CN115436025A - Method for measuring numerical aperture of optical system based on grating shearing interference - Google Patents

Abstract

The method for measuring the numerical aperture of the optical system based on grating shearing interference comprises the following steps: the device comprises an optical and illumination system, an optical system to be measured, an object plane diffraction grating plate, an image plane diffraction grating plate, a two-dimensional photoelectric sensor and a calculation processing unit. The object plane diffraction grating plate and the image plane diffraction grating plate are respectively arranged on the object plane and the image plane of the optical system to be measured. During measurement, differential wavefronts at two or more axial positions are measured and fitted to obtain an inclination term coefficient by an axial scanning method, and the numerical aperture of the system to be measured is directly calculated by utilizing the difference value of the inclination term coefficients of the differential wavefronts at the adjacent positions and the axial distance of the adjacent positions. The method does not need to manufacture extra gratings, can obtain the measurement of the numerical aperture of the optical system to be measured by only adding one step of measurement of the shearing phase on the basis of the wave aberration measurement, and has the advantages of simple measurement process, convenient operation and the like.

Description

Measuring method of numerical aperture of optical system based on grating shearing interference

technical field

The invention relates to the technical field of optical measurement, in particular to a method for measuring the numerical aperture (NA) of an optical system based on grating shearing interferometer, which is applicable to the numerical value of the projection objective lens of a photolithography machine or other optical imaging systems based on a grating shearing interferometer. Aperture measurement.

Background technique

Ronchi grating shearing interferometer is a shearing interferometer that uses an extended light source and uses a grating on the object plane to modulate the coherence of the light source. It has a common optical path, a large dynamic range, no separate ideal reference wave surface, and high precision. Advantages such as simple structure. For example, prior art 1 (Lu Yunjun, Tang Feng, Wang Xiangchao, Wave aberration detection method for grating shearing interference optical imaging system, Chinese invention patent, patent number: 109900201B) proposed a differential wavefront extraction algorithm for Ronchi shearing interferometer , the phase-shifted interferogram can be processed to obtain the differential wavefront, and on this basis, the wavefront aberration of the system under test can be obtained by wavefront reconstruction.

As an important parameter of the optical system, the numerical aperture (NA) determines the imaging resolution of the optical system. When using a double-grating Ronchi shearing interferometer to measure the wave aberration of the optical system to be tested, it is also necessary to accurately calibrate the NA in advance. . In addition, for the development of high NA shearing interferometer systems, it is also necessary to calibrate the NA to establish a non-uniformly distributed shear volume model to achieve high-precision measurement of wave aberration.

The traditional NA measurement method needs to calibrate the focal length and the diameter of the exit pupil. Although there are many measurement methods for the focal length, the exit pupil diameter cannot be directly measured in many cases. Prior art 2 (Sukmock Lee, Direct determination off-number by using Ronchi test, Optics Express, 17 (7), 5107-5111.) A kind of f-number measurement method based on Ronchi shearing interferometer that proposes, this method can From the wave aberration at two different locations, the defocus term in the reconstructed wavefront is established as a function of f. The numerical aperture of the objective lens to be measured can be obtained by converting the f number. At that time, this method needed to measure the shear phase in the x direction and the y direction at the same time, and then perform wavefront reconstruction to obtain the reconstructed wavefront. The test process and data processing were relatively complicated, and it was necessary to switch the x direction and The y-direction grating is easy to introduce errors in the wavefront reconstruction process, which reduces the accuracy of NA calibration.

At present, there is no simple and high-precision numerical aperture detection method based on a grating shearing interferometer.

Contents of the invention

The purpose of the present invention is to overcome the deficiencies of the above-mentioned prior art, and propose a method for measuring the numerical aperture of an optical system with a simpler process and higher measurement accuracy. Measurement, the NA of the optical system to be tested is calculated directly through the difference of the coefficient of the tilt item Z2 (or Z3) of the differential wavefront. This method does not require wavefront reconstruction, and only needs to measure the x or y directions of two different positions The differential wavefront simplifies the measurement process and data processing process, improves measurement efficiency and measurement accuracy, and the method is easily integrated into the Ronchi shearing interferometer system.

