] The following is a detailed discussion of each step:

[0061] Step S2: Process the 2D FROG trace map to generate a standardized FROG trace map. Specifically, determine whether the 2D FROG trace map originates from experimental measurements. If it does, standardize the 2D FROG trace information to generate a standardized FROG trace map. If it originates from simulation processing, unify the intensity scale of the 2D FROG trace map and use it directly as the standardized FROG trace map. Standardization processing includes, but is not limited to, background subtraction, effective region extraction, intensity scale unification, delay axis calibration, and frequency axis calibration.

[0062] Step S3: Construct the initial complex electric field based on the standardized FROG trace plot, specifically including:

[0063] Step S31: Determine the sampling range required for complex electric field reconstruction based on the frequency axis and delay axis of the standardized FROG trace plot.

[0064] Step S32: Estimate the initial spectral intensity of the femtosecond pulse to be measured within the sampling range based on the intensity distribution of the standardized FROG trace plot.

[0065] Step S33: Normalize and square root the initial spectral intensity to obtain the initial spectral amplitude.

[0066] Step S34: Combine the initial spectral amplitude with the preset initial phase to construct a complex electric field in the frequency domain. The preset initial phase can be zero phase, a small-amplitude random phase, or an initial phase set according to the system's prior dispersion.

[0067] Step S35: Obtain the time-domain complex electric field by performing an inverse Fourier transform on the frequency-domain complex electric field.

[0068] Step S36: Use the time-domain complex electric field as the initial complex electric field.

[0069] Step S4: Employing a dynamic relaxation update control mechanism, the complex electric field is iteratively updated based on the initial complex electric field and the standardized FROG trace map, outputting the reconstruction parameters corresponding to the femtosecond pulse under test, specifically including:

[0070] Step S41: Based on the extended stacked imaging engine, amplitude constraints are applied according to the initial complex electric field and the delay position in the normalized FROG trace map to obtain the amplitude-constrained temporal nonlinear signal, specifically including:

[0071] Step S411: Based on the extended stacked imaging engine, calculate the time-domain nonlinear signal at different delay positions according to the initial complex electric field and the delay position in the normalized FROG trace map.

[0072] Step S412: Using the measured amplitude information in the standardized FROG trace plot, amplitude constraints are applied to the time-domain nonlinear signal at different delay positions to obtain the amplitude-constrained frequency-domain nonlinear signal. The specific formula is as follows:

[0073] ;

[0074] ;

[0075] in, For the frequency domain nonlinear signal after amplitude constraint at the k-th iteration and j-th delay position, To standardize the intensity distribution at the j-th delay position in the FROG trace plot, To standardize the amplitude information corresponding to the FROG trace plot, Let j be the delay time corresponding to the j-th delay position. For the frequency domain nonlinear signal before amplitude constraint at the k-th iteration and j-th delay position, for amplitude, For Fourier transform operators, This represents the time-domain nonlinear signal before amplitude constraint at the k-th iteration and j-th delay position.

[0076] Step S413: Perform an inverse Fourier transform on the amplitude-constrained frequency-domain nonlinear signal to obtain the amplitude-constrained time-domain nonlinear signal.

[0077] Step S42: Based on the dynamic relaxation update control mechanism, generate dynamic relaxation update coefficients according to the current iteration number. The specific formula is as follows:

[0078] ;

[0079] in, These are the dynamic relaxation update coefficients during the k-th iteration. For the initial update strength, For the amplitude of random disturbance, This refers to the random perturbation term during the k-th iteration update process. , As the attenuation factor, The maximum number of iterations, For minimum update intensity, It follows a standard normal distribution with a mean of 0 and a variance of 1. The dynamic relaxation update coefficients change dynamically with the iteration process, enabling the reconstruction process to have matching search capabilities and convergence stability at different stages.

