CN114547855A - Multi-objective automatic optimization method for optical imaging system - Google Patents
Multi-objective automatic optimization method for optical imaging system Download PDFInfo
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Abstract
The invention provides a multi-target automatic optimization method of an optical imaging system, which adopts an index intermediate quantity BlProgressive approximation of each to-be-optimized performance TlCorresponding optimal index AlWhen the multi-performance optimization is carried out, the invention can avoid the process that the optimization process falls into the process of local optimal solution which is realized by some optimal indexes of the performance to be optimized but cannot be realized by other optimal indexes of the performance to be optimized, namely, progressive approximation, and can ensure that all the optimal indexes corresponding to the performance to be optimized can be realized; meanwhile, according to the result after each round of iterative optimization design, the invention automatically updates the position of the field of view point to be optimized in each round and the constraint conditions adopted in the optical design softwareBy the mutual influence of the optimal indexes of various performances to be optimized in the optimization process, the comprehensive optimization of the performances of various imaging systems is realized, and the imaging quality of the imaging systems is effectively improved.
Description
Technical Field
The invention belongs to the technical field of optical design, and particularly relates to a multi-objective automatic optimization method for an optical imaging system.
Background
Any optical system, wherever it is used, is used to transmit the light emitted from the target into the receiver of the instrument by changing its propagation direction and position according to the requirements of the instrument's working principle, so as to obtain various information of the target, including the geometry, energy intensity, etc. of the target. Therefore, there are two aspects to the requirements for the imaging performance of the optical system: the first aspect is the optical characteristics including focal length, object distance, image distance, magnification, entrance pupil position and distance, etc.; the second aspect is the imaging quality, the image formed by the optical system should be clear enough, and the object image should be similar with less distortion. The content of the first aspect, i.e. meeting the requirements in terms of optical performance, falls within the category of discussion of applied optics; the content of the second aspect, namely meeting the requirements in terms of imaging quality, belongs to the research content of optical design.
The optical design work included: structure form selection and initial structure determination, aberration correction, image quality evaluation, optical tolerance making and the like. The aberration correction is a step with large workload and strong artistry, and is the most important step. Generally, aberration correction is a progressive process, especially for some demanding and complex systems. The physical law of light propagation in an optical system, namely the catadioptric law, is nonlinear, so that the optical system generally has aberration, and the relationship between the aberration and structural parameters is also a complex nonlinear problem, so that the imaging quality of an objective lens is guided to a better state from a poor state in an initial structure through adjusting part or all of the structural parameters step by step, which is essentially to search a 'tortuous' but feasible route in a solution space of the problem, so that the lens is gradually moved from a position with poor image quality to a position with better image quality, and the structure of the lens is not only reasonable, but also can be processed and manufactured. The process is a complex process which extremely depends on the experience of designers, and after an electronic computer appears, the process is introduced into the aberration calculation, so that the aberration calculation speed is greatly improved; but the modification of the system structure parameters still depends on the optical designer to determine. With the increase of computer speed, the time required for calculating aberration is less and less, and analyzing the current design result and determining how to modify the parameters in the next step becomes a major problem for optical designers, so that the automatic design of the optical system occurs, that is, the computer automatically changes the curvature radius, interval or thickness of the system, even the refractive index of the optical material according to a certain program.
When automatic optimization design is carried out, firstly, an evaluation function representing the relationship between various aberration performance indexes and structural parameters is constructed. When the optical aberration and the performance index tend to be the minimum value, the optical aberration and the performance index approach to the target value, and in the automatic design process, the structural parameter is called as iteration once when being changed; after each iteration, the merit function tends toward a minimum, mathematically called "convergence", and deviation from the minimum is called "divergence". Therefore, the designer should pay attention at any time that manual intervention is necessary to change some factor in the evaluation function or damping factor of the independent variable to increase the convergence speed when the divergence or convergence speed is slow. If not, it is judged whether the selected configuration has a possibility of effective correction, whether it is necessary to exchange the optical material or change the configuration, or the like.
The automatic design work of an optical system has been 60 years old, in 1950, beck (j.g. baker) at harvard university in the united states starts organizing an optical automatic design research group, and technologically developed countries develop the work, and a plurality of methods such as a gradual change Method (Variation Method), a most rapid Descent Method (steel Gradient Method), an optimal Gradient Method (optimal Gradient Method) and a Least Square Method (Least Square Method) do not achieve ideal effects; in 1950, Wen (G.G.Wynne) of the university of London, Imperial's institute of technology, published a Damped Least Squares (DLS) method, which greatly improved the convergence rate of the evaluation function and made the automatic optimization technique one of the more commonly applied methods.
At the final stage of lens optimization, chengdan in 2010 proposes an automatic optimization method for automatically adjusting and determining proper sampling view field and azimuth angle weight. According to the method, on the basis of local optimization, the weight is automatically adjusted in an outer ring, and the imaging performance of a sampling field point is automatically and effectively balanced; however, the selection of the sampling field point in the optical design still depends on the experience of the optical designer, and the problems that the imaging quality of the sampling field point is good, but the imaging quality of the positions of other field points is poor in the optical design process easily occur.
Disclosure of Invention
In order to solve the problems, the invention provides a multi-objective automatic optimization method for an optical imaging system, which can realize the comprehensive optimization of the performance of various imaging systems and effectively improve the imaging quality of the imaging system.
