WO2021160086A1 - 非零干涉非球面测量回程误差去除方法及装置 - Google Patents

非零干涉非球面测量回程误差去除方法及装置 Download PDF

Info

Publication number
WO2021160086A1
WO2021160086A1 PCT/CN2021/075989 CN2021075989W WO2021160086A1 WO 2021160086 A1 WO2021160086 A1 WO 2021160086A1 CN 2021075989 W CN2021075989 W CN 2021075989W WO 2021160086 A1 WO2021160086 A1 WO 2021160086A1
Authority
WO
WIPO (PCT)
Prior art keywords
error
neural network
interference
aspheric
backhaul
Prior art date
Application number
PCT/CN2021/075989
Other languages
English (en)
French (fr)
Inventor
郝群
胡摇
汪文莉
袁诗翥
Original Assignee
北京理工大学
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by 北京理工大学 filed Critical 北京理工大学
Publication of WO2021160086A1 publication Critical patent/WO2021160086A1/zh

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods

Definitions

  • the invention relates to the technical field of optical measurement, in particular to a method for removing return error of non-zero interference aspheric surface measurement, and a device for removing return error of non-zero interference aspheric surface measurement, and is mainly used for rapid and high-precision measurement of aspheric surface error.
  • Aspheric optical element refers to a type of optical element whose surface curvature is not a fixed value. It can simplify the structure in the optical design, realize the function of multiple aspheric mirrors with a single aspheric mirror, and at the same time has the advantages of correcting various aberrations and increasing the freedom of optical design. It is widely used in precision telescopes and aerospace cameras. In the optical system. Therefore, strict requirements are put forward on the precision measurement of the aspheric surface error.
  • the zero compensation method refers to a type of interferometric method in which the compensator can completely compensate the aberrations generated by the ideal aspheric surface. Its measurement accuracy is high, but the design and installation of the zero compensator are complicated and not universal.
  • the non-zero compensation method means that the compensator cannot fully compensate the aberrations generated by the ideal aspheric surface, resulting in residual wavefront aberrations, which makes the measurement light unable to return to the original path. In this way, the compensator and the measured lens do not need to correspond to each other, which can reduce The design and installation and adjustment requirements of the compensator.
  • the non-zero compensation method is currently the main method to expand the dynamic range to achieve high-precision measurement, but the design of the residual error introduces the return error to the optical system, which is extremely disadvantageous for the precise measurement when the aspheric surface error is large.
  • the accuracy of the inverse optimization method to solve the aspheric surface error mainly depends on the modeling accuracy of the system, including the inaccuracy of the optical component parameters and the inconsistency of the component position with the actual system, the randomness of temperature, humidity, and air velocity. And the selection of the detector resolution and the number of Zernike polynomial terms in the reverse optimization algorithm will affect the accuracy of the final measurement results.
  • the inverse optimization method requires multiple iterative optimization of the optimization variables, which greatly reduces the efficiency of solving the surface error, and is not suitable for rapid measurement of industrial production.
  • the technical problem to be solved by the present invention is to provide a method for removing the return error of non-zero interference aspheric surface measurement, which has good universality and can eliminate the return error.
  • the combination of trace function realizes fast and high-precision measurement of aspheric surface error.
  • the method for removing the return error of the non-zero interference aspheric surface measurement includes the following steps:
  • the training set includes several sets of surface shape error data and corresponding optical system interference wavefront data, all of which are generated by computer simulation;
  • the invention uses a computer to simulate the optical system of the non-zero compensation method and generates a training set to complete the training of the neural network, which is convenient and fast.
  • a set of interference wavefront data of the actual optical system no prior knowledge and preprocessing are required. That is to say, the return error in the actual optical system is eliminated, and it has good universality; the method for eliminating the return error based on the neural network proposed by the present invention, in the process of solving the aspheric surface error, there is no inherent systematic error and the solution
  • the accuracy does not depend on the modeling accuracy of the system, including the inaccuracy of the optical component parameters and the inconsistency of the component position with the actual system, and the randomness of temperature, humidity, and airflow speed will not affect the final result.
  • the complex assembly and calibration process realizes fast and high-precision aspheric surface error measurement.
  • non-zero interference aspheric surface measurement return error removal device which includes:
  • Optical model establishment module which is configured to use optical software simulation to establish the optical model of the aspheric interference system to be tested;
  • the training set acquisition module is configured to acquire a training set for eliminating backhaul errors.
  • the training set includes several sets of surface shape error data and corresponding optical system interference wavefront data, which are all generated by computer simulation;
  • Neural network building module which is configured to construct a neural network that eliminates backhaul errors
  • Neural network training module which is configured to train a neural network that eliminates backhaul errors
