CN111209689A - Non-zero interference aspheric surface measurement return error removing method and device - Google Patents
Non-zero interference aspheric surface measurement return error removing method and device Download PDFInfo
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Abstract
The method and the device for removing the return error of the non-zero interference aspheric surface measurement have good universality, can eliminate the return error, and are combined with the light ray tracing function of optical software to realize the rapid and high-precision measurement of the aspheric surface shape error. The method comprises the following steps: (1) establishing an optical model of the aspheric interference system to be tested by utilizing optical software simulation; (2) acquiring a training set for eliminating return errors, wherein the training set comprises a plurality of groups of surface shape error data of the surface to be detected and corresponding optical system interference wavefront data, and the training set is generated by utilizing computer simulation; (3) constructing a neural network for eliminating return errors; (4) training a neural network for eliminating return errors; (5) and solving the aspheric surface shape error by using the trained neural network.
Description
Technical Field
The invention relates to the technical field of optical measurement, in particular to a non-zero interference aspheric surface measurement return error removing method and a non-zero interference aspheric surface measurement return error removing device, which are mainly used for rapid high-precision measurement of aspheric surface shape errors.
Background
An aspheric optical element refers to a type of optical element in which the surface curvature is not a fixed value. The structure can be simplified in the optical design, the function of a plurality of aspheric mirrors is realized by a single aspheric mirror, and the optical system has the advantages of correcting various aberrations, increasing the freedom degree of the optical design and the like, and is widely applied to precision optical systems such as astronomical telescopes, space cameras and the like. Therefore, strict requirements are put on the precision measurement of the surface shape error of the aspheric surface.
Among various measurement techniques, the interferometry has the advantages of high precision, non-contact, short measurement time and the like. The zero compensation method is an interference measurement method in which a compensator can completely compensate aberration generated by an ideal aspheric surface, and has high measurement accuracy, but the design and the adjustment of the zero compensator are complex and have no universality.
The non-zero compensation method means that the compensator cannot completely compensate aberration generated by an ideal aspheric surface, residual wavefront aberration is generated, and measuring light cannot return to the original path, so that the compensator and a measured mirror do not need to correspond one to one, and the requirements on the design and the assembly and debugging of the compensator can be reduced. The non-zero compensation method is a main method for realizing high-precision measurement by expanding a dynamic range at present, but the design of residual errors introduces return errors into an optical system, which is extremely disadvantageous to precision measurement when the surface shape error of an aspheric surface is large.
In order to eliminate the influence of the return error, a half method and a reverse optimization method based on light ray tracing are respectively proposed in the non-zero compensation interference method aspheric surface measurement to eliminate the return error.
When the surface shape error of the aspheric surface is large, the half method has a large system error.
The precision of the inverse optimization method for solving the aspheric surface shape error mainly depends on the modeling precision of the system, and the precision of the final measurement result is influenced by the inaccuracy of optical element parameters, the inconsistency of element positions with an actual system, the randomness of temperature, humidity and air flow speed, the selection of the resolution of a detector in the inverse optimization algorithm, the Zernike polynomial terms and the like. In addition, the reverse optimization method needs to perform iterative optimization on the optimization variables for many times, so that the efficiency of solving the surface shape error is greatly reduced, and the method is not suitable for rapid measurement of industrial production.
Therefore, the demand for online measurement of surface shape errors of aspheric surfaces with high precision still puts an urgent demand on the technology for eliminating return errors.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a non-zero interference aspheric surface measurement return error removing method which has good universality, can eliminate return errors, and is combined with the light ray tracing function of optical software to realize the rapid and high-precision measurement of aspheric surface shape errors.
The technical scheme of the invention is as follows: the method for removing the return error of the non-zero interference aspheric surface measurement comprises the following steps:
(1) establishing an optical model of the aspheric interference system to be tested by utilizing optical software simulation;
(2) acquiring a training set for eliminating return errors, wherein the training set comprises a plurality of groups of surface shape error data of the surface to be detected and corresponding optical system interference wavefront data, and the training set is generated by utilizing computer simulation;
(3) constructing a neural network for eliminating return errors;
(4) training a neural network for eliminating return errors;
(5) and solving the aspheric surface shape error by using the trained neural network.