A multi-objective automatic optimization method for an optical imaging system comprises the following steps:
s1: determining the performance T to be optimized of the initial structure of the imaging system to be optimized according to the design requirementlAnd each property T to be optimizedlCorresponding optimal index AlAnd selecting a field-of-view point F to be optimized from the full field of view of the imaging system to be optimizediForming a set of view points, wherein L is 1,2, …, L, and L is at least 3, I is 1,2, …, I, and I is at least 3;
s2: obtaining each performance T to be optimized under the initial structure of the imaging system to be optimizedlCorresponding index intermediate BlThe method specifically comprises the following steps: respectively judging the performance T of the initial structure to be optimizedlActual performance value oflWhether or not less than the corresponding optimum index AlIf yes, let Bl＝Al(ii) a If not, calculating B according to the following formulal：
Bl＝Cl-kB×(Al-Cl)
Wherein k isBSetting a weight coefficient;
s3: respectively setting each field of view point F to be optimized in the initial field of view point setiAre all marked as all properties T to be optimizedlAnd correlating the view points with the intermediate quantity B of the indexlAs per each and to be optimized performance TlPerformance T to be optimized for the associated field of view pointlIn which ifAny field point to be optimized is marked as any associated field point of performance to be optimized, which indicates that the field point to be optimized can cause the performance to be optimized to generate fluctuation exceeding a set value;
s4: optimizing the initial structure by using a damped least square method according to constraint conditions in optical design software to obtain a new optical structure and finish the updating of an imaging system;
s5: judging whether the updating times of the imaging system are larger than the set internal circulation times N or whether the performance T to be optimized of the imaging system to be optimized under the current optical structurelActual performance value C oflWhether or not B is reachedlIf no, the process proceeds to step S6, and if one is satisfied, the process proceeds to step S7;
s6: after the constraint conditions adopted currently in the optical design software are updated according to the set rules, the steps S4-S5 are executed again;
s7: judging whether the updating times of the imaging system are larger than the set external circulation times M or whether the performance T to be optimized of the imaging system to be optimized under the current optical structurelActual performance value C oflWhether or not it reaches AlAnd if the optical structure of the imaging system to be optimized is not the current optical structure of the imaging system to be optimized, executing the step S2 again, and then executing the steps S4-S5, and if the optical structure of the imaging system to be optimized meets one of the steps S4-S5, finishing the automatic optimization design of the imaging system.
Further, the actual performance value C in step S3lThe acquisition method comprises the following steps:
respectively evaluating L performances to be optimized T corresponding to each view field point of the full view field of the imaging system to be optimizedlAnd for each performance T to be optimizedlTaking the performance value corresponding to the view field point with the worst performance as the initial structure of the imaging system to be optimized in the performance T to be optimizedlActual performance value ofl。
Further, the step S6 of updating the current field-of-view point set and the constraint conditions adopted in the optical design software according to the set rules specifically includes:
s61: sequentially judging the performance T to be optimized of the imaging system to be optimized under the current optical structure one by onelActual performance value C oflWhether or not B is reachedlUntil the first miss is found BlC of (A)lAnd mixing the ClThe corresponding field of view point is taken as an alternative field of view point F*While simultaneously reacting C with ClCorresponding performance T to be optimizedlIs marked as T*；
S62: judging alternative view point F*Whether the current view point set belongs to, if not, the weight average value of all the view points to be optimized in the current view point set is used as an alternative view point F*And the alternative field of view point F*Adding the current view point set to obtain an updated view point set, marking a selected view point F as an associated view point with performance T to be optimized, and then entering step S63; if so, firstly judging the alternative view point F*Whether or not it has been marked as a performance to be optimized T*If not, marking F as the associated view point of the performance T to be optimized, and proceeding to step S63, if yes, performing the following operations, and then proceeding to step S63:
the weights are updated as follows:
wherein, W (Fi)nextUpdating the updated weight value k of the ith field point to be optimized in the current field point set1、k2、ShAnd SlAre all set convergence rate factors, W (Fi)nowUpdating a weight value before the ith field point to be optimized in the current field point set, wherein omega (F) is a set threshold value of comprehensive aberration, and omega' (Fi) is an aberration comprehensive evaluation index of each field point to be optimized in the current field point set;
for each field point to be optimized in the updated field point set, if the weight value of the field point to be optimized is smaller than the weight threshold value delta, and the field point to be optimized does not belong to a field boundary point or is a field point which appears for multiple times, deleting the field point to be optimized, otherwise, keeping the field point to be optimized, obtaining an updated field point set, and then entering step S63;
s63: judging whether the number of the field points to be optimized in the updated field point set is larger than the set maximum number H of the field points, if not, entering step S64, and if so, entering S65;
s64: executing the updating constraint operation, and then re-executing the steps S4-S5; wherein the update constraint operation is: if an operation of deleting a field point to be optimized is performed, deleting all constraints related to the deleted field point to be optimized in the constraint conditions of step S4, and if an operation of adding a field point to be optimized in association with optimization performance is performed, adding corresponding constraints related to the field point to be optimized in the performance to be optimized in association with the field point to be optimized in the constraint conditions of step S4;
s65: and keeping the field points to be optimized which belong to the field boundary points or appear for multiple times in the current field point set to obtain a final optimized field point set, executing updating constraint operation based on the final optimized field point set, and then executing the steps S4-S5 again.
Further, a calculation formula of the aberration comprehensive evaluation index ω' (Fi) of each field-of-view point to be optimized in the field-of-view point set is as follows:
wherein, α l (Fi), β l (Fi) and γ l (Fi) represent the ith field point F to be optimized in the current field point setiAt the time of optimizing the performance TlThe corresponding weight coefficients Cl (Fi) and Bl (Fi) respectively represent the ith field point F to be optimized in the field point setiTo be optimized performance TlActual performance value and intermediate index.