  • the error solving module is configured to use a trained neural network to solve the aspheric surface error.
  • Fig. 1 is an overall flow chart of the method for removing the return error of non-zero interference aspheric surface measurement according to the present invention.
  • Figure 2 is a simulated wavefront diagram of the shape error of the surface to be measured.
  • Fig. 3 is an interference wavefront diagram of a simulated optical system.
  • Fig. 4 is the interference wavefront diagram of the optical system when the simulated surface to be measured does not contain the shape error.
  • Figure 5 is half of the point-to-point subtraction error of Figures 3 and 4.
  • Figure 6 is the point-to-point subtraction error of Figure 5 and Figure 2.
  • Figure 7 is a diagram of the neural network structure.
  • Figure 8 is the declining curve of the loss function during neural network training.
  • Figure 9 is a wavefront diagram of the surface shape error of the tested surface obtained by the test.
  • Fig. 10 is the point-to-point subtraction error of Fig. 9 and Fig. 2.
  • the problem to be solved by the neural network-based backhaul error removal technology disclosed in the present invention is to eliminate the backhaul error and combine with the ray tracing function of the optical software to realize the rapid and high-precision measurement of the aspheric surface error.
  • this method for removing the return error of non-zero interference aspheric measurement includes the following steps:
  • the training set includes several sets of surface shape error data and corresponding optical system interference wavefront data, all of which are generated by computer simulation;
  • the invention uses a computer to simulate the optical system of the non-zero compensation method and generates a training set to complete the training of the neural network, which is convenient and fast.
  • a set of interference wavefront data of the actual optical system no prior knowledge and preprocessing are required. That is to say, the return error in the actual optical system is eliminated, and it has good universality; the method for eliminating the return error based on the neural network proposed by the present invention, in the process of solving the aspheric surface error, there is no inherent systematic error and the solution
  • the accuracy does not depend on the modeling accuracy of the system, including the inaccuracy of the optical component parameters and the inconsistency of the component position with the actual system, and the randomness of temperature, humidity, and airflow speed will not affect the final result.
  • the complex assembly and calibration process realizes fast and high-precision aspheric surface error measurement.
  • the optical model in the step (1) includes: a non-zero compensator and an aspheric surface to be measured.
  • the surface shape error of the surface to be measured is randomly generated using Zernike polynomials, and the number of terms and coefficients of the Zernike polynomial are controlled to be within a certain range.
  • the upper limit of the specific coefficients is determined by the surface shape of the surface to be measured in the actual measurement process. The upper limit corresponding to the error is determined.
  • the interference wavefront of the optical system is generated after ray tracing in the optical software based on the corresponding surface shape error of the measured surface, and the specific number of Zernike polynomial terms and coefficients are derived by the optical software.
  • the input of the neural network is the Zernike polynomial coefficients corresponding to the interference wavefront of the optical system, and the output is the Zernike polynomial coefficients of the surface error.
  • the neural network is used to simulate the input and Non-linear relationship between outputs.
  • step (4) using the training set obtained in the step (2) to train the neural network constructed in the step (3), a better training effect is obtained, and the loss function is reduced to a level that meets the accuracy requirements.
  • the Zernike polynomial coefficients corresponding to the interference wavefront of the actual optical system are used as the input of the trained neural network, and after calculation by the neural network, the output is the Zernike polynomial corresponding to the aspheric surface error The coefficient of each item, so as to realize the elimination of the backhaul error.
  • a fully connected neural network is constructed.
  • the input of the network is 37 Zernike coefficients.
  • 15 Zernike coefficients are output; in order to suppress over-fitting, it is Part of the fully connected layer applies L2 regularization method, and adds several randomly closed layers to the network.
  • the training of the network uses 64 sets of samples for batch processing each time, and randomly shuffles the training set at the beginning of each training generation; the loss function is the root mean square of the predicted value and the true value Error RMS;
  • the optimization method first use Adam (adaptive moment estimation) with a fixed learning rate of 1 ⁇ 10 -3 to train for 400 generations, and then use a fixed learning rate of 1 ⁇ 10 -5 SGD (stochastic gradient descent). , Stochastic gradient descent method) training for 600 generations.
  • the present invention also includes a non-zero interference aspheric measurement backhaul error removal device, which is usually expressed in the form of functional modules corresponding to the steps of the method.
  • the device includes:
  • Optical model establishment module which is configured to use optical software simulation to establish the optical model of the aspheric interference system to be tested;
  • the training set acquisition module is configured to acquire a training set for eliminating backhaul errors.
  • the training set includes several sets of surface shape error data and corresponding optical system interference wavefront data, which are all generated by computer simulation;
  • Neural network building module which is configured to construct a neural network that eliminates backhaul errors
