WO2020001646A1 - Polarization aberration measuring method for projection objective lens - Google Patents

Polarization aberration measuring method for projection objective lens Download PDF

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WO2020001646A1
WO2020001646A1 PCT/CN2019/093838 CN2019093838W WO2020001646A1 WO 2020001646 A1 WO2020001646 A1 WO 2020001646A1 CN 2019093838 W CN2019093838 W CN 2019093838W WO 2020001646 A1 WO2020001646 A1 WO 2020001646A1
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projection objective
matrix
jones matrix
light intensity
polarizer
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PCT/CN2019/093838
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French (fr)
Chinese (zh)
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倪晟
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上海微电子装备(集团)股份有限公司
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01MTESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M11/00Testing of optical apparatus; Testing structures by optical methods not otherwise provided for
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01MTESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M11/00Testing of optical apparatus; Testing structures by optical methods not otherwise provided for
    • G01M11/02Testing optical properties
    • GPHYSICS
    • G03PHOTOGRAPHY; CINEMATOGRAPHY; ANALOGOUS TECHNIQUES USING WAVES OTHER THAN OPTICAL WAVES; ELECTROGRAPHY; HOLOGRAPHY
    • G03FPHOTOMECHANICAL PRODUCTION OF TEXTURED OR PATTERNED SURFACES, e.g. FOR PRINTING, FOR PROCESSING OF SEMICONDUCTOR DEVICES; MATERIALS THEREFOR; ORIGINALS THEREFOR; APPARATUS SPECIALLY ADAPTED THEREFOR
    • G03F7/00Photomechanical, e.g. photolithographic, production of textured or patterned surfaces, e.g. printing surfaces; Materials therefor, e.g. comprising photoresists; Apparatus specially adapted therefor
    • G03F7/20Exposure; Apparatus therefor

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  • the invention relates to the technical field of integrated circuit manufacturing, in particular to a method for measuring polarization aberration of a projection objective.
  • Ellipsometer is the most widely used measurement instrument in the field of ellipsometric measurement. It is a general optical measurement instrument that uses the polarization characteristics of light to obtain the information of the sample to be measured.
  • the basic principle is to project special elliptical polarized light onto the surface of the sample to be measured through a polarizer, and measure the reflected light (or transmitted light) of the sample to be measured to obtain the polarization state change of the polarized light before and after reflection (or transmission). (Including amplitude ratio and phase difference), and then extract the information of the sample to be tested from it.
  • the parameter optimization of the ellipsometer system is mainly focused on the optimization of the phase delay of the ellipsometer compensator.
  • an optimal phase delay of 127 ° is proposed to reduce the effect of the deviation on the measurement results of the ellipsometer.
  • parameters of the ellipsometer such as the azimuth of the polarizer and analyzer, the number of sampling points, and the azimuth of the compensator. These parameters are also important factors affecting the relationship between the deviation and the measurement results of the ellipsometer.
  • the prior art CN103426031B discloses a method for optimizing the parameters of an ellipsometer system. The measurement result of this method is the Muller matrix of the sample.
  • the Muller matrix contains the depolarization effect, and the measurement of the projection lens of the lithography machine cannot be used directly
  • the Muller matrix needs to obtain the polarization aberration of the projection objective after converting the Muller matrix to the Jones matrix.
  • the actual measurement error is directly equivalent to the depolarization effect of the conversion of the Mueller matrix to the Jones matrix, the final measurement result is not accurate enough, resulting in poor imaging results of the produced product.
  • the purpose of the present invention is to provide a method for measuring the polarization aberration of a projection objective to solve the problem that the measurement result of the polarization aberration measurement method of the projection objective in the prior art is a Muller matrix, and the Muller matrix has a depolarization effect, resulting in a final measurement result
  • the problem is that the accuracy is not high, which affects the imaging effect of the product.
  • the present invention provides a method for measuring polarization aberration of a projection objective.
  • the method for measuring polarization aberration of a projection objective includes the following steps:
  • S1 A first polarizing plate (P1), a first quarter wave plate (Q1), a first condensing lens (L1), a projection objective (PO), a second converging lens (L2), The second quarter-wave plate (Q2), the second polarizer (P2), and the light intensity measuring device (IS);
  • a rotation angle group set is established, and the elements in the rotation angle group set are the rotation angle of the first polarizer (P1), the rotation angle of the first quarter wave plate (Q1), and the second polarizer ( The combination of the rotation angle formed by the rotation angle of P2) and the rotation angle of the second quarter wave plate (Q2).
  • the elements in the rotation angle group set are different from each other, where the rotation angle is the brightness of the polarizer. The angle between the fast axis of the axis or waveplate and the given direction;
  • S3 Select an element from the set of rotation angle groups, and adjust the first polarizing plate (P1), the first quarter wave plate (Q1), and the second quarter wave plate ( Q2) and the rotation angle of the second polarizer (P2);
  • S4 the light intensity measuring device (IS) measures a set of light intensity values corresponding to the current element
  • S5 Repeat S3 and S4 at least 16 times to obtain multiple groups of light intensity values, wherein each time S3 is performed, a different element is selected and the multiple groups of light intensity values obtained by the light intensity measurement device (IS) measurement are constructed Is a light intensity matrix. All selected elements are constructed as a lambda function matrix. The elements in the lambda function matrix are the first polarizer (P1), the first quarter wave plate (Q1), and the second quarter. The coefficients of the elements in the Jones matrix of the wave plate (Q2) and the second polarizer (P2) and their complex conjugate products;
  • the light intensity value is calculated in S4.
  • the calculation formula used is as follows:
  • I is the light intensity value
  • E out is the energy of the outgoing light
  • E out J P2 ⁇ J Q2 ⁇ J PO ⁇ J Q1 ⁇ J P1 ⁇ E in ; * represents the conjugate transpose
  • J P1 is the first polarization Jones matrix of the plate (P1)
  • J P2 is the Jones matrix of the second polarizer (P2)
  • J Q1 is the Jones matrix of the first quarter wave plate (Q1)
  • J Q2 is the second quarter wave Jones matrix of lens (Q2)
  • J PO is the Jones matrix of projection objective (PO)
  • Jones matrix of wave plate and polarizer are with R is the rotation matrix
  • is the rotation angle of the corresponding wave plate or polarizer
  • E in is the energy of the incident light.
  • the constructing all selected elements into a lambda function matrix includes the following steps:
  • calculating the Jones matrix of the projection objective lens (PO) according to the light intensity matrix and the lambda function matrix includes the following steps:
  • J i, j are the elements in the Jones matrix of the projection objective (PO)
  • the least square method is used in S6 to calculate the approximate value of the Jones matrix of the projection objective lens.
  • an adjustment step of each rotation angle in the selected element ranges from 30 to 60 degrees.
  • the given direction is an X-axis or Y-axis direction.
  • the first condensing lens (L1) and the second condensing lens (L2) are both collimating lenses, and the two have different focal lengths.
  • the first condensing lens (L1) enables the light incident on the projection objective (PO) to have a first numerical aperture
  • the second condensing lens (L2) ) Converting light having a second numerical aperture emitted by the projection objective (PO) into parallel light, the second numerical aperture being larger than the first numerical aperture
  • each point in the light intensity map obtained by the light intensity measurement device (IS) measurement corresponds to a point on the pupil surface of the projection objective lens (PO).
  • a stable light beam is selected as the incident light.
  • the method for measuring the polarization aberration of a projection objective is obtained by measuring a light intensity matrix constructed by all groups of light intensity values based on a light intensity measurement device and constructed by all selected elements.
  • the lambda function matrix calculates the Jones matrix of the projection objective lens, that is, the method of the present invention can directly calculate and obtain the Jones matrix of the projection objective lens.
  • the method of measuring the Mueller matrix first and then converting the Mueller matrix to the Jones matrix , Effectively avoids the result error caused by the depolarization effect of the conversion of the Mueller matrix to the Jones matrix, improves the measurement and calculation accuracy, and improves the product imaging effect.
  • FIG. 1 is a schematic structural diagram of a measurement system used in a method for measuring polarization aberration of a projection objective lens according to an embodiment of the present invention
  • FIG. 2 is a flowchart of a method for measuring polarization aberration of a projection objective lens according to an embodiment of the present invention.
  • FIG. 1 is a schematic structural diagram of a measurement system used by the projection objective lens polarization aberration measurement method of the present invention.
  • the measurement system includes a first polarizing plate P1, a first quarter-wave plate Q1, a first condensing lens L1, a projection objective PO, and a second condensing lens L2, which are sequentially arranged along the propagation direction of the optical path.
  • Polarizer Polarizer for short: Light passes through the polarizer, and only components with a certain angle can pass through the polarizer, and the light transmittance of the vertical angle is 0.
