CN114216575A - Ultra-short pulse reconstruction system and method based on BP neural network - Google Patents

Ultra-short pulse reconstruction system and method based on BP neural network Download PDF

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CN114216575A
CN114216575A CN202111383297.0A CN202111383297A CN114216575A CN 114216575 A CN114216575 A CN 114216575A CN 202111383297 A CN202111383297 A CN 202111383297A CN 114216575 A CN114216575 A CN 114216575A
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CN114216575B (en
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张飒飒
王韬
田遴博
杨易
迟庆金
王昭
赵峰榕
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Abstract

The invention belongs to the technical field of ultrashort pulse characterization, and relates to an ultrashort pulse reconstruction system and method based on a deep learning BP neural network. An ultrashort pulse reconstruction system based on a BP neural network comprises a double-beam autocorrelation light path unit and a main control unit; the double-beam autocorrelation light path unit is used for acquiring a delay scanning spectrum trace diagram of the ultrashort pulse; the main control unit is used for controlling the system and processing data and comprises a control module and a data processing module; the data processing module comprises a BP neural network model; and the BP neural network model predicts the input scanning spectrum trace graph and outputs the amplitude and the phase of the ultrashort pulse to be detected. The invention provides the calculation of the cutting angle of the BBO crystal aiming at the difference of the pulse wavelength to be measured, thereby improving the applicability of the system and the success rate of the experiment. And the to-be-detected pulse information is reconstructed by combining the BP neural network, so that the reconstruction efficiency of the ultrashort pulse is greatly improved.

Description

Ultra-short pulse reconstruction system and method based on BP neural network
Technical Field
The invention belongs to the technical field of ultrashort pulse characterization, and relates to an ultrashort pulse reconstruction system and method based on deep learning BP neural network
Background
Since the advent of ultrashort pulse laser, the ultrashort pulse laser has irreplaceable important application in numerous fields such as microscopic imaging, laser processing, medical treatment and the like, has attracted extensive attention and great interest of society, and particularly has very key significance in the research of the quantum field.
The ultrashort pulse laser has very short laser pulse width, generally in picosecond or femtosecond level, and when the pulse width is femtosecond level, the pulse width exceeds the electronic response limit and cannot be represented by a general detector, so that the method for accurately and efficiently representing ultrashort pulses is very critical. In the sixties of the twentieth century, the problem of ultrashort pulse characterization was solved to some extent by the proposal of the autocorrelation method, and in the following decades, the self-referenced spectral interferometry, the frequency-resolved optical switching method, and the like were successively proposed. Compared with the former two methods, the frequency-resolved optical switching method, especially the second harmonic frequency-resolved optical switching method, has the characteristics of high resolution, high accuracy, simple optical path and the like, and is a mainstream method for representing ultrashort pulses at present, but the method needs a long time to calculate and restore the required data result from the spectrum trace, cannot detect in real time, has low signal-to-noise ratio and poor performance, and is widely subject to defects.
Disclosure of Invention
Aiming at the defects of low resolution, low accuracy (autocorrelation method), complex light path (self-reference spectrum interference method), low efficiency (frequency-resolved optical switching method), poor performance (all) of low signal-to-noise ratio and the like in the prior art, the invention provides a system for representing ultrashort pulses by using a double-reflection second harmonic frequency-resolved optical switching method based on a BP neural network, preferably selects an optical part of the system consisting of the double-reflection autocorrelation light path and a second harmonic nonlinear crystal, and uses the BP neural network to replace the traditional inversion algorithm (such as PCGPA) to calculate and obtain amplitude phase data.
The technical scheme adopted by the invention for solving the technical problems is as follows: the ultrashort pulse reconstruction system based on the BP neural network is characterized in that: the system comprises a double-beam autocorrelation light path unit and a main control unit; the double-beam autocorrelation light path unit is used for acquiring a scanning spectrum trace diagram of the ultrashort pulse; the main control unit is used for controlling the system and processing data and comprises a control module and a data processing module; the data processing module comprises a BP neural network model; and the BP neural network model predicts the input scanning spectrum trace graph and outputs the amplitude and the phase of the ultrashort pulse to be detected.