  • Neural network training module which is configured to train a neural network that eliminates backhaul errors
  • the error solving module is configured to use a trained neural network to solve the aspheric surface error.
  • This example specifically illustrates the implementation method of the non-zero compensation method in the interferometric measurement of the aspheric surface error based on the neural network to remove the return error and realize the fast and high-precision measurement of the aspheric surface error.
  • the neural network-based backhaul error removal technology disclosed in this example has specific implementation steps as follows:
  • Step 1 Establish the optical model of the aspheric interference system to be tested
  • the above-mentioned optical model mainly includes a plano-convex lens as a non-zero compensator and a concave mirror as the surface to be measured.
  • the convex curvature radius of the plano-convex lens is -760mm, the thickness is 15mm, and the aperture is 110mm.
  • the material is ZF6, and the distance between its convex surface and the surface to be measured is set to 1100mm.
  • the selected surface to be measured is a concave mirror with a radius of curvature of -100mm and a diameter of 10mm.
  • Step 2 Obtain the training set that eliminates the backhaul error
  • the training set to eliminate the backhaul error generally includes 6000-10000 sets of corresponding surface shape error data of the measured surface and the interference wavefront data of the optical system, which are all generated by computer simulation without actual experimentation, which is convenient and quick.
  • the surface error of the surface to be measured as described above can be randomly generated using Zernike polynomials.
  • the number of terms of the Zernike polynomial is controlled to 15 items, and the coefficient range is 0-0.002mm.
  • Figure 2 shows the wavefront diagram of the surface shape error generated by the simulation, and its PV value is 3.397 ⁇ .
  • the interference wavefront of the optical system described above is generated after ray tracing in the optical software based on the surface shape error of the measured surface.
  • the light enters the surface to be measured through the non-zero compensator, returns to the non-zero compensator after being reflected by the surface to be measured, and then converges through the ideal lens.
  • the interference wavefront data of the optical system that is, the corresponding Zernike polynomial coefficients, can be derived from the software.
  • Figure 3 shows the interference wavefront diagram of the optical system generated by simulation, and its PV value is 6.4636 ⁇ 10 4 ⁇ .
  • Figure 4 shows the interference wavefront diagram of the optical system generated by simulation when there is no surface error on the surface to be measured, and its PV value is 3.1578 ⁇ 10 4 ⁇ .
  • Figure 5 shows the wavefront diagram of the surface shape error measured by the backhaul error of the optical system during this ray tracing process, and its PV value is 3.2325 ⁇ 10 4 ⁇ .
  • Fig. 6 is the point-to-point subtraction error of Fig. 5 and Fig. 2, and its PV value is 3.2325 ⁇ 10 4 ⁇ . It can be seen that the influence of the backhaul error is very serious.
  • the data set contains 10,000 sets of samples, the first 9900 sets of samples are taken as the training set, and the last 100 sets of samples are taken as the test set.
  • Step 3 Build a neural network to eliminate backhaul errors
  • the input of the network is 37 Zernike coefficients, and after four fully connected layers (Dense Layer), 15 Zernike coefficients are output.
  • the L2 regularization method is applied to part of the dense layer in the network, and several random off layers (Dropout layers) are added to the network.
  • Step 4 Train the neural network to eliminate the backhaul error
  • the training of the network uses 64 sets of samples for batch processing each time, and randomly shuffles the training set at the beginning of each training generation.
  • the loss function is the root mean square error (RMS) of the predicted value and the true value.
  • RMS root mean square error
  • the network has been trained for 1000 generations, and the change of the loss function value of the test set is shown in Figure 8. It can be seen that as the training generation increases, the performance of the network is continuously improved.
  • the loss function value of the test set at the final 1000 generations is 1.7217 ⁇ 10 -4 .
  • Step 5 Use the trained neural network to solve the aspheric surface error
  • step 2 Take the actual optical interference wavefront data obtained in step 2, that is, the coefficients of the Zernike polynomial and the corresponding terms as the input of the trained neural network. After the neural network is calculated, the output is read and substituted into the Zernike polynomial calculation.
  • the profile error of the measuring surface is shown in Figure 9, and its PV value is 3.2996 ⁇ .
  • Figure 10 is the point-to-point subtraction error (0.1694 ⁇ ) of Figure 9 and Figure 2. It can be seen that, comparing Fig. 10 with Fig. 6, the PV value of the error has dropped from 3.2325 ⁇ 10 4 ⁇ to 0.1694 ⁇ , the amplitude has dropped significantly, and the return error has been effectively eliminated.
  • the neural network that removes the backhaul error as described above will have a certain universality. For a set of interference wavefront data of the actual optical system, it can eliminate the backhaul in the actual optical system without any prior knowledge and preprocessing. Error, to achieve rapid measurement of the aspheric surface error.
  • the neural network-based backhaul error removal technology disclosed in the present invention has no inherent system error in the process of solving the aspheric surface shape error, and the solution accuracy does not depend on the modeling accuracy of the system, avoiding the complicated assembly, adjustment and calibration process , To achieve high-precision aspheric surface error measurement.