[0080] Step S43: Based on the difference between the time-domain nonlinear signals before and after amplitude constraint, and combined with the dynamic relaxation update coefficients, update the complex electric field of the femtosecond pulse to be reconstructed. The specific formula is as follows:

[0081]

[0082] in, This represents the complex electric field after updating the j-th delayed position in the k-th iteration. The complex electric field before the update of the j-th delayed position in the k-th iteration. Let j be the displacement index corresponding to the j-th delay position. The delay step size between adjacent delay positions. Let be the gate function formed by the current complex electric field at the k-th iteration and the j-th delay position. For the time-domain nonlinear signal after amplitude constraint at the k-th iteration and j-th delay position, For the time-domain nonlinear signal before amplitude constraint at the k-th iteration and j-th delay position, is the dynamic relaxation update coefficient during the k-th iteration. Let be the delay gate function formed by the current complex electric field at the k-th iteration and the j-th delay position. The complex conjugate of the delay gate function is... This represents the maximum value of the delay gate function strength over the time range. This represents the correction amount for the time-domain nonlinear signal generated before and after amplitude constraint. Therefore, the complex electric field update formula expresses the following: first, the correction amount is obtained based on the difference in nonlinear signals before and after amplitude constraint; then, the correction direction and scale are determined through the delay gate function and its normalization term; finally, the coefficients are updated by dynamic relaxation. Adjust the correction intensity to thus Updated to .

[0083] Step S44: Determine whether the preset conditions are met based on the updated complex electric field corresponding to the last delay position under the current iteration number; if the preset conditions are met, stop reconstruction and output the reconstruction parameters corresponding to the femtosecond pulse to be measured; if the preset conditions are not met, use the updated complex electric field corresponding to the last delay position under the current iteration number as the initial complex electric field and return to S41. The reconstruction parameters corresponding to the femtosecond pulse to be measured include: time-domain intensity, time-domain phase, and the corresponding reconstructed FROG trace. The time-domain intensity and time-domain phase are obtained by demodulating the updated complex electric field corresponding to the last delay position of the last iteration. This invention assumes there are N delay positions and a preset maximum number of iterations of M, then the updated complex electric field corresponding to the last delay position of the last iteration is the updated complex electric field corresponding to the Nth delay position of the Mth iteration. If the preset stopping condition is met after the Kth iteration, where K≤M, then the updated complex electric field corresponding to the last delay position in the Kth iteration is used as the final reconstructed complex electric field.

[0084] Step S44: Determine whether the updated complex electric field corresponding to the last delay position at the current iteration number meets the preset conditions, specifically including:

[0085] Step S441: Input the updated complex electric field corresponding to the last delay position under the current iteration number into the FROG forward model, and calculate the reconstructed FROG trace map corresponding to the current iteration state.

[0086] Step S442: Compare the reconstructed FROG trace plot corresponding to the current iteration state with the standardized FROG trace plot to obtain the current reconstruction error.

[0087] Step S443: Determine whether the current reconstruction error is less than the error threshold; if the current reconstruction error is less than the error threshold, it means that the preset condition is met; if the current reconstruction error is greater than or equal to the error threshold, determine whether the number of iterations has reached the preset maximum number of iterations; if the preset maximum number of iterations has been reached, it means that the preset condition is met; if the preset maximum number of iterations has not been reached, it means that the preset condition is not met.

[0088] Alternatively, step S441: determine whether the number of iterations has reached the preset maximum number of iterations; if the preset maximum number of iterations has been reached, it means that the preset condition is met; if the preset maximum number of iterations has not been reached, input the updated complex electric field corresponding to the last delay position under the current iteration number into the FROG forward model, and calculate the reconstructed FROG trace map corresponding to the current iteration state.

[0089] Step S442: Compare the reconstructed FROG trace plot corresponding to the current iteration state with the standardized FROG trace plot to obtain the current reconstruction error.

[0090] Step S443: Determine whether the current reconstruction error is less than the error threshold; if the current reconstruction error is less than the error threshold, it means that the preset condition is met; if the current reconstruction error is greater than or equal to the error threshold, it means that the preset condition is not met.

[0091] Alternatively, step S441: Input the updated complex electric field corresponding to the last delay position under the current iteration number into the FROG forward model, and calculate the reconstructed FROG trace map corresponding to the current iteration state.

[0092] Step S442: Compare the reconstructed FROG trace plot corresponding to the current iteration state with the standardized FROG trace plot to obtain the current reconstruction error.