Preferably, the training set of the BP neural network model is composed of simulated scanning spectrum trace graphs, and the same group of noiseless pulse amplitudes and phases correspond to n simulated scanning spectrum trace graphs with different signal-to-noise ratios; n is more than or equal to 1 and less than or equal to 30.
Preferably, the simulated scanning spectrum trace diagram is obtained by the following steps:
(1) collecting pulse amplitude data, and carrying out N-point sampling on each group of collected pulse amplitude data, wherein N is more than or equal to 100 and less than or equal to 500;
(2) selecting N data from N sampling points of the pulse amplitude data, and performing random number processing of different degrees;
(3) and (3) according to the formula, the pulse amplitude data processed in the step (2) and the pulse phase data generated by the function:
Figure BDA0003366363030000021
in the formula
Figure BDA0003366363030000022
The spectrum is a scanning spectrum of second harmonic, E (t) is a pulse to be detected, E (t-tau) is a time-shifting copy, namely a gate function, of the pulse to be detected, omega is the frequency of the pulse to be detected, and tau is delay;
and calculating to obtain data of the simulated scanning spectrum trace graph, and generating n simulated scanning spectrum trace graphs with different signal-to-noise ratios.
Preferably, the different degrees of random numeralization processing are: respectively taking different random numbers between 0 and 1 for the selected n pulse amplitude data; and, the selected random number is different from the corresponding original value.
Preferably, the control module is configured to control a delay system of the dual-beam autocorrelation optical path unit to delay.
Preferably, the control module is further configured to control the spectrometer to continuously scan the frequency-doubled pulse spectrum while the delay system generates the delay, so as to generate a delay-scanned spectrum trace pattern.
Preferably, the nonlinear crystal in the two-beam autocorrelation optical path unit is a barium metaborate crystal; the cutting angle of the barium metaborate crystal is a main section collinear phase matching frequency doubling angle, and the calculation method comprises the following steps: setting two beams of pulse to be measured as k1And k2The frequency multiplication pulse is k3The phase matching condition under the condition of the main section is to satisfy the wave vector superposition, i.e.
Figure BDA0003366363030000023
Decomposing the vector to obtain a formula:
Figure BDA0003366363030000031
Figure BDA0003366363030000032
since the three pulses satisfy the vector superposition, so
Figure BDA0003366363030000033
The square addition operation is performed on the formulas (2) and (3), and the result is substituted into
Figure BDA0003366363030000034
To obtain:
Figure BDA0003366363030000035
according to the frequency multiplication, omega can be known3＝2ω1＝2ω2Therefore, it is
Figure BDA0003366363030000036
Wherein n isp(θ3) The angle between the frequency-doubled light and the main axis is theta3The refractive index of the time-doubled light; n isp(θ1)、np(θ2) For the pulse to be measured and the main shaft to form an included angle theta1、θ2The refractive index of the pulse to be measured;
the optical refractive index of the frequency doubling light e is calculated according to a formula:
Figure BDA0003366363030000037
wherein n isp(θ3) Is that
Figure BDA0003366363030000038
Combining the formulas (5) and (6), and drawing by matlab to obtain theta3With theta1The change map of (1), theta corresponding to the vertex of the image3The value is the desired cutting angle.
The invention also provides an ultrashort pulse reconstruction method based on the BP neural network, which comprises the following steps:
(1) acquiring an ultrashort pulse slow scanning spectrum trace diagram to be detected;
(2) and inputting the scanning spectrum trace graph into a pre-trained BP neural network model, and outputting the amplitude and the phase of the ultrashort pulse to be detected.
The ultra-short pulse reconstruction system and method based on the BP neural network have the advantages that: on the basis of measuring ultrashort pulses by the traditional FROG method, double reflection improvement is carried out on an autocorrelation light path, and mutual interference among the light paths is reduced. The cutting angle calculation of the BBO crystal is carried out according to the difference of the pulse wavelengths to be detected, and the applicability of the system and the success rate of the experiment are improved. The BP neural network is combined to replace traditional algorithms such as PCGPA and the like to reconstruct pulse information to be detected from the FROG trace, and the neural network is trained by using training sets with different signal-to-noise ratios, so that the ultra-short pulse reconstruction efficiency is greatly improved, and the accuracy of reconstructing ultra-short pulses under the condition of low signal-to-noise ratio is improved.