The method utilizes the computer to simulate the optical system of the non-zero compensation method and generate the training set, completes the training of the neural network, is convenient and quick, can eliminate the return error in the actual optical system without any prior knowledge and pretreatment for the interference wavefront data of a group of actual optical systems, and has good universality; in the method for removing the return error based on the neural network, in the process of solving the aspheric surface shape error, inherent system errors do not exist, the solving precision does not depend on the modeling precision of a system, the final result cannot be influenced by the inaccuracy of optical element parameters, the inconsistency of element positions with an actual system, the randomness of temperature, humidity and air flow speed and the like, the complex adjusting and calibrating process is avoided, and the rapid and high-precision aspheric surface shape error measurement is realized.
Still provide a nonzero interference aspheric surface and measure return stroke error remove device, it includes:
the optical model establishing module is configured to utilize optical software simulation to establish an optical model of the aspheric interference system to be tested;
a training set acquisition module configured to acquire a training set for eliminating return errors, wherein the training set comprises a plurality of groups of surface shape error data of the surface to be detected and corresponding interference wavefront data of the optical system,
all generated by computer simulation;
a neural network construction module configured to construct a neural network that eliminates a backhaul error;
a neural network training module configured to train a neural network that eliminates a backhaul error;
and the error solving module is configured to solve the aspheric surface shape error by using the trained neural network.
Drawings
Fig. 1 is an overall flowchart of a non-zero interference aspheric surface measurement return error removing method according to the present invention.
FIG. 2 is a simulated wavefront error plot of the measured surface profile.
FIG. 3 is a diagram of an interference wavefront for a simulated optical system.
FIG. 4 is a diagram of an interference wavefront of an optical system when a simulated surface to be measured does not contain surface shape errors.
Fig. 5 is one half of the point-to-point subtraction error of fig. 3 and 4.
Fig. 6 is a point-to-point subtraction error of fig. 5 and fig. 2.
Fig. 7 is a diagram of a neural network architecture.
FIG. 8 is a loss function decline curve during neural network training.
FIG. 9 is a diagram of the surface shape error wavefront of the surface to be measured.
Fig. 10 is a point-to-point subtraction error of fig. 9 from fig. 2.
Detailed Description
In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the term "comprises/comprising" and any variations thereof in the description and claims of the present invention and the above-described drawings is intended to cover non-exclusive inclusions, such that a process, method, apparatus, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
In order to solve the problems of measurement precision caused by system error and system modeling precision respectively in the process of solving aspheric surface shape errors by a half method and a reverse optimization method based on ray tracing and the problem that online measurement cannot be realized by multiple iterations of the reverse optimization method, the invention discloses a return error removal technology based on a neural network, which aims to solve the problems that: and the return error is eliminated, and the quick high-precision measurement of the aspheric surface shape error is realized by combining the return error with the light ray tracing function of optical software.
As shown in fig. 1, the method for removing return error of non-zero interference aspheric surface measurement includes the following steps:
(1) establishing an optical model of the aspheric interference system to be tested by utilizing optical software simulation;
(2) acquiring a training set for eliminating return errors, wherein the training set comprises a plurality of groups of surface shape error data of the surface to be detected and corresponding optical system interference wavefront data, and the training set is generated by utilizing computer simulation;
(3) constructing a neural network for eliminating return errors;
(4) training a neural network for eliminating return errors;
(5) and solving the aspheric surface shape error by using the trained neural network.
The method utilizes the computer to simulate the optical system of the non-zero compensation method and generate the training set, completes the training of the neural network, is convenient and quick, can eliminate the return error in the actual optical system without any prior knowledge and pretreatment for the interference wavefront data of a group of actual optical systems, and has good universality; in the method for removing the return error based on the neural network, in the process of solving the aspheric surface shape error, inherent system errors do not exist, the solving precision does not depend on the modeling precision of a system, the final result cannot be influenced by the inaccuracy of optical element parameters, the inconsistency of element positions with an actual system, the randomness of temperature, humidity and air flow speed and the like, the complex adjusting and calibrating process is avoided, and the rapid and high-precision aspheric surface shape error measurement is realized.
Preferably, the optical model in step (1) comprises: a non-zero compensator and an aspheric surface to be measured.