  • QWP Quarter-wave plate
  • Condensing lens (Lens, abbreviated as L): It is a kind of lens that is thick in the middle and thin in the periphery, that is, a convex lens; it has the ability to condense light, and is also called a "positive lens”.
  • the first condensing lens L1 and the second condensing lens L2 in this embodiment are both collimating lenses, and the two have different focal lengths.
  • the first polarizing plate P1 is used To ensure that the light incident on the projection objective PO is linearly polarized light; the first condensing lens L1 causes the light incident on the projection objective PO to have a first numerical aperture, and the second condensing lens L2 emits the light of the second numerical aperture emitted from the projection objective PO. Converted into parallel light, the second numerical aperture is larger than the first numerical aperture.
  • the present invention provides a method for measuring the polarization aberration of a projection objective.
  • the specific measurement process of the method for measuring the polarization aberration of a projection objective of the present invention is described below with reference to FIGS. 1 and 2.
  • step S1 is performed, and a first polarizing plate P1, a first quarter wave plate Q1, a first condensing lens L1, a projection objective lens PO, a second converging lens L2, and a second quarter are set in order along the propagation direction of the optical path.
  • step S2 is executed to establish a rotation angle group set, where the elements in the rotation angle group set are the rotation angle of the first polarizer P1, the rotation angle of the first quarter wave plate Q1, and the second polarizer P2.
  • the combination of the rotation angle and the rotation angle of the second quarter wave plate Q2 is a combination of rotation angles.
  • the elements in the rotation angle group set are different from each other.
  • the rotation angle is the bright axis of the polarizer and the speed of the wave plate. The angle between the axis and a given direction (usually the X direction).
  • step S3 is executed, an element is selected from the set of rotation angles, and the first polarizing plate P1, the first quarter wave plate Q1, the second quarter wave plate Q2, and The second polarizer P2, so that the four elements have a rotation angle corresponding to the selected element.
  • step S4 is performed, and the light intensity measuring device IS measures a group of light intensity values under the current element.
  • Each point in the light intensity map obtained by the light intensity measurement device IS corresponds to a point on the pupil surface of the projection objective PO, and each point on the pupil surface of the projection objective PO has an independent Jones matrix.
  • the projection objective of the present invention has polarization
  • the aberration measurement method is based on the correspondence between the points in the light intensity map and the points in the pupil plane of the projection objective lens. Since each point in the pupil surface of the projection objective lens has a set of light intensity values, by separately Solve, measure and obtain the Jones matrix of the pupil plane point of the corresponding projection objective lens, and then obtain the Jones matrix distribution of the pupil plane of the entire projection objective lens.
  • the light intensity measurement The calculation formula used by the device IS to measure a group of light intensity values under the current element is:
  • step S5 is performed, and S3 and S4 are repeatedly performed at least 16 times to obtain multiple groups of light intensity values, wherein each time S3 is performed, a different element is selected, and the multiple groups of light intensity obtained by the light intensity measurement device IS are measured.
  • the value is constructed as a light intensity matrix, and all selected elements are constructed as a lambda function matrix.
  • the elements in the lambda function matrix are the first polarizer P1, the first quarter wave plate Q1, and the second quarter wave plate.
  • the adjustment step of each rotation angle in the selected elements is 30 to 60 degrees, that is, two adjacent selected elements The difference between the rotation angles of the same object in the range of 30 to 60 degrees. In this embodiment, the adjustment step of the rotation angle of the same object in two adjacent selected elements is 45 degrees.
  • the polarization aberration measurement method of the projection objective lens can also measure the polarization aberration of other elements.
  • formula (3) is based on different elements selected in the set of rotation angle groups, and different groups of light intensity values can be obtained based on the light intensity measuring device IS. Using a linear algebraic relationship, it can be obtained:
  • x, y 1,2; to the left of the equal sign is the light intensity column I, which represents the measurement of different rotation angles of the four elements; to the right of the equal sign, the number of rows of the ⁇ function matrix represents the number of measurements, and each column of the ⁇ function matrix is The coefficient corresponding to the product of the Jones matrix element of the projection objective PO; the subscript indicates the product form of the Jones matrix element of the projection objective PO, and the superscript indicates the group number of the light intensity group.
  • I is a light intensity matrix
  • is a lambda function matrix
  • X is a matrix composed of a projection objective Jones matrix element and a complex conjugate product thereof.
  • step S6 is performed to calculate a Jones matrix of the projection objective PO according to the light intensity matrix and the lambda function matrix.
  • the Jones matrix of the projection objective PO can be adjusted. Solve unknown parameters involved in.
  • the least square method is used in S6 to calculate the approximate value of the Jones matrix of the projection objective lens, thereby effectively avoiding calculation errors and improving the calculation accuracy.
  • X ( ⁇ T (n) ⁇ (n)) -1 ⁇ ⁇ (n) T ⁇ I, by adjusting the first polarizer P1 and the first quarter with different rotation angles
  • the wave plate Q1, the second quarter wave plate Q2, and the second polarizing plate P2 can solve the 7 unknown parameters involved in the Jones matrix of the projection objective PO:
  • J xx is set to a real number and does not include a phase portion, so this method cannot measure wave aberrations.
  • the projection objective lens polarization aberration measurement method of the present invention uses the least square method to calculate the Jones matrix of the projection objective lens
  • the main error source lies in the least square method, that is, the ⁇ function matrix ⁇ .
  • the ⁇ function matrix can be reduced The condition number of ⁇ .
  • the analysis of the ⁇ function matrix ⁇ shows that ⁇ is composed of two parts, that is, the part in front of the projection objective (P1, Q1) and the part behind the projection objective (Q2, P2).
  • the Jones matrix of the two parts determines the ⁇ of each row Coefficient, so the condition number of ⁇ is determined by the rotation angle (direction angle) of the front and back parts. For each group of rotation angle combinations determined, the condition number of ⁇ can be calculated, so that a rotation angle combination with a smaller number of conditions can be found to reduce the effect of random errors on the measurement results.
  • the description is relatively simple, and the relevant part may refer to the description of the structure part.
  • the projection objective lens polarization aberration measurement method obtains a light intensity matrix constructed by all groups of light intensity values and all selected
  • the lambda function matrix constructed by the elements calculates the Jones matrix of the projection objective lens, that is, the measurement method of the present invention can directly calculate and obtain the Jones matrix of the projection objective lens.
  • the Mueller matrix is obtained by measuring first, and then the Mueller matrix is converted to Jones.
  • the matrix method effectively avoids the result error caused by the depolarization effect of the conversion of the Mueller matrix to the Jones matrix, improves the measurement and calculation accuracy, and improves the product imaging effect.

Abstract

A polarization aberration measuring method for a projection objective lens, comprising: calculating the Jones matrix of a projection objective lens (PO) by means of a light intensity matrix constructed by all groups of light intensity values that is measured on the basis of a light intensity measuring device (IS) and a λ function matrix constructed by all selected elements, so as to directly calculate the Jones matrix of the projection objective lens (PO), effectively avoiding the resultant error caused by the depolarization effect of transitioning the Mueller matrix to the Jones matrix, improving the measurement and calculation accuracy.

Description

投影物镜偏振像差测量方法Method for measuring polarization aberration of projection objective 技术领域Technical field
本发明涉及集成电路制造技术领域,特别涉及一种投影物镜偏振像差测量方法。The invention relates to the technical field of integrated circuit manufacturing, in particular to a method for measuring polarization aberration of a projection objective.
背景技术Background technique
椭偏仪是椭偏测量领域使用最广泛的一种测量仪器,它是一种利用光的偏振特性获取待测样品信息的通用光学测量仪器。其基本原理是通过起偏器将特殊的椭圆偏振光投射到待测样品表面,通过测量待测样品的反射光(或透射光),以获得偏振光在反射(或透射)前后的偏振状态变化(包括振幅比和相位差),进而从中提取出待测样品的信息。Ellipsometer is the most widely used measurement instrument in the field of ellipsometric measurement. It is a general optical measurement instrument that uses the polarization characteristics of light to obtain the information of the sample to be measured. The basic principle is to project special elliptical polarized light onto the surface of the sample to be measured through a polarizer, and measure the reflected light (or transmitted light) of the sample to be measured to obtain the polarization state change of the polarized light before and after reflection (or transmission). (Including amplitude ratio and phase difference), and then extract the information of the sample to be tested from it.