Drawings
Fig. 1 is a schematic structural diagram of an ultra-short pulse reconstruction system based on a BP neural network according to an embodiment of the present invention;
FIG. 2 is a BBO crystal collinear phase matching calculation result when the pulse wavelength to be measured is 800 nm;
FIG. 3 is a schematic diagram of a BP neural network structure;
FIG. 4 is a schematic diagram of a random number process;
fig. 5 is a flowchart of an ultra-short pulse reconstruction method based on a BP neural network according to an embodiment of the present invention;
in fig. 1: 1. a femtosecond laser; 2-1. a first silvered mirror; 2-2 a second silvered mirror; 2-3 a third silvered mirror; 3. a femtosecond beam splitter; 4. a converging mirror; 5. a nonlinear crystal; 6. a diaphragm; 7. a spectrometer; 8. a stepping motor; 9. a computer; 10 external electrical pulse generator.
Detailed Description
In order to facilitate an understanding of the invention, the invention is described in more detail below with reference to the accompanying drawings and specific examples. Preferred embodiments of the present invention are shown in the drawings. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.
Embodiment 1 the ultrashort pulse reconstruction system based on a BP neural network provided in this embodiment mainly includes a hardware system and a software system, where the hardware system is a dual-beam autocorrelation optical path system using a BBO crystal as a nonlinear crystal, and the software system includes a BP neural network model and a control module.
The structure of a dual-beam autocorrelation optical path system with a BBO crystal as a nonlinear crystal is shown in fig. 1, and includes: the device comprises a femtosecond laser 1, 5 silvered reflectors, a femtosecond beam splitter 3, a converging reflector 4, a nonlinear crystal 5, a data acquisition system, a delay system and a delay system controller.
The data acquisition system consists of a spectrometer 7 and a computer 9. The delay system consists of two second silvered reflectors 2-2 and a stepping motor 8, a delay system controller consists of an external electric pulse generator 10 and a control module built in a computer 9 and is used for controlling the delay system to generate displacement, and a BP neural network model is built in the computer 9.
The fixed optical path is composed of two first silvered mirrors 2-1. The emergent light of the fixed light path is incident on the converging mirror 4. The emergent light of the delay system enters the converging reflector 4 after passing through the third silvered reflector.
The nonlinear crystal 5 is used for generating frequency doubling pulse signals, and the diaphragm 6 is used for blocking other pulses except the frequency doubling pulses.
In order to facilitate movement, the light path part and the stepping motor of the embodiment are arranged on a 25-by-25-hole aluminum honeycomb plate, the stepping motor 8 is connected with an external pulse generator 10 through a data line, the external pulse generator 10 is connected with a computer 9 through an RS232 data bus, the spectrometer 7 is connected with the computer 9 through an instrument control line, and all instruments in the system are controlled by the computer 9.
The femtosecond laser device 1 outputs ultrashort pulses to be detected, and the femtosecond beam splitter 3 is 1: 1 splitting ratio, and dividing the ultrashort pulse to be detected into two input delay systems and a fixed light path. The fixed light path and the delay system are reflected twice to separate the incident light beam from the emergent light beam.
The data acquisition system acquires a scanning spectrum by a spectrometer 7, and generates a scanning spectrum trace pattern by a computer 9. The delay system generates optical path delay through the stepping motor 8, the delay system controller is composed of a control module in the computer 9 and an external electric pulse generator 10, the control module in the computer 9 writes a program for controlling delay amount by labview and controls the external electric pulse generator 10 to output pulse electric signals to the stepping motor 8.