Further, the calculated weight W (Fi)nextAfter normalization is carried out according to the following formula, the normalized weight is compared with a weight threshold value delta, wherein the normalization formula is as follows:
wherein, W (F)next-maxAnd updating the maximum value of the updated weight values of the field points to be optimized.
Further, the imaging system to be optimized is a total refraction type imaging system, a total reflection type imaging system or a refraction and reflection type imaging system.
Further, the performance to be optimized comprises a focal length, an object distance, an image distance, a magnification, an entrance pupil position, an entrance pupil distance, a total system length, a maximum passing aperture of the optical lens, spherical aberration, coma aberration, astigmatism, field curvature, distortion, sine difference, wave aberration, telecentricity, polarization aberration, aberration uniformity and/or imaging quality.
Has the advantages that:
1. the invention provides a multi-target automatic optimization method of an optical imaging system, which adopts an index intermediate quantity BlProgressive approximation of each to-be-optimized performance TlCorresponding optimal index AlWhen the multi-performance optimization is carried out, the invention can avoid the process that the optimization process falls into the process of local optimal solution which is realized by some optimal indexes of the performance to be optimized but cannot be realized by other optimal indexes of the performance to be optimized, namely, progressive approximation, and can ensure that all the optimal indexes corresponding to the performance to be optimized can be realized; meanwhile, according to the result after each round of iterative optimization design, the position of the field of view to be optimized and the constraint condition adopted in the optical design software are automatically updated, the problem that the imaging quality at the optimized field of view is good but the imaging quality between two optimized field of view points is poor is avoided, meanwhile, the comprehensive optimization of the performance of various imaging systems is realized through the mutual influence of the optimal indexes of the performance to be optimized in the optimization process, and the imaging quality of the imaging systems is effectively improved.
2. The invention provides a multi-objective automatic optimization method of an optical imaging system, which can automatically select an optimized field point according to input design indexes, automatically adjust optimization weight and constraint variable, realize comprehensive optimization of various design indexes through mutual influence of various design indexes in the optimization process, effectively reduce the dependence of the optimization design of the imaging system on the experience of an optical designer, and improve the optimization efficiency; meanwhile, the invention solves the problems that the imaging quality at the optimized view field point in the optical design software is good, but the imaging quality between the two optimized view field points is poor in the optical design, and improves the full view field imaging quality.
3. The invention provides a multi-objective automatic optimization method for an optical imaging system, which is characterized in that each performance to be optimized is cooperatively optimized, and each design index of the performance to be optimized is influenced mutually in the optimization process, so that the comprehensive optimization of various performance indexes is realized, and the imaging quality of the system is effectively improved.
4. The invention provides a multi-objective automatic optimization method for an optical imaging system, which has strong universality in the optimization design process of the imaging system and can obtain good optimization design results.
Drawings
FIG. 1 is a flow chart of a method for multi-objective automatic optimization of an optical imaging system;
FIG. 2(a) is a diagram of a NA0.75 full refraction type deep ultraviolet projection lithography imaging system;
FIG. 2(b) is a distortion diagram of an NA0.75 full refraction type deep ultraviolet projection lithography imaging system;
FIG. 2(c) is a wave aberration diagram of an NA0.75 full refraction type deep ultraviolet projection lithography imaging system;
FIG. 2(d) is an image space telecentric degree diagram of the NA0.75 full refraction type deep ultraviolet projection photoetching imaging system;
FIG. 3(a) is a structural diagram of an NA0.33 total reflection type extreme ultraviolet projection lithography imaging system;
FIG. 3(b) is a distortion diagram of the NA0.33 total reflection type EUV projection lithography imaging system;
FIG. 3(c) is a wave aberration diagram of the NA0.33 total reflection type EUV projection lithography imaging system;
FIG. 3(d) is an image space telecentric degree diagram of the NA0.33 total reflection type extreme ultraviolet projection lithography imaging system;
FIG. 4(a) is a diagram of a NA1.35 catadioptric deep ultraviolet projection lithography imaging system;
FIG. 4(b) is a distortion diagram of the NA1.35 catadioptric deep ultraviolet projection lithography imaging system;
FIG. 4(c) is the wave aberration diagram of the NA1.35 catadioptric deep ultraviolet projection lithography imaging system;
FIG. 4(d) is the image space telecentricity diagram of the NA1.35 catadioptric deep ultraviolet projection lithography imaging system.
Detailed Description
In order to make the technical solutions better understood by those skilled in the art, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application.
In order to solve the selection problem of the optimized field of view points more efficiently, the invention provides a multi-objective automatic optimization design method of an optical imaging system. As shown in fig. 1, a method for multi-objective automatic optimization of an optical imaging system includes the following steps:
s1: determining the performance T to be optimized of the initial structure of the imaging system to be optimized according to the design requirementlAnd each property T to be optimizedlCorresponding optimal index AlAnd selecting a field-of-view point F to be optimized from the full field of view of the imaging system to be optimizediA set of view points is formed, where L is 1,2, …, L, and L is at least 3, I is 1,2, …, I, and I is at least 3.
It should be noted that the performance to be optimized of the imaging system can be divided into two aspects, the first aspect is optical characteristics including a focal length, an object distance, an image distance magnification, an entrance pupil position, an entrance pupil distance, and the like; the second aspect is the imaging quality, the image formed by the optical system should be clear enough, and the object image is similar, the deformation size, etc.; meanwhile, the optimal indexes corresponding to the performances to be optimized can be determined according to actual requirements.