近年来,为适应不同测量条件与用户群体的需要,多种配置类型的椭偏仪取得了长足的发展,包括旋转起偏器型、旋转检偏器型、单旋转补偿器型和双旋转补偿器型等。在使用椭偏仪对待测样品进行测量时,测量结果往往会在一定程度上偏离其真实值。产生这些偏差的原因很多,包括椭偏仪随机噪声、椭偏仪系统误差、环境随机噪声以及测量人为误差因素等。即使在同等偏差下,椭偏仪不同配置的系统参数,其测量结果对偏差的敏感度也不相同。因此为了减小偏差对椭偏仪测量结果的影响,必须利用一定的方法对椭偏仪的系统参数进行优化分析,从而得到椭偏仪最优的系统参数,进而尽量降低偏差对椭偏仪测量结果的影响。所以在椭偏仪设计过程中,必须找到针对当前椭偏仪系统结构的最优系统参数配置。In recent years, in order to meet the needs of different measurement conditions and user groups, many configurations of ellipsometer have made great progress, including rotary polarizer type, rotary analyzer type, single rotation compensator type and dual rotation compensation. Type and so on. When the ellipsometer is used to measure the sample to be measured, the measurement result often deviates from its true value to a certain extent. There are many reasons for these deviations, including ellipsometer random noise, ellipsometer system error, environmental random noise, and measurement human error factors. Even under the same deviation, the sensitivity of the measurement results to the deviation of the system parameters of different configurations of the ellipsometer is not the same. Therefore, in order to reduce the influence of the deviation on the measurement results of the ellipsometer, a certain method must be used to optimize the analysis of the ellipsometer system parameters, so as to obtain the optimal system parameters of the ellipsometer, and then minimize the deviation to the ellipsometer measurement. Impact of results. Therefore, in the process of ellipsometer design, it is necessary to find the optimal system parameter configuration for the current ellipsometer system structure.
目前对于椭偏仪系统的参数优化,主要关注在对椭偏仪补偿器的相位延迟量的优化,例如提出了127°的最优相位延迟量,以实现降低偏差对椭偏仪测量结果的影响。但是,椭偏仪的参数很多,如起偏器、检偏器的方位角, 采样点数,补偿器方位角等,这些参数同样是对偏差与椭偏仪测量结果关系的重要影响因素,必须综合考虑以进行优化处理。现有技术CN103426031B中公开了一种椭偏仪系统参数的优化方法,该方法测量的结果是样品的穆勒矩阵,穆勒矩阵含有退偏效果,而在光刻机投影物镜的测量不能直接采用穆勒矩阵,需要将穆勒矩阵转换至琼斯矩阵之后获得投影物镜偏振像差。但是,由于实际测量的误差会直接等效成穆勒矩阵转换至琼斯矩阵的退偏效应,使最终量测结果不够精确,导致生产的产品成像效果不佳。At present, the parameter optimization of the ellipsometer system is mainly focused on the optimization of the phase delay of the ellipsometer compensator. For example, an optimal phase delay of 127 ° is proposed to reduce the effect of the deviation on the measurement results of the ellipsometer. . However, there are many parameters of the ellipsometer, such as the azimuth of the polarizer and analyzer, the number of sampling points, and the azimuth of the compensator. These parameters are also important factors affecting the relationship between the deviation and the measurement results of the ellipsometer. Consider for optimization. The prior art CN103426031B discloses a method for optimizing the parameters of an ellipsometer system. The measurement result of this method is the Muller matrix of the sample. The Muller matrix contains the depolarization effect, and the measurement of the projection lens of the lithography machine cannot be used directly The Muller matrix needs to obtain the polarization aberration of the projection objective after converting the Muller matrix to the Jones matrix. However, because the actual measurement error is directly equivalent to the depolarization effect of the conversion of the Mueller matrix to the Jones matrix, the final measurement result is not accurate enough, resulting in poor imaging results of the produced product.
针对现有技术中投影物镜偏振像差测量方法存在的不足,本领域技术人员一直在寻找解决的方法。In view of the shortcomings of the measurement methods for polarization aberrations of projection objectives in the prior art, those skilled in the art have been searching for a solution.
发明内容Summary of the invention
本发明的目的在于提供一种投影物镜偏振像差测量方法,以解决使用现有技术中投影物镜偏振像差测量方法的测量结果为穆勒矩阵,穆勒矩阵存在退偏效应,导致最终测量结果精准度不高,影响产品成像效果的问题。The purpose of the present invention is to provide a method for measuring the polarization aberration of a projection objective to solve the problem that the measurement result of the polarization aberration measurement method of the projection objective in the prior art is a Muller matrix, and the Muller matrix has a depolarization effect, resulting in a final measurement result The problem is that the accuracy is not high, which affects the imaging effect of the product.
为解决上述技术问题,本发明提供一种投影物镜偏振像差测量方法,所述投影物镜偏振像差测量方法包括如下步骤:To solve the above technical problems, the present invention provides a method for measuring polarization aberration of a projection objective. The method for measuring polarization aberration of a projection objective includes the following steps:
S1:沿光路传播方向依次设置第一偏振片(P1)、第一四分之一波片(Q1)、第一会聚透镜(L1)、投影物镜(PO)、第二会聚透镜(L2)、第二四分之一波片(Q2)、第二偏振片(P2)及光强测量装置(IS);S1: A first polarizing plate (P1), a first quarter wave plate (Q1), a first condensing lens (L1), a projection objective (PO), a second converging lens (L2), The second quarter-wave plate (Q2), the second polarizer (P2), and the light intensity measuring device (IS);
S2:建立旋转角组集合,所述旋转角组集合中的元素为由第一偏振片(P1)的旋转角、第一四分之一波片(Q1)的旋转角、第二偏振片(P2)的旋转角和第二四分之一波片(Q2)的旋转角共同构成的旋转角的组合,所述旋转角组集合中的元素互不相同,其中,旋转角为偏振片的亮轴或波片的快轴与给定方向的夹角;S2: A rotation angle group set is established, and the elements in the rotation angle group set are the rotation angle of the first polarizer (P1), the rotation angle of the first quarter wave plate (Q1), and the second polarizer ( The combination of the rotation angle formed by the rotation angle of P2) and the rotation angle of the second quarter wave plate (Q2). The elements in the rotation angle group set are different from each other, where the rotation angle is the brightness of the polarizer. The angle between the fast axis of the axis or waveplate and the given direction;
S3:在所述旋转角组集合中选取一元素,并按照选取的元素分别调节第一偏振片(P1)、第一四分之一波片(Q1)、第二四分之一波片(Q2)和第二偏振片(P2)的旋转角;S3: Select an element from the set of rotation angle groups, and adjust the first polarizing plate (P1), the first quarter wave plate (Q1), and the second quarter wave plate ( Q2) and the rotation angle of the second polarizer (P2);
S4:所述光强测量装置(IS)测得对应于当前元素的一组光强值;S4: the light intensity measuring device (IS) measures a set of light intensity values corresponding to the current element;
S5:反复执行S3和S4至少16次以获得多组光强值,其中,每次执行S3选取一个不同的元素,并将光强测量装置(IS)测量获得的所述多组光强值构建为一光强矩阵,将所有选取的元素构建为一λ函数矩阵,λ函数矩阵中元素为第一偏振片(P1)、第一四分之一波片(Q1)、第二四分之一波片(Q2)和第二偏振片(P2)的琼斯矩阵中元素及其复共轭乘积的系数;S5: Repeat S3 and S4 at least 16 times to obtain multiple groups of light intensity values, wherein each time S3 is performed, a different element is selected and the multiple groups of light intensity values obtained by the light intensity measurement device (IS) measurement are constructed Is a light intensity matrix. All selected elements are constructed as a lambda function matrix. The elements in the lambda function matrix are the first polarizer (P1), the first quarter wave plate (Q1), and the second quarter. The coefficients of the elements in the Jones matrix of the wave plate (Q2) and the second polarizer (P2) and their complex conjugate products;
S6:根据所述光强矩阵和所述λ函数矩阵计算投影物镜(PO)的琼斯矩阵。S6: Calculate a Jones matrix of a projection objective (PO) according to the light intensity matrix and the lambda function matrix.