In this embodiment, the nonlinear crystal 5 is a barium metaborate crystal (BBO crystal) having a large phase matching angle. The cutting angle of the BBO crystal is calculated according to the wavelength to be measured, and the calculation method comprises the following steps:
setting two beams of pulse to be measured as k1And k2The frequency multiplication pulse is k3The phase matching condition under the condition of the main section is that the wave vectors meet the vector superposition, namely
Figure BDA0003366363030000051
Decomposing the vector to obtain a formula:
Figure BDA0003366363030000052
Figure BDA0003366363030000053
since the three pulses satisfy the vector superposition, so
Figure BDA0003366363030000054
The square addition operation is performed on the formulas (2) and (3), and the result is substituted into
Figure BDA0003366363030000055
To obtain:
Figure BDA0003366363030000056
according to the frequency multiplication, omega can be known3＝2ω1＝2ω2Therefore, it is
Figure BDA0003366363030000057
Wherein n isp(θ3) The angle between the frequency-doubled light and the main axis is theta3The refractive index of the time-doubled light; n isp(θ1)、np(θ2) For the pulse to be measured and the main shaft to form an included angle theta1、θ2The refractive index of the pulse to be measured; in this embodiment, a class of phase matching ooes is adopted, the refractive index of the pulse o to be measured does not change with the included angle of the main shaft, and the refractive index of the frequency doubling e is calculated according to a formula:
Figure BDA0003366363030000061
wherein n isp(θ3) Is that
Figure BDA0003366363030000062
Combining the formulas (5) and (6), and drawing by matlab to obtain theta3With theta1The change map of (1), theta corresponding to the vertex of the image3The value is the desired cutting angle.
Compared with the prior art, the nonlinear crystal cut angle calculation method provided by the embodiment is more intuitive, and phase matching types such as ooe, eoe and the like can be calculated. The angle of the pulse to be measured entering the nonlinear crystal in a real experiment is difficult to control, and the calculation is based on the fact that the pulse to be measured can generate frequency doubling pulses when entering the nonlinear crystal at any angle, so that the feasibility of the experiment is improved.
In this embodiment, the wavelength of the femtosecond laser is 800nm, the cutting angle of the nonlinear crystal is a main-section collinear phase matching frequency doubling angle calculated to be 29.3 °, and the calculation result is shown in fig. 2.
In this embodiment, the working principle of the hardware system is as follows:
the femtosecond pulse to be detected is divided into light intensity of 1: 1, one beam of the same pulse is incident to a converging reflector after passing through a fixed light path, the other beam of the same pulse is reflected to the converging reflector through a silver-plated reflector after passing through a delay system, the two beams of pulses to be detected are converged to the center of a BBO crystal by the converging reflector, a frequency doubling pulse is generated between the two pulses after the nonlinear effect of the BBO crystal, and the pinhole diaphragm blocks other pulses except the frequency doubling pulse so as to ensure that only the frequency doubling pulse is incident to a probe of a spectrometer. The spectrometer transmits the collected frequency doubling pulse signals to a computer, and a scanning spectrum trace pattern is obtained through the processing of the computer.
In this embodiment, the software system selects a back-propagation (back-propagation) neural network structure, and compared with a multi-layer perceptron, the back-propagation optimization parameter weight is adopted by the BP neural network, so that the accuracy is higher and more reliable, and the convolutional neural network structure is simpler.
Setting the neuron number of a model input layer to be 49152, adding an input layer bias unit to be 1, setting the neuron number of a hidden layer to be 49152, adding a hidden layer bias unit to be 1, setting the neuron number of the hidden layer to be 49152 according to a picture matrix with a to-be-detected scanning spectrum trace graph of 128 × 3, setting the neuron number of an output layer to be 256 according to 128 points of amplitude data and phase data of two types of output pulses, and introducing a nonlinear factor by using a relu activation function to complete the neural network setting, as shown in fig. 3.
In this embodiment, the training set of the BP neural network model adopts a constructed simulated scanning spectrum trace atlas, and the construction method and process of the training set are as follows:
(A) placing a femtosecond laser with the wavelength of 800nm to be detected in front of the built double-beam autocorrelation light path system, and adjusting light path collimation to focus two beams of pulses to be detected on a BBO crystal to generate second harmonic.
(B) The step length displacement of a stepping motor is controlled by using a program compiled by labview, delay is realized, a spectrometer collects the scanning spectrum of each displacement, and a scanning spectrum tracing diagram is generated at a computer end.