Preferably, in the step (2), the surface shape error of the surface to be measured is randomly generated by using a Zernike polynomial, the number of terms and coefficients of the Zernike polynomial are controlled within a certain range, and the specific upper limit of the coefficient is determined by the upper limit corresponding to the surface shape error of the surface to be measured in the actual measurement process.
Or, in the step (2), the interference wavefront of the optical system is generated after optical ray tracing in the optical software based on the corresponding surface shape error of the surface to be measured, and the specific Zernike polynomial term and coefficient are derived by the optical software.
Preferably, in the step (3), the input of the neural network is Zernike polynomial coefficients corresponding to the interference wavefront of the optical system, and the output is Zernike polynomial coefficients of the surface shape error, and the neural network is used for simulating the nonlinear relation between the input and the output as much as possible through training.
Preferably, in the step (4), the neural network constructed in the step (3) is trained by using the training set obtained in the step (2), so that a good training effect is obtained, and the loss function is reduced to a level meeting the precision requirement.
Preferably, in the step (5), the Zernike polynomial coefficients corresponding to the interference wavefront of the actual optical system are input as a trained neural network, and after calculation of the neural network, the coefficients of each term of the Zernike polynomial corresponding to the aspheric surface shape error are output, so as to eliminate the return error.
Preferably, in the step (3), a fully-connected neural network is constructed, the input of the network is 37 Zernike coefficients, and after passing through four fully-connected layers, 15 Zernike coefficients are output; to suppress overfitting, an L2 regularization method was applied to some of the fully connected layers in the network and several random shutdown layers were added to the network.
Preferably, in the step (4), training of the network is batch-processed by using 64 groups of samples each time, and the training set is randomly disturbed 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; in the optimization method, a fixed learning rate of 1 × 10 is used first-3Training 400 generations by adaptive moment estimation, and then using a fixed learning rate of 1 × 10-5SGD (stochastic gradient device) of (g) 600 generations of training.
It will be understood by those skilled in the art that all or part of the steps in the method of the above embodiments may be implemented by hardware instructions related to a program, the program may be stored in a computer-readable storage medium, and when executed, the program includes the steps of the method of the above embodiments, and the storage medium may be: ROM/RAM, magnetic disks, optical disks, memory cards, and the like. Therefore, in accordance with the method of the present invention, the present invention also includes a non-zero interference aspheric measurement return error removing device, which is generally expressed in the form of functional blocks corresponding to the steps of the method. The device includes:
the optical model establishing module is configured to utilize optical software simulation to establish an optical model of the aspheric interference system to be tested;
the training set acquisition module is configured to acquire a training set for eliminating return errors, wherein the training set comprises a plurality of groups of surface shape error data of the surface to be detected and corresponding optical system interference wavefront data, and the training set is generated by computer simulation;
a neural network construction module configured to construct a neural network that eliminates a backhaul error;
a neural network training module configured to train a neural network that eliminates a backhaul error;
and the error solving module is configured to solve the aspheric surface shape error by using the trained neural network.
Specific examples of the present invention are described in detail below.
The present example specifically illustrates an implementation method for removing a return error and realizing rapid and high-precision measurement of an aspheric surface shape error based on a neural network in a process of interferometric measurement of the aspheric surface shape error by a nonzero-digit compensation method.
As shown in fig. 1, the backhaul error removal technique based on the neural network disclosed in this example includes the following specific implementation steps:
The optical model as described above mainly includes a plano-convex lens as a non-zero compensator and a concave mirror as a surface to be measured. The curvature radius of the convex surface of the plano-convex lens is-760 mm, the thickness is 15mm, the caliber is 110mm, ZF6 is selected as the material, and the distance between the convex surface and the surface to be measured is set to be 1100 mm. The selected surface to be measured is a concave mirror with the curvature radius of-100 mm and the caliber of 10 mm.
The training set for eliminating the return error generally comprises 6000-10000 groups of corresponding surface shape error data of the surface to be detected and interference wavefront data of the optical system, and is generated by computer simulation, actual experiments are not needed, and the method is convenient and fast.
The surface shape error of the surface to be measured can be randomly generated by using a Zernike polynomial, in order to be matched with the surface shape error existing in actual processing, the number of terms of the Zernike polynomial is controlled to be 15 terms, and the coefficient range is 0-0.002 mm. Fig. 2 is a diagram of the surface shape error wavefront of the surface to be measured generated by simulation, and the PV value of the diagram is 3.397 λ.