可选的,在所述的投影物镜偏振像差测量方法中,在未考虑所述第一会聚透镜(L1)和所述第二会聚透镜(L2)的琼斯矩阵时,S4中计算光强值采用的计算公式如下:Optionally, in the method for measuring the polarization aberration of the projection objective lens, when the Jones matrix of the first condensing lens (L1) and the second converging lens (L2) is not considered, the light intensity value is calculated in S4. The calculation formula used is as follows:
Figure PCTCN2019093838-appb-000001
Figure PCTCN2019093838-appb-000001
其中,I为光强值,E out为出射光的能量,E out=J P2·J Q2·J PO·J Q1·J P1·E in;*表示共轭转置;J P1为第一偏振片(P1)的琼斯矩阵,J P2为第二偏振片(P2)的琼斯矩阵,J Q1为第一四分之一波片(Q1)的琼斯矩阵,J Q2为第二四分之一波片(Q2)的琼斯矩阵;J PO为投影物镜(PO)的琼斯矩阵;波片和偏振片的琼斯矩阵分别为
Figure PCTCN2019093838-appb-000002
Figure PCTCN2019093838-appb-000003
R为旋转 矩阵,
Figure PCTCN2019093838-appb-000004
α为对应波片或偏振片的旋转角;E in为入射光的能量。
Among them, I is the light intensity value, E out is the energy of the outgoing light, E out = J P2 · J Q2 · J PO · J Q1 · J P1 · E in ; * represents the conjugate transpose; J P1 is the first polarization Jones matrix of the plate (P1), J P2 is the Jones matrix of the second polarizer (P2), J Q1 is the Jones matrix of the first quarter wave plate (Q1), and J Q2 is the second quarter wave Jones matrix of lens (Q2); J PO is the Jones matrix of projection objective (PO); Jones matrix of wave plate and polarizer are
Figure PCTCN2019093838-appb-000002
with
Figure PCTCN2019093838-appb-000003
R is the rotation matrix,
Figure PCTCN2019093838-appb-000004
α is the rotation angle of the corresponding wave plate or polarizer; E in is the energy of the incident light.
可选的,在所述的投影物镜偏振像差测量方法中,S5中,所述将所有选取的元素构建为一λ函数矩阵包括如下步骤:Optionally, in the method for measuring the polarization aberration of the projection objective lens, in S5, the constructing all selected elements into a lambda function matrix includes the following steps:
S50:定义
Figure PCTCN2019093838-appb-000005
D=J Q1·J P1·E in
S50: Definition
Figure PCTCN2019093838-appb-000005
D = J Q1 · J P1 · E in ;
S51:获得λ函数矩阵中元素计算公式:λ i,j,k,l=U l·M ki·D j,并计算λ函数矩阵中所有元素,以构建λ函数矩阵; S51: Obtain a formula for calculating the elements in the λ function matrix: λ i, j, k, l = U l · M ki · D j , and calculate all elements in the λ function matrix to construct a λ function matrix;
其中,U,M,D为简化后的矩阵,用矩阵分别表示为U=[U 1 U 2],
Figure PCTCN2019093838-appb-000006
J P1为第一偏振片(P1)的琼斯矩阵,J P2为第二偏振片(P2)的琼斯矩阵,J Q1为第一四分之一波片(Q1)的琼斯矩阵,J Q2为第二四分之一波片(Q2)的琼斯矩阵;E in为入射光的能量;*表示共轭转置;其中,i,j,k,l表示琼斯矩阵中元素的下标,分别取值1或2;λ i,j,k,l为λ函数矩阵中元素。
Among them, U, M, and D are simplified matrices, and the matrices are expressed as U = [U 1 U 2 ],
Figure PCTCN2019093838-appb-000006
J P1 is the Jones matrix of the first polarizer (P1), J P2 is the Jones matrix of the second polarizer (P2), J Q1 is the Jones matrix of the first quarter wave plate (Q1), and J Q2 is the first Jones matrix of the quarter-wave plate (Q2); E in is the energy of the incident light; * represents the conjugate transpose; where i, j, k, l represent the subscripts of the elements in the Jones matrix, and take values respectively 1 or 2; λ i, j, k, l are the elements in the λ function matrix.
可选的,在所述的投影物镜偏振像差测量方法中,S6中,根据所述光强矩阵和所述λ函数矩阵计算投影物镜(PO)的琼斯矩阵包括如下步骤:Optionally, in the method for measuring the polarization aberration of the projection objective lens, in S6, calculating the Jones matrix of the projection objective lens (PO) according to the light intensity matrix and the lambda function matrix includes the following steps:
S60:简化公式(1)为:S60: The simplified formula (1) is:
Figure PCTCN2019093838-appb-000007
Figure PCTCN2019093838-appb-000007
S61:将公式(2)简化为投影物镜琼斯矩阵元素及其复共轭乘积的一次函数:
Figure PCTCN2019093838-appb-000008
S61: Simplify the formula (2) into a linear function of the projection objective Jones matrix element and its complex conjugate product:
Figure PCTCN2019093838-appb-000008
S62:计算投影物镜(PO)的琼斯矩阵中元素,以得到投影物镜(PO)的琼斯矩阵;S62: Calculate elements in the Jones matrix of the projection objective (PO) to obtain the Jones matrix of the projection objective (PO);
其中,J i,j为投影物镜(PO)的琼斯矩阵中元素,
Figure PCTCN2019093838-appb-000009
为投影物镜(PO) 的琼斯矩阵中元素的复共轭。
Where J i, j are the elements in the Jones matrix of the projection objective (PO),
Figure PCTCN2019093838-appb-000009
Complex conjugates of the elements in the Jones matrix of the projection objective (PO).
可选的,在所述的投影物镜偏振像差测量方法中,若S5中反复执行S3和S4的次数大于16次,则S6中采用最小二乘法计算投影物镜的琼斯矩阵的近似值。Optionally, in the method for measuring the polarization aberration of the projection objective lens, if S3 and S4 are repeatedly performed more than 16 times in S5, the least square method is used in S6 to calculate the approximate value of the Jones matrix of the projection objective lens.
可选的,在所述的投影物镜偏振像差测量方法中,S5中,选取的元素中各个旋转角的调整步长范围为30~60度。Optionally, in the method for measuring the polarization aberration of the projection objective lens, in S5, an adjustment step of each rotation angle in the selected element ranges from 30 to 60 degrees.
可选的,在所述的投影物镜偏振像差测量方法中,所述给定方向为X轴或Y轴方向。Optionally, in the method for measuring the polarization aberration of the projection objective lens, the given direction is an X-axis or Y-axis direction.
可选的,在所述的投影物镜偏振像差测量方法中,所述第一会聚透镜(L1)和所述第二会聚透镜(L2)均为准直透镜,且两者具有不同的焦距。Optionally, in the method for measuring the polarization aberration of the projection objective lens, the first condensing lens (L1) and the second condensing lens (L2) are both collimating lenses, and the two have different focal lengths.
可选的,在所述的投影物镜偏振像差测量方法中,所述第一会聚透镜(L1)使得入射至投影物镜(PO)的光具有第一数值孔径,所述第二会聚透镜(L2)将所述投影物镜(PO)出射的具有第二数值孔径的光转换为平行光,所述第二数值孔径大于所述第一数值孔径。Optionally, in the method for measuring the polarization aberration of the projection objective lens, the first condensing lens (L1) enables the light incident on the projection objective (PO) to have a first numerical aperture, and the second condensing lens (L2) ) Converting light having a second numerical aperture emitted by the projection objective (PO) into parallel light, the second numerical aperture being larger than the first numerical aperture.
可选的,在所述的投影物镜偏振像差测量方法中,所述光强测量装置(IS)测量获得的光强图中每一个点对应投影物镜(PO)的光瞳面的一点。Optionally, in the method for measuring the polarization aberration of the projection objective lens, each point in the light intensity map obtained by the light intensity measurement device (IS) measurement corresponds to a point on the pupil surface of the projection objective lens (PO).
可选的,在所述的投影物镜偏振像差测量方法中,测量开始前,选取稳定的光束作为入射光。Optionally, in the method for measuring the polarization aberration of the projection objective lens, before the measurement is started, a stable light beam is selected as the incident light.
在本发明所提供的投影物镜偏振像差测量方法中,所述投影物镜偏振像差测量方法通过基于光强测量装置测量获得所有组光强值构建为的光强矩阵和所有选取的元素构建的λ函数矩阵计算投影物镜的琼斯矩阵,即本发明的测量方法可以直接计算获得投影物镜的琼斯矩阵,相比现有方法中先测量获得穆勒矩阵,再将穆勒矩阵转换至琼斯矩阵的方法,有效避免因穆勒矩阵转换至琼斯矩阵的退偏效应造成的结果误差,提高了测量和计算精准度,提升 了产品成像效果。In the method for measuring the polarization aberration of a projection objective provided by the present invention, the method for measuring the polarization aberration of a projection objective is obtained by measuring a light intensity matrix constructed by all groups of light intensity values based on a light intensity measurement device and constructed by all selected elements. The lambda function matrix calculates the Jones matrix of the projection objective lens, that is, the method of the present invention can directly calculate and obtain the Jones matrix of the projection objective lens. Compared with the existing method, the method of measuring the Mueller matrix first and then converting the Mueller matrix to the Jones matrix , Effectively avoids the result error caused by the depolarization effect of the conversion of the Mueller matrix to the Jones matrix, improves the measurement and calculation accuracy, and improves the product imaging effect.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1是本发明一实施例中投影物镜偏振像差测量方法采用的测量系统的结构示意图;FIG. 1 is a schematic structural diagram of a measurement system used in a method for measuring polarization aberration of a projection objective lens according to an embodiment of the present invention; FIG.