[0093] Step S443: Determine whether the trajectory error has converged based on the current reconstruction error; if the trajectory error has converged, it means that the preset conditions are met; if the trajectory error has not converged, determine whether the number of iterations has reached the preset maximum number of iterations; if the preset maximum number of iterations has been reached, it means that the preset conditions are met; if the preset maximum number of iterations has not been reached, it means that the preset conditions are not met.

[0094] This invention can also use a single parameter condition as the stopping condition, which will not be discussed again here.

[0095] This invention introduces a dynamically relaxed update coefficient that evolves with the reconstruction process during the complex electric field update. This allows early iterations to maintain an effective search capability in the solution space, preventing premature convergence to local optima. Simultaneously, it reduces the impact of overcorrection and noise disturbances in later iterations, gradually leading the reconstruction process to a stable convergence state. Therefore, iterative reconstruction is no longer a simple single-step error correction, but a closed-loop optimization process composed of amplitude constraints and dynamic relaxed update coefficient transformation.

[0096] This invention proposes a femtosecond pulse reconstruction method based on a combination of dynamic relaxation update and extended layered imaging. This method transforms the static or random update method in the traditional iterative process into a dynamic relaxation update mechanism that evolves with the reconstruction process. This allows the pulse complex electric field recovery process to smoothly transition from an effective search in the early stage to stable convergence in the later stage, thereby improving the convergence efficiency and reliability of the algorithm in complex pulse reconstruction. The method disclosed in this invention has promising applications in ultrafast optical pulse measurement, femtosecond laser diagnostics, pulse compression optimization, FROG pulse characterization, and phase retrieval computation.

[0097] like Figure 2 As shown, this invention also discloses a dynamic relaxation stacked imaging reconstruction system for femtosecond pulse temporal characterization, the system comprising:

[0098] The FROG measurement module is used to measure the trajectory of the femtosecond pulse to be measured and obtain the two-dimensional FROG trace map corresponding to the femtosecond pulse to be measured.

[0099] The data preprocessing module is used to process the two-dimensional FROG trace map to generate a standardized FROG trace map.

[0100] The initial complex electric field generation module is used to construct the initial complex electric field based on the standardized FROG trace diagram.

[0101] The dynamic relaxation update reconstruction module is used to perform iterative update processing of the complex electric field based on the initial complex electric field and the standardized FROG trace map using a dynamic relaxation update control mechanism, and output the reconstruction parameters corresponding to the femtosecond pulse to be measured.

[0102] As an optional implementation, the dynamic relaxation update and reconstruction module of the present invention includes:

[0103] The frequency domain amplitude constraint unit is used to perform amplitude constraint based on the extended stacked imaging engine, according to the initial complex electric field and the delay position in the normalized FROG trace map, to obtain the amplitude-constrained time-domain nonlinear signal.

[0104] The dynamic relaxation coefficient update unit is used to generate dynamic relaxation update coefficients based on the current iteration number, according to the dynamic relaxation update control mechanism.

[0105] The complex electric field update unit is used to update the complex electric field of the femtosecond pulse to be reconstructed based on the difference between the time-domain nonlinear signals before and after amplitude constraint, and in combination with the dynamic relaxation update coefficients.

[0106] The judgment unit is used to determine whether the updated complex electric field corresponding to the last delay position under the current iteration number meets the preset conditions. If the preset conditions are met, the reconstruction is stopped and the reconstruction parameters corresponding to the femtosecond pulse to be measured are output. If the preset conditions are not met, the updated complex electric field corresponding to the last delay position under the current iteration number is used as the initial complex electric field and the result is returned to the frequency domain amplitude constraint unit.

[0107] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0108] Specific example 1:

[0109] Step 1: Use the FROG measurement module to measure the complex femtosecond pulse and the simple femtosecond pulse to be measured respectively, and obtain the two-dimensional FROG trace image corresponding to the complex femtosecond pulse and the simple femtosecond pulse to be measured.