In order to achieve the above object, the technical solution of the present invention is as follows:

A method for measuring the numerical aperture of an optical system based on grating shearing interference. The grating shearing interferometer used in this method includes: a light source and an illumination system, an object plane diffraction grating plate, a first three-dimensional translation stage, an image plane diffraction grating plate, a second A three-dimensional translation platform, a two-dimensional photoelectric sensor and a calculation processing unit, the light source and the lighting system output spatially incoherent light, the object plane diffraction grating plate is fixed on the first three-dimensional translation platform, and the image plane diffraction grating The plate is fixed on the second three-dimensional translation stage, the image plane diffraction grating plate is fixed on the second three-dimensional translation stage, and the object plane diffraction grating plate contains two groups of one-dimensional gratings whose grating directions are perpendicular to each other. The image surface diffraction grating plate contains a set of checkerboard gratings or two sets of one-dimensional gratings whose grating lines are perpendicular to each other. The output end of the two-dimensional photoelectric sensor is connected to the calculation and processing unit to establish an xyz coordinate system, and the z-axis direction is along the The direction of the optical axis of the system, the x-axis is along the grating line direction of the second grating on the object plane diffraction grating plate, the y axis is along the grating line direction of the first grating on the object plane diffraction grating plate, and the first three-dimensional displacement stage and the second three-dimensional The motion axis of displacement stage is respectively x-axis, y-axis and z-axis; The included angle of described checkerboard grating diagonal direction and x-axis (or y-axis) is 45 degrees; Its characteristic is that the steps of this method are as follows:

(1) Place the optical system to be tested in the grating shearing interferometer, so that the light source and illumination system are located on the object side of the optical system to be tested, and the image plane diffraction grating plate is located on the image side of the optical system to be tested, adjust the first A three-dimensional translation stage, so that the object plane diffraction grating plate is located on the object plane of the optical system to be tested, and the second three-dimensional translation platform is adjusted so that the image plane diffraction grating plate is located on the image plane of the optical system to be tested;

(2) Adjust the first three-dimensional translation stage so that the second grating or the first grating on the object plane diffraction grating plate enters the field of view of the optical system to be tested, adjust the second three-dimensional translation stage so that the checkerboard grating on the image plane diffraction grating plate Or the one-dimensional grating in the corresponding direction enters the field of view, and is conjugate to the position of the second grating on the object plane diffraction grating plate. Record the position of the image plane grating at this time, denoted as P ₁ ;

(3) Taking P1 as the starting point, define N positions (N>=2) of the second translation stage scanning along the z direction, as the axial scanning position, denoted as P _i , wherein i=1, 2, 3...N;

对

进行Zernike拟合，提取Z2项系数c_2,i，其中，i＝1，2，3…N；(4) If the second grating 102 enters the field of view of the optical system 3 to be tested, use the prior art 1 to obtain a series of shear interferograms in the x-axis direction through the phase shift of the object plane or image plane grating, and measure the x-axis directional differential wavefront

right

Carry out Zernike fitting and extract the Z2 term coefficient c _2,i , where i=1, 2, 3...N;

对

进行Zernike拟合，提取Z3项系数c_3,i，其中，i＝1，2，3…N；If the first grating 101 enters the field of view of the optical system under test 3, using the prior art 1, a series of shear interferograms in the y-axis direction are obtained through the phase shift of the object plane or image plane grating, and the differential wave in the y-axis direction is obtained by measurement forward

right

Carry out Zernike fitting and extract the Z3 term coefficient c _3,i , where i=1, 2, 3...N;

(5) If the current z-direction position P _i of the second displacement platform is P _N , then enter step 6), otherwise the second displacement platform moves to the next position P _i+1 , so that P _i = P _i+1 , return to step 4);

(6) If the second grating 102 enters the field of view of the optical system 3 to be tested, the Z2 coefficient c ₂ ,i is subtracted from the Z2 coefficient c _2,i-1 of the previous position to obtain N-1 Z2 coefficients Difference △c _2,i , subtract the position P _i from the previous position P _i-1 to get the corresponding axial distance △Z _i , where i=2, 3...N; according to the formula (1) Calculate the size of numerical aperture NA of N-1 groups of optical systems to be tested:

If the first grating 101 enters the field of view of the optical system under test _3, the Z3 coefficient c 3,i is subtracted from the Z3 coefficient c _3,i-1 of the previous position to obtain the difference △ of N-1 Z3 coefficients c _3,i , subtract the position P _i from the previous position P _i-1 , and get the corresponding axial distance △Z _i , where i=2, 3...N, at this time, calculate according to the formula (2) The size of the numerical aperture NA of the optical system to be tested (3) of N-1 group:

(7) The final numerical aperture of the optical system to be tested (3) is the average value of the NA of the N-1 groups.