图2是本发明一实施例中投影物镜偏振像差测量方法的流程图。FIG. 2 is a flowchart of a method for measuring polarization aberration of a projection objective lens according to an embodiment of the present invention.
具体实施方式detailed description
以下结合附图和具体实施例对本发明提出的投影物镜偏振像差测量方法作进一步详细说明。根据下面说明和权利要求书,本发明的优点和特征将更清楚。需说明的是,附图均采用非常简化的形式且均使用非精准的比例,仅用以方便、明晰地辅助说明本发明实施例的目的。The method for measuring the polarization aberration of the projection objective lens proposed by the present invention is described in further detail below with reference to the drawings and specific embodiments. The advantages and features of the invention will be apparent from the following description and claims. It should be noted that the drawings are in a very simplified form and all use inaccurate proportions, which are only used to facilitate and clearly assist the description of the embodiments of the present invention.
请参考图1,其为本发明的投影物镜偏振像差测量方法采用的测量系统的结构示意图。如图1所示,所述测量系统包括:沿光路传播方向依次设置的第一偏振片P1、第一四分之一波片Q1、第一会聚透镜L1、投影物镜PO、第二会聚透镜L2、第二四分之一波片Q2、第二偏振片P2及光强测量装置IS。Please refer to FIG. 1, which is a schematic structural diagram of a measurement system used by the projection objective lens polarization aberration measurement method of the present invention. As shown in FIG. 1, the measurement system includes a first polarizing plate P1, a first quarter-wave plate Q1, a first condensing lens L1, a projection objective PO, and a second condensing lens L2, which are sequentially arranged along the propagation direction of the optical path. , The second quarter-wave plate Q2, the second polarizing plate P2, and the light intensity measuring device IS.
为了便于理解本发明的测量系统,下面对其中涉及的元件进行详细的解释:In order to facilitate the understanding of the measurement system of the present invention, the elements involved therein are explained in detail below:
1)偏振片(Polarizer,简称P):光通过偏振片,只有一定角度的分量能够通过偏振片,其垂直角度的光透过率为0。1) Polarizer (Polarizer for short): Light passes through the polarizer, and only components with a certain angle can pass through the polarizer, and the light transmittance of the vertical angle is 0.
2)四分之一波片(QWP,简称Q):光通过四分之一波片,两垂直方向的相位差改变pi/4。因此通过偏振片和四分之一波片的不同组合,可以得到不同偏振态的光。2) Quarter-wave plate (QWP, referred to as Q): Light passes through the quarter-wave plate, and the phase difference between the two vertical directions changes pi / 4. Therefore, through different combinations of polarizers and quarter-wave plates, light with different polarization states can be obtained.
3)会聚透镜(Lens,简称L):是中间厚、周边薄的一种透镜,即凸透镜; 它具有会聚光的能力,又叫作“正透镜”。3) Condensing lens (Lens, abbreviated as L): It is a kind of lens that is thick in the middle and thin in the periphery, that is, a convex lens; it has the ability to condense light, and is also called a "positive lens".
较佳的,本实施例中所述第一会聚透镜L1和所述第二会聚透镜L2均为准直透镜,且两者具有不同的焦距,本实施例中,所述第一偏振片P1用于确保入射至投影物镜PO的光为线偏振光;第一会聚透镜L1使得入射至投影物镜PO的光具有第一数值孔径,第二会聚透镜L2将投影物镜PO出射的第二数值孔径的光转换为平行光,所述第二数值孔径大于所述第一数值孔径。Preferably, the first condensing lens L1 and the second condensing lens L2 in this embodiment are both collimating lenses, and the two have different focal lengths. In this embodiment, the first polarizing plate P1 is used To ensure that the light incident on the projection objective PO is linearly polarized light; the first condensing lens L1 causes the light incident on the projection objective PO to have a first numerical aperture, and the second condensing lens L2 emits the light of the second numerical aperture emitted from the projection objective PO. Converted into parallel light, the second numerical aperture is larger than the first numerical aperture.
本发明提供了一种投影物镜偏振像差测量方法,下面结合图1及图2理解本发明的投影物镜偏振像差测量方法的具体测量过程。The present invention provides a method for measuring the polarization aberration of a projection objective. The specific measurement process of the method for measuring the polarization aberration of a projection objective of the present invention is described below with reference to FIGS. 1 and 2.
首先,执行步骤S1,沿光路传播方向依次设置第一偏振片P1、第一四分之一波片Q1、第一会聚透镜L1、投影物镜PO、第二会聚透镜L2、第二四分之一波片Q2、第二偏振片P2及光强测量装置IS;测量开始前,选取稳定的光束作为入射光,由于本发明测量方案前端包含的偏振片和波片会对入射光进行调制,所以只要求入射光相对稳定即可。First, step S1 is performed, and a first polarizing plate P1, a first quarter wave plate Q1, a first condensing lens L1, a projection objective lens PO, a second converging lens L2, and a second quarter are set in order along the propagation direction of the optical path. Wave plate Q2, second polarizing plate P2, and light intensity measuring device IS; before the measurement starts, a stable light beam is selected as the incident light. Since the polarizing plate and the wave plate included in the front end of the measurement solution of the present invention modulate the incident light, only the It is only required that the incident light is relatively stable.
接着,执行步骤S2,建立旋转角组集合,所述旋转角组集合中的元素为由第一偏振片P1的旋转角、第一四分之一波片Q1的旋转角、第二偏振片P2的旋转角和第二四分之一波片Q2的旋转角共同构成的旋转角的组合,所述旋转角组集合中的元素互不相同,旋转角为偏振片的亮轴、波片的快轴与给定方向(一般为X方向)的夹角。Next, step S2 is executed to establish a rotation angle group set, where the elements in the rotation angle group set are the rotation angle of the first polarizer P1, the rotation angle of the first quarter wave plate Q1, and the second polarizer P2. The combination of the rotation angle and the rotation angle of the second quarter wave plate Q2 is a combination of rotation angles. The elements in the rotation angle group set are different from each other. The rotation angle is the bright axis of the polarizer and the speed of the wave plate. The angle between the axis and a given direction (usually the X direction).
接着,执行步骤S3,在所述旋转角组集合选取一元素,并按照选取的元素分别调节第一偏振片P1、第一四分之一波片Q1、第二四分之一波片Q2和第二偏振片P2,从而使得四个元件具有对应所选取的元素的旋转角。Next, step S3 is executed, an element is selected from the set of rotation angles, and the first polarizing plate P1, the first quarter wave plate Q1, the second quarter wave plate Q2, and The second polarizer P2, so that the four elements have a rotation angle corresponding to the selected element.
接着,执行步骤S4,所述光强测量装置IS测得当前元素下的一组光强值。Next, step S4 is performed, and the light intensity measuring device IS measures a group of light intensity values under the current element.
所述光强测量装置IS测量获得的光强图中每一个点对应投影物镜PO的光瞳面的一点,投影物镜PO光瞳面的每一点具有一个独立的琼斯矩阵,本发 明的投影物镜偏振像差测量方法基于光强图中的点与投影物镜的光瞳面中的点的对应关系,由于投影物镜光瞳面中每一个点都有一组光强值,通过对这组光强值单独求解,测量获得与之对应的投影物镜的光瞳面点的琼斯矩阵,进而获得整个投影物镜的光瞳面的琼斯矩阵分布。Each point in the light intensity map obtained by the light intensity measurement device IS corresponds to a point on the pupil surface of the projection objective PO, and each point on the pupil surface of the projection objective PO has an independent Jones matrix. The projection objective of the present invention has polarization The aberration measurement method is based on the correspondence between the points in the light intensity map and the points in the pupil plane of the projection objective lens. Since each point in the pupil surface of the projection objective lens has a set of light intensity values, by separately Solve, measure and obtain the Jones matrix of the pupil plane point of the corresponding projection objective lens, and then obtain the Jones matrix distribution of the pupil plane of the entire projection objective lens.