(C) Collecting pulse amplitude data from documents and experiments, and performing 128-point sampling on each group of collected pulse amplitude data;
(D) selecting 1-30 data from 128 sampling points of the amplitude data to carry out random number processing with different degrees, specifically:
as shown in fig. 4a, the collected pulse amplitude data is a gaussian pulse, which is a continuous gaussian curve, and 128 points are equally divided on the abscissa, and the value of the middle point of each part represents the part, so as to obtain a scatter diagram shown in fig. 4b, which is composed of 128 points and is subjected to random number processing of different degrees, as shown in fig. 4c, 6 data points are subjected to random number processing, and as shown in fig. 4c, the data of 27 th, 45 th, 61 th, 70 th, 81 th, and 101 th points are given a value between 0 and 1 which is different from the original value, so as to obtain a scatter diagram shown in fig. 4c, which is the random number processing.
(E) And (3) the 6 processed pulse amplitude data and the pulse phase data generated by the function are processed according to a formula:
Figure BDA0003366363030000071
in the formula
Figure BDA0003366363030000072
The second harmonic scanning spectrum, E (t), the pulse to be measured, E (t-tau) the time-shifted copy of the pulse to be measured, i.e. the gate function, omega the frequency of the pulse to be measured, tau the delay.
And calculating to obtain data of the simulated scanning spectrum trace graph, and generating 6 simulated scanning spectrum trace graphs with different signal-to-noise ratios. FIG. 4d is a plot of a scatter plot as shown in FIG. 4 c.
Through the random number processing, the generated simulated scanning spectrum trace graph presents different signal-to-noise ratios, and a real spectrum trace graph can be simulated better.
In the training set in this embodiment, if 30 data are selected for randomization, the same group of noiseless pulse amplitudes and phases correspond to 30 simulated scanning spectrum trace patterns with different signal-to-noise ratios.
In this embodiment, a spectrometer is used to collect a delay scanning spectrum trace pattern of a frequency doubling pulse generated through an autocorrelation light path, and a PCGPA algorithm is used to perform inversion calculation to obtain amplitude pulse width phase information of the pulse to be measured, which is used as a test data set.
Inputting the constructed training data set into a BP neural network model, training and optimizing the model, wherein a loss function adopts cross entropy:
Figure BDA0003366363030000081
when loss is reduced to 10-3The expectation is considered to be reached.
And inputting the test data set and a part of the training data set into the trained model, predicting pulse information to be tested, and comparing the pulse information with the original data to test the performance of the BP neural network.
Through prediction and comparison, under the condition that the scanning spectrum trace diagram presents a high signal-to-noise ratio (is not subjected to random number processing), the reconstruction accuracy of the BP neural network is about 95.1% (95.3% of the traditional PCGPA), which is basically consistent with that of the traditional method, and under the condition that the scanning spectrum trace diagram presents a low signal-to-noise ratio (10 random number processing), the reconstruction accuracy of the BP neural network is 61.7% (40% of the traditional PCGPA), which is greatly improved compared with the traditional method. In the aspect of reconstruction speed, the time for reconstructing data from a group of scanning spectrum trace maps by the BP neural network is 0.5 second (about 30 minutes in the traditional PCGPA), which is greatly improved compared with the traditional method.
Embodiment 2 this embodiment provides an ultrashort pulse reconstruction method based on a BP neural network, and the flow is shown in fig. 5, including the following steps:
(1) acquiring a scanning spectrum trace diagram of the short wave pulse to be detected by using a built double-beam autocorrelation light path system which takes a BBO crystal as a nonlinear crystal;
(2) inputting the obtained scanning spectrum trace map into a built-in BP neural network model in a computer, and outputting corresponding amplitude and phase through model prediction.

Claims (8)

1. An ultrashort pulse reconstruction system based on a BP neural network is characterized in that: the system comprises a double-beam autocorrelation light path unit and a main control unit; the double-beam autocorrelation light path unit is used for acquiring a scanning spectrum trace diagram of the ultrashort pulse; the main control unit is used for controlling the system and processing data and comprises a control module and a data processing module; the data processing module comprises a BP neural network model; and the BP neural network model predicts the input scanning spectrum trace graph and outputs the amplitude and the phase of the ultrashort pulse to be detected.