The interference wavefront of the optical system is generated after the light ray is traced in the optical software based on the surface shape error of the surface to be measured. The light is incident to the surface to be measured through the nonzero compensator, is reflected by the surface to be measured, returns to the nonzero compensator and is converged through the ideal lens. After the tracking is completed, the interference wavefront data of the optical system, i.e. the corresponding Zernike polynomial coefficients, can be derived by software, and FIG. 3 is a diagram of the interference wavefront of the optical system generated by simulation, and the PV value is 6.4636 × 104Lambda is measured. FIG. 4 is a diagram showing an interference wavefront of an optical system generated by simulation when the surface to be measured has no surface shape error, and the PV value is 3.1578 × 104Lambda is measured. FIG. 5 is a diagram showing a wavefront chart of the profile error measured by the return error of the optical system during the current ray tracing process, in which the PV value is 3.2325 × 104Lambda is measured. FIG. 6 is a point-to-point subtraction error of FIG. 5 and FIG. 2 with a PV value of 3.2325 × 104Lambda is measured. It can be seen that the effect of the backhaul error is very severe.
A data set is first generated using the method described above. The data set comprises 10000 groups of samples, the front 9900 groups of samples are taken as a training set, and the rear 100 groups of samples are taken as a testing set.
The fully-connected neural network shown in fig. 7 and table 1 is constructed, the input of the network is 37-term Zernike coefficients, and after passing through four fully-connected layers (sense Layer), 15-term Zernike coefficients are output. To suppress the overfitting, an L2 regularization method was applied to the partially fully connected Layer (density Layer) in the network and several random shutdown layers (Dropout layers) were added to the network.
TABLE 1
| Serial number | Layer(s) | Activating a | Regularization term | |
| 1 | Dense(400) | | L2 | |
| 2 | Dropout(0.2) | |||
| 3 | Dense(400) | | L2 | |
| 4 | Dropout(0.2) | |||
| 5 | Dense(15) |
Training of the network was batch processed using 64 samples each time, and followed at the beginning of each training generationThe machine shuffles the training set. The loss function is the root mean square error (RMS) of the predicted and true values. In the optimization method, Adam (fixed learning rate 1 × 10) is used first-3) Training 400 generations, and then using SGD (fixed learning Rate 1X 10)-5) The training 600 generation. After the network is trained for 1000 generations, the variation of the loss function value of the test set is shown in fig. 8, and it can be seen that the performance of the network is also continuously improved with the increase of training generations. The loss function value of the test set at the final 1000 generations was 1.7217 × 10-4。
And (3) taking the actual optical interference wavefront data obtained in the step (2), namely the Zernike polynomial and the coefficient of the corresponding term as the input of the trained neural network, reading the output after the calculation of the neural network, substituting the output into the Zernike polynomial for calculation, and obtaining the surface shape error of the surface to be measured as shown in the figure 9, wherein the PV value is 3.2996 lambda. Fig. 10 is a point-to-point subtraction error (0.1694 λ) of fig. 9 from fig. 2. It can be seen that the error PV value of FIG. 10 is from 3.2325X 10 compared to FIG. 64The lambda is reduced to 0.1694 lambda, the amplitude is obviously reduced, and the return error is effectively eliminated.
Once trained, the neural network with the return error removed has certain universality, and for interference wavefront data of a group of actual optical systems, the return error in the actual optical systems can be eliminated without any priori knowledge and preprocessing, so that the aspheric surface shape error can be rapidly measured.
According to the return error removing technology based on the neural network, in the aspheric surface shape error solving process, inherent system errors do not exist, the solving precision does not depend on the modeling precision of a system, the complex adjusting and calibrating process is avoided, and high-precision aspheric surface shape error measurement is realized.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, and all simple modifications, equivalent variations and modifications made to the above embodiment according to the technical spirit of the present invention still belong to the protection scope of the technical solution of the present invention.