具体的,在未考虑所述第一会聚透镜L1和所述第二会聚透镜L2的琼斯矩阵时(由于会聚透镜的琼斯矩阵较理想透镜误差很小,因此这里忽略不计),所述光强测量装置IS测得当前元素下的一组光强值采用的计算公式为:Specifically, when the Jones matrix of the first condensing lens L1 and the second condensing lens L2 is not considered (because the Jones matrix of the condensing lens has a smaller error than the ideal lens, it is ignored here), the light intensity measurement The calculation formula used by the device IS to measure a group of light intensity values under the current element is:
Figure PCTCN2019093838-appb-000010
Figure PCTCN2019093838-appb-000010
其中,I为光强值,E out为出射光的能量,根据光的传播公式可知:E out=J P2·J Q2·J PO·J Q1·J P1·E in(其中,忽略了第一会聚透镜L1和第二会聚透镜L2的琼斯矩阵);
Figure PCTCN2019093838-appb-000011
D=J Q1·J P1·E in;E in为入射光的能量;*表示共轭转置;J P1为第一偏振片P1的琼斯矩阵,J P2为第二偏振片P2的琼斯矩阵,J Q1为第一四分之一波片Q1的琼斯矩阵,J Q2为第二四分之一波片Q2的琼斯矩阵;波片和偏振片的琼斯矩阵分别为
Figure PCTCN2019093838-appb-000012
Figure PCTCN2019093838-appb-000013
J PO为投影物镜PO的琼斯矩阵;R为旋转矩阵,
Figure PCTCN2019093838-appb-000014
α为对应波片或偏振片的旋转角,由旋转矩阵R的公式可以获知:光强测量装置IS测得的光强与投影物镜PO的琼斯矩阵有关,同时也与四个元件的旋转角度相关。
Among them, I is the light intensity value and E out is the energy of the outgoing light. According to the light propagation formula, it can be known that E out = J P2 · J Q2 · J PO · J Q1 · J P1 · E in (where the first is ignored Jones matrix of the condenser lens L1 and the second condenser lens L2);
Figure PCTCN2019093838-appb-000011
D = J Q1 · J P1 · E in ; E in is the energy of the incident light; * represents the conjugate transpose; J P1 is the Jones matrix of the first polarizer P1, J P2 is the Jones matrix of the second polarizer P2, J Q1 is the Jones matrix of the first quarter wave plate Q1, J Q2 is the Jones matrix of the second quarter wave plate Q2; the Jones matrices of the wave plate and the polarizer are
Figure PCTCN2019093838-appb-000012
with
Figure PCTCN2019093838-appb-000013
J PO is the Jones matrix of the projection objective PO; R is the rotation matrix,
Figure PCTCN2019093838-appb-000014
α is the rotation angle of the corresponding wave plate or polarizing plate. It can be known from the formula of the rotation matrix R that the light intensity measured by the light intensity measuring device IS is related to the Jones matrix of the projection objective PO and is also related to the rotation angle of the four elements .
接着,执行步骤S5,反复执行S3、S4至少16次以获得多组光强值,其中,每次执行S3选取一个不同的元素,并将光强测量装置IS测量获得的所 述多组光强值构建为一光强矩阵,将所有选取的元素构建为一λ函数矩阵,λ函数矩阵中元素为第一偏振片P1、第一四分之一波片Q1、第二四分之一波片Q2和第二偏振片P2的琼斯矩阵中元素及其复共轭乘积的系数;优选的,选取的元素中各个旋转角的调整步长范围为30~60度,即相邻两个选取的元素中同一对象的旋转角的差值介于30~60度,本实施例中相邻两个选取的元素中同一对象的旋转角的调整步长为45度。Next, step S5 is performed, and S3 and S4 are repeatedly performed at least 16 times to obtain multiple groups of light intensity values, wherein each time S3 is performed, a different element is selected, and the multiple groups of light intensity obtained by the light intensity measurement device IS are measured. The value is constructed as a light intensity matrix, and all selected elements are constructed as a lambda function matrix. The elements in the lambda function matrix are the first polarizer P1, the first quarter wave plate Q1, and the second quarter wave plate. Coefficients of the elements in the Jones matrix of Q2 and the second polarizer P2 and their complex conjugate products; preferably, the adjustment step of each rotation angle in the selected elements is 30 to 60 degrees, that is, two adjacent selected elements The difference between the rotation angles of the same object in the range of 30 to 60 degrees. In this embodiment, the adjustment step of the rotation angle of the same object in two adjacent selected elements is 45 degrees.
本发明的投影物镜偏振像差测量方法除了可以测量投影物镜的偏振像差外,还可以测量其他元件的偏振像差。In addition to the polarization aberration measurement method of the projection objective lens of the present invention, the polarization aberration measurement method of the projection objective lens can also measure the polarization aberration of other elements.
其中,所述将所有选取的元素构建为一λ函数矩阵以及获取投影物镜PO的琼斯矩阵的过程如下:The process of constructing all selected elements into a lambda function matrix and obtaining the Jones matrix of the projection objective PO is as follows:
S50:定义
Figure PCTCN2019093838-appb-000015
D=J Q1·J P1·E in
S50: Definition
Figure PCTCN2019093838-appb-000015
D = J Q1 · J P1 · E in ;
S51:简化公式(1)为:S51: The simplified formula (1) is:
Figure PCTCN2019093838-appb-000016
Figure PCTCN2019093838-appb-000016
S52:将公式(2)简化为投影物镜琼斯矩阵元素及其复共轭乘积的一次函数:S52: Simplify the formula (2) into a linear function of the projection objective Jones matrix element and its complex conjugate product:
Figure PCTCN2019093838-appb-000017
Figure PCTCN2019093838-appb-000017
具体的,公式(3)是基于在所述旋转角组集合中的选取的不同元素,可以基于光强测量装置IS测量得到不同组光强值,利用线性代数关系,可以得到:Specifically, formula (3) is based on different elements selected in the set of rotation angle groups, and different groups of light intensity values can be obtained based on the light intensity measuring device IS. Using a linear algebraic relationship, it can be obtained:
Figure PCTCN2019093838-appb-000018
Figure PCTCN2019093838-appb-000018
其中,x,y=1,2;等号左边为光强列I,代表四个元件的不同旋转角度的 测量;等号右边λ函数矩阵的行数表示测量次数,λ函数矩阵的每列分别对应投影物镜PO的琼斯矩阵元素乘积的系数;下标表示的是投影物镜PO的琼斯矩阵元素乘积形式,上标表示光强组的组号。Among them, x, y = 1,2; to the left of the equal sign is the light intensity column I, which represents the measurement of different rotation angles of the four elements; to the right of the equal sign, the number of rows of the λ function matrix represents the number of measurements, and each column of the λ function matrix is The coefficient corresponding to the product of the Jones matrix element of the projection objective PO; the subscript indicates the product form of the Jones matrix element of the projection objective PO, and the superscript indicates the group number of the light intensity group.
将公式(4)改写成矩阵形式,可以得到:Rewriting formula (4) into matrix form, we can get:
I=Γ(n)XI = Γ (n) X
其中,I为光强矩阵,Γ为λ函数矩阵,X为投影物镜琼斯矩阵元素及其复共轭乘积构成的矩阵。Among them, I is a light intensity matrix, Γ is a lambda function matrix, and X is a matrix composed of a projection objective Jones matrix element and a complex conjugate product thereof.
S53:获得λ函数矩阵中元素计算公式:λ i,j,k,l=U l·M ki·D j,并计算λ函数矩阵Γ中所有元素,以构建λ函数矩阵Γ; S53: Obtain a formula for calculating the elements in the λ function matrix: λ i, j, k, l = U l · M ki · D j , and calculate all elements in the λ function matrix Γ to construct a λ function matrix Γ;
其中,U,M,D为简化后的矩阵,用矩阵分别表示为U=[U 1 U 2],
Figure PCTCN2019093838-appb-000019
J P1为第一偏振片P1的琼斯矩阵,J P2为第二偏振片P2的琼斯矩阵,J Q1为第一四分之一波片Q1的琼斯矩阵,J Q2为第二四分之一波片Q2的琼斯矩阵;E in为入射光的能量;*表示共轭转置;其中,i,j,k,l表示投影物镜PO的琼斯矩阵中元素的下标,分别取值1或2;λ i,j,k,l为λ函数矩阵中元素。
Among them, U, M, and D are simplified matrices, and the matrices are expressed as U = [U 1 U 2 ],
Figure PCTCN2019093838-appb-000019
J P1 is the Jones matrix of the first polarizer P1, J P2 is the Jones matrix of the second polarizer P2, J Q1 is the Jones matrix of the first quarter wave plate Q1, and J Q2 is the second quarter wave Jones matrix of slice Q2; E in is the energy of the incident light; * represents the conjugate transpose; where i, j, k, l represent the subscripts of the elements in the Jones matrix of the projection objective PO, which take values 1 or 2 respectively; λ i, j, k, l are the elements in the λ function matrix.
接着,执行步骤S6,根据所述光强矩阵和所述λ函数矩阵计算投影物镜PO的琼斯矩阵。Next, step S6 is performed to calculate a Jones matrix of the projection objective PO according to the light intensity matrix and the lambda function matrix.
