CN114547855B - 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
本发明提供一种光学成像系统多目标自动优化方法，采用指标中间量Bl渐进式的逼近各待优化性能Tl对应的最优指标Al，使得本发明在进行多性能优化的时候，可以避免优化过程陷入某些待优化性能的最优指标已经实现，但是其余某些待优化性能的最优指标无法实现的局部最优解的过程，也即渐进式的逼近，可以确保所有待优化性能对应的最优指标均能实现；同时，本发明根据每轮迭代优化设计后的结果，自动更新每一轮待优化视场点位置与光学设计软件中采用的约束条件，通过各项待优化性能的最优指标在优化过程中的相互影响，实现了多种成像系统性能的综合优化，有效的提升了成像系统的成像质量。
The present invention provides a multi-objective automatic optimization method for an optical imaging system, which uses an intermediate indicator B l to gradually approximate the optimal indicator A l corresponding to each performance T l to be optimized, so that when the present invention performs multi-performance optimization, it can avoid the optimization process from falling into a process of local optimal solution in which the optimal indicators of some performances to be optimized have been achieved, but the optimal indicators of other performances to be optimized cannot be achieved, that is, the gradual approximation can ensure that the optimal indicators corresponding to all performances to be optimized can be achieved; at the same time, the present 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 software according to the result after each round of iterative optimization design, and realizes the comprehensive optimization of multiple imaging system performances through the mutual influence of the optimal indicators of various performances to be optimized in the optimization process, and effectively improves the imaging quality of the imaging system.
Description
Technical Field
The invention belongs to the technical field of optical design, and particularly relates to a multi-objective automatic optimization method of an optical imaging system.
Background
Any optical system is used wherever, and the effect is to change the propagation direction and position of the light emitted by the target according to the requirement of the working principle of the instrument, and send the light into the receiver of the instrument, so as to obtain various information of the target, including the geometry of the target, the intensity of energy and the like. Thus, there are two aspects to the requirements for imaging performance of an optical system: the first aspect is optical characteristics including focal length, object distance, image distance, magnification, entrance pupil position, entrance pupil distance, and the like; the second aspect is the imaging quality, the imaging by the optical system should be sufficiently clear, and the object image is similar with little distortion. The content of the first aspect, namely meeting the requirements in terms of optical performance, belongs to the field of discussion of application optics; the second aspect, i.e. meeting the requirements in terms of imaging quality, is then part of the study of the optical design.
The optical design work includes: structural form selection, initial structure determination, aberration correction, image quality evaluation, optical tolerance establishment and the like. The aberration correction is the most important step, and the workload is large, the artistry is strong. Aberration correction is generally a progressive process, especially for some demanding, complex systems. The physical law of light propagation in an optical system, namely the law of refraction and reflection, is nonlinear, so that aberration generally exists in the optical system, the relation between the aberration and structural parameters is a complex nonlinear problem, so that the imaging quality of an objective lens is guided to a better state from a poorer state in the initial structure through adjusting part or all of the structural parameters step by step, and a 'zigzag' but feasible route is actually found in a solution space of the problem, so that a lens gradually moves from a position with poor image quality to a position with better image quality, and the lens structure is reasonable and can be manufactured. This process is a complex and extremely dependent on the experience of the designer, and after the electronic computer appears, it is introduced into the calculation of the aberration, greatly improving the calculation speed of the aberration; modification of system configuration parameters is still determined by the optical designer. With the increase of computer speed, the time required for calculating aberrations is smaller and smaller, and analyzing the current design result and deciding how to modify parameters in the next step becomes a major problem for optical designers, so that automatic design of optical systems occurs, that is, the computer automatically changes the radius of curvature, spacing or thickness of the system, and even the refractive index of the optical material according to a certain program.
In the automatic optimization design, first, an "evaluation function" is constructed that characterizes the relationship between various aberration performance indicators and structural parameters. When the system tends to be extremely small, the system represents that the aberration and performance index approach target values, and each time the structural parameter is changed in the process of automatic design is called 'iteration'; after each iteration, the evaluation function tends towards a minimum, mathematically called "convergence", and away from the minimum called "divergence". Therefore, the designer should notice at any time that when the divergence or convergence speed is slow, a manual intervention must be performed to change the damping factor of some factors or arguments in the evaluation function to increase the convergence speed. If not, it is determined whether the selected form has a possibility of effective correction, whether it is necessary to exchange an optical material or change the form, or the like.
The automatic design work of optical systems has been 60 years old, the university of harvard bekker (j.g. baker) in 1950 began to organize an optical automatic design research group, and the developed-technology countries developed this work successively, and many methods, such as a change-by-change Method (change Method), a steepest descent Method (STEEPEST DESCENT Method), an optimal gradient Method (Optimum Gradient Method) and a least square Method (Least Square Method), have not achieved ideal effects; damping least Square method (DAMPED LEAST Square, DLS) was published by Imperial institute of technology Wen En (G.G.Wynne) at university of London in 1950, which greatly increases the convergence rate of the evaluation function and makes the automatic optimization technology one of the more popular methods of application.