Landscapes

  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Health & Medical Sciences (AREA)
  • Computing Systems (AREA)
  • Biomedical Technology (AREA)
  • Biophysics (AREA)
  • Computational Linguistics (AREA)
  • Data Mining & Analysis (AREA)
  • Evolutionary Computation (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Molecular Biology (AREA)
  • Artificial Intelligence (AREA)
  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Software Systems (AREA)
  • Health & Medical Sciences (AREA)
  • Instruments For Measurement Of Length By Optical Means (AREA)
  • Length Measuring Devices By Optical Means (AREA)

Abstract

非零干涉非球面测量回程误差去除方法及装置，其具有良好的普适性，能够消除回程误差，与光学软件的光线追迹功能相结合，实现非球面面形误差的快速且高精度的测量。方法包括：(1)利用光学软件模拟，建立待测非球面干涉***的光学模型；(2)获取消除回程误差的训练集，训练集包括若干组的待测面面形误差数据和对应的光学***干涉波前数据，均利用计算机模拟生成；(3)构建消除回程误差的神经网络；(4)训练消除回程误差的神经网络；(5)利用训练好的神经网络求解非球面面形误差。

Description

非零干涉非球面测量回程误差去除方法及装置 技术领域
本发明涉及光学测量的技术领域，尤其涉及一种非零干涉非球面测量回程误差去除方法，以及非零干涉非球面测量回程误差去除装置，主要用于非球面面形误差的快速高精度测量。
背景技术
非球面光学元件是指表面曲率为非固定值的一类光学元件。其在光学设计中可以简化结构，以单片非球面镜实现多片非球面镜的功能，同时具有校正多种像差，增加光学设计的自由度等优势，被广泛应用于天文望远镜和航天相机等精密光学***中。由此，对非球面面形误差的精密测量提出严格要求。
在各种测量技术中，干涉法具有高精度、非接触、测量时间短等优势。其中零位补偿法是指补偿器能够完全补偿理想非球面产生的像差的一类干涉测量方法，其测量精度高，但零补偿器的设计和装调复杂，且不具有通用性。
非零位补偿法是指补偿器不能完全补偿理想非球面产生的像差，产生剩余波前像差，导致测量光无法原路返回，这样，补偿器与被测镜无需一一对应，能够降低对补偿器的设计和装调要求。非零位补偿法是目前扩大动态范围实现高精度测量的主要方法，但剩余误差的设计给光学***引入了回程误差，这对非球面面形误差较大时的精密测 量是极为不利的。
为消除回程误差的影响，人们在非零位补偿干涉法非球面测量中分别提出了基于光线追迹的二分之一法、逆向优化法来消除回程误差。
在非球面面形误差较大时，二分之一法本身存在较大的***误差。
而逆向优化法求解非球面面形误差的精度主要依赖于对***的建模精度，包括光学元件参数的不准确性和元件位置与实际***的不一致性，温度、湿度、气流速度的随机性，以及逆向优化算法中探测器分辨率和Zernike多项式项数的选取等都会影响最终测量结果的精度。此外，逆向优化法需要对优化变量进行多次迭代优化，大大降低了求解面形误差的效率，不适用于工业生产的快速测量。
因此，加工在线的高精度非球面面形误差测量需求对消除回程误差的技术依然提出迫切要求。
发明内容
为克服现有技术的缺陷，本发明要解决的技术问题是提供了一种非零干涉非球面测量回程误差去除方法，其具有良好的普适性，能够消除回程误差，与光学软件的光线追迹功能相结合，实现非球面面形误差的快速且高精度的测量。
本发明的技术方案是：这种非零干涉非球面测量回程误差去除方法，其包括以下步骤：
(1)利用光学软件模拟，建立待测非球面干涉***的光学模型；
(2)获取消除回程误差的训练集，训练集包括若干组的待测面面形误差数据和对应的光学***干涉波前数据，均利用计算机模拟生成；
(3)构建消除回程误差的神经网络；
(4)训练消除回程误差的神经网络；
(5)利用训练好的神经网络求解非球面面形误差。
本发明利用计算机模拟非零位补偿法的光学***并生成了训练集，完成了神经网络的训练，方便快捷，对于一组实际光学***的干涉波前数据，无需任何先验知识及预处理，即可消除实际光学***中的回程误差，具有良好的普适性；本发明提出的基于神经网络的回程误差去除方法，在非球面面形误差求解过程中，本身不存在固有的***误差且求解精度不依赖于***的建模精度，包括光学元件参数的不准确性和元件位置与实际***的不一致性，温度、湿度、气流速度的随机性等都不会对最终的结果产生影响，避免了复杂的装调和校准过程，实现了快速且高精度的非球面面形误差测量。