[0110] Step 2: Perform dark background subtraction, effective region extraction, intensity normalization, delay axis calibration, and frequency axis calibration on the two two-dimensional FROG trace images to obtain standardized FROG trace data;

[0111] Step 3: Input the standardized FROG trace data into the dynamic relaxation update reconstruction module. During the iteration process, apply amplitude constraints to the calculated frequency domain nonlinear signal field based on the standardized FROG trace data, and adjust the update amplitude of the complex electric field in combination with the dynamic relaxation update mechanism to improve the stability and accuracy of the complex femtosecond pulse reconstruction process.

[0112] Step four: When the reconstruction error meets the preset requirements, or the number of iterations reaches the set upper limit, the iteration stops, and the reconstructed complex electric field corresponding to the complex femtosecond pulse to be measured and the reconstructed complex electric field corresponding to the simple femtosecond pulse to be measured are output. The corresponding time-domain intensity and time-domain phase, as well as the reconstructed FROG trace diagram, are demodulated. Figure 3 shows the reconstruction results of different types of femtosecond pulses by the method of the present invention. Figure 3(a) is the standardized FROG trace diagram corresponding to the simple femtosecond pulse obtained by actual measurement; Figure 3(b) is the reconstructed FROG trace diagram of the simple femtosecond pulse obtained by the method of the present invention obtained by actual measurement. It can be seen that its main energy distribution area, delay direction broadening characteristics and frequency direction distribution characteristics are basically consistent with those of Figure 3(a), indicating that the method of the present invention can recover the FROG trace corresponding to the simple femtosecond pulse well; Figure 3(c) is the time-domain intensity and time-domain phase results obtained by reconstructing the simple femtosecond pulse obtained by actual measurement. The time-domain intensity shows a single-peak distribution, and the phase curve is continuous and smooth, indicating that the method of the present invention can output complete pulse time-domain information. Figure 3(d) shows the standardized FROG trace of the complex femtosecond pulse obtained from the simulation. Its energy distribution is more complex than that of the simple pulse, reflecting the asymmetric or multi-structure characteristics of the complex pulse in the delay and frequency directions. Figure 3(e) shows the reconstructed FROG trace of the complex femtosecond pulse obtained from the simulation using the method of this invention. It can be seen that the reconstruction result can better maintain the main structural features of the original complex trace, indicating that the method of this invention is not only applicable to simple pulses, but also to femtosecond pulses with complex temporal structures. Figure 3(f) shows the time-domain intensity and time-domain phase results of the complex femtosecond pulse reconstructed from the simulation. The reconstruction curve can reflect the multi-peak, chirp, or phase change characteristics of the complex pulse, indicating that the method of this invention can realize the recovery of the complex electric field of the complex femtosecond pulse. Figure 3(g) and Figure 3(h) show the time-domain intensity recovery results obtained by different methods under the same noise conditions in the simulation. Figure 3(g) shows the time-domain intensity recovery result obtained by the extended layered imaging engine method. It can be seen that there are obvious curve jitter and noise residue, indicating that noise has a certain impact on the complex electric field update process. Figure 3(h) shows the temporal intensity recovery result obtained using the dynamic relaxation stacked imaging reconstruction method of the present invention. It can be seen that the reconstructed curve and the original curve are well consistent, the curve is smoother overall, and the noise disturbance is significantly reduced. This indicates that, under the same noise conditions, the method of the present invention can reduce the impact of noise disturbance on the complex electric field recovery result and improve the stability of femtosecond pulse temporal intensity reconstruction.

[0113] Example 2:

[0114] This invention takes the monitoring of the processing light source status in a femtosecond laser processing system as an example, such as... Figure 4As shown, the femtosecond laser processing system, as a peripheral application system, acquires the monitoring signal of the processing beam through beam splitting sampling, and sequentially completes FROG measurement, data acquisition, image preprocessing, femtosecond pulse reconstruction, parameter demodulation, and feedback control. This structure can achieve online monitoring and feedback adjustment of the processing light source state without changing the basic structure of the main processing optical path. The specific implementation process includes:

[0115] Step 1: The femtosecond pulses output by the femtosecond laser are modulated or shaped to generate a processing beam, which enters the femtosecond laser processing system and is then applied to the material to be processed by the processing optical path and focusing system.