S2: at the beginning of the imaging system to be optimizedUnder the structure, acquiring each performance T to be optimizedlCorresponding index intermediate BlThe method specifically comprises the following steps:
s31: respectively evaluating L performances to be optimized T corresponding to each view field point of the full view field of the imaging system to be optimizedlAnd for each performance T to be optimizedlTaking the performance value corresponding to the view field point with the worst performance as the initial structure of the imaging system to be optimized in the performance T to be optimizedlActual performance value ofl；
S32: respectively judging the initial structure of the imaging system to be optimized at each performance T to be optimizedlActual performance value oflWhether or not less than the corresponding optimum index AlIf yes, let Bl＝Al(ii) a If not, calculating B according to the following formulal：
Bl＝Cl-kB×(Al-Cl)
Wherein k isBTo calculate BlThe set weight coefficient of (2);
s3: respectively setting each field of view point F to be optimized in the initial field of view point setiAre all marked as all properties T to be optimizedlAnd correlating the view points with the intermediate quantity B of the indexlAs per each and to be optimized performance TlPerformance T to be optimized for the associated field of view pointlIf any field of view point to be optimized is marked as any associated field of view point of the performance to be optimized, it indicates that the field of view point to be optimized can cause the performance to be optimized to fluctuate beyond a set value.
That is, if a certain view point to be optimized is marked as a related view point of a certain performance to be optimized, it indicates that the view point to be optimized has a large influence on the performance to be optimized, and meanwhile, in the initial setting of the present invention, it is considered that each view point to be optimized in the initial view point set has a large influence on each performance to be optimized, thereby forming a fully-related mark.
For example, assuming that the current field-of-view point set includes three field-of-view points F1, F2, F3 to be optimized, the performance to be optimized of the current imaging system is T1, T2, T3, and the association relationship between the field-of-view point to be optimized and the performance to be optimized is expressed as follows:
correlation table of to-be-optimized view field point and to-be-optimized performance
| T1 | | T3 | |
| F1 | |||
| 1 | 0 | 1 | |
| |
1 | 0 | 0 |
| |
0 | 1 | 0 |
In the above table, 1 indicates that the field of view point to be optimized is correlated with the performance to be optimized, 0 indicates that the field of view point to be optimized is not correlated, if the performance to be optimized T1 is only associated with the field of view points F1 and F2 to be optimized, that is, in the full field of view of the imaging system, the field of view points F1 and F2 to be optimized have a large influence on the performance to be optimized T1 of the entire imaging system, when the initial structure is optimized by using the damped least squares method in the optical design software, the optimization of the field of view points F1 and F2 with respect to the performance to be optimized T1 takes the intermediate index amount B1 as a constraint condition, and the optimization performance T1 of the entire imaging system can be well controlled by only controlling the actual performance values of the performance to be optimized T1 at the field of view points F1 and F2 to be optimized.
S4: and optimizing the initial structure of the imaging system by using a damped least square method according to the constraint conditions in optical design software to obtain a new optical structure of the imaging system, thereby completing the updating of the imaging system.
It should be noted that, in the optical design software, the initial structure of the imaging system can be optimized by using the damped least squares method only by determining good constraint conditions, and the specific process of the optimization of the present invention is not described in detail.
S5: judging whether the updating times of the imaging system are larger than the set internal circulation times N or whether the performance T to be optimized of the imaging system to be optimized under the current optical structurelActual performance value C oflWhether or not B is reachedlIf no, the process proceeds to step S6, and if one is satisfied, the process proceeds to step S7;
s6: after updating the current view point set and the constraint conditions adopted in the optical design software according to the set rules, re-executing the steps S4-S5, wherein the updating process specifically comprises the following steps:
s61: sequentially judging the performance T to be optimized of the imaging system to be optimized under the current optical structure one by onelActual performance value C oflWhether or not it reaches BlUntil the first one is found not to reach BlC of (A)lAnd combining the ClThe corresponding field of view point is taken as an alternative field of view point F*While simultaneously reacting C with ClCorresponding performance T to be optimizedlIs marked as T*；
S62: judging alternative field of view point F*Whether the current view point set belongs to, if not, the weight average value of all the view points to be optimized in the current view point set is used as an alternative view point F*And the alternative field of view point F*Adding the current view point set to obtain an updated view point setMarking the selected field point F as an associated field point of the performance T to be optimized, and then proceeding to step S63; if so, firstly judging the alternative view point F*Whether or not it has been marked as a performance to be optimized T*If no, marking F as the associated view point of performance T to be optimized, and proceeding to step S63, if yes, performing the following operations, and then proceeding to step S63:
the weights are updated as follows:
wherein k is1、k2、ShAnd SlAre all set convergence rate factors, W (Fi)nextUpdating the updated weight value of the ith field point to be optimized in the current field point set, W (Fi)nowFor the weight before updating of the ith field point to be optimized in the current field point set, ω (F) is a set threshold value of the comprehensive aberration, and ω' (Fi) is an aberration comprehensive evaluation index of each field point to be optimized in the current field point set, the calculation formula is as follows:
wherein, α l (Fi), β l (Fi) and γ l (Fi) represent the ith field point F to be optimized in the current field point setiAt the time of optimizing the performance TlThe corresponding weight coefficients Cl (Fi) and Bl (Fi) respectively represent the ith field point F to be optimized in the field point setiTo be optimized performance TlActual performance value and intermediate index quantity of (1);
will calculate the weight W (Fi)nextAnd carrying out normalization, wherein the normalization formula is as follows:
wherein, W (F)next-maxFor each field to be optimizedThe maximum value of the updated weight values.
