Pulse focal spot digital detection method based on variable sampling matrix

Abstract

The present application relates to a kind of based on the digital detection method of pulse focal spot of variable sampling matrix, this method is completed by variable sampling matrix to replace digital frequency domain algorithm to three-dimensional pulse far field light spot digital detection;For the three-dimensional space-time pulse signal generated by pulsed light source, the wavefront curvature of incident pulse is obtained by wavefront sensor, combined with the digital three-dimensional complex amplitude matrix of pulsed light parameter, then the far field focal spot calculation is completed by variable sampling matrix modification sampling boundary condition, and the focal spot distribution of the arbitrary sampling parameter of three-dimensional space-time focal spot is obtained.The present application can effectively extend the near field or far field transmission calculation range of the surface distribution of the measured pulse signal, avoid the signal aliasing caused by the calculation window of low space bandwidth product, improve the sampling resolution while reducing the required time of calculation, and can obtain the high sampling resolution synchronized with the upper limit of hardware device calculation.

Description

Technical Field

[0001] This invention belongs to the field of optical systems and optical simulation, and in particular relates to a pulse focal spot digital detection method based on a variable sampling matrix. Background Technology

[0002] In high-power laser devices, dispersion occurs at various stages of the system, such as stretching, amplification, compression, and pulse transmission. Compared to other processes, the spatiotemporal coupling effect of the pulse in the stretcher and compressor is more pronounced. In early studies, due to the relatively wide output pulse width, the stretching factor provided by the system was small, and the minor aberrations generated by the structure could be ignored. However, as the achievable pulse width becomes shorter and the required stretching factor increases, the influence of minor aberrations on the pulse becomes significant, affecting the uniformity control of the focal spot. In the digital management phase, high-energy laser systems require complete control over pulse transmission and focusing, necessitating a comprehensive consideration of both two-dimensional space and one-dimensional time to fully grasp the three-dimensional characteristics of the pulsed light field.

[0003] Different calculation methods are generally used for different computational regions and media when calculating light wave propagation. When the light wave propagation distance is approximately one wavelength, correlation methods in computational electromagnetics are usually used. For calculations in the far field, scalar diffraction numerical calculations in Fourier optics are commonly used. For calculating the intensity distribution of far-field light spots or Fresnel zones, scalar diffraction calculations can provide rigorous solutions that strictly satisfy the Helmholtz equations. The core technique of correlation calculations is to use Fourier transforms to shift the signal frequency by different components. This method largely restricts the boundary conditions of the diffraction process. The Fast Fourier Transform (FFT) calculation method can reduce the time complexity of multiplication operations by utilizing the symmetry of the transform matrix, and is widely used because it greatly improves the computational efficiency of signal processing. However, using the FFT algorithm introduces a fixed sampling relationship between the input and output domains. This deterministic sampling relationship affects broadband phase retrieval and phase retrieval when significant chromatic aberration exists, which has a certain impact on the accuracy of the calculation results. If a fast algorithm is used to calculate the pulse propagation process, especially the far-field distribution, there may be insufficient sampling resolution or wasted computational resources. Summary of the Invention

[0004] The technical problem this invention aims to solve is to provide a digital detection method for pulsed focal spots based on a variable sampling matrix. This method replaces the digital frequency domain algorithm with a variable sampling matrix to complete the digital detection of three-dimensional pulsed far-field light spots. For a three-dimensional spatiotemporal pulse signal generated by a pulsed light source, the wavefront curvature of the incident pulse is obtained through a wavefront sensor. Combined with the pulse light parameters, a digital three-dimensional complex amplitude matrix is ​​obtained. Then, the sampling boundary conditions are modified by the variable sampling matrix to complete the far-field focal spot calculation, obtaining the focal spot distribution of the three-dimensional spatiotemporal focal spot with arbitrary sampling parameters. This method can adapt to recording information and simulation processes with different basic parameters, and can significantly reduce the calculation time while improving sampling resolution.

[0005] The technical solution of the present invention is as follows:

[0006] To address the limitations of sampling parameters and insufficient surface information in three-dimensional pulse focal spots, this invention provides a pulse focal spot digital detection method based on a variable sampling matrix. This method adapts to different pulse calculation windows for pulse aberration measurement systems, expands the effective range of calculation by employing a variable sampling matrix to complete the transmission algorithm, and ensures that the sampling parameters of the calculation windows are independent and can be freely and flexibly controlled.