In the final stage of lens optimization, cheng Dewen in 2010 proposes an automatic optimization method that automatically adjusts and determines appropriate sampling field of view and azimuth weights. On the basis of local optimization, the method automatically adjusts the weight on the outer ring, and automatically and effectively balances the imaging performance of the sampling view field point; but the selection of sampling field points in the optical design still depends on the experience of an optical designer, and the problems that the imaging quality of the sampling field points is good in the optical design process, but the imaging quality of the rest field points is poor easily occur.
Disclosure of Invention
In order to solve the problems, the invention provides a multi-objective automatic optimization method of an optical imaging system, which can realize comprehensive optimization of various imaging system performances and effectively improve the imaging quality of the imaging system.
An automatic multi-objective optimization method for an optical imaging system, comprising the following steps:
S1: determining the performance T l to be optimized of an initial structure of the imaging system to be optimized and the optimal index A l corresponding to each performance T l to be optimized according to design requirements, and selecting a field point F i to be optimized from the full field of view of the imaging system to be optimized to form a field point set, wherein l=1, 2, …, L is at least 3,i =1, 2, …, I, and I is at least 3;
S2: under the initial structure of the imaging system to be optimized, acquiring index intermediate quantity B l corresponding to each performance T l to be optimized, wherein the index intermediate quantity B l specifically comprises: respectively judging whether the actual performance value C l of the initial structure under each performance T l to be optimized is smaller than the corresponding optimal index A l, and if so, letting B l＝Al; if not, B l is calculated according to the following formula:
Bl＝Cl-kB×(Al-Cl)
Wherein k B is a set weight coefficient;
S3: marking each field point F i to be optimized in the initial field point set as an associated field point of all the properties T l to be optimized, and taking the index intermediate quantity B l as a constraint condition of the properties T l to be optimized of each associated field point associated with the properties T l to be optimized, wherein if any field point to be optimized is marked as an associated field point of any property to be optimized, the fact that the field point to be optimized can cause the property to be optimized to generate fluctuation exceeding a set value is indicated;
s4: optimizing the initial structure by using a damping least square method according to constraint conditions in optical design software to obtain a new optical structure, and finishing 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 actual performance values C l of the to-be-optimized performances T l of the imaging system to be optimized under the current optical structure reach B l, if not, entering a step S6, and if one of the updating times is satisfied, entering a step S7;
s6: updating the constraint conditions currently adopted in the optical design software according to the set rules, and re-executing the steps S4 to S5;
S7: judging whether the updating times of the imaging system are larger than the set outer circulation times M or whether the actual performance value C l of each performance T l to be optimized of the imaging system to be optimized under the current optical structure reaches A l, if not, executing the step S2 again by adopting the current optical structure of the imaging system to be optimized, executing the step S4 to the step S5 again, and if one of the steps is met, completing the automatic optimization design of the imaging system.
Further, the method for obtaining the actual performance value C l in step S3 is as follows:
And respectively evaluating the performance values of L to-be-optimized performances T l corresponding to each field point of the full field of the imaging system to be optimized, and taking the performance value corresponding to the field point with the worst performance as an actual performance value C l of the initial structure of the imaging system to be optimized under the to-be-optimized performance T l for each to-be-optimized performance T l.
Further, the updating of the current field point set according to the set rule and the constraint condition adopted in the optical design software in step S6 specifically includes:
S61: judging whether the actual performance value C l of each performance T l to be optimized of the imaging system to be optimized under the current optical structure reaches B l or not one by one in sequence until the first C l which does not reach B l is found, taking the view field point corresponding to the C l as an alternative view field point F *, and simultaneously marking the performance T l to be optimized corresponding to the C l as T *;
S62: judging whether the alternative view field point F * belongs to the current view field point set, if not, taking the weight average value of all view field points to be optimized in the current view field point set as the weight of the alternative view field point F *, adding the alternative view field point F * into the current view field point set to obtain an updated view field point set, marking the selected view field point F as an associated view field point with the performance T to be optimized, and then entering step S63; if so, firstly judging whether the alternative view field point F * is marked as the associated view field point of the performance to be optimized T *, if not, marking F as the associated view field point of the performance to be optimized T, and entering the step S63, if so, executing the following operations, and then entering the step S63:
the weights are updated according to the following formula:
wherein, W (Fi) next is the weight value after the i-th view field point to be optimized in the current view field point set is updated, k 1、k2、Sh and S l are both set convergence speed factors, W (Fi) now is the weight value before the i-th view field point to be optimized in the current view field point set is updated, ω (F) is the set threshold value of the comprehensive aberration, ω' (Fi) is the comprehensive evaluation index of the aberration of each view field point to be optimized in the current view field point set;
for each view field point to be optimized in the updated view field point set, if the weight value is smaller than the weight threshold delta, and meanwhile, the view field point to be optimized does not belong to the view field boundary point or is a view field point which appears for many times, deleting the view field point to be optimized, otherwise, reserving the view field point to be optimized, obtaining an updated view field point set, and then entering step S63;
S63: judging whether the number of field points to be optimized in the updated field point set is larger than the set maximum number H of field points, if not, entering step S64, and if so, entering step S65;
S64: executing update constraint operation, and then re-executing the steps S4-S5; wherein, the update constraint operation is: if the operation of deleting the to-be-optimized view field point is performed, deleting all constraints related to the deleted to-be-optimized view field point in the constraint condition of the step S4, and if the operation of increasing the to-be-optimized view field point to be associated with the optimization performance is performed, increasing the corresponding constraint related to the to-be-optimized view field point in the to-be-optimized performance associated with the to-be-optimized view field point in the constraint condition of the step S4;
s65: and reserving field points to be optimized, which belong to field boundary points or appear for many times, in the current field point set to obtain a final optimized field point set, executing update constraint operation based on the final optimized field point set, and then re-executing the steps S4-S5.