For each field point to be optimized in the updated field point set, if the normalized weight is smaller than the weight threshold value delta and the field point to be optimized does not belong to a field boundary point or a field point appearing for multiple times, if the field point to be optimized appears for more than three times, deleting the field point to be optimized, otherwise, keeping the field point to be optimized, obtaining an updated field point set, and then entering step S63;
s63: judging whether the number of the field points to be optimized in the updated field point set is larger than the set maximum number H of the field points, if not, entering step S64, and if so, entering S65;
s64: replacing the field point to be optimized and the weight thereof in the field point set before updating with the field point to be optimized and the weight thereof in the field point set after updating, executing updating constraint operation, and then executing the steps S4-S5 again; wherein the update constraint operation is: if an operation of deleting a field point to be optimized is performed, deleting all constraints related to the deleted field point to be optimized in the constraint conditions of step S4, and if an operation of adding a field point to be optimized in association with optimization performance is performed, adding corresponding constraints related to the field point to be optimized in the performance to be optimized in association with the field point to be optimized in the constraint conditions of step S4;
s65: and (4) retaining the field points to be optimized which belong to the field boundary points or appear for multiple times in the current field point set to obtain a final optimized field point set, executing updating constraint operation based on the final optimized field point set, and then executing the steps S4-S5 again.
S7: judging whether the updating times of the imaging system are larger than the set external circulation times M or whether the performance T to be optimized of the imaging system to be optimized under the current optical structurelActual performance value C oflWhether or not it reaches AlIf the optical structure of the imaging system to be optimized is not the current optical structure of the imaging system to be optimized, the step S2 is executed again, and then S4-S5 are executed, if the optical structure meets one of the steps, the automatic optimization design of the imaging system is completed, and the current optimization design result is used as the final optimization design result to be ensuredAnd (4) storing.
Further, the optical system may be classified into a refractive system, a reflective system and a catadioptric system according to the type of lens used. The photoetching objective lens system has higher requirement and more uniform image quality in a large field of view and is one of the most precise optical systems, so that the invention selects three sets of photoetching objective lens systems to carry out automatic optimization design on the imaging performance of the photoetching objective lens systems, including distortion, wave aberration, full-field wave aberration uniformity, image space telecentricity, multiplying power, object distance, image distance and system total length, and verifies the universality of the invention.
The definition principles of the positive and negative signs of the optical system structure parameters given by the embodiment of the invention are respectively as follows:
the positive and negative signs of the curvature radius are defined as follows: the direction from the curvature center of the lens surface to the vertex of the lens surface is defined as negative when the direction is the same as the direction of the light path, and vice versa;
the positive and negative signs of the interval are defined as follows: if the direction from the intersection point of the current surface and the reference axis to the intersection point of the next surface and the reference axis is positive along with the direction of the light path, otherwise, the direction is negative;
wherein the XYZ coordinate system is defined as: the Z axis is parallel to the reference axis and is in the same direction with the direction of the light path, the Y axis is vertical to the Z axis, and the X axis is vertical to a plane formed by the Y axis and the Z axis.
The Q-bfs free-form surface used in the embodiment of the invention is given the structural parameters of the Q-bfs surface type according to the Q-bfs coefficient giving principle, and the Q-bfs surface type formula is as follows:
wherein r is2＝x2+y2(ii) a u is a normalized radial coordinate; z is the rise of the free-form surface Q-bfs parallel to the z-axis; c is the vertex curvature of the free-form surface Q-bfs; k is the conic constant, pmaxThe maximum clear radius of the curved surface; biIs the coefficient corresponding to the Q-bfs polynomial.
The Q-con free-form surface used in the embodiment of the invention is given the structural parameters of the Q-con surface type according to the Q-con coefficient given principle, and the Q-con surface type formula is as follows:
wherein r is2＝x2+y2(ii) a u is a normalized radial coordinate; z is the rise of the Q-type free curved surface parallel to the z axis; c is the vertex curvature of the Q-type free curved surface; k is a conic constant; a isiIs the coefficient corresponding to Q-con polynomial.
The structure of the NA0.75 total refraction type deep ultraviolet projection photoetching imaging system is shown in fig. 2(a), the specific structure parameters of each lens are given in table 1, and the Q-bfs surface type coefficient is given in table 2.
TABLE 1 NA0.75 full refraction type deep ultraviolet projection photoetching imaging system structure parameter
TABLE 2NA0.75 Total refractive type deep ultraviolet projection lithography imaging System Q-bfs surface form factor
| Surface numbering | 2 | 3 | 12 | 21 |
| Normalized radius | 6.90E+01 | 6.90E+01 | 7.71E+01 | 6.86E+01 |
| K | -9.15E-01 | 2.32E-01 | -8.32E-03 | 6.68E-02 |
| 4th | 2.87E-01 | 4.59E-01 | -5.93E-03 | -4.21E-02 |
| 6th | 6.08E-02 | 6.62E-02 | 1.32E-02 | -7.63E-04 |
| 8th | -3.35E-03 | -3.82E-03 | -2.42E-04 | 3.42E-05 |
| 10th | 1.37E-03 | 1.45E-03 | 6.29E-05 | 3.25E-05 |
| 12th | 3.71E-04 | 3.92E-04 | -2.62E-06 | 8.83E-06 |
| 14th | 2.43E-04 | 2.59E-04 | -4.31E-06 | 7.72E-07 |
| 16th | 1.45E-04 | 1.55E-04 | -2.64E-06 | -5.30E-07 |
| 18th | 8.41E-05 | 9.04E-05 | -1.26E-06 | -6.65E-07 |
| 20th | 5.30E-05 | 5.69E-05 | -1.22E-07 | -3.14E-07 |
| 22nd | 2.99E-05 | 3.22E-05 | 3.75E-07 | -2.29E-08 |
| 24th | 1.51E-05 | 1.62E-05 | 6.77E-07 | 1.98E-07 |
| 26th | 3.85E-06 | 4.36E-06 | 4.48E-07 | 1.95E-07 |
| 28th | -3.47E-07 | -1.25E-07 | 2.72E-07 | 1.81E-07 |
| 30th | -1.63E-06 | -1.56E-06 | 1.43E-07 | 4.36E-08 |
NA0.75 total refraction type deep ultravioletThe image-placing static working field of the projection photoetching imaging system is a rectangular working field of 26mm multiplied by 10.5mm, and fig. 2(b) is a distortion diagram of an NA0.75 total refraction type deep ultraviolet projection photoetching imaging system, so that the distortion of the chief ray of the imaging system in the total field is less than 0.316 nm; FIG. 2(c) is the wave aberration diagram of NA0.75 full refraction type deep ultraviolet projection lithography imaging system, it can be seen that the full field wave aberration of the imaging system is less than 0.235nm, and the standard deviation of the wave aberration of different field points of the full field is 5 × 10-5The wave aberration uniformity of the full field of view is good; FIG. 2(d) is an image space telecentricity diagram of the NA0.75 full refraction type deep ultraviolet projection lithography imaging system, and it can be seen that the image space telecentricity of the imaging system in full field of view is less than 1 mrad.