In the method for measuring the numerical aperture of an optical system based on grating shear interference, the ratio of the period of the one-dimensional grating on the object plane diffraction grating plate to the period of the checkerboard grating or one-dimensional grating on the image plane diffraction grating plate is equal to the optical system to be measured. System magnification.

In the method for measuring the numerical aperture of the optical system based on grating shear interference, the grating duty ratios on the object plane diffraction grating plate and on the image plane diffraction grating plate are both 50%.

The technical effect of the present invention is, based on the grating shearing interferometer, using the method of axial scanning, measuring the differential wavefront at two or more positions in the axial direction, and fitting the tilt term of the differential wavefront (x direction differential wavefront Z2 or the Z3) coefficient of the differential wavefront in the y direction, using the distance between two adjacent positions and the difference between the coefficients of the tilt term of the differential wavefront, directly calculate the NA of the optical system to be tested. This method does not need to make additional gratings, and the structure of the shearing interferometer does not need any change, only needs to add a measurement of the shearing phase, and has the characteristics of simple measurement process and simple output processing.

Description of drawings

Fig. 1 is the schematic diagram of the measurement device of the optical system numerical aperture based on grating shear interference;

Fig. 2 is the schematic diagram of object plane diffraction grating plate;

Fig. 3 is a schematic diagram of a checkerboard grating of an image plane diffraction grating;

Fig. 4 is a schematic diagram of grating defocus optical path difference;

Fig. 5 is a schematic diagram of the Z2 coefficient of the differential wavefront in the x direction and the Z3 coefficient of the differential wavefront in the y direction and the z-direction position of the grating;

Among them, 1. The object plane diffraction grating plate; 2. The first three-dimensional translation stage; 3. The optical system to be tested; 4. The image plane diffraction grating plate; 5. The second three-dimensional translation stage; 6. Two-dimensional photoelectric sensor; 7. Calculation processing unit; 8. Light source and lighting system.

detailed description

In order to better understand the purpose, technical solutions and advantages of the present invention, the present invention will be further described below in conjunction with the accompanying drawings and embodiments, but the protection scope of the present invention should not be limited thereby.

The invention discloses a method for measuring the numerical aperture of an optical system based on grating shearing interference. The grating shearing interferometer used in the method is shown in Figure 1. The system includes: a light source and an illumination system 8, an object plane diffraction grating plate 1, and A three-dimensional translation stage 2, an image plane diffraction grating plate 4, a second three-dimensional translation stage 5, a two-dimensional photoelectric sensor 6 and a calculation processing unit 7, the light source and the lighting system 8 output spatially incoherent light, and the object surface Diffraction grating plate 1 is fixed on the first three-dimensional translation stage 2, the image plane diffraction grating plate 4 is fixed on the second three-dimensional translation stage 5, and the output end of the two-dimensional photoelectric sensor 6 is connected to the calculation processing unit 7 ;

Establish an xyz coordinate system, the z-axis direction is along the optical axis direction of the shearing interferometer, the x-axis is along the grating line direction of the second grating 102 on the object-plane diffraction grating plate 1, and the y-axis is along the first grating line direction of the object-plane diffraction grating plate 1 For the grating line direction of the grating 101, the motion axes of the first three-dimensional translation stage 2 and the second three-dimensional translation stage 5 are respectively x-axis, y-axis and z-axis;

The first three-dimensional translation stage 2 is used to move the first grating 101 and the second grating 102 in the object plane diffraction grating plate 1 to the center of the object plane field of view of the optical system 3 to be tested;

The second three-dimensional displacement stage 5 is used to move the checkerboard grating in the image plane diffraction grating plate 4 to the center of the image plane field of view of the optical system to be tested 3, and carry out the x-axis direction and y axis direction of the image plane diffraction grating plate 4. Axis specific periodic movement;

The two-dimensional photoelectric sensor 6 can be a charge-coupled device CCD or a CMOS image sensor, and the detection surface receives the shear interference fringes generated by the diffraction of the checkerboard grating;

The calculation processing unit 7 is used to collect and store the interferogram, and to process and analyze the interferogram;

Fig. 2 is a schematic diagram of the object plane diffraction grating plate 1, which includes two one-dimensional diffraction gratings, respectively a first grating 101 with grating lines along the y-axis direction and a second grating 102 with grating lines along the x-axis direction , the period of the one-dimensional diffraction grating is P1, and the duty cycle is 50%;

The first grating 101 and the second grating 102 are phase gratings or amplitude gratings;

Fig. 3 is a schematic diagram of the 4 checkerboard gratings of the image plane diffraction grating version, which is a checkerboard grating with a period of P2 and a duty cycle of 50%; the checkerboard grating is composed of square grids, and the diagonal direction of the square is along the x-axis direction or y-axis direction;

The period P1 of a one-dimensional grating and the period P2 of a two-dimensional grating satisfy:

P1=M·P2 (1)

Wherein, M is the magnification of the imaging optical system 3 to be tested.