[0116] Step 2: Set up a beam splitting and sampling module in the processing optical path, extract a portion of the beam from the processing beam as a monitoring beam, and input the monitoring beam into the FROG measurement module to obtain the two-dimensional FROG trace corresponding to the current processing light source;

[0117] Step 3: Perform image normalization processing on the two-dimensional FROG traces to obtain normalized FROG trace data;

[0118] Step four: Input the standardized FROG trace data into the dynamic relaxation update reconstruction module of this invention to reconstruct the complex electric field, restore the femtosecond pulse complex electric field of the current processing light source, and demodulate to obtain the time domain intensity and time domain phase.

[0119] Step 5: Compare the demodulated state parameters with the preset processing light source parameters. When the state parameters deviate from the preset range, the feedback control module generates an adjustment command and applies it to the femtosecond laser, pulse modulation unit, beam shaping unit, or processing control unit to bring the processing light source state closer to the preset state.

[0120] The above examples are simplified; please refer to the method section of the instruction manual for detailed procedures.

[0121] The present invention also discloses a computer-storable medium storing a computer program, which, when executed by a processor, implements the steps of the above-described dynamic relaxation stacked imaging reconstruction method for femtosecond pulse phase characterization.

[0122] The present invention also discloses a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the above-described dynamic relaxation stacked imaging reconstruction method for femtosecond pulse phase characterization.

[0123] This invention may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this invention may take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0124] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0125] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0126] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0127] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A dynamic relaxation stacked imaging reconstruction method for femtosecond pulse temporal characterization, characterized in that, The method includes: The trajectory of the femtosecond pulse to be tested is measured to obtain a two-dimensional FROG trace map corresponding to the femtosecond pulse to be tested. The two-dimensional FROG trace map is processed to generate a standardized FROG trace map; Construct the initial complex electric field based on the standardized FROG trace plot; A dynamic relaxation update control mechanism is adopted to perform iterative update processing of the complex electric field based on the initial complex electric field and the standardized FROG trace map, and output the reconstruction parameters corresponding to the femtosecond pulse to be measured.

2. The dynamic relaxation stacked imaging reconstruction method for femtosecond pulse temporal characterization according to claim 1, characterized in that, The process of processing the two-dimensional FROG trace map to generate a standardized FROG trace map specifically includes: Determine whether the two-dimensional FROG trace map originates from experimental measurements; if the two-dimensional FROG trace map originates from experimental measurements, then standardize the two-dimensional FROG trace information to generate the standardized FROG trace map; if the two-dimensional FROG trace map originates from simulation processing, then directly use the two-dimensional FROG trace map as the standardized FROG trace map after unifying the intensity scale.

3. The dynamic relaxation stacked imaging reconstruction method for femtosecond pulse temporal characterization according to claim 1, characterized in that, The construction of the initial complex electric field based on the standardized FROG trace plot specifically includes: The sampling range required for complex electric field reconstruction is determined based on the frequency axis and delay axis of the standardized FROG trace plot; The initial spectral intensity of the femtosecond pulse to be measured is estimated within the sampling range based on the intensity distribution of the standardized FROG trace plot. The initial spectral intensity is normalized and square-rooted to obtain the initial spectral amplitude; The initial spectral amplitude is combined with a preset initial phase to construct a frequency domain complex electric field; The frequency domain complex electric field is transformed by inverse Fourier transform to obtain the time domain complex electric field; The time-domain complex electric field is used as the initial complex electric field.

4. The dynamic relaxation stacked imaging reconstruction method for femtosecond pulse temporal characterization according to claim 1, characterized in that, The dynamic relaxation update control mechanism employs an iterative update process for the complex electric field based on the initial complex electric field and the standardized FROG trace map, outputting the reconstruction parameters corresponding to the femtosecond pulse under test. Specifically, this includes: Step S41: Based on the extended stacked imaging engine, amplitude constraints are performed according to the initial complex electric field and the delay position in the normalized FROG trace map to obtain the amplitude-constrained time-domain nonlinear signal; Step S42: Based on the dynamic relaxation update control mechanism, generate dynamic relaxation update coefficients according to the current iteration number; Step S43: Update the complex electric field of the femtosecond pulse to be reconstructed based on the difference between the time-domain nonlinear signals before and after amplitude constraint, and in conjunction with the dynamic relaxation update coefficients. Step S44: Determine whether the preset conditions are met based on the updated complex electric field corresponding to the last delay position under the current iteration number; if the preset conditions are met, stop reconstruction and output the reconstruction parameters corresponding to the femtosecond pulse to be measured; if the preset conditions are not met, use the updated complex electric field corresponding to the last delay position under the current iteration number as the initial complex electric field and return to step S41.