The structure of the NA0.33 total reflection type euv projection lithography imaging system is shown in fig. 3(a), wherein table 3 shows specific structural parameters of each lens, and table 4 shows Q-con surface type coefficients:
TABLE 3NA0.33 Total reflection type extreme ultraviolet projection photoetching imaging system structure parameters
| Surface of | Surface type | Radius/mm | Distance/mm | Catadioptric form |
| Article surface | 0.00000 | 688.08944 | ||
| 1 | Q-bfs | -6078.54080 | -538.03308 | Reflection |
| 2 | Q-bfs | 1144.55074 | 738.07763 | Reflection |
| 3 | Q-bfs | 291.60624 | -161.40134 | Reflection |
| 4 | Q-bfs | 416.47319 | 711.30120 | Reflection |
| 5 | Q-bfs | 374.21899 | -293.40192 | Reflection |
| 6 | Q-bfs | 374.62071 | 337.40192 | Reflection |
| Image plane | 0.00000 | 0.00000 |
TABLE 4 NA0.33 Total reflection type extreme ultraviolet projection lithography imaging system Q-bfs surface type coefficient
The NA0.33 total refraction type deep ultraviolet projection photoetching imaging system image-placing static working visual field is an arc-shaped working visual field with 26mm multiplied by 2mm, and the diagram (b) is a NA0.33 total reflection type extreme ultraviolet projection photoetching imaging system distortion diagram, so that the distortion of the main light ray of the imaging system total visual field is less than 0.224 nm; FIG. 3(c) is a wave aberration diagram of NA0.33 total reflection type EUV projection lithography imaging system, which shows that the full field wave aberration of the imaging system is less than 0.198nm, the standard deviation of the wave aberration at different field points of the full field is 7.823X 10-4, and the uniformity of the full field wave aberration is good; fig. 3(d) is an image space telecentricity diagram of the NA0.33 total reflection type euv projection lithography imaging system, and it can be seen that the image space telecentricity of the imaging system in the total field of view is less than 1.97 mrad.
The structure of the NA1.35 catadioptric extreme ultraviolet projection photoetching imaging system is shown in fig. 4(a), specific structural parameters of each lens are given in table 5, the surface type coefficient of Q-bfs is given in table 6, and the surface type coefficient of Q-con is given in table 7.
TABLE 5 NA1.35 Refraction-reflection type extreme ultraviolet projection photoetching imaging system structure parameters
TABLE 6 NA1.35 Refraction-reflection type extreme ultraviolet projection photoetching imaging system Q-bfs surface type coefficient
| Surface numbering | 2 | 4 | 7 | 10 | 14 |
| Normalized radius | 8.46E+01 | 7.21E+01 | 7.81E+01 | 6.16E+01 | 4.73E+01 |
| |
0 | 0 | 0 | 0 | 0 |
| 4th | -3.34E+00 | 9.78E-04 | 6.37E+00 | -1.60E+00 | -1.07E-02 |
| 6th | -7.95E-02 | -1.12E-03 | 8.76E-01 | 4.29E-01 | -1.50E-04 |
| 8th | -9.87E-03 | -1.90E-03 | 2.15E-01 | 6.85E-03 | 6.61E-05 |
| 10th | 7.53E-03 | -1.33E-03 | -3.31E-02 | 1.47E-03 | 1.09E-04 |
| 12th | -1.10E-03 | 1.76E-04 | -5.78E-03 | 6.35E-04 | -1.05E-04 |
| 14th | 1.93E-03 | -7.07E-04 | 1.22E-03 | 7.54E-04 | 8.18E-06 |
| 16th | -7.32E-04 | 1.95E-04 | -2.04E-05 | 3.12E-04 | 3.95E-05 |
| 18th | 6.47E-04 | -1.68E-04 | -8.18E-04 | -9.77E-05 | 1.50E-05 |
| 20th | -3.33E-04 | 2.28E-05 | 6.10E-04 | 2.18E-05 | 1.63E-06 |
| 22nd | 2.81E-04 | -1.89E-05 | -9.87E-05 | -1.36E-05 | -6.25E-06 |
| 24th | -1.46E-04 | -2.46E-05 | -2.89E-05 | -9.31E-06 | 1.50E-05 |
| 26th | 9.31E-05 | 2.25E-05 | 3.17E-05 | 5.71E-06 | -1.12E-05 |
| 28th | -3.30E-05 | -1.08E-05 | -1.15E-05 | -2.82E-07 | 3.21E-06 |
| 30th | 9.36E-06 | 2.17E-06 | 5.47E-06 | 2.52E-06 | 2.15E-06 |
| Surface numbering | 44 | 47 | 49 | 50 |
| Normalized radius | 1.56E+02 | 1.48E+02 | 8.89E+01 | 5.09E+01 |
| |
0 | 0 | 0 | 0 |
| 4th | -9.96E+00 | 5.09E+00 | -3.85E+00 | -2.50E-02 |
| 6th | 3.66E+00 | -2.28E-01 | -2.27E-02 | -6.42E-03 |
| 8th | 9.82E-01 | -6.12E-01 | 3.70E-02 | 2.89E-03 |
| 10th | 2.92E-02 | -1.32E-01 | 1.66E-02 | -1.43E-03 |
| 12th | 1.44E-02 | 2.83E-03 | 2.66E-04 | 8.11E-04 |
| 14th | 7.03E-03 | 3.22E-03 | 1.33E-03 | 8.82E-05 |
| 16th | -8.57E-03 | 1.29E-03 | 3.63E-04 | -1.09E-04 |
| 18th | -1.67E-03 | 5.83E-04 | 3.73E-04 | 5.57E-05 |
| 20th | -8.76E-04 | 1.01E-03 | 5.60E-05 | -3.04E-05 |
| 22nd | -1.65E-04 | 3.45E-04 | 1.07E-04 | 1.77E-05 |
| 24th | -1.09E-04 | 2.22E-04 | -3.02E-06 | -7.28E-06 |
| 26th | -8.43E-06 | 2.39E-05 | 3.22E-05 | 1.76E-07 |
| 28th | -4.83E-06 | 3.30E-05 | -4.70E-06 | 3.81E-06 |
| 30th | 1.14E-06 | 2.97E-06 | 4.90E-06 | -2.01E-06 |
TABLE 7 NA1.35 Refraction-reflection type extreme ultraviolet projection photoetching imaging system Q-con surface type coefficient
The NA1.35 catadioptric deep ultraviolet projection lithography imaging system has a rectangular working field of image static working field of 26mm multiplied by 5.5mm, and the image distortion of the NA1.35 catadioptric deep ultraviolet projection lithography imaging system is shown in FIG. 4(b), so that the distortion of the main light ray of the imaging system in the whole field of view is less than 0.238 nm; FIG. 4(c) is a wave aberration diagram of NA1.35 catadioptric deep ultraviolet projection lithography imaging system, which shows that the full-field wave aberration of the imaging system is less than 0.570nm, the standard deviation of the wave aberration at different field points of the full field is 8 × 10-5, and the uniformity of the full-field wave aberration is good; FIG. 4(d) is an image space telecentricity diagram of the NA1.35 catadioptric deep ultraviolet projection lithography imaging system, and it can be seen that the image space telecentricity of the imaging system in full field is less than 1.33 mrad;