FIG. 4 is a schematic diagram of the optical path difference at any point M on the CCD when the image plane grating is defocused. The distance between the image plane grating 4 and the focal plane is △Z. Taking the shearing in the x direction as an example, the optical path difference introduced by +1 order light and -1 order light due to the defocusing of the image plane grating is:

Among them, P is the image plane grating period, NA is the numerical aperture of the optical system, and λ is the wavelength. It can be seen that the main component of the optical path difference is the tilt term (the Z2 term in the Zernike polynomial). Similarly, if it is shearing in the y direction, the main component of the optical path difference is the tilt term (Z3 term).

FIG. 5 shows the relationship curve between the shear phase tilt term coefficient (the Z2 term coefficient of the shear phase in the x direction or the Z3 coefficient of the shear phase in the y direction) and the defocus distance of the image plane grating.

Example 1:

Utilize the above-mentioned measuring method of optical system numerical aperture based on grating shearing interference, it is characterized in that the method comprises the following steps:

(1) The optical system 3 to be measured is placed in the grating shearing interferometer, so that the light source and the illumination system 8 are located on the object side of the optical system 3 to be measured, and the image plane diffraction grating plate 4 is located on the image of the optical system 3 to be measured. Adjust the first three-dimensional translation stage 2 so that the object plane diffraction grating plate 1 is located on the object plane of the optical system 3 to be tested, adjust the second three-dimensional translation stage 5 so that the image plane diffraction grating plate 4 is located on the image plane of the optical system 3 to be tested noodle;

(2) Adjust the first three-dimensional translation stage 2, so that the second grating 102 on the object plane diffraction grating plate 1 enters the field of view of the optical system 3 to be measured, and adjust the second three-dimensional translation stage 5, so that the second grating 102 on the image plane diffraction grating plate 4 The checkerboard grating or the one-dimensional grating in the corresponding direction enters the field of view and is conjugate to the position of the second grating 102 on the object plane diffraction grating plate 1 . Record the position of the image plane grating at this time, denoted as P ₁ ;

( ₃ ) Taking P1 as the starting point, define N positions (N>=2) of the second translation stage 5 scanning along the z direction, as the axial scanning position, denoted as P _i , where i=1, 2, 3... N;

对

进行Zernike拟合，提取Z2项系数c_2,i，其中，i＝1，2，3…N；(4) Utilize the prior art 1 to obtain a series of shear interferograms in the x-axis direction through the phase shift of the object plane or image plane grating, and measure the differential wavefront in the x-axis direction

right

Carry out Zernike fitting and extract the Z2 term coefficient c _2,i , where i=1, 2, 3...N;

(5) If the current z-direction position P _i of the second displacement table 5 is P _N , then enter step 6), otherwise the second displacement table 5 moves to the next position P _i+1 , so that P _i =P _i+1 , return to step 4);

(6) Subtract the Z2 coefficient c 2, _i from the Z2 coefficient c _2,i-1 of the previous position to obtain the difference △c _2,i of N-1 Z2 coefficients, and compare the position P _i with the previous position Subtract P _i-1 to get the corresponding axial distance as △Z _i , where i=2, 3...N;

(7) Calculate the size of the numerical aperture NA of N-1 groups of optical systems to be measured 3 according to formula (1):

The final numerical aperture of the optical system to be tested (3) is the average value of the NA of the N-1 groups.