还提供了一种非零干涉非球面测量回程误差去除装置，其包括：
光学模型建立模块，其配置来利用光学软件模拟，建立待测非球面干涉***的光学模型；
训练集获取模块，其配置来获取消除回程误差的训练集，训练集包括若干组的待测面面形误差数据和对应的光学***干涉波前数据，均利用计算机模拟生成；
神经网络构建模块，其配置来构建消除回程误差的神经网络；
神经网络训练模块，其配置来训练消除回程误差的神经网络；
误差求解模块，其配置利用训练好的神经网络求解非球面面形误差。
附图说明
图1是根据本发明的非零干涉非球面测量回程误差去除方法的整体流程图。
图2是模拟的待测面面形误差波前图。
图3是模拟的光学***的干涉波前图。
图4是模拟的待测面不含面形误差时光学***的干涉波前图。
图5是图3与图4点对点相减误差的一半。
图6是图5与图2点对点相减误差。
图7是神经网络结构图。
图8是神经网络训练过程中的损失函数下降曲线。
图9是测试得到的待测面面形误差波前图。
图10是图9与图2点对点相减误差。
具体实施方式
为了使本技术领域的人员更好地理解本发明方案，下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分的实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都应当属于本发明保护的范围。
需要说明的是，本发明的说明书和权利要求书及上述附图中的术语“包括”以及任何变形，意图在于覆盖不排他的包含，例如，包含了一系列步骤或单元的过程、方法、装置、产品或设备不必限于清楚 地列出的那些步骤或单元，而是可包括没有清楚地列出的或对于这些过程、方法、产品或设备固有的其他步骤或单元。
为解决基于光线追迹的二分之一法、逆向优化法求解非球面面形误差过程中，分别由于***误差和***建模精度导致的测量精度问题，以及逆向优化法多次迭代无法实现在线测量的问题，本发明公开的基于神经网络的回程误差去除技术要解决的问题是：消除回程误差，与光学软件的光线追迹功能相结合，实现非球面面形误差的快速高精度测量。
如图1所示，这种非零干涉非球面测量回程误差去除方法，其包括以下步骤：
(1)利用光学软件模拟，建立待测非球面干涉***的光学模型；
(2)获取消除回程误差的训练集，训练集包括若干组的待测面面形误差数据和对应的光学***干涉波前数据，均利用计算机模拟生成；
(3)构建消除回程误差的神经网络；
(4)训练消除回程误差的神经网络；
(5)利用训练好的神经网络求解非球面面形误差。
本发明利用计算机模拟非零位补偿法的光学***并生成了训练集，完成了神经网络的训练，方便快捷，对于一组实际光学***的干涉波前数据，无需任何先验知识及预处理，即可消除实际光学***中的回程误差，具有良好的普适性；本发明提出的基于神经网络的回程误差去除方法，在非球面面形误差求解过程中，本身不存在固有的***误差且求解精度不依赖于***的建模精度，包括光学元件参数的不 准确性和元件位置与实际***的不一致性，温度、湿度、气流速度的随机性等都不会对最终的结果产生影响，避免了复杂的装调和校准过程，实现了快速且高精度的非球面面形误差测量。
优选地，所述步骤(1)中的光学模型包括：非零位补偿器和待测非球面。
优选地，所述步骤(2)中，待测面的面形误差利用Zernike多项式随机生成，控制Zernike多项式的项数和系数在一定范围以内，具体系数上限由实际测量过程中待测面面形误差对应的上限决定。
或者，所述步骤(2)中，光学***的干涉波前是基于相应的待测面面形误差在光学软件中光线追迹后生成的，具体的Zernike多项式项数和系数由光学软件导出。
优选地，所述步骤(3)中，神经网络的输入是光学***的干涉波前对应的Zernike多项式系数，输出是面形误差的Zernike多项式系数，该神经网络用于通过训练尽可能模拟输入与输出之间的非线性关系。
优选地，所述步骤(4)中，利用步骤(2)获得的训练集训练步骤(3)构建的神经网络，得到较好的训练效果，使损失函数下降到符合精度要求的水平。
优选地，所述步骤(5)中，将实际光学***的干涉波前对应的Zernike多项式系数作为训练好的神经网络输入，经过神经网络的计算后，输出为非球面面形误差对应的Zernike多项式每一项的系数，从而实现回程误差的消除。
优选地，所述步骤(3)中，构建全连接神经网络，网络的输入为37项Zernike系数，经过四个全连接层后，输出15项Zernike系数； 为了抑制过拟合，为网络中的部分全连接层应用L2正则化方法，并在网络中加入数个随机关闭层。
优选地，所述步骤(4)中，网络的训练每次使用64组样本进行批处理，并在每个训练世代的开始随机打乱训练集；损失函数为预测值和真实值的均方根误差RMS；优化方法上，首先使用固定学习率1×10 -3的Adam(adaptive moment estimation，自适应矩估计法)训练400世代，再使用固定学习率1×10 -5的SGD(stochastic gradient descent，随机梯度下降法)训练600世代。