table 8 shows the performance parameters of refractive, reflective, and catadioptric lithography imaging systems, where the table shows that the full refractive deep ultraviolet projection lithography imaging system with NA0.75 and the full reflective extreme ultraviolet projection lithography imaging system with NA0.33 and the catadioptric deep ultraviolet projection lithography imaging system with NA1.35 have excellent imaging performances such as distortion, wave aberration, full field aberration uniformity, image space telecentricity, magnification, object distance, image distance, and total system length.
TABLE 8 PROPERTIES PARAMETER TABLE FOR REFRACTIVE, REFLECTIVE AND REFLECTIVE LITHOGRAPHIC IMAGING SYSTEMS
In summary, according to the optical imaging system multi-objective automatic optimization design method, the optimization field point can be automatically selected according to the input design index, the optimization weight and the constraint variable are automatically adjusted, comprehensive optimization of various design indexes is realized through mutual influence of various design indexes in the optimization process, dependence of optimization design of the imaging optical system on experience of an optical designer is effectively reduced, and optimization efficiency is improved. The problem that imaging quality at optimized view field points in optical design software is good, but imaging quality between two optimized view field points is poor in optical design is solved, uniformity of full view field imaging quality is improved, good optimized design results can be obtained in a full refraction type imaging optical system, a total reflection type imaging optical system and a refraction and reflection type imaging optical system, and good universality is achieved in design of an imaging relation system.
The present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof, and it will be understood by those skilled in the art that various changes and modifications may be made herein without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (7)
1. A multi-objective automatic optimization method for an optical imaging system is characterized by comprising the following steps:
s1: determining the performance T to be optimized of the initial structure of the imaging system to be optimized according to the design requirementlAnd each property T to be optimizedlCorresponding optimal index AlAnd selecting a field-of-view point F to be optimized from the full field of view of the imaging system to be optimizediForming a set of view points, wherein L is 1,2, …, L, and L is at least 3, I is 1,2, …, I, and I is at least 3;
s2: obtaining each performance T to be optimized under the initial structure of the imaging system to be optimizedlCorresponding index intermediate BlThe method specifically comprises the following steps: respectively judging the performance T of the initial structure to be optimizedlActual performance value oflWhether or not less than the corresponding optimum index AlIf yes, let Bl＝Al(ii) a If not, calculating B according to the following formulal：
Bl＝Cl-kB×(Al-Cl)
Wherein k isBSetting a weight coefficient;
s3: respectively setting each field of view point F to be optimized in the initial field of view point setiAre all marked as all properties T to be optimizedlAnd correlating the view points with the intermediate quantity B of the indexlAs per each and to be optimized performance TlPerformance T to be optimized for the associated field of view pointlIf any field of view point to be optimized is marked as any associated field of view point of the performance to be optimized, the field of view point to be optimized can cause the performance to be optimized to generate fluctuation exceeding a set value;
s4: optimizing the initial structure by using a damped least square method according to constraint conditions in optical design software to obtain a new optical structure and finish the updating of an imaging system;
s5: judging whether the updating times of the imaging system are larger than the set internal circulation times N or whether the performance T to be optimized of the imaging system to be optimized under the current optical structurelActual performance value C oflWhether or not B is reachedlIf no, the process proceeds to step S6, and if one is satisfied, the process proceeds to step S7;
s6: after the constraint conditions adopted currently in the optical design software are updated according to the set rules, the steps S4 to S5 are executed again;
s7: judging whether the updating times of the imaging system are larger than the set external circulation times M or whether the performance T to be optimized of the imaging system to be optimized under the current optical structurelActual performance value C oflWhether or not it reaches AlIf yes, thenAnd executing the step S2 again by adopting the current optical structure of the imaging system to be optimized, then executing the steps S4-S5, and if one of the steps is met, finishing the automatic optimization design of the imaging system.