5. The dynamic relaxation stacked imaging reconstruction method for femtosecond pulse temporal characterization according to claim 4, characterized in that, The extended layered imaging engine performs amplitude constraints based on the initial complex electric field and the delay position in the normalized FROG trace map to obtain an amplitude-constrained time-domain nonlinear signal, specifically including: Based on the extended stacked imaging engine, the time-domain nonlinear signal at different delay positions is calculated according to the initial complex electric field and the delay position in the normalized FROG trace map; The amplitude of the time-domain nonlinear signal at different delay positions is constrained using the measured amplitude information in the standardized FROG trace plot to obtain the amplitude-constrained frequency-domain nonlinear signal. The amplitude-constrained frequency-domain nonlinear signal is subjected to an inverse Fourier transform to obtain the amplitude-constrained time-domain nonlinear signal.

6. The dynamic relaxation stacked imaging reconstruction method for femtosecond pulse temporal characterization according to claim 4, characterized in that, The dynamic relaxation update control mechanism generates dynamic relaxation update coefficients based on the current iteration number, and the specific formula is as follows: ； in, These are the dynamic relaxation update coefficients during the k-th iteration. For the initial update strength, For the amplitude of random disturbance, This refers to the random perturbation term during the k-th iteration update process. As the attenuation factor, The maximum number of iterations, This represents the minimum update intensity.

7. A dynamic relaxation stacked imaging reconstruction system for femtosecond pulse temporal characterization, characterized in that, The system includes: The FROG measurement module is used to measure the trajectory of the femtosecond pulse to be measured and obtain the two-dimensional FROG trace map corresponding to the femtosecond pulse to be measured. The data preprocessing module is used to process the two-dimensional FROG trace map to generate a standardized FROG trace map. An initial complex electric field generation module is used to construct an initial complex electric field based on the standardized FROG trace diagram; The dynamic relaxation update reconstruction module is used to perform iterative update processing of the complex electric field based on the initial complex electric field and the standardized FROG trace map using a dynamic relaxation update control mechanism, and output the reconstruction parameters corresponding to the femtosecond pulse to be measured.

8. The dynamic relaxation stacked imaging reconstruction system for femtosecond pulse temporal characterization according to claim 7, characterized in that, The dynamic relaxation update and reconstruction module includes: The frequency domain amplitude constraint unit is used to perform amplitude constraint based on the extended stacked imaging engine, according to the initial complex electric field and the delay position in the normalized FROG trace map, to obtain the amplitude-constrained time-domain nonlinear signal. The dynamic relaxation coefficient update unit is used to generate dynamic relaxation update coefficients based on the current iteration number, according to the dynamic relaxation update control mechanism. The complex electric field update unit is used to update the complex electric field of the femtosecond pulse to be reconstructed based on the difference between the time-domain nonlinear signals before and after amplitude constraint, and in combination with the dynamic relaxation update coefficients. The judgment unit is used to determine whether the updated complex electric field corresponding to the last delay position under the current iteration number meets the preset conditions. If the preset conditions are met, the reconstruction is stopped and the reconstruction parameters corresponding to the femtosecond pulse to be measured are output. If the preset conditions are not met, the updated complex electric field corresponding to the last delay position under the current iteration number is used as the initial complex electric field and the result is returned to the frequency domain amplitude constraint unit.

9. A computer-storable medium, characterized in that, The device stores a computer program, which, when executed by a processor, implements the steps of a dynamic relaxation stacked imaging reconstruction method for femtosecond pulse phase characterization as described in any one of claims 1-6.

10. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, it implements the steps of the dynamic relaxation stacked imaging reconstruction method for femtosecond pulse phase characterization as described in any one of claims 1-6.

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