具体的,通过调节具有不同旋转角度的第一偏振片P1、第一四分之一波片Q1、第二四分之一波片Q2和第二偏振片P2,可以将投影物镜PO的琼斯矩阵中涉及的未知参数求解出来。Specifically, by adjusting the first polarizer P1, the first quarter-wave plate Q1, the second quarter-wave plate Q2, and the second polarizer P2 with different rotation angles, the Jones matrix of the projection objective PO can be adjusted. Solve unknown parameters involved in.
较佳的,若S5中反复执行S3、S4的次数大于16次,S6中采用最小二乘法计算投影物镜的琼斯矩阵的近似值,从而有效避免计算误差,提高计算精准度。Preferably, if S3 and S4 are repeatedly performed more than 16 times in S5, the least square method is used in S6 to calculate the approximate value of the Jones matrix of the projection objective lens, thereby effectively avoiding calculation errors and improving the calculation accuracy.
采用最小二乘法计算时,X=(Γ T(n)Γ(n)) -1·Γ(n) T·I,通过调节具有不同旋转角度的第一偏振片P1、第一四分之一波片Q1、第二四分之一波片Q2和第二偏振片P2,可以将投影物镜PO的琼斯矩阵中涉及的7个未知参数求解出来: When using the least squares calculation, X = (Γ T (n) Γ (n)) -1 · Γ (n) T · I, by adjusting the first polarizer P1 and the first quarter with different rotation angles The wave plate Q1, the second quarter wave plate Q2, and the second polarizing plate P2 can solve the 7 unknown parameters involved in the Jones matrix of the projection objective PO:
Figure PCTCN2019093838-appb-000020
Figure PCTCN2019093838-appb-000020
这里J xx设为实数,不包含相位部分,因此该方法不能测量波像差。 Here J xx is set to a real number and does not include a phase portion, so this method cannot measure wave aberrations.
在本发明的投影物镜偏振像差测量方法采用最小二乘法计算投影物镜的琼斯矩阵时,其主要误差来源在于最小二乘法,即λ函数矩阵Γ,想要降低计算误差,可以减小λ函数矩阵Γ的条件数。When the projection objective lens polarization aberration measurement method of the present invention uses the least square method to calculate the Jones matrix of the projection objective lens, the main error source lies in the least square method, that is, the λ function matrix Γ. To reduce the calculation error, the λ function matrix can be reduced The condition number of Γ.
经对λ函数矩阵Γ分析可知,Γ由两部分构成,即投影物镜前面的部分(P1,Q1)和投影物镜后面的部分(Q2,P2),该两部分的琼斯矩阵决定了每一行的λ系数,所以,Γ的条件数由前后两个部分的旋转角(方向角)决定。对每一组确定的旋转角度组合,可以计算得到Γ的条件数,这样就可以找到一个条件数较小的旋转角度组合,减小随机误差对量测结果造成的影响。The analysis of the λ function matrix Γ shows that Γ is composed of two parts, that is, the part in front of the projection objective (P1, Q1) and the part behind the projection objective (Q2, P2). The Jones matrix of the two parts determines the λ of each row Coefficient, so the condition number of Γ is determined by the rotation angle (direction angle) of the front and back parts. For each group of rotation angle combinations determined, the condition number of Γ can be calculated, so that a rotation angle combination with a smaller number of conditions can be found to reduce the effect of random errors on the measurement results.
对于实施例公开的方法而言,由于与实施例公开的结构相对应,所以描述的比较简单,相关之处参见结构部分说明即可。As for the method disclosed in the embodiment, since it corresponds to the structure disclosed in the embodiment, the description is relatively simple, and the relevant part may refer to the description of the structure part.
综上,在本发明所提供的投影物镜偏振像差测量方法中,所述投影物镜偏振像差测量方法通过基于光强测量装置测量获得所有组光强值构建为的光强矩阵和所有选取的元素构建的λ函数矩阵计算投影物镜的琼斯矩阵,即本发明的测量方法可以直接计算获得投影物镜的琼斯矩阵,相比现有方法中先测量获得穆勒矩阵,再将穆勒矩阵转换至琼斯矩阵的方法,有效避免因穆勒矩阵转换至琼斯矩阵的退偏效应造成的结果误差,提高了测量和计算精准度,提升了产品成像效果。In summary, in the projection objective lens polarization aberration measurement method provided by the present invention, the projection objective lens polarization aberration measurement method obtains a light intensity matrix constructed by all groups of light intensity values and all selected The lambda function matrix constructed by the elements calculates the Jones matrix of the projection objective lens, that is, the measurement method of the present invention can directly calculate and obtain the Jones matrix of the projection objective lens. Compared with the existing method, the Mueller matrix is obtained by measuring first, and then the Mueller matrix is converted to Jones. The matrix method effectively avoids the result error caused by the depolarization effect of the conversion of the Mueller matrix to the Jones matrix, improves the measurement and calculation accuracy, and improves the product imaging effect.
上述描述仅是对本发明较佳实施例的描述,并非对本发明范围的任何限定,本发明领域的普通技术人员根据上述揭示内容做的任何变更、修饰,均属于权利要求书的保护范围。The above description is only a description of the preferred embodiments of the present invention, and does not limit the scope of the present invention. Any changes and modifications made by those of ordinary skill in the art according to the above disclosure shall fall into the protection scope of the claims.

Claims (11)

  1. 一种投影物镜偏振像差测量方法,其特征在于,所述投影物镜偏振像差测量方法包括如下步骤:A method for measuring the polarization aberration of a projection objective, characterized in that the method for measuring the polarization aberration of a projection objective includes the following steps:
    S1:沿光路传播方向依次设置第一偏振片(P1)、第一四分之一波片(Q1)、第一会聚透镜(L1)、投影物镜(PO)、第二会聚透镜(L2)、第二四分之一波片(Q2)、第二偏振片(P2)及光强测量装置(IS);S1: A first polarizing plate (P1), a first quarter wave plate (Q1), a first condensing lens (L1), a projection objective (PO), a second converging lens (L2), The second quarter-wave plate (Q2), the second polarizer (P2), and the light intensity measuring device (IS);
    S2:建立旋转角组集合,所述旋转角组集合中的元素为由第一偏振片(P1)的旋转角、第一四分之一波片(Q1)的旋转角、第二偏振片(P2)的旋转角和第二四分之一波片(Q2)的旋转角共同构成的旋转角的组合,所述旋转角组集合中的元素互不相同,其中,旋转角为偏振片的亮轴或波片的快轴与给定方向的夹角;S2: A rotation angle group set is established, and the elements in the rotation angle group set are the rotation angle of the first polarizer (P1), the rotation angle of the first quarter wave plate (Q1), and the second polarizer ( The combination of the rotation angle formed by the rotation angle of P2) and the rotation angle of the second quarter wave plate (Q2). The elements in the rotation angle group set are different from each other, where the rotation angle is the brightness of the polarizer. The angle between the fast axis of the axis or waveplate and the given direction;
    S3:在所述旋转角组集合中选取一元素,并按照选取的元素分别调节第一偏振片(P1)、第一四分之一波片(Q1)、第二四分之一波片(Q2)和第二偏振片(P2)的旋转角;S3: Select an element from the set of rotation angle groups, and adjust the first polarizing plate (P1), the first quarter wave plate (Q1), and the second quarter wave plate ( Q2) and the rotation angle of the second polarizer (P2);
    S4:所述光强测量装置(IS)测得对应于当前元素的一组光强值;S4: the light intensity measuring device (IS) measures a set of light intensity values corresponding to the current element;
    S5:反复执行S3和S4至少16次以获得多组光强值,其中,每次执行S3选取一个不同的元素,并将光强测量装置(IS)测量获得的所述多组光强值构建为一光强矩阵,将所有选取的元素构建为一λ函数矩阵,λ函数矩阵中元素为第一偏振片(P1)、第一四分之一波片(Q1)、第二四分之一波片(Q2)和第二偏振片(P2)的琼斯矩阵中元素及其复共轭乘积的系数;S5: Repeat S3 and S4 at least 16 times to obtain multiple groups of light intensity values, wherein each time S3 is performed, a different element is selected and the multiple groups of light intensity values obtained by the light intensity measurement device (IS) measurement are constructed Is a light intensity matrix. All selected elements are constructed as a lambda function matrix. The elements in the lambda function matrix are the first polarizer (P1), the first quarter wave plate (Q1), and the second quarter. The coefficients of the elements in the Jones matrix of the wave plate (Q2) and the second polarizer (P2) and their complex conjugate products;
    S6:根据所述光强矩阵和所述λ函数矩阵计算投影物镜(PO)的琼斯矩阵。S6: Calculate a Jones matrix of a projection objective (PO) according to the light intensity matrix and the lambda function matrix.
