A method for determining ion beam polishing removal function based on BP neural network

Abstract

The present invention relates to a method for determining an ion beam polishing removal function based on a BP neural network. A database is established through a limited number of Faraday scans and line scan experiments to determine the relationship between the ion beam current density and the removal function distribution coefficient. According to the Faraday scan result, the removal function peak removal rate is calculated through a linear formula, and the removal function distribution coefficient is predicted through a BP neural network. The removal function information obtained by the method is basically the same as the removal function information obtained by the experimental method, but the time for determining the removal function is greatly shortened; at the same time, the removal function is determined based on the Faraday scan result, and there is no need to perform a removal function experiment on the surface of the component, thereby saving costs; and the present invention determines the distribution information of the removal function through a linear formula and a BP neural network. This method is applicable to all materials that can be used for ion beam processing, is not limited by material properties, and can be used for all ion beam processing processes.

Description

Technical Field

[0001] The invention relates to the technical field of optical precision manufacturing, and in particular to a method for determining an ion beam polishing removal function based on a BP neural network. Background Art

[0002] Ion beam polishing is usually used for the final processing of ultra-precision optical components. Ion beam polishing achieves material removal based on the principle of atomic sputtering, so that the removal accuracy of component materials by ion beam polishing reaches the atomic level and the processing accuracy reaches the nanometer level. It is considered to be the optical component polishing technology with the highest processing accuracy and the best shaping effect. When processing optical components, the traditional contact polishing method inevitably has problems such as polishing head wear, edge effect and sub-surface damage due to its contact processing method, which restricts the improvement of processing accuracy. Ion beam polishing uses an ion beam instead of a traditional polishing head to remove the surface material of the optical component through the ion sputtering effect between the ion beam and the optical component. It can not only avoid the above problems, but also has the characteristics of high precision and high convergence.

[0003] During the ion beam polishing process, the solution of the dwell time is completed under the assumption that the removal function remains unchanged during the entire polishing process. Therefore, the solution of the removal function is a prerequisite for ion beam processing. The long single processing time causes the grid loss of the ion source to affect the characteristics of the removal function. Therefore, in order to ensure the processing accuracy, the removal function information needs to be re-determined before each processing of large-aperture optical components. The determination of the removal function information is generally completed through experimental methods, that is, controlling the ion beam to etch the surface of the optical component, using an interferometer to measure the surface shape of the optical component before and after the experiment, and obtaining the material removal amount of the experimental process by subtracting the component surface shape before and after the experiment, and then calculating the removal function information based on the etching parameters. This method is complex to operate, time-consuming and costly.

[0004] Ion beam polishing is based on the removal of materials by ion sputtering. This process can be explained by the Sigmund principle, that is, when the ion beam bombards the optical element, the removal function is proportional to the ion concentration distribution on the surface of the element. Using a Faraday cup to scan the ion beam can obtain the spatial distribution of the ion beam current density, which is proportional to the ion concentration distribution. Therefore, when the distance between the ion source and the Faraday cup and the surface of the processed optical element is the same, the current density distribution obtained by scanning the ion beam with a Faraday cup is positively correlated with the ion beam current distribution on the surface of the optical element. Therefore, the current density distribution obtained by scanning the ion beam with a Faraday cup can be used to represent the distribution of the removal function, but the relationship between the two parameters is nonlinear and related to the material properties. The current method cannot be applied to all types of optical elements.

[0005] In summary, there is a need for a method of determining ion beam polishing removal function that is cost-effective, efficient, and applicable to all types of optical components. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a method for determining an ion beam polishing removal function based on a BP neural network, which is cost-saving, efficient and applicable to all types of optical elements, in view of the current state of the prior art.

[0007] The technical solution adopted by the present invention to solve the above technical problem is: a method for determining an ion beam polishing removal function based on a BP neural network, comprising the following steps:

[0008] S1. Establish a database of Faraday scanning and removal functions:

[0009] After selecting the optical element material, set the ion source process parameters and turn on the ion source. The ion source process parameters include ion beam voltage, acceleration voltage, radio frequency power, argon gas flow rate, neutralization current and working distance. Change other parameters except the ion beam voltage each time to obtain ion beam currents with the same energy but different spatial distributions. After the ion source is stable, perform a Faraday scan and a removal function experiment to obtain ion beam current density and removal function distribution information.