本领域普通技术人员可以理解，实现上述实施例方法中的全部或部分步骤是可以通过程序来指令相关的硬件来完成，所述的程序可以存储于一计算机可读取存储介质中，该程序在执行时，包括上述实施例方法的各步骤，而所述的存储介质可以是：ROM/RAM、磁碟、光盘、存储卡等。因此，与本发明的方法相对应的，本发明还同时包括一种非零干涉非球面测量回程误差去除装置，该装置通常以与方法各步骤相对应的功能模块的形式表示。该装置包括：
光学模型建立模块，其配置来利用光学软件模拟，建立待测非球面干涉***的光学模型；
训练集获取模块，其配置来获取消除回程误差的训练集，训练集包括若干组的待测面面形误差数据和对应的光学***干涉波前数据，均利用计算机模拟生成；
神经网络构建模块，其配置来构建消除回程误差的神经网络；
神经网络训练模块，其配置来训练消除回程误差的神经网络；
误差求解模块，其配置利用训练好的神经网络求解非球面面形误差。
以下详细说明本发明的具体实施例。
本实例具体说明非零位补偿法干涉测量非球面面形误差的过程中，基于神经网络，去除回程误差，实现非球面面形误差的快速高精度测量的实施方法。
如图1所示，本实例公开的基于神经网络的回程误差去除技术，具体实现步骤如下：
步骤1、建立待测非球面干涉***的光学模型
如上所述的光学模型主要包括一个作为非零位补偿器的平凸透镜和一个作为待测面的凹面镜。平凸透镜的凸面曲率半径为-760mm，厚度为15mm，口径为110mm，材质选用ZF6，并将它的凸面与待测面的距离设定为1100mm。选用的待测面是曲率半径为-100mm、口径为10mm的凹面镜。
步骤2、获取消除回程误差的训练集
消除回程误差的训练集一般包括6000-10000组对应的待测面的面形误差数据和光学***的干涉波前数据，均利用计算机模拟生成，无需进行实际实验，方便快捷。
如上所述的待测面面形误差可利用Zernike多项式随机生成，为了与实际加工存在的面形误差相吻合，控制Zernike多项式的项数为15项，系数范围为0-0.002mm。图2所示是模拟生成的待测面面形误差波前图，其PV值为3.397λ。
如上所述的光学***的干涉波前是基于待测面面形误差在光学软 件中光线追迹后生成的。光线经非零位补偿器入射至待测面，经待测面反射后返回至非零位补偿器，再经过理想透镜会聚。完成追迹后，光学***的干涉波前数据，即对应的Zernike多项式系数，可由软件导出，图3所示是模拟生成的光学***的干涉波前图，其PV值为6.4636×10 4λ。图4所示是待测面无面形误差时，模拟生成的光学***的干涉波前图，其PV值为3.1578×10 4λ。图5所示是本次光线追迹过程中，受光学***回程误差影响测得的面形误差波前图，其PV值为3.2325×10 4λ。图6是图5与图2点对点相减误差，其PV值为3.2325×10 4λ。可见，回程误差的影响非常严重。
利用上述方法先生成数据集。数据集包含10000组样本，取前9900组样本作为训练集，取后100组样本作为测试集。
步骤3、构建消除回程误差的神经网络
构建如图7和表1所示的全连接神经网络，网络的输入为37项Zernike系数，经过四个全连接层(Dense Layer)后，输出15项Zernike系数。为了抑制过拟合，为网络中的部分全连接层(Dense Layer)应用L2正则化方法，并在网络中加入了数个随机关闭层(Dropout层)。
表1
序号 层 激活函数 正则项
1 Dense(400) tanh L2
2 Dropout(0.2)    
3 Dense(400) tanh L2
4 Dropout(0.2)    
5 Dense(15)    
步骤4、训练消除回程误差的神经网络
网络的训练每次使用64组样本进行批处理，并在每个训练世代的 开始随机打乱训练集。损失函数为预测值和真实值的均方根误差(RMS)。优化方法上，首先使用Adam(固定学习率1×10 -3)训练400世代，再使用SGD(固定学习率1×10 -5)训练600世代。网络经过了1000世代的训练，测试集损失函数值的变化如图8所示，可见随着训练世代的增加，网络的性能也不断提高。最终1000世代处测试集的损失函数值为1.7217×10 -4。
步骤5、利用训练好的神经网络求解非球面面形误差
将步骤2中得到的实际光学干涉波前数据，即Zernike多项式及对应项的系数作为训练好的神经网络的输入，经过神经网络的计算后，读取输出并代入Zernike多项式计算后，得到的待测面面形误差如图9所示，其PV值为3.2996λ。图10是图9与图2点对点相减误差(0.1694λ)。可见，图10与图6相比，误差的PV值从3.2325×10 4λ下降到0.1694λ，幅值有显著下降，回程误差得到有效消除。
如上所述去除回程误差的神经网络一旦训练好将具有一定的普适性，对于一组实际光学***的干涉波前数据，无需任何先验知识及预处理，即可消除实际光学***中的回程误差，实现非球面面形误差的快速测量。
本发明公开的基于神经网络的回程误差去除技术，在非球面面形误差求解过程中，本身不存在固有的***误差且求解精度不依赖于***的建模精度，避免了复杂的装调和校准过程，实现了高精度的非球面面形误差测量。
以上所述，仅是本发明的较佳实施例，并非对本发明作任何形式上的限制，凡是依据本发明的技术实质对以上实施例所作的任何简单修改、等同变化与修饰，均仍属本发明技术方案的保护范围。