[0007] The present invention provides a pulse focal spot digital detection method based on a variable sampling matrix, comprising the following steps S1 to S3:

[0008] S1. The wavefront curvature of the Gaussian pulse light signal is recorded using a Hartmann wavefront sensor. The wavefront curvature is then processed in conjunction with the pulse light parameters to obtain the corresponding digital three-dimensional complex amplitude matrix. Taking a Gaussian pulse as an example, let the phase distribution of the pulse light on the spatial cross-section corresponding to the wavefront curvature distribution be... The radius of the Gaussian beam is r g The spatial distribution u at the two-dimensional cross-section of the pulse g It can be represented in the following form:

[0009]

[0010] In the formula, j is the imaginary unit. g It is expressed as a three-dimensional matrix with N rows and N columns and K layers in the digital matrix, where the expression of each layer is the same as that described in formula (1);

[0011] The time distribution of the Gaussian pulse u t It can be expressed in the following form:

[0012]

[0013] In the formula, τ is the full width at half maximum (FWHM) of the pulse. t Within the digitization matrix, it is expressed as a one-dimensional form with K sampling points. The three-dimensional complex amplitude matrix can be expressed as U = u g ·ut ;

[0014] S2. Set a variable sampling input window for the aforementioned three-dimensional complex amplitude matrix, and set the variable sampling matrix through the sampling parameters of the input and output windows. The sampling parameters of the input window are the sampling interval δ1 and the number of sampling points N, while the sampling parameters of the output window are the sampling interval δ2 and the number of sampling points M. The expression for the variable sampling matrix can be described as follows:

[0015]

[0016] In formula (3), d is the transmission distance, w is the center wavelength of the pulse beam used, n is the row vector of the input window dimension and satisfies n=[1,2,…,N]-(N+1) / 2, m is the row vector of the output window dimension and satisfies m=[1,2,…,M]-(M+1) / 2, and j is the imaginary unit;

[0017] S3. Based on the input window, set the quadratic phase shift matrix and the lens quadratic phase matrix, and combine the variable sampling matrix to complete the variable sampling transmission calculation of the input three-dimensional complex amplitude matrix, and obtain its far-field three-dimensional focal spot matrix.

[0018] The expression for the quadratic phase shift matrix set in the input window is as follows:

[0019]

[0020] The expression for the lens's second phase matrix set in the input window is as follows:

[0021]

[0022] In formula (5), f is the lens focal length, and k is the wavenumber corresponding to the pulse center wavelength. The variable sampling transmission calculation process can be written as the following expression:

[0023] W = V T (U·L·C)V (6)

[0024] In formula (6), W is the variable sampling three-dimensional focal spot matrix.

[0025] In step S1, the wavefront sensor used is not limited to the Hartmann wavefront sensor, and the recording process is applicable to any sensor that records and reconstructs wavefront information in a single instance.

[0026] In step S2, the transmission distance d should satisfy the sampling constraint d>max(N,M)·δ1δ2 / w.

[0027] Compared with the prior art, the beneficial effects of the present invention are:

[0028] 1. The present invention adopts a variable sampling matrix transmission method, which can remove the fixed sampling relationship from the recording device during the pulse transmission calculation process, greatly improving the flexibility of the calculation.

[0029] 2. The calculation windows of the present invention are independent of each other, which can expand the calculation range of a single transmission process while maintaining the original calculation results, and improve the calculation range of the three-dimensional focal spot in the time domain and spatial domain.

[0030] 3. This invention saves more computation time than widely used traditional algorithms at the same computational accuracy, and can greatly improve the efficiency of processing and judging the details of three-dimensional far-field signals. Attached Figure Description

[0031] Figure 1 This is a flowchart of a pulse focal spot digital detection method based on a variable sampling matrix according to the present invention.

[0032] Figure 2 This is a schematic diagram of the variable sampling matrix calculation window for a pulse focal spot digital detection method based on a variable sampling matrix according to the present invention.

[0033] Figure 3 This is a comparison chart showing the computation time of various embodiments of the pulse focal spot digital detection method based on a variable sampling matrix according to the present invention. Figure 3 (a) represents the eight coherent input bundles. Figure 3 (b) Comparison of calculation results and time consumption for the Fast Fourier Transform algorithm. Figure 3 (c) shows the result and time consumption of the variable sampling transfer matrix calculation using this method. Figure 3 (d) is the calculation of the Fast Fourier Transform algorithm and Figure 3 (c) shows the calculation results and time consumption for the same resolution accuracy.