Further, the calculation formula of the aberration comprehensive evaluation index ω' (Fi) of each field point to be optimized in the field point set is as follows:
wherein, αl (Fi), βl (Fi) and γl (Fi) represent weight coefficients corresponding to the i-th field point to be optimized F i in the current field point set at the performance to be optimized T l, and Cl (Fi) and Bl (Fi) represent actual performance values and index intermediate quantities of the performance to be optimized T l of the i-th field point to be optimized F i in the field point set respectively.
Further, after normalizing the calculated weight W (Fi) next according to the following formula, comparing the normalized weight with the weight threshold Δ, where the normalized formula is:
Wherein W (F) next-max is the maximum value in the updated weight of each view field point to be optimized.
Further, the imaging system to be optimized is a total refraction imaging system, a total reflection imaging system or a refraction-reflection imaging system.
Further, the performance to be optimized includes focal length, object distance, image distance, magnification, entrance pupil position, entrance pupil distance, total system length, maximum passing aperture of optical lens, spherical aberration, coma, astigmatism, field curvature, distortion, sinusoidal difference, wave aberration, telecentricity, polarization aberration, aberration uniformity, and/or imaging quality.
The beneficial effects are that:
1. The invention provides a multi-target automatic optimization method of an optical imaging system, which adopts index intermediate quantity B l to gradually approach an optimal index A l corresponding to each performance to be optimized T l, so that the optimization process can be prevented from being involved in the process of optimizing the multi-performance, but the rest of optimal indexes of the performance to be optimized can not be realized in the process of locally optimizing solutions, namely the gradual approximation can ensure that all the optimal indexes corresponding to the performance to be optimized can be realized; meanwhile, according to the result of each round of iterative optimization design, the constraint conditions adopted in the position of the field point to be optimized and the optical design software of each round are automatically updated, so that the problems that the imaging quality at the optimized field point is good but the imaging quality between two optimized field points is poor are avoided, meanwhile, the comprehensive optimization of the performances of various imaging systems is realized through the mutual influence of the optimal indexes of each item of performance to be optimized in the optimization process, and the imaging quality of the imaging system is effectively improved.
2. The invention provides a multi-objective automatic optimization method of an optical imaging system, which can automatically select an optimized view field point according to input design indexes, automatically adjust optimization weights and constraint variables, realize the comprehensive optimization of various design indexes through the 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 problem that the imaging quality at the optimized view field point in the optical design software is good, but the imaging quality between two optimized view field points is poor, 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 all performances to be optimized are optimized in a coordinated manner, all design indexes of the performances to be optimized are mutually influenced in the optimization process, comprehensive optimization of various performance indexes is realized, and the imaging quality of the system is effectively improved.
4. The multi-objective automatic optimization method of the optical imaging system has strong universality in the optimization design process of the imaging system, and can obtain good optimization design results in all aspects.