  2. 如权利要求1所述的投影物镜偏振像差测量方法,其特征在于,在未 考虑所述第一会聚透镜(L1)和所述第二会聚透镜(L2)的琼斯矩阵时,S4中计算光强值采用的计算公式如下:The method for measuring the polarization aberration of a projection objective according to claim 1, wherein the light is calculated in S4 when the Jones matrix of the first condensing lens (L1) and the second condensing lens (L2) is not considered. The calculation formula for the strong value is as follows:
    Figure PCTCN2019093838-appb-100001
    Figure PCTCN2019093838-appb-100001
    其中,I为光强值,E out为出射光的能量,E out=J P2·J Q2·J PO·J Q1·J P1·E in;*表示共轭转置;J P1为第一偏振片(P1)的琼斯矩阵,J P2为第二偏振片(P2)的琼斯矩阵,J Q1为第一四分之一波片(Q1)的琼斯矩阵,J Q2为第二四分之一波片(Q2)的琼斯矩阵;J PO为投影物镜(PO)的琼斯矩阵;波片和偏振片的琼斯矩阵分别为
    Figure PCTCN2019093838-appb-100002
    Figure PCTCN2019093838-appb-100003
    R为旋转矩阵,
    Figure PCTCN2019093838-appb-100004
    α为对应波片或偏振片的旋转角;Ein为入射光的能量。
    Among them, I is the light intensity value, E out is the energy of the outgoing light, E out = J P2 · J Q2 · J PO · J Q1 · J P1 · E in ; * represents the conjugate transpose; J P1 is the first polarization Jones matrix of the plate (P1), J P2 is the Jones matrix of the second polarizer (P2), J Q1 is the Jones matrix of the first quarter wave plate (Q1), and J Q2 is the second quarter wave Jones matrix of lens (Q2); J PO is the Jones matrix of projection objective (PO); Jones matrix of wave plate and polarizer are
    Figure PCTCN2019093838-appb-100002
    with
    Figure PCTCN2019093838-appb-100003
    R is the rotation matrix,
    Figure PCTCN2019093838-appb-100004
    α is the rotation angle of the corresponding wave plate or polarizer; Ein is the energy of incident light.
  3. 如权利要求2所述的投影物镜偏振像差测量方法,其特征在于,S5中,所述将所有选取的元素构建为一λ函数矩阵包括如下步骤:The method for measuring the polarization aberration of a projection objective according to claim 2, wherein in S5, the step of constructing all selected elements into a lambda function matrix comprises the following steps:
    S50:定义
    Figure PCTCN2019093838-appb-100005
    D=J Q1·J P1·E in
    S50: Definition
    Figure PCTCN2019093838-appb-100005
    D = J Q1 · J P1 · E in ;
    S51:获得λ函数矩阵中元素计算公式:λ i,j,k,l=U l·M ki·D j,并计算λ函数矩阵中所有元素,以构建λ函数矩阵; S51: Obtain a formula for calculating the elements in the λ function matrix: λ i, j, k, l = U l · M ki · D j , and calculate all elements in the λ function matrix to construct a λ function matrix;
    其中,U,M,D为简化后的矩阵,用矩阵分别表示为U=[U 1 U 2],
    Figure PCTCN2019093838-appb-100006
    J P1为第一偏振片(P1)的琼斯矩阵,J P2为第二偏振片(P2)的琼斯矩阵,J Q1为第一四分之一波片(Q1)的琼斯矩阵,J Q2为第二四分之一波片(Q2)的琼斯矩阵;E in为入射光的能量;*表示共轭 转置;其中,i,j,k,l表示琼斯矩阵中元素的下标,分别取值1或2;λ i,j,k,l为λ函数矩阵中元素。
    Among them, U, M, and D are simplified matrices, and the matrices are expressed as U = [U 1 U 2 ],
    Figure PCTCN2019093838-appb-100006
    J P1 is the Jones matrix of the first polarizer (P1), J P2 is the Jones matrix of the second polarizer (P2), J Q1 is the Jones matrix of the first quarter wave plate (Q1), and J Q2 is the first Jones matrix of the quarter-wave plate (Q2); E in is the energy of the incident light; * represents the conjugate transpose; where i, j, k, l represent the subscripts of the elements in the Jones matrix, and take values respectively 1 or 2; λ i, j, k, l are the elements in the λ function matrix.
  4. 如权利要求3所述的投影物镜偏振像差测量方法,其特征在于,S6中,根据所述光强矩阵和所述λ函数矩阵计算投影物镜(PO)的琼斯矩阵包括如下步骤:The method for measuring polarization aberration of a projection objective according to claim 3, wherein in S6, calculating the Jones matrix of the projection objective (PO) according to the light intensity matrix and the lambda function matrix comprises the following steps:
    S60:简化公式(1)为:S60: The simplified formula (1) is:
    Figure PCTCN2019093838-appb-100007
    Figure PCTCN2019093838-appb-100007
    S61:将公式(2)简化为投影物镜琼斯矩阵元素及其复共轭乘积的一次函数:
    Figure PCTCN2019093838-appb-100008
    S61: Simplify the formula (2) into a linear function of the projection objective Jones matrix element and its complex conjugate product:
    Figure PCTCN2019093838-appb-100008
    S62:计算投影物镜(PO)的琼斯矩阵中元素,以得到投影物镜(PO)的琼斯矩阵;S62: Calculate elements in the Jones matrix of the projection objective (PO) to obtain the Jones matrix of the projection objective (PO);
    其中,J i,j为投影物镜(PO)的琼斯矩阵中元素,
    Figure PCTCN2019093838-appb-100009
    为投影物镜(PO)的琼斯矩阵中元素的复共轭。
    Where J i, j are the elements in the Jones matrix of the projection objective (PO),
    Figure PCTCN2019093838-appb-100009
    Complex conjugate of the elements in the Jones matrix of the projection objective (PO).
  5. 如权利要求1所述的投影物镜偏振像差测量方法,其特征在于,若S5中反复执行S3和S4的次数大于16次,则S6中采用最小二乘法计算投影物镜的琼斯矩阵的近似值。The method for measuring the polarization aberration of a projection objective according to claim 1, wherein if S3 and S4 are repeatedly performed more than 16 times in S5, the least square method is used in S6 to calculate an approximate value of the Jones matrix of the projection objective.
  6. 如权利要求5所述的投影物镜偏振像差测量方法,其特征在于,S5中,选取的元素中各个旋转角的调整步长范围为30~60度。The method for measuring the polarization aberration of a projection objective according to claim 5, characterized in that, in S5, an adjustment step of each rotation angle in the selected element ranges from 30 to 60 degrees.
  7. 如权利要求6所述的投影物镜偏振像差测量方法,其特征在于,所述给定方向为X轴或Y轴方向。The method for measuring the polarization aberration of a projection objective according to claim 6, wherein the given direction is an X-axis or Y-axis direction.
  8. 如权利要求1所述的投影物镜偏振像差测量方法,其特征在于,所述第一会聚透镜(L1)和所述第二会聚透镜(L2)均为准直透镜,且两者具有不同的焦距。The method of measuring the polarization aberration of a projection objective according to claim 1, wherein the first condensing lens (L1) and the second condensing lens (L2) are collimating lenses, and the two have different focal length.
  9. 如权利要求1所述的投影物镜偏振像差测量方法,其特征在于,所述 第一会聚透镜(L1)使得入射至投影物镜(PO)的光具有第一数值孔径,所述第二会聚透镜(L2)将所述投影物镜(PO)出射的具有第二数值孔径的光转换为平行光,所述第二数值孔径大于所述第一数值孔径。The method of measuring the polarization aberration of a projection objective according to claim 1, wherein the first condensing lens (L1) enables light incident on the projection objective (PO) to have a first numerical aperture, and the second condensing lens (L2) converting light having a second numerical aperture emitted by the projection objective (PO) into parallel light, the second numerical aperture being larger than the first numerical aperture.
  10. 如权利要求1所述的投影物镜偏振像差测量方法,其特征在于,所述光强测量装置(IS)测量获得的光强图中每一个点对应投影物镜(PO)的光瞳面的一点。The method for measuring polarization aberration of a projection objective according to claim 1, characterized in that each point in the light intensity map obtained by the light intensity measurement device (IS) measurement corresponds to a point on the pupil surface of the projection objective (PO) .
  11. 如权利要求1所述的投影物镜偏振像差测量方法,其特征在于,测量开始前,选取稳定的光束作为入射光。The method for measuring the polarization aberration of a projection objective according to claim 1, wherein before the measurement is started, a stable light beam is selected as the incident light.
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