Claims (10)
1. The method for removing the return error of the non-zero interference aspheric surface measurement is characterized by comprising the following steps of: which comprises the following steps:
(1) establishing an optical model of the aspheric interference system to be tested by utilizing optical software simulation;
(2) acquiring a training set for eliminating return errors, wherein the training set comprises a plurality of groups of surface shape error data of the surface to be detected and corresponding optical system interference wavefront data, and the training set is generated by utilizing computer simulation;
(3) constructing a neural network for eliminating return errors;
(4) training a neural network for eliminating return errors;
(5) and solving the aspheric surface shape error by using the trained neural network.
2. The non-zero interferometric aspheric measurement return error removal method of claim 1, characterized by: the optical model in the step (1) comprises: a non-zero compensator and an aspheric surface to be measured.
3. The non-zero interferometric aspheric measurement return error removal method of claim 2, characterized by: in the step (2), the surface shape error of the surface to be measured is randomly generated by using a Zernike polynomial, the number of terms and the coefficient of the Zernike polynomial are controlled within a certain range, and the specific upper limit of the coefficient is determined by the upper limit corresponding to the surface shape error of the surface to be measured in the actual measurement process.
4. The non-zero interferometric aspheric measurement return error removal method of claim 2, characterized by: in the step (2), the interference wavefront of the optical system is generated after the optical line tracing in the optical software based on the corresponding surface shape error of the surface to be measured, and the specific Zernike polynomial term and coefficient are derived by the optical software.
5. The non-zero interferometric aspheric measurement return error removal method of claim 3 or 4, characterized in that: in the step (3), the input of the neural network is the Zernike polynomial coefficient corresponding to the interference wavefront of the optical system, and the output is the Zernike polynomial coefficient of the surface shape error, and the neural network is used for simulating the nonlinear relation between the input and the output as much as possible through training.
6. The non-zero interferometric aspheric measurement return error removal method of claim 5, characterized in that: in the step (4), the neural network constructed in the step (3) is trained by using the training set obtained in the step (2), so that a good training effect is obtained, and the loss function is reduced to a level meeting the precision requirement.
7. The non-zero interferometric aspheric measurement return error removal method of claim 6, characterized by: in the step (5), the Zernike polynomial coefficient corresponding to the interference wavefront of the actual optical system is used as the trained neural network input, and after calculation of the neural network, the coefficient of each term of the Zernike polynomial corresponding to the aspheric surface shape error is output, so that the return error is eliminated.
8. The non-zero interferometric aspheric measurement return error removal method of claim 7, characterized by: in the step (3), a fully-connected neural network is constructed, the input of the network is 37 Zernike coefficients, and after passing through four fully-connected layers, 15 Zernike coefficients are output; to suppress overfitting, an L2 regularization method was applied to some of the fully connected layers in the network and several random shutdown layers were added to the network.
9. The method of claim 8, wherein the step of removing the return error of the non-zero interferometric aspheric measurement comprises: in the step (4), 64 groups of samples are used for batch processing each time for training the network, and the training set is randomly disturbed 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; in the optimization method, a fixed learning rate of 1 × 10 is used first-3The adaptive moment estimation method Adam trains 400 generations, and then uses a fixed learning rate of 1 multiplied by 10-5Random gradient descent ofFasgd training 600 generations.
10. Non-zero interference aspheric surface measurement return error removing device, its characterized in that: it includes:
the optical model establishing module is configured to utilize optical software simulation to establish an optical model of the aspheric interference system to be tested;
the training set acquisition module is configured to acquire a training set for eliminating return errors, wherein the training set comprises a plurality of groups of surface shape error data of the surface to be detected and corresponding optical system interference wavefront data, and the training set is generated by computer simulation;
a neural network construction module configured to construct a neural network that eliminates a backhaul error;
a neural network training module configured to train a neural network that eliminates a backhaul error;
and the error solving module is configured to solve the aspheric surface shape error by using the trained neural network.
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| CN113091638A (en) * | 2021-03-25 | 2021-07-09 | 中国科学院光电技术研究所 | Device and method for calibrating return error in surface shape measurement by interferometry |
| WO2021160086A1 (en) * | 2020-02-14 | 2021-08-19 | 北京理工大学 | Method and apparatus for eliminating non-zero interference aspheric measurement hysteresis error |
| CN113283162A (en) * | 2021-04-30 | 2021-08-20 | 晋城鸿智纳米光机电研究院有限公司 | Plastic optical lens surface shape error prediction method, electronic device and storage medium |
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