Drawings
FIG. 1 is a flow chart of a method of multi-objective automatic optimization of an optical imaging system;
FIG. 2 (a) is a block diagram of a NA0.75 total refractive deep ultraviolet projection lithography imaging system;
FIG. 2 (b) is a distortion chart of a NA0.75 full refractive deep ultraviolet projection lithography imaging system;
FIG. 2 (c) is a wave aberration diagram of a NA0.75 total refractive deep ultraviolet projection lithography imaging system;
FIG. 2 (d) is an image side telecentricity diagram of an NA0.75 full refractive deep ultraviolet projection lithography imaging system;
FIG. 3 (a) is a block diagram of an NA0.33 total reflection EUV projection lithography imaging system;
FIG. 3 (b) is a distortion chart of a NA0.33 total reflection EUV projection lithography imaging system;
FIG. 3 (c) is a wave aberration diagram of a NA0.33 total reflection EUV projection lithography imaging system;
FIG. 3 (d) is an image side telecentricity diagram of a NA0.33 total reflection EUV projection lithography imaging system;
FIG. 4 (a) is a block diagram of a NA1.35 catadioptric deep ultraviolet projection lithography imaging system;
FIG. 4 (b) is a distortion chart of a NA1.35 catadioptric deep ultraviolet projection lithography imaging system;
FIG. 4 (c) is a wave aberration diagram of a NA1.35 catadioptric deep ultraviolet projection lithography imaging system;
fig. 4 (d) is an image-side telecentricity diagram of a NA1.35 catadioptric deep ultraviolet projection lithography imaging system.
Detailed Description
In order to enable those skilled in the art to better understand the present application, the following description will make clear and complete descriptions of the technical solutions according to the embodiments of the present application with reference to the accompanying drawings.
In order to more efficiently solve the selection problem of the optimized view field points, the invention provides a multi-target automatic optimization design method of an optical imaging system, which automatically selects the position of each round of optimized sampling view field point according to the result of each round of optimized design, and simultaneously adaptively sets optimization weights and constraint conditions for different sampling view field points, and realizes the comprehensive optimization of various design indexes through the mutual influence among various design indexes in the optimization process, thereby effectively improving the imaging quality of the system. As shown in fig. 1, a multi-objective automatic optimization method of an optical imaging system includes the following steps:
S1: and determining the performance T l to be optimized of the initial structure of the imaging system to be optimized and the optimal index A l corresponding to each performance T l to be optimized according to design requirements, and selecting a field point F i to be optimized from the full field of view of the imaging system to be optimized to form a field point set, wherein l=1, 2, …, L is at least 3,i =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 focal length, object distance, image distance magnification, entrance pupil position, entrance pupil distance, and the like; the second aspect is imaging quality, the imaging of the optical system should be clear enough, and the object images are similar, the deformation size, etc.; meanwhile, the optimal index corresponding to each performance to be optimized can be determined according to actual requirements.
S2: under the initial structure of the imaging system to be optimized, acquiring index intermediate quantity B l corresponding to each performance T l to be optimized, wherein the method specifically comprises the following steps:
S31: respectively evaluating the performance values of L to-be-optimized performances T l corresponding to each field point of a full field of the imaging system to be optimized, and regarding the performance value corresponding to the field point with the worst performance as an actual performance value C l of an initial structure of the imaging system to be optimized under the to-be-optimized performance T l for each to-be-optimized performance T l;
S32: respectively judging whether the actual performance value C l of the initial structure of the imaging system to be optimized under each performance T l to be optimized is smaller than the corresponding optimal index A l, and if so, letting B l＝Al; if not, B l is calculated according to the following formula:
Bl＝Cl-kB×(Al-Cl)
Wherein k B is a set weight coefficient for calculating B l;
S3: each field point F i to be optimized in the initial field point set is marked as an associated field point of all the performances T l to be optimized, and the index intermediate quantity B l is used as a constraint condition of the performances T l to be optimized of each associated field point associated with the performances T l to be optimized, wherein if any field point to be optimized is marked as an associated field point of any performances to be optimized, the fact that the field point to be optimized can cause the performances to be optimized to generate fluctuation exceeding a set value is indicated.
That is, if a certain view field point to be optimized is marked as an associated view field point of a certain performance to be optimized, the effect of the view field point to be optimized on the performance to be optimized is greatly indicated, and meanwhile, when the method and the device are initially set, the effect of each view field point to be optimized in the initial view field point set on the performance to be optimized is greatly considered, so that a full-association mark is formed.
For example, assuming that the current field point set includes three field points F1, F2, and F3 to be optimized, the performance to be optimized of the current imaging system is T1, T2, and T3, and the association relationship between the field points to be optimized and the performance to be optimized is expressed as follows:
correlation table of field point to be optimized and performance to be optimized
| T1 | T2 | T3 | |
| F1 | 1 | 0 | 1 |
| F2 | 1 | 0 | 0 |
| F3 | 0 | 1 | 0 |
In the table, 1 represents that the field point to be optimized and the performance to be optimized are related to each other, 0 represents that the field point to be optimized and the performance to be optimized are not related to each other, for example, the performance to be optimized T1, only the field points to be optimized F1 and F2 are related to each other, that is, in the whole field of view of the imaging system, the field points to be optimized F1 and F2 have a larger influence on the performance to be optimized T1 of the whole imaging system, and when the initial structure is optimized in the optical design software by using the damping least square method, the optimization of the field points to be optimized F1 and F2 about the performance to be optimized T1 adopts the index intermediate quantity B1 as a constraint condition, and only the actual performance value of the performance to be optimized T1 at the field points to be optimized F1 and F2 needs to be controlled, so that the optimization performance T1 of the whole imaging system can be well controlled.