Claims (10)

  1. 非零干涉非球面测量回程误差去除方法，其特征在于：其包括以下步骤：
    (1)利用光学软件模拟，建立待测非球面干涉***的光学模型；
    (2)获取消除回程误差的训练集，训练集包括若干组的待测面面形误差数据和对应的光学***干涉波前数据，均利用计算机模拟生成；
    (3)构建消除回程误差的神经网络；
    (4)训练消除回程误差的神经网络；
    (5)利用训练好的神经网络求解非球面面形误差。
  2. 根据权利要求1所述的非零干涉非球面测量回程误差去除方法，其特征在于：所述步骤(1)中的光学模型包括：非零位补偿器和待测非球面。
  3. 根据权利要求2所述的非零干涉非球面测量回程误差去除方法，其特征在于：所述步骤(2)中，待测面的面形误差利用Zernike多项式随机生成，控制Zernike多项式的项数和系数在一定范围以内，具体系数上限由实际测量过程中待测面面形误差对应的上限决定。
  4. 根据权利要求2所述的非零干涉非球面测量回程误差去除方法，其特征在于：所述步骤(2)中，光学***的干涉波前是基于相应的待测面面形误差在光学软件中光线追迹后生成的，具体的Zernike多项式项数和系数由光学软件导出。
  5. 根据权利要求3或4所述的非零干涉非球面测量回程误差去除方法，其特征在于：所述步骤(3)中，神经网络的输入是光学***的干涉波前对应的Zernike多项式系数，输出是面形误差的Zernike多项式系数，该神经网络用于通过训练尽可能模拟输入与输出之间的非线性关系。
  6. 根据权利要求5所述的非零干涉非球面测量回程误差去除方法，其特征在于：所述步骤(4)中，利用步骤(2)获得的训练集训练步骤(3)构建的神经网络，得到较好的训练效果，使损失函数下降到符合精度要求的水平。
  7. 根据权利要求6所述的非零干涉非球面测量回程误差去除方法，其特征在于：所述步骤(5)中，将实际光学***的干涉波前对应的Zernike多项式系数作为训练好的神经网络输入，经过神经网络的计算后，输出为非球面面形误差对应的Zernike多项式每一项的系数，从而实现回程误差的消除。
  8. 根据权利要求7所述的非零干涉非球面测量回程误差去除方法，其特征在于：所述步骤(3)中，构建全连接神经网络，网络的输入为37项Zernike系数，经过四个全连接层后，输出15项Zernike系数；为了抑制过拟合，为网络中的部分全连接层应用L2正则化方法，并在网络中加入数个随机关闭层。
  9. 根据权利要求8所述的非零干涉非球面测量回程误差去除方法，其特征在于：所述步骤(4)中，网络的训练每次使用64组样本进行批处理，并在每个训练世代的开始随机打乱训练集；损失函数为预测值和真实值的均方根误差RMS；优化方 法上，首先使用固定学习率1×10 -3的自适应矩估计法Adam训练400世代，再使用固定学习率1×10 -5的随机梯度下降法SGD训练600世代。
  10. 非零干涉非球面测量回程误差去除装置，其特征在于：其包括：光学模型建立模块，其配置来利用光学软件模拟，建立待测非球面干涉***的光学模型；
    训练集获取模块，其配置来获取消除回程误差的训练集，训练集包括若干组的待测面面形误差数据和对应的光学***干涉波前数据，均利用计算机模拟生成；
    神经网络构建模块，其配置来构建消除回程误差的神经网络；
    神经网络训练模块，其配置来训练消除回程误差的神经网络；
    误差求解模块，其配置利用训练好的神经网络求解非球面面形误差。
PCT/CN2021/075989 2020-02-14 2021-02-08 非零干涉非球面测量回程误差去除方法及装置 WO2021160086A1 (zh)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
CN202010105329.XA CN111209689B (zh) 2020-02-14 2020-02-14 非零干涉非球面测量回程误差去除方法及装置
CN202010105329.X 2020-02-14

Publications (1)

Publication Number Publication Date
WO2021160086A1 true WO2021160086A1 (zh) 2021-08-19

Family

ID=70788524

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/CN2021/075989 WO2021160086A1 (zh) 2020-02-14 2021-02-08 非零干涉非球面测量回程误差去除方法及装置

Country Status (2)

Country Link
CN (1) CN111209689B (zh)
WO (1) WO2021160086A1 (zh)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114662047A (zh) * 2022-04-06 2022-06-24 中国工程物理研究院激光聚变研究中心 一种去除函数误差修正能力表征方法、***和介质

Families Citing this family (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111209689B (zh) * 2020-02-14 2022-07-26 北京理工大学 非零干涉非球面测量回程误差去除方法及装置
CN112985300B (zh) * 2021-02-24 2022-03-25 中国科学院长春光学精密机械与物理研究所 基于条纹追踪的光学元件轮廓检测方法、设备及存储介质
CN112949197B (zh) * 2021-03-08 2022-09-09 北京理工大学 一种基于深度学***凸透镜曲率半径在线测量方法
CN113091638B (zh) * 2021-03-25 2022-06-28 中国科学院光电技术研究所 一种标定干涉法测量面形中的回程误差的装置及方法
CN113283162B (zh) * 2021-04-30 2022-10-28 晋城鸿智纳米光机电研究院有限公司 塑料光学镜片面形误差预测方法、电子装置及存储介质

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105318847A (zh) * 2015-11-12 2016-02-10 浙江大学 基于***建模的非球面非零位环形子孔径拼接方法
CN105352453A (zh) * 2015-11-12 2016-02-24 浙江大学 非零位干涉检测***中非球面顶点球曲率半径测量方法
US20190288401A1 (en) * 2016-12-01 2019-09-19 At&T Intellectual Property I, L.P. Dielectric dish antenna system and methods for use therewith
CN110715619A (zh) * 2019-11-22 2020-01-21 北京理工大学 基于自适应非零干涉法的光学自由曲面面形误差测量方法
CN111209689A (zh) * 2020-02-14 2020-05-29 北京理工大学 非零干涉非球面测量回程误差去除方法及装置