[0010] S2. Use the linear formula to determine the peak removal rate of the removal function:

[0011] The peak value J of the ion beam current density obtained by S1 max The peak removal rate R of the removal function obtained with S1 max Linear fitting is performed to obtain the proportional coefficient a, and the peak removal rate R of the removal function is calculated based on the energy of the incident ions, the incident angle of the ion beam, and the etched material when the energy of the incident ions, the incident angle of the ion beam, and the etched material are the same for ion beams with different spatial distributions. max and the peak value of the ion beam current density J max Satisfy the linear relationship R max =aJ max (6), with the peak current density J of the ion beam max To determine the peak removal rate R of the removal function max ;

[0012] S3. Use neural network to determine the removal function distribution coefficient:

[0013] (1) Constructing a neural network

[0014] A 3-layer BP network with 1 hidden layer was selected, and the peak value of ion beam current density J max and the ion beam current distribution coefficient σ FAs the input signal, the removal function distribution coefficient σ is used as the output signal to construct a neural network, in which the transfer function of the network hidden layer neuron and the transfer function of the output layer neuron both use the S-type tangent function;

[0015] (2) Training the Neural Network

[0016] Initialize the network structure and weights, select the data in the database established in S1 to train the neural network, forward calculate the input signal and output signal of each layer of neurons in the BP network according to the input samples, calculate the reverse error according to the expected output, and modify the weights. If the error is less than the given value T or the number of iterations exceeds the set value H, the learning ends;

[0017] (3) Prediction of removal function distribution coefficients through neural network

[0018] Use the Faraday cup to scan the ion beam current to obtain the peak ion beam current density J' under the current conditions max and the distribution parameter σ under the current conditions F’ , and input into the neural network as prediction data to predict the removal function distribution coefficient σ' under the current conditions;

[0019] S4. Determine the removal function:

[0020] The removal function peak removal rate R calculated in S2 and S3 max Substitute the removal function distribution coefficient σ' under the current situation into the general expression formula of the removal function In the removal function, we get

[0021] Furthermore, the specific process of obtaining the ion beam current density distribution information in S1 includes:

[0022] S11, close the neutralizer, control the ion beam to be incident vertically on the Faraday cup, keep the center line of the ion source and the Faraday cup in the same vertical plane, move the ion source horizontally through the Faraday cup, and obtain the distribution coefficient of the ion beam current density in one-dimensional direction;

[0023] S12, using the method of collecting data at equal intervals to perform Faraday scanning experiments, setting the ion source scanning range, movement speed, working distance and number of sampling points in the scanning direction to perform Faraday scanning to obtain current density data, and performing Gaussian fitting on the sampled data to obtain the peak ion beam current density J at the current moment max and the ion beam distribution coefficient σ F ;

[0024] S13. According to the rotationally symmetric Gaussian distribution of current density space, the ion beam current density distribution is expressed by the following formula (1):

[0025]

[0026] Among them, J max and σ F are the peak value and distribution coefficient of ion beam current density, respectively.

[0027] Furthermore, the specific process of obtaining the removal function distribution information in S1 includes:

[0028] S14, after completing S13, the neutralizer is turned on, the ion beam is controlled to be incident vertically on the surface of the optical element, and a line scanning experiment is performed n times along the X direction at a speed v, and the surface shape of the optical element before and after the experiment is measured using an interferometer and a difference is made to obtain the material removal amount during the line scanning experiment;

[0029] S15, calculating the average value r(y) of the material removal amount along the Y direction of the component;

[0030] S16. Perform Gaussian fitting on r(y) to obtain a one-dimensional material removal function along the Y direction, as shown in the following formula (2):

[0031]

[0032] Among them, R y and σ y are the peak removal rate and distribution coefficient of the one-dimensional material removal function, respectively;

[0033] S17, according to formula (3) and formula (4), R y and σ y Calculate the peak removal rate R of the removal function max and the distribution coefficient σ,

[0034]

[0035] σ=σ y (4)

[0036] S18, R max Substitute σ into the following formula

[0037] Find the removal function.

[0038] Furthermore, the stabilization of the ion source in S1 specifically includes that the fluctuation of the ion beam current is less than 5%.

[0039] Compared with the prior art, the advantages of the present invention are:

[0040] 1. The present invention establishes a database through a limited number of Faraday scans and line scan experiments to determine the relationship between the ion beam current density and the removal function distribution coefficient. According to the Faraday scan results, the removal function peak removal rate is calculated by a linear formula, and the removal function distribution coefficient is predicted by a BP neural network. The removal function information obtained by this method is basically the same as the removal function information obtained by the experimental method, and the time for determining the removal function is greatly shortened from 3 hours to 1 minute. At the same time, the method determines the removal function based on the Faraday scan results, and there is no need to perform a removal function experiment on the component surface, thereby saving costs.