S4: and optimizing the initial structure of the imaging system by using a damping least square method according to constraint conditions in optical design software to obtain a new optical structure of the imaging system, and finishing 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 damping least square method only by determining the constraint condition, and the specific process of the optimization of the invention is not repeated.
S5: judging whether the updating times of the imaging system are larger than the set internal circulation times N or whether the actual performance values C l of the to-be-optimized performances T l of the imaging system to be optimized under the current optical structure reach B l, if not, entering a step S6, and if one of the updating times is satisfied, entering a step S7;
s6: after updating the current view field point set and the constraint conditions adopted in the optical design software according to the set rule, the steps S4 to S5 are re-executed, and the updating process specifically comprises the following steps:
S61: judging whether the actual performance value C l of each performance T l to be optimized of the imaging system to be optimized under the current optical structure reaches B l one by one in sequence until the first C l which does not reach B l is found, taking the view field point corresponding to the C l as an alternative view field point F *, and simultaneously marking the performance T l to be optimized corresponding to the C l as T *;
S62: judging whether the alternative view field point F * belongs to the current view field point set, if not, taking the weight average value of all view field points to be optimized in the current view field point set as the weight of the alternative view field point F *, adding the alternative view field point F * into the current view field point set to obtain an updated view field point set, marking the selected view field point F as an associated view field point with the performance T to be optimized, and then entering step S63; if so, firstly judging whether the alternative view field point F * is marked as the associated view field point of the performance to be optimized T *, if not, marking F as the associated view field point of the performance to be optimized T, and entering the step S63, if so, executing the following operations, and then entering the step S63:
the weights are updated according to the following formula:
Wherein, k 1、k2、Sh and S l are both set convergence rate factors, W (Fi) next is a weight value after the i-th field point to be optimized is updated in the current field point set, W (Fi) now is a weight value before the i-th field point to be optimized is updated in the current field point set, ω (F) is a set threshold value of comprehensive aberration, ω' (Fi) is an aberration comprehensive evaluation index of each field point to be optimized in the current field point set, and a calculation formula is as follows:
Wherein, alpha l (Fi), beta l (Fi) and gamma l (Fi) represent the corresponding weight coefficients of the ith view field point F i to be optimized in the current view field point set at the position of the performance T l to be optimized, and Cl (Fi) and Bl (Fi) represent the actual performance value and index intermediate quantity of the performance T l to be optimized of the ith view field point F i to be optimized in the view field point set respectively;
Normalizing the calculated weight W (Fi) next, wherein the normalized formula is as follows:
Wherein W (F) next-max is the maximum value in the updated weight of each view field point to be optimized.
For each view field point to be optimized in the updated view field point set, if the normalized weight value is smaller than the weight threshold delta, and meanwhile, the view field point to be optimized does not belong to the view field boundary point or is a view field point which appears for more than three times, if the view field point to be optimized appears for more than three times, deleting the view field point to be optimized, otherwise, reserving the view field point to be optimized to obtain an updated view field point set, and then entering step S63;
S63: judging whether the number of field points to be optimized in the updated field point set is larger than the set maximum number H of field points, if not, entering step S64, and if so, entering step S65;
S64: replacing the field points to be optimized and the weights thereof in the field point set before updating with the field points to be optimized and the weights 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 the operation of deleting the to-be-optimized view field point is performed, deleting all constraints related to the deleted to-be-optimized view field point in the constraint condition of the step S4, and if the operation of increasing the to-be-optimized view field point to be associated with the optimization performance is performed, increasing the corresponding constraint related to the to-be-optimized view field point in the to-be-optimized performance associated with the to-be-optimized view field point in the constraint condition of the step S4;
s65: and reserving field points to be optimized, which belong to field boundary points or appear for many times, in the current field point set to obtain a final optimized field point set, and then executing update constraint operation based on the final optimized field point set, and then executing steps S4-S5 again.
S7: judging whether the updating times of the imaging system are larger than the set outer circulation times M or whether the actual performance value C l of each performance T l to be optimized of the imaging system to be optimized under the current optical structure reaches A l, if not, executing the step S2 again by adopting the current optical structure of the imaging system to be optimized, executing the step S4-S5 again, and if one of the steps is met, completing the automatic optimization design of the imaging system, and storing the existing optimization design result as a final optimization design result.
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 and more uniform image quality in a large view field, and is one of the most precise optical systems, so the invention selects three sets of photoetching objective lens systems, and performs automatic optimization design on imaging performance, including distortion, wave aberration, full-view field wave aberration uniformity, image space telecentricity, multiplying power, object distance, image distance and total system length, and verifies the universality of the invention.