Family Cites Families (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN101290218B (zh) * 2008-05-23 2010-06-09 浙江大学 用于校正非球面非零位检测时的原理误差的方法
CN106918303B (zh) * 2017-03-14 2019-02-19 安徽大学 光学自由曲面自适应非零位干涉检测***
CN107764203B (zh) * 2017-10-27 2019-08-23 北京理工大学 基于部分补偿法的双波长相移干涉非球面测量方法及装置
CN110188321B (zh) * 2019-05-22 2022-07-19 中国科学院光电技术研究所 一种基于神经网络算法的主次镜校准方法
CN110751268B (zh) * 2019-09-27 2022-07-26 北京理工大学 基于端到端卷积神经网络的相位混叠误差去除方法及装置
CN110646100B (zh) * 2019-09-30 2021-02-19 中国科学院光电技术研究所 一种基于bp神经网络的倍频波前探测方法

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105318847A (zh) * 2015-11-12 2016-02-10 浙江大学 基于***建模的非球面非零位环形子孔径拼接方法
CN105352453A (zh) * 2015-11-12 2016-02-24 浙江大学 非零位干涉检测***中非球面顶点球曲率半径测量方法
US20190288401A1 (en) * 2016-12-01 2019-09-19 At&T Intellectual Property I, L.P. Dielectric dish antenna system and methods for use therewith
CN110715619A (zh) * 2019-11-22 2020-01-21 北京理工大学 基于自适应非零干涉法的光学自由曲面面形误差测量方法
CN111209689A (zh) * 2020-02-14 2020-05-29 北京理工大学 非零干涉非球面测量回程误差去除方法及装置

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114662047A (zh) * 2022-04-06 2022-06-24 中国工程物理研究院激光聚变研究中心 一种去除函数误差修正能力表征方法、***和介质
CN114662047B (zh) * 2022-04-06 2022-10-28 中国工程物理研究院激光聚变研究中心 一种去除函数误差修正能力表征方法、***和介质

Also Published As

Publication number Publication date
CN111209689B (zh) 2022-07-26
CN111209689A (zh) 2020-05-29

Similar Documents

Publication Publication Date Title
WO2021160086A1 (zh) 非零干涉非球面测量回程误差去除方法及装置
Liu et al. Robust modeling method for thermal error of CNC machine tools based on ridge regression algorithm
CN111414977B (zh) 机床主轴热误差建模的加权集成温度敏感点组合选取方法
CN109240204B (zh) 一种基于两步法的数控机床热误差建模方法
CN112445131A (zh) 一种线性***自适应最优跟踪控制方法
CN109800449B (zh) 一种基于神经网络的航空发动机压缩部件特性修正方法
CN110030953B (zh) 一种圆光栅测角误差补偿方法
CN110715619B (zh) 基于自适应非零干涉法的光学自由曲面面形误差测量方法
Wang et al. A Back Propagation neural network based optimizing model of space-based large mirror structure
CN111444619B (zh) 一种注塑模具冷却***在线分析方法及设备
CN110108271B (zh) 一种气动光学效应引起的星光偏折补偿方法
CN112946880B (zh) 一种基于模型的无波前传感器光学***自动装调方法
CN103744269A (zh) 光刻投影物镜波像差和成像最佳焦面的检测方法
CN115423881A (zh) 一种基于神经网络和光斑形态的主次镜快速校准方法
CN114165338B (zh) 发动机冷却气流温度预测方法和装置、控制方法和设备
CN114186477A (zh) 一种基于Elman神经网络的轨道预测算法
CN108846499B (zh) 一种气象要素超短期预测方法和装置
Berlakovich et al. Improving the precision of parallel registration by incorporating a priori information
CN111177894B (zh) 基于支持向量机模型的红外笼加热功率修正方法
CN111191377A (zh) 光机热耦合中非线性拟合方法
CN112949197B (zh) 一种基于深度学***凸透镜曲率半径在线测量方法
Lerro et al. Neural network techniques to solve a model-free scheme for flow angle estimation
Urban III et al. Numerical ellipsometry: enhancement of new algorithm for real-time, in situ film growth monitoring
CN114859552B (zh) 一种基于深度学习的离轴望远镜低阶像差校正方法
CN114528880B (zh) 一种基于计算全息的波前像差测量方法

Legal Events

Date Code Title Description
121 Ep: the epo has been informed by wipo that ep was designated in this application

Ref document number: 21753024

Country of ref document: EP

Kind code of ref document: A1

NENP Non-entry into the national phase

Ref country code: DE

122 Ep: pct application non-entry in european phase

Ref document number: 21753024

Country of ref document: EP

Kind code of ref document: A1

32PN Ep: public notification in the ep bulletin as address of the adressee cannot be established

Free format text: NOTING OF LOSS OF RIGHTS PURSUANT TO RULE 112(1) EPC (EPO FORM 1205A DATED 03.04.2023)

122 Ep: pct application non-entry in european phase

Ref document number: 21753024

Country of ref document: EP

Kind code of ref document: A1