[0041] 2. The present invention determines the distribution information of the removal function through a linear formula and a BP neural network. This method is applicable to all materials that can be used for ion beam processing, is not limited by material properties, and can be used in all ion beam processing processes. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is a flow chart of determining the ion beam polishing removal function based on the BP neural network in an embodiment of the present invention;

[0043] Figure 2 The Faraday scanning results and data fitting results in the embodiment of the present invention;

[0044] Figure 3 This is a flow chart of determining removal function information by a line scanning experimental method in an embodiment of the present invention;

[0045] Figure 4 The results of the line scanning experiment in the embodiment of the present invention;

[0046] Figure 5 is the peak removal rate R of the ion beam removal function in the embodiment of the present invention max The peak value of the current density J max Linear fitting graph of proportionality coefficient a;

[0047] Figure 6 The neural network establishment process in the embodiment of the present invention;

[0048] Figure 7 A schematic diagram of a neural network model established in an embodiment of the present invention;

[0049] Figure 8 This is the neural network training process in the embodiment of the present invention. DETAILED DESCRIPTION

[0050] The specific implementation of the present invention is further described in detail below in conjunction with the drawings and examples.

[0051] like Figure 1The specific operation steps of a method for determining an ion beam polishing removal function based on a BP neural network of the present invention include:

[0052] 1. Establish a database of Faraday scan and removal functions:

[0053] (1) After selecting the optical element material, set the ion source process parameters (the initial ion source parameters are ion beam voltage 1100 V, acceleration voltage 300 V, RF power 95 W, argon flow rate 5 sccm and working distance 25 mm) and turn on the ion source. Change the other parameters except the ion beam voltage each time to obtain ion beam currents with the same energy but different spatial distributions. After the ion source is stable (the fluctuation of the ion beam current is less than 5%), perform a Faraday scan and a removal function experiment to obtain current density and removal function distribution information. The specific process is shown in (2) and (3) in step 1;

[0054] (2) Obtain current density distribution information by Faraday scanning the ion beam. Turn off the neutralizer and control the ion beam to be incident vertically on the Faraday cup. The center line of the ion source and the Faraday cup is always in the same vertical plane. Move the ion source horizontally through the Faraday cup to obtain the distribution coefficient of the current density in one dimension. The spatial distribution of current density is a rotationally symmetric Gaussian type, so the ion beam current density distribution can be expressed by formula 1, where J max and σ F are the peak value and distribution coefficient of ion beam current density, respectively.

[0055]

[0056] The Faraday scanning experiment was carried out by using the method of collecting data at equal intervals: the ion source scanning range was set to (-15 mm, +15 mm) in the scanning direction, the movement speed was 1 mm / s, the working distance was 25 mm, and the number of sampling points was 31 to perform Faraday scanning to obtain current density data, and then the sampled data was Gaussian fitted ( Figure 2 is the measured data and fitting result of a Faraday scan result), and the peak value J of the ion beam current density at the current moment is obtained. max and the distribution coefficient σ F .

[0057] (3) The flow chart of obtaining the removal function distribution information through line scanning experiment is as follows Figure 3 After completing (2) in step 1, turn on the neutralizer and perform a line scan experiment to determine the removal function information. Control the ion beam to be incident vertically on the surface of the optical element, and perform a line scan experiment n = 25 times along the X direction at a speed v = 1 mm / s (the result of one line scan experiment is shown in Figure 4The interferometer is used to measure the surface shape of the optical element before and after the experiment and to obtain the material removal amount during the line scanning experiment by subtraction. The removal function information is calculated by the following steps:

[0058] 1) Calculate the average material removal amount r(y) along the Y direction of the component;

[0059] 2) Perform Gaussian fitting on r(y) to obtain the one-dimensional material removal function along the Y direction, as shown in Equation 2, where R y and σ y are the peak removal rate and distribution coefficient of the one-dimensional material removal function, respectively;

[0060]

[0061] 3) According to formula 3 and formula 4, R y and σ y Calculate the removal function peak removal rate R max and the distribution coefficient σ;

[0062]

[0063] σ=σ y (4)

[0064] 4) R max Substituting σ and σ into Equation 5, we can obtain the removal function.