The definition principle of positive and negative signs of the structural parameters of the optical system given by the embodiment of the invention is as follows:
The positive and negative sign definition principle of the curvature radius is 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 in the same direction as the direction of the light path, and vice versa;
the positive and negative sign of the interval is defined as: if the direction from the intersection point of the current surface and the reference axis to the intersection point of the latter surface and the reference axis is positive in the same direction as the direction of the light path, otherwise, is negative;
Wherein, the definition of XYZ coordinate system is: the Z axis is parallel to the reference axis and is in the same direction as the direction of the light path, the Y axis is perpendicular to the Z axis, and the X axis is perpendicular 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 gives structural parameters of Q-bfs surface type according to the Q-bfs coefficient given principle, and the Q-bfs surface type formula is as follows:
Wherein r 2＝x2+y2; u is the normalized radial coordinate; z is the sagittal height of the Q-bfs free-form surface parallel to the z-axis; c is Q-bfs free-form surface vertex curvature; k is a conical constant, and ρ max is the maximum light transmission radius of the curved surface; b i is the coefficient corresponding to the Q-bfs polynomial.
The Q-con free curved surface used in the embodiment of the invention gives the structural parameter 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 2＝x2+y2; u is the normalized radial coordinate; z is the sagittal height of the Q-type freeform surface parallel to the z-axis; c is the curvature of the vertex of the Q-type free-form surface; k is a conic constant; a i is the coefficient corresponding to the Q-con polynomial.
The structure of the NA0.75 full-refraction type deep ultraviolet projection lithography imaging system is shown in fig. 2 (a), specific structural parameters of each lens are given in table 1, and the Q-bfs face type coefficients are given in table 2.
TABLE 1 NA0.75 Total refractive deep ultraviolet projection lithography imaging System structural parameters
Surface coefficient of Q-bfs type deep ultraviolet projection lithography imaging system with full refraction type surface coefficient of Table 2NA0.75
The distortion diagram of the NA0.75 full-refraction type deep ultraviolet projection lithography imaging system is shown in FIG. 2 (b), wherein the image static working field of the imaging system is a rectangular working field of view of 26mm multiplied by 10.5mm, and the distortion diagram of the NA0.75 full-refraction type deep ultraviolet projection lithography imaging system can be seen that the distortion of the full-field chief ray of the imaging system is less than 0.316nm; FIG. 2 (c) is a wave aberration diagram of an NA0.75 full refraction type deep ultraviolet projection lithography imaging system, and it can be seen that the wave aberration of the full field of view of the imaging system is less than 0.235nm, the standard deviation of the wave aberration of different field points of the full field of view is 5×10 -5, and the uniformity of the wave aberration of the full field of view is good; fig. 2 (d) is an image-side telecentricity diagram of an NA0.75 total refraction type deep ultraviolet projection lithography imaging system, and it can be seen that the image-side telecentricity of the imaging system is less than 1mrad.
NA0.33 total reflection type extreme ultraviolet projection lithography imaging system structure is shown in FIG. 3 (a), specific structural parameters of each lens are given in Table 3, and Q-con surface type coefficients are given in Table 4:
Table 3NA0.33 total reflection type extreme ultraviolet projection lithography imaging system structural parameter
| Surface of the body | Surface type | Radius/mm | Distance/mm | Form of refraction and reflection |
| Object plane | 0.00000 | 688.08944 | ||
| 1 | Q-bfs | -6078.54080 | -538.03308 | Reflection of |
| 2 | Q-bfs | 1144.55074 | 738.07763 | Reflection of |
| 3 | Q-bfs | 291.60624 | -161.40134 | Reflection of |
| 4 | Q-bfs | 416.47319 | 711.30120 | Reflection of |
| 5 | Q-bfs | 374.21899 | -293.40192 | Reflection of |
| 6 | Q-bfs | 374.62071 | 337.40192 | Reflection of |
| Image plane | 0.00000 | 0.00000 |
TABLE 4 NA0.33 Total reflection extreme ultraviolet projection lithography imaging System Q-bfs plane coefficients
The distortion of the total view field chief ray of the imaging system can be seen to be less than 0.224nm by using an arc-shaped working view field with an image static working view field of 26mm multiplied by 2mm of an NA0.33 total refraction type deep ultraviolet projection photoetching imaging system and a distortion chart of the NA0.33 total reflection type extreme ultraviolet projection photoetching imaging system shown in the figure 3 (b); FIG. 3 (c) is a wave aberration diagram of an NA0.33 total reflection type extreme ultraviolet projection lithography imaging system, and can be seen that the wave aberration of the full field of view of the imaging system is smaller than 0.198nm, the standard deviation of the wave aberration of different field points of the full field of view is 7.823X10-4, and the uniformity of the wave aberration of the full field of view is good; fig. 3 (d) is an image side telecentricity diagram of an NA0.33 total reflection euv projection lithography imaging system, which can be seen to have a total field of view image side telecentricity of less than 1.97mrad.