2. The BP neural network-based ultrashort pulse reconstruction system of claim 1, wherein: the training set of the BP neural network model consists of simulated scanning spectrum trace graphs, and the same group of noiseless pulse amplitude and phase correspond to n simulated scanning spectrum trace graphs with different signal-to-noise ratios; n is more than or equal to 1 and less than or equal to 30.
3. The BP neural network-based ultrashort pulse reconstruction system of claim 2, wherein: the simulated scanning spectrum trace diagram is obtained by adopting the following steps:
(1) collecting pulse amplitude data, and carrying out N-point sampling on each group of collected pulse amplitude data, wherein N is more than or equal to 100 and less than or equal to 500;
(2) selecting N data from N sampling points of the pulse amplitude data, and performing random number processing of different degrees;
(3) and (3) according to the formula, the pulse amplitude data processed in the step (2) and the pulse phase data generated by the function:
Figure FDA0003366363020000011
in the formula
Figure FDA0003366363020000012
The spectrum is a scanning spectrum of second harmonic, E (t) is a pulse to be detected, E (t-tau) is a time-shifting copy, namely a gate function, of the pulse to be detected, omega is the frequency of the pulse to be detected, and tau is delay;
and calculating to obtain data of the simulated scanning spectrum trace graph, and generating n simulated scanning spectrum trace graphs with different signal-to-noise ratios.
4. The BP neural network-based ultrashort pulse reconstruction system of claim 3, wherein: the random number processing of different degrees is as follows: respectively taking different random numbers between 0 and 1 for the selected n pulse amplitude data; and, the selected random number is different from the corresponding original value.
5. The BP neural network-based ultrashort pulse reconstruction system of claim 1, wherein: the control module is used for controlling the delay system of the double-beam autocorrelation light path unit to delay.
6. The BP neural network-based ultrashort pulse reconstruction system of claim 5, wherein: the control module is also used for controlling the spectrometer to continuously scan the frequency doubling pulse spectrum while the delay system generates delay, and generating a delay scanning spectrum trace diagram.
7. The BP neural network-based ultrashort pulse reconstruction system of claim 1, wherein: the nonlinear crystal in the double-beam autocorrelation light path unit is a barium metaborate crystal; the cutting angle of the barium metaborate crystal is a main section collinear phase matching frequency doubling angle, and the calculation method comprises the following steps:
setting two beams of pulse to be measured as k1And k2The frequency multiplication pulse is k3The phase matching condition under the condition of the main section is to satisfy the wave vector superposition, i.e.
Figure FDA0003366363020000021
Decomposing the vector to obtain a formula:
Figure FDA0003366363020000022
Figure FDA0003366363020000023
since the three pulses satisfy the vector superposition, so
Figure FDA0003366363020000024
The square addition operation is performed on the formulas (2) and (3), and the result is substituted into
Figure FDA0003366363020000025
To obtain:
Figure FDA0003366363020000026
according to the frequency multiplication, omega can be known3＝2ω1＝2ω2Therefore, it is
Figure FDA0003366363020000027
Wherein n isp(θ3) The angle between the frequency-doubled light and the main axis is theta3The refractive index of the time-doubled light; n isp(θ1)、np(θ2) For the pulse to be measured and the main shaft to form an included angle theta1、θ2The refractive index of the pulse to be measured;
the optical refractive index of the frequency doubling light e is calculated according to a formula:
Figure FDA0003366363020000028
wherein n isp(θ3) Is that
Figure FDA0003366363020000029
Combining the formulas (5) and (6), and drawing by matlab to obtain theta3With theta1The change map of (1), theta corresponding to the vertex of the image3The value is the desired cutting angle.
8. An ultrashort pulse reconstruction method based on a BP neural network is characterized by comprising the following steps:
(1) acquiring a scanning spectrum trace diagram of the ultrashort pulse to be detected;
(2) and inputting the scanning spectrum trace graph into a pre-trained BP neural network model, and outputting the amplitude and the phase of the ultrashort pulse to be detected.
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