[0065]

[0066] 2. Use the linear formula to determine the peak removal rate of the removal function:

[0067] When the incident ion energy, the incident angle of the ion beam, and the etched material are the same, for ion beams with different spatial distributions, the peak removal rate R of the removal function is max and the peak value of the ion beam current density J max It is a linear relationship, as shown in Formula 6:

[0068] R max =aJ max (6)

[0069] Therefore, the peak value J of the ion beam current density obtained in step 1 (2) is max The peak removal rate R of the removal function obtained in step 1 (3) max The proportional coefficient a can be determined by linear fitting. The fitting result is as follows: Figure 5 As shown in the figure, each group of discrete points represents the peak removal rate, R max and the peak current density J maxThe measured value of J can be obtained by linear fitting curve, and the proportional coefficient a is 1.5962, so max To determine the R of the removal function max The expression R max =1.5962J max .

[0070] 3. Use neural network to determine the removal function distribution coefficient:

[0071] BP neural network refers to a multi-layer forward neural network based on the error back propagation algorithm, which can approximate any nonlinear mapping with arbitrary accuracy. The nonlinear fitting algorithm flow of BP neural network is as follows: Figure 6 As shown, it can be divided into three steps: BP neural network construction, BP neural network training and BP neural network prediction.

[0072] (1) Constructing a neural network

[0073] A three-layer BP neural network can describe all nonlinear functions, so a three-layer network with one hidden layer is selected. The direct factors affecting the removal function include the current density peak value and the distribution coefficient, so the current density peak value J is selected. max and the distribution coefficient σ F As the input signal, select the removal function distribution coefficient σ as the output signal. The input vector is X = (x1, x2) T , the hidden layer input vector is Y = (y1, y2, y3, y4, y5) T , the output vector is O = (o1) T , the expected response is D = (d) T , the weight matrix between the input layer and the hidden layer is represented by W, W = (w 11 , w 12 , w 13 , w 14 , w 15 , w 21 , w 22 , w 23 , w 24 , w 25 ) T , the weight matrix between the hidden layer and the output layer is represented by V, V = (v1, v2, v3, v4, v5) T , the transfer function of the hidden layer neurons and the transfer function of the output layer neurons both use the S-type tangent function, and the constructed neural network model is as follows Figure 7 shown.

[0074] The data relationship between the signals of each layer is:

[0075] Input of each hidden layer:

[0076] The output of each hidden layer:

[0077] Output layer input:

[0078] Output layer output: o = f(v)

[0079] (2) Training the Neural Network

[0080] The training process of the neural network is as follows Figure 8 As shown in the figure, the network structure and weights are initialized first, and then the input signal and output signal of each layer of neurons in the BP network are calculated forward according to the input sample. The reverse error is calculated according to the expected output, and the weight is corrected. If the error is less than the given value or the number of iterations exceeds the set value, the learning ends. The deviation of the output layer is: e(1) = d(1) - o(1), and the error T is set to 1×10 -9 , the maximum number of iterations H is 5000.

[0081] Select the data in the database established in step 1 to train the neural network.

[0082] (3) Prediction of removal function distribution coefficients through neural network

[0083] Use the Faraday cup to scan the ion beam current to obtain the peak ion beam current density J' under the current conditions max and the distribution parameter σ under the current conditions F’ And it is input into the neural network as prediction data to predict the removal function distribution coefficient σ' under the current conditions.

[0084] 4. Determine the removal function:

[0085] The removal function peak removal rate R calculated in steps 2 and 3 is max Substituting the removal function distribution coefficient σ' under the current conditions into the general expression formula 5 of the removal function, the removal function can be obtained for ion beam polishing.

[0086] In this embodiment, it should also be mentioned that the range of the Faraday scanning ion beam flow is L, and L should be more than 4 times the diameter of the ion beam to ensure that the ion concentration at the scanning point reaches more than 95% of the total number within the range of diameter L. In the line scanning experiment, the distance between the starting point and the end point when the ion beam scans the surface of the component is L1, and L1 should be more than 4 times the diameter of the ion beam to ensure that the ion beam can achieve sufficient length of equal removal in the middle of the scanning area to calculate the removal function information.

[0087] At the same time, the number of input layer elements of the 3-layer neural network of the present application is 2, which are the current density peak value J max and the distribution coefficient σ F, the number of elements in the output layer is 1, which is the removal function distribution coefficient σ, and the number of hidden layers is 5.

[0088] In this way, the present invention establishes a database through a limited number of Faraday scans and line scan experiments, so as to determine the relationship between the ion beam current density and the removal function distribution coefficient. According to the Faraday scan results, the removal function peak removal rate is calculated by a linear formula, and the removal function distribution coefficient is predicted by a BP neural network. The removal function information obtained by this method is basically the same as the removal function information obtained by the experimental method, and at the same time, the time for determining the removal function is greatly shortened from 3 hours to 1 minute. At the same time, this method determines the removal function based on the Faraday scan results, and there is no need to perform a removal function experiment on the component surface, thereby saving costs.