[0034] Figure 4 To compare the results of digital calculations of three-dimensional pulse focal spot distribution based on traditional calculation methods in the case study. Figure 4 (a) and Figure 4 (b) shows the extreme value cross-section and time-domain intensity line diagram at the vertical plane. Figure 4 (c) and Figure 4 (d) shows the extreme value cross-section and time-domain intensity line diagram at the horizontal plane. Figure 4 (e) is a three-dimensional spatiotemporal distribution extreme value slice diagram. Figure 4 (f) and Figure 4 (g) shows the transmission cross-section diagram and the spatial intensity line diagram.

[0035] Figure 5 The above represents the simulation results of the far-field three-dimensional pulsed focal spot distribution in an embodiment of the present invention. Figure 5 (a) and Figure 5 (b) shows the extreme value cross-section and time-domain intensity line diagram at the vertical plane. Figure 5 (c) and Figure 5 (d) shows the extreme value cross-section and time-domain intensity line diagram at the horizontal plane. Figure 5 (e) is a three-dimensional focal spot spatiotemporal distribution extreme value slice map. Figure 5 (f) and Figure 5 (g) shows the transmission cross-section diagram and the spatial intensity line diagram. Detailed Implementation

[0036] The present invention will be further described below with reference to embodiments and accompanying drawings, but this should not be construed as limiting the scope of protection of the present invention.

[0037] Please refer to Figure 1 , Figure 1 The flowchart of the pulse focal spot digital detection method based on a variable sampling matrix of the present invention is shown in the figure. As can be seen from the figure, the pulse focal spot digital detection method based on a variable sampling matrix of the present invention includes steps S1 to S3, specifically: recording the wavefront curvature of the pulse light signal through a wavefront sensor, processing the wavefront curvature in combination with pulse light parameters to obtain the corresponding digital three-dimensional complex amplitude matrix U; setting a variable sampling input window and an output window for the three-dimensional complex amplitude matrix, and setting the variable sampling matrix V by calculating the sampling parameters of the input window and the output window; setting a quadratic phase shift matrix C and a lens quadratic phase matrix L based on the input window, and completing the variable sampling transmission calculation of the input three-dimensional complex amplitude matrix in combination with the variable sampling matrix to obtain the far-field three-dimensional focal spot matrix W = V. T (ULC)V.

[0038] The pulse focal spot digital detection method based on variable sampling matrix, wherein the calculation window of the variable sampling matrix transmission algorithm is as follows: Figure 2 As shown, both the input window and the output window are sampling parameters that satisfy their own window resolution.

[0039] The calculation window of the pulse focal spot digital detection method based on the variable sampling matrix satisfies the sampling parameters of the sampling device. The second phase shift matrix C of the input window and the second phase shift matrix L of the lens have a conjugate relationship when the transmission distance is equal to the lens focal length, i.e., d = f, and can be omitted during calculation.

[0040] Example 1 demonstrates a comparison of computation time for calculating coherent bundles using the variable sampling matrix transmission algorithm; relevant data can be found in [link to example]. Figure 3 .exist Figure 3 (a) shows eight rays with a diameter of 150 μm, spaced 1.15 μm apart, distributed at the vertices of a regular octagon, with 1000 sampling points. Figure 3 (b) shows the far-field results of coherent bundle combining calculated using the Fast Fourier Transform (FFT) algorithm. In this process, the FFT algorithm saves 90% of the computation time compared to the Discrete Fourier Transform (DFT) algorithm. Figure 3(c) shows the computation results using the variable sampling matrix transmission algorithm, where the region of the main signal is narrowed down by the variable sampling matrix to observe details. Figure 3 (d) shows the result obtained using the Fast Fourier Transform algorithm. Figure 3 (c) The computation time required for the same sampling resolution is 20,000 for the Fast Fourier Algorithm to obtain the same resolution distribution result, while the method of the present invention only requires the original number of sampling points of 1,000 to obtain the same level of fineness sampling resolution. Comparing the computation time, it can be seen that the computation time of the variable sampling matrix transmission algorithm to obtain the computation result is about 98% less than that of the widely used Fast Fourier Algorithm.