2. The method for multi-objective automatic optimization of optical imaging system as claimed in claim 1, wherein the actual performance value C in step S3lThe acquisition method comprises the following steps:
respectively evaluating L performances to be optimized T corresponding to each view field point of the full view field of the imaging system to be optimizedlAnd for each performance T to be optimizedlTaking the performance value corresponding to the view field point with the worst performance as the initial structure of the imaging system to be optimized in the performance T to be optimizedlActual performance value ofl。
3. The method for multi-objective automatic optimization of optical imaging system as claimed in claim 2, wherein the step S6 of updating the current field of view point set and the constraint conditions adopted in the optical design software according to the set rules is specifically as follows:
s61: sequentially judging the performance T to be optimized of the imaging system to be optimized under the current optical structure one by onelActual performance value C oflWhether or not B is reachedlUntil the first miss is found BlC of (A)lAnd mixing the ClThe corresponding field of view point is taken as an alternative field of view point F*While simultaneously reacting C with ClCorresponding performance T to be optimizedlIs marked as T*；
S62: judging alternative view point F*Whether the current view point set belongs to, if not, the weight average value of all the view points to be optimized in the current view point set is used as an alternative view point F*And the alternative field of view point F*Adding the current view point set to obtain an updated view point set, marking a selected view point F as an associated view point with performance T to be optimized, and then entering step S63; if so, firstly judging the alternative view point F*Whether or not it has been marked as a performance to be optimized T*In a given context of the correlationIf no, marking F as the associated view point of the performance T to be optimized, and proceeding to step S63, if yes, performing the following operations, and then proceeding to step S63:
the weights are updated as follows:
wherein, W (Fi)nextUpdating the updated weight value k of the ith field point to be optimized in the current field point set1、k2、ShAnd SlAre all set convergence rate factors, W (Fi)nowUpdating a weight value before the ith field point to be optimized in the current field point set, wherein omega (F) is a set threshold value of comprehensive aberration, and omega' (Fi) is an aberration comprehensive evaluation index of each field point to be optimized in the current field point set;
for each field point to be optimized in the updated field point set, if the weight value of the field point to be optimized is smaller than the weight threshold value delta, and the field point to be optimized does not belong to a field boundary point or is a field point which appears for multiple times, deleting the field point to be optimized, otherwise, keeping the field point to be optimized, obtaining an updated field point set, and then entering step S63;
s63: judging whether the number of the field points to be optimized in the updated field point set is larger than the set maximum number H of the field points, if not, entering step S64, and if so, entering S65;
s64: executing the updating constraint operation, and then re-executing the steps S4-S5; wherein the update constraint operation is: if an operation of deleting a field point to be optimized is performed, deleting all constraints related to the deleted field point to be optimized in the constraint conditions of step S4, and if an operation of adding a field point to be optimized in association with optimization performance is performed, adding corresponding constraints related to the field point to be optimized in the performance to be optimized in association with the field point to be optimized in the constraint conditions of step S4;
s65: and keeping the field points to be optimized which belong to the field boundary points or appear for multiple times in the current field point set to obtain a final optimized field point set, executing updating constraint operation based on the final optimized field point set, and then executing the steps S4-S5 again.
4. The multi-objective automatic optimization method of the optical imaging system according to claim 1, wherein the calculation formula of the integrated evaluation index ω' (Fi) of the aberration of each field-of-view point to be optimized in the field-of-view point set is as follows:
wherein, α l (Fi), β l (Fi) and γ l (Fi) represent the ith field point F to be optimized in the current field point setiAt the time of optimizing the performance TlThe corresponding weight coefficients Cl (Fi) and Bl (Fi) respectively represent the ith field point F to be optimized in the field point setiTo be optimized performance TlActual performance value and intermediate index values.
5. The method of claim 1, wherein the calculated weight W (Fi)nextAfter normalization is carried out according to the following formula, the normalized weight is compared with a weight threshold value delta, wherein the normalization formula is as follows:
wherein, W (F)next-maxAnd updating the maximum value of the updated weight values of the field points to be optimized.
6. The method for multi-objective automatic optimization of optical imaging system according to any one of claims 1 to 5, wherein the imaging system to be optimized is a total refraction type imaging system, a total reflection type imaging system or a refraction and reflection type imaging system.
7. The method as claimed in any one of claims 1 to 5, wherein the performance to be optimized includes focal length, object distance, image distance, magnification, entrance pupil position, entrance pupil distance, total system length, maximum optical lens pass aperture, spherical aberration, coma aberration, astigmatism, field curvature, distortion, sinusoidal aberration, wave aberration, telecentricity, polarization aberration, aberration uniformity and/or imaging quality.
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