[0089] At the same time, the present invention determines the distribution information of the removal function through a linear formula and a BP neural network. This method is applicable to all materials that can be used for ion beam processing, is not limited by material properties, and can be used for all ion beam processing processes.

Claims

1. A method for determining ion beam polishing removal function based on BP neural network, characterized in that The following steps are involved: S1. Establish a database of Faraday scanning and removal functions: After selecting the optical element material, set the ion source process parameters and turn on the ion source. The ion source process parameters include ion beam voltage, acceleration voltage, radio frequency power, argon gas flow rate, neutralization current and working distance. Change other parameters except the ion beam voltage each time to obtain ion beam currents with the same energy but different spatial distributions. After the ion source is stable, perform a Faraday scan and a removal function experiment to obtain ion beam current density and removal function distribution information. The ion source being stabilized in S1 specifically includes the fluctuation of the ion beam current being less than 5%; The specific process of obtaining the ion beam current density distribution information in S1 includes: S11, close the neutralizer, control the ion beam to be incident vertically on the Faraday cup, keep the center line of the ion source and the Faraday cup in the same vertical plane, move the ion source horizontally through the Faraday cup, and obtain the distribution coefficient of the ion beam current density in one-dimensional direction; S12, using the method of collecting data at equal intervals to perform Faraday scanning experiments, setting the ion source scanning range, movement speed, working distance and number of sampling points in the scanning direction to perform Faraday scanning to obtain current density data, and performing Gaussian fitting on the sampled data to obtain the peak ion beam current density J at the current moment max and the ion beam distribution coefficient σ F ; S13. According to the rotationally symmetric Gaussian distribution of current density space, the ion beam current density distribution is expressed by the following formula (1): Among them, J max and σ F are the peak value and distribution coefficient of ion beam current density, respectively; The specific process of obtaining the removal function distribution information in S1 includes: S14, after completing S13, the neutralizer is turned on, the ion beam is controlled to be incident vertically on the surface of the optical element, and a line scanning experiment is performed n times along the X direction at a speed v, and the surface shape of the optical element before and after the experiment is measured using an interferometer and a difference is made to obtain the material removal amount during the line scanning experiment; S15, calculating the average value r(y) of the material removal amount along the Y direction of the component; S16. Perform Gaussian fitting on r(y) to obtain a one-dimensional material removal function along the Y direction, as shown in the following formula (2): Among them, R y and σ y are the peak removal rate and distribution coefficient of the one-dimensional material removal function, respectively; S17, according to formula (3) and formula (4), R y and σ y Calculate the peak removal rate R of the removal function max and the distribution coefficient σ, s = s y (4) S18, R max Substitute σ into the following formula Find the removal function; S2. Use the linear formula to determine the peak removal rate of the removal function: The peak value J of the ion beam current density obtained by S1 max The peak removal rate R of the removal function obtained with S1 max Linear fitting is performed to obtain the proportional coefficient a, and the peak removal rate R of the removal function is calculated based on the energy of the incident ions, the incident angle of the ion beam, and the etched material when the energy of the incident ions, the incident angle of the ion beam, and the etched material are the same for ion beams with different spatial distributions. max and the peak value of the ion beam current density J max Satisfy the linear relationship R max =aJ max (6), with the peak current density J of the ion beam max To determine the peak removal rate R of the removal function max ; S3. Use neural network to determine the removal function distribution coefficient: (1) Constructing a neural network A 3-layer BP network with 1 hidden layer was selected, and the peak value of ion beam current density J max and the ion beam current distribution coefficient σ F As the input signal, the removal function distribution coefficient σ is used as the output signal to construct a neural network, in which the transfer function of the network hidden layer neuron and the transfer function of the output layer neuron both use the S-type tangent function; (2) Training the Neural Network Initialize the network structure and weights, select the data in the database established in S1 to train the neural network, forward calculate the input signal and output signal of each layer of neurons in the BP network according to the input samples, calculate the reverse error according to the expected output, and modify the weights. If the error is less than the given value T or the number of iterations exceeds the set value H, the learning ends; (3) Prediction of removal function distribution coefficients through neural network Use the Faraday cup to scan the ion beam current to obtain the peak ion beam current density J' under the current conditions max and the distribution parameter σ under the current conditions F’ , and input into the neural network as prediction data to predict the removal function distribution coefficient σ' under the current conditions; S4. Determine the removal function: The removal function peak removal rate R calculated in S2 and S3 max Substitute the removal function distribution coefficient σ' under the current situation into the general expression formula of the removal function In the removal function, we get

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