NA1.35 catadioptric extreme ultraviolet projection lithography imaging system structure is shown in FIG. 4 (a), the specific structural parameters of each lens are given in Table 5, the Q-bfs face type coefficients are given in Table 6, and the Q-con face type coefficients are given in Table 7.
TABLE 5 NA1.35 catadioptric extreme ultraviolet projection lithography imaging system structural parameters
TABLE 6Q-bfs face coefficients for NA1.35 catadioptric extreme ultraviolet projection lithography imaging system
TABLE 7 NA1.35 refraction and reflection type extreme ultraviolet projection lithography imaging system Q-con surface coefficient
The aberration of the total view field chief ray of the imaging system can be seen to be less than 0.238nm as shown in the figure 4 (b) which is a distortion chart of the NA1.35 catadioptric deep ultraviolet projection lithography imaging system, wherein the image static working view field of the NA1.35 catadioptric deep ultraviolet projection lithography imaging system is a rectangular working view field of 26mm multiplied by 5.5 mm; FIG. 4 (c) is a wave aberration diagram of an NA1.35 catadioptric deep ultraviolet projection lithography imaging system, and it can be seen that the wave aberration of the full field of view of the imaging system is less than 0.570nm, the standard deviation of the wave aberrations of different field points of the full field of view is 8×10-5, and the uniformity of the wave aberration of the full field of view is good; FIG. 4 (d) is an image side telecentricity diagram of an NA1.35 catadioptric deep ultraviolet projection lithography imaging system, which can be seen to have a full field image side telecentricity of less than 1.33mrad;
Table 8 shows the performance parameters of three sets of refraction, reflection and refraction imaging systems, and can show that the total refraction type deep ultraviolet projection imaging system with NA of 0.75, the total reflection type extreme ultraviolet projection imaging system with NA of 0.33, the total reflection type deep ultraviolet projection imaging system with NA of 1.35, and the imaging performance such as distortion, wave aberration, uniformity of aberration of the total field of view, telecentricity of image space, multiplying power, object distance, image distance, total length of system and the like are excellent.
Table 8 table of performance parameters for refractive, reflective and catadioptric lithography imaging systems
In summary, according to the multi-objective automatic optimization design method for the optical imaging system, the optimal view field point can be automatically selected according to the input design indexes, the optimization weight and the constraint variable can be automatically adjusted, the comprehensive optimization of various design indexes is realized through the mutual influence of various design indexes in the optimization process, the dependence of the optimal design of the imaging optical system on the experience of an optical designer is effectively reduced, and the optimization efficiency is improved. The imaging quality of 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, the uniformity of the imaging quality of the full view field is improved, the full-refraction imaging optical system, the full-reflection imaging optical system and the refraction-reflection optical imaging system can obtain good optimal design results, and the imaging system has good universality in the design of an imaging relation system.
Of course, the present invention is capable of other various embodiments and its several details are capable of modification and variation in light of the present invention by one skilled in the art without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (4)
1. An automatic multi-objective optimization method for an optical imaging system is characterized by comprising the following steps:
S1: determining the performance T l to be optimized of an initial structure of the imaging system to be optimized and the optimal index A l corresponding to each performance T l to be optimized according to design requirements, and selecting a field point F i to be optimized from the full field of view of the imaging system to be optimized to form a field point set, wherein l=1, 2, …, L is at least 3,i =1, 2, …, I, and I is at least 3;
S2: under the initial structure of the imaging system to be optimized, acquiring index intermediate quantity B l corresponding to each performance T l to be optimized, wherein the index intermediate quantity B l specifically comprises: respectively judging whether the actual performance value C l of the initial structure under each performance T l to be optimized is smaller than the corresponding optimal index A l, and if so, letting B l＝Al; if not, B l is calculated according to the following formula:
Bl＝Cl-kB×(Al-Cl)
Wherein k B is a set weight coefficient;
S3: marking each field point F i to be optimized in the initial field point set as an associated field point of all the properties T l to be optimized, and taking the index intermediate quantity B l as a constraint condition of the properties T l to be optimized of each associated field point associated with the properties T l to be optimized, wherein if any field point to be optimized is marked as an associated field point of any property to be optimized, the fact that the field point to be optimized can cause the property to be optimized to generate fluctuation exceeding a set value is indicated;
s4: optimizing the initial structure by using a damping least square method according to constraint conditions in optical design software to obtain a new optical structure, and finishing 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 actual performance values C l of the to-be-optimized performances T l of the imaging system to be optimized under the current optical structure reach B l, if not, entering a step S6, and if one of the updating times is satisfied, entering a step S7;
s6: updating the constraint conditions currently adopted in the optical design software according to the set rules, and re-executing the steps S4 to S5;
S7: judging whether the updating times of the imaging system are larger than the set outer circulation times M or whether the actual performance value C l of each performance T l to be optimized of the imaging system to be optimized under the current optical structure reaches A l, if not, executing the step S2 again by adopting the current optical structure of the imaging system to be optimized, executing the step S4 to the step S5 again, and if one of the steps is met, completing the automatic optimization design of the imaging system;