[0041] Example 2 presents a comparison between the simulation results of far-field three-dimensional pulse focal spot distribution calculated by the traditional method and the digital detection method for pulse focal spots using the variable sampling matrix provided by this invention. Relevant data can be found in [link to relevant data]. Figure 4 and Figure 5 During data acquisition, both schemes use the same recording method: the incident pulse signal is expanded by a beam expander and then modulated by the same array lens. The results of the traditional method are shown in... Figure 4 In the middle. As you can see, Figure 4 (a)~ Figure 4 (d) shows the extreme value cross-sections and time-domain intensity lines at the vertical and horizontal planes. The spatiotemporal distribution of the pulses along this cross-section exhibits characteristics of enhanced aliasing signals and low resolution. Figure 4 (e) is a three-dimensional spatiotemporal distribution of the main signal extreme value slice. Here, the three-dimensional spatiotemporal slice shows the details of the aliased pulse in the spatiotemporal coordinates. Since the aliased signal and the main signal jointly divide the coordinate units in the calculation window, the main signal has a low sampling resolution in different dimensions. Figure 4 (f) and Figure 4 (g) shows the transmission cross-section and spatial intensity line diagram, which clearly demonstrates that the aliasing signal uniformly occupies the calculation window, affecting the detailed observation of the calculated information. The results provided by this invention are shown in... Figure 5 middle. Figure 5 (a)~ Figure 5 (d) shows the extreme value cross-sections and time-domain intensity lines at the vertical and horizontal planes. Figure 5 (e) is a three-dimensional focal spot spatiotemporal distribution extreme value slice map. Figure 5 (f) and Figure 5 (g) shows the transmission cross-section and spatial intensity line diagram. Clearly, the digital reconstruction results provided by this method do not exhibit aliasing signals, and the sampling resolution for observations in different dimensions is significantly improved compared to traditional methods. The noise fringes at the edges of the main signal are very clearly distributed. Figure 4The distribution in this area is clearly blurry, and the image details and sampling resolution provided are far lower than those of the method provided in this invention.

[0042] The parts of this invention not described in detail are common knowledge to those skilled in the art.

[0043] This method acquires pulse information from a wavefront sensor, pre-sets three-dimensional pulse data, and then changes the sampling boundary conditions using a variable sampling matrix to obtain three-dimensional pulse spot information with higher sampling resolution and more flexible transmission parameters. This method can adapt to recording information and simulation processes with different basic parameters, and can significantly reduce computation time while improving sampling resolution, providing calculation results more quickly and flexibly.

[0044] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific implementation examples of the present invention and are not intended to limit the invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A variable sampling matrix based pulsed focal spot digital detection method, characterized in that, The method comprises the following steps: S1. recording the wavefront curvature of a Gaussian pulse light signal by a wavefront sensor, processing the wavefront curvature in combination with pulse light parameters to obtain a corresponding three-dimensional complex amplitude matrix; S2. setting a variable sampling input window for the three-dimensional complex amplitude matrix, and setting a variable sampling matrix through the sampling parameter of the input window and the output window; S3. setting a quadratic phase shift matrix and a lens quadratic phase matrix through the input window, and completing variable sampling transmission calculation of the input three-dimensional complex amplitude matrix in combination with the variable sampling matrix to obtain a far-field three-dimensional focal spot matrix thereof; The three-dimensional complex amplitude matrix U in the step S1 is a Gaussian pulse, and the phase distribution of the pulse light corresponding to the wavefront curvature distribution on a spatial section is The Gaussian beam radius is r g At the two-dimensional section of the pulse, its spatial distribution u g is expressed as follows: where j is the imaginary unit, u g In the digitalized matrix, it is expressed as a three-dimensional matrix with N rows, N columns and K layers, and the expression of each layer is the same as described in formula (1). The time profile u of the Gaussian pulse t is expressed as: where τ is the full width at half maximum of the pulse, u t In the digitalized matrix, expressed in one dimension with K samples, the three-dimensional complex amplitude matrix U = u g ·u t .

2. The variable decimation matrix based pulsed focal spot digital detection method of claim 1, wherein, The sampling parameters of the input window in the step S2 are a sampling interval δ1 and a sampling point number N, the sampling parameters of the output window are a sampling interval δ2 and a sampling point number M, and the expression of the variable sampling matrix is as follows: In the formula, d is a transmission distance, d>max(N,M)·δ1δ2 / w is satisfied, w is the central wavelength of the used pulse light beam, n is an input window dimension row vector, n=[1,2,…,N]-(N+1) / 2 is satisfied, m is an output window dimension row vector, m=[1,2,…,M]-(M+1) / 2 is satisfied, and j is an imaginary unit.

3. The variable decimation matrix based pulsed focal spot digital detection method of claim 1, wherein, The expression of the quadratic phase shift matrix in the step S3 is as follows: The expression of the lens quadratic phase matrix is as follows: In the formula, f is a lens focal length, and k is a wave number corresponding to the central wavelength of the pulse.

4. The variable decimation matrix based pulsed focal spot digital detection method of claim 1, wherein, The variable sampling transmission calculation formula in the step S3 is as follows: W = V T (U·L·C)V (6) In the formula, W is a variable sampling three-dimensional focal spot matrix, and U is a three-dimensional complex amplitude matrix.

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