the method for obtaining the actual performance value C l in the step S3 is as follows:
Respectively evaluating the performance values of L to-be-optimized performances T l corresponding to each field point of a full field of the imaging system to be optimized, and regarding the performance value corresponding to the field point with the worst performance as an actual performance value C l of an initial structure of the imaging system to be optimized under the to-be-optimized performance T l for each to-be-optimized performance T l;
The updating of the current view field point set and the constraint condition adopted in the optical design software according to the set rule in the step S6 specifically includes:
S61: judging whether the actual performance value C l of each performance T l to be optimized of the imaging system to be optimized under the current optical structure reaches B l or not one by one in sequence until the first C l which does not reach B l is found, taking the view field point corresponding to the C l as an alternative view field point F *, and simultaneously marking the performance T l to be optimized corresponding to the C l as T *;
S62: judging whether the alternative view field point F * belongs to the current view field point set, if not, taking the weight average value of all view field points to be optimized in the current view field point set as the weight of the alternative view field point F *, adding the alternative view field point F * into the current view field point set to obtain an updated view field point set, marking the selected view field point F as an associated view field point with the performance T to be optimized, and then entering step S63; if so, firstly judging whether the alternative view field point F * is marked as the associated view field point of the performance to be optimized T *, if not, marking F as the associated view field point of the performance to be optimized T, and entering the step S63, if so, executing the following operations, and then entering the step S63:
the weights are updated according to the following formula:
wherein, W (Fi) next is the weight value after the i-th view field point to be optimized in the current view field point set is updated, k 1、k2、Sh and S l are both set convergence speed factors, W (Fi) now is the weight value before the i-th view field point to be optimized in the current view field point set is updated, ω (F) is the set threshold value of the comprehensive aberration, ω' (Fi) is the comprehensive evaluation index of the aberration of each view field point to be optimized in the current view field point set;
for each view field point to be optimized in the updated view field point set, if the weight value is smaller than the weight threshold delta, and meanwhile, the view field point to be optimized does not belong to the view field boundary point or is a view field point which appears for many times, deleting the view field point to be optimized, otherwise, reserving the view field point to be optimized, obtaining an updated view field point set, and then entering step S63;
S63: judging whether the number of field points to be optimized in the updated field point set is larger than the set maximum number H of field points, if not, entering step S64, and if so, entering step S65;
S64: executing update constraint operation, and then re-executing the steps S4-S5; wherein, the update constraint operation is: if the operation of deleting the to-be-optimized view field point is performed, deleting all constraints related to the deleted to-be-optimized view field point in the constraint condition of the step S4, and if the operation of increasing the to-be-optimized view field point to be associated with the optimization performance is performed, increasing the corresponding constraint related to the to-be-optimized view field point in the to-be-optimized performance associated with the to-be-optimized view field point in the constraint condition of the step S4;
S65: reserving field points to be optimized, which belong to field boundary points or appear for many times, in the current field point set to obtain a final optimized field point set, executing update constraint operation based on the final optimized field point set, and then re-executing the steps S4-S5;
the calculation formula of the comprehensive evaluation index omega' (Fi) of the aberration of each view field point to be optimized in the view field point set is as follows:
wherein, αl (Fi), βl (Fi) and γl (Fi) represent weight coefficients corresponding to the i-th field point to be optimized F i in the current field point set at the performance to be optimized T l, and Cl (Fi) and Bl (Fi) represent actual performance values and index intermediate quantities of the performance to be optimized T l of the i-th field point to be optimized F i in the field point set respectively.
2. The multi-objective automatic optimization method of an optical imaging system according to claim 1, wherein the calculated weight W (Fi) next is normalized according to the following formula, and the normalized weight is compared with the weight threshold Δ, where the normalized formula is:
Wherein W (F) next-max is the maximum value in the updated weight of each view field point to be optimized.
3. A multi-objective automatic optimization method of an optical imaging system according to any one of claims 1 or 2, wherein the imaging system to be optimized is a total refraction imaging system, a total reflection imaging system or a catadioptric imaging system.
4. A method of multi-objective automatic optimization of an optical imaging system according to any of claims 1 or 2, wherein the properties to be optimized include focal length, object distance, image distance, magnification, entrance pupil position, entrance pupil distance, total system length, maximum optical lens pass-through aperture, spherical aberration, coma, astigmatism, field curvature, distortion, sinusoidal aberration, wave aberration, telecentricity, polarization aberration, aberration uniformity and/or imaging quality.
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