Example 2:

Utilize the measuring method of the numerical aperture of the optical system to be tested of above-mentioned Ronchi grating shearing interferometer, comprise the following steps:

(1) The optical system 3 to be measured is placed in the grating shearing interferometer, so that the light source and the illumination system 8 are located on the object side of the optical system 3 to be measured, and the image plane diffraction grating plate 4 is located on the image of the optical system 3 to be measured. Adjust the first three-dimensional translation stage 2 so that the object plane diffraction grating plate 1 is located on the object plane of the optical system 3 to be tested, adjust the second three-dimensional translation stage 5 so that the image plane diffraction grating plate 4 is located on the image plane of the optical system 3 to be tested noodle;

(2) Adjust the first three-dimensional translation stage 2, so that the first grating 101 on the object plane diffraction grating plate 1 enters the field of view of the optical system 3 to be measured, adjust the second three-dimensional translation stage 5, and make the grating on the image plane diffraction grating plate 4 The checkerboard grating or the one-dimensional grating in the corresponding direction enters the field of view and is conjugate to the position of the first grating 101 on the object plane diffraction grating plate 1 . Record the position of the image plane grating at this time, denoted as P ₁ ;

( ₃ ) Taking P1 as the starting point, define N positions (N>=2) of the second translation stage 5 scanning along the z direction, as the axial scanning position, denoted as P _i , where i=1, 2, 3... N;

对

进行Zernike拟合，提取Z3项系数c_3,i，其中，i＝1，2，3…N；(4) Using prior art 1, a series of shear interferograms in the y-axis direction are obtained through the phase shift of the object plane or image plane grating, and the differential wavefront in the y-axis direction is obtained by measurement

right

Carry out Zernike fitting and extract the Z3 term coefficient c _3,i , where i=1, 2, 3...N;

(5) If the current z-direction position P _i of the second displacement table 5 is P _N , then enter step 6), otherwise the second displacement table 5 moves to the next position P _i+1 , so that P _i =P _i+1 , return to step 4);

(6) Subtract the Z3 coefficient c 3, _i from the Z3 coefficient c _3,i-1 of the previous position to obtain the difference △c _3,i of N-1 Z3 coefficients, and compare the position P _i with the previous position Subtract P _i-1 to get the corresponding axial distance as △Z _i , where i=2, 3...N;

(7) Calculate the size of the numerical aperture NA of N-1 groups of optical systems to be measured 3 according to formula (1):

The final numerical aperture of the optical system to be tested (3) is the average value of NA _i of the N-1 groups.

The method for measuring the numerical aperture of an optical system based on grating shear interference proposed by the present invention, by measuring the differential wavefront at two or more positions in the axial direction and fitting the tilt term of the differential wavefront, combined with the difference between the coefficients of the tilt term and The distance between adjacent positions is calculated to obtain the numerical aperture of the objective lens to be measured. This method does not need to make additional gratings. On the basis of wave aberration measurement, it only needs to add one step of shear phase measurement to obtain the measurement of numerical aperture of the optical system to be tested. It has the advantages of simple measurement process and convenient operation. .

Claims (3)

1. The method for measuring the numerical aperture of the optical system based on grating shearing interference comprises the following steps: the system comprises a light source and lighting system (8), an object plane diffraction grating plate (1), a first three-dimensional displacement table (2), an image plane diffraction grating plate (4), a second three-dimensional displacement table (5), a two-dimensional photoelectric sensor (6) and a calculation processing unit (7), wherein the light source and lighting system (8) outputs spatial incoherent light, the object plane diffraction grating plate (1) is fixed on the first three-dimensional displacement table (2), the image plane diffraction grating plate (4) is fixed on the second three-dimensional displacement table (5), the object plane diffraction grating plate (1) comprises two groups of one-dimensional gratings vertical to the grating line direction, the image plane diffraction grating plate (4) comprises one group of chessboard gratings or two groups of one-dimensional gratings vertical to the grating line direction, the output end of the two-dimensional photoelectric sensor (6) is connected with the calculation processing unit (7) to establish an xyz coordinate system, the z-axis direction is along the optical axis direction of a shearing interferometer, the x-axis is along the grating line direction of the second grating (102) on the object plane diffraction grating plate (1), the y-axis is along the first grating line direction of the grating plate (1), and the three-dimensional displacement table (2) and the object plane diffraction grating plate (4) and the object plane diffraction grating plate (1) are respectively arranged as follows:

step 1), placing an optical system (3) to be measured in the grating shearing interferometer, enabling a light source and an illumination system (8) to be located in an object space of the optical system (3) to be measured, enabling an image plane diffraction grating plate (4) to be located in an image space of the optical system (3) to be measured, adjusting a first three-dimensional displacement table (2), enabling the object plane diffraction grating plate (1) to be located in an object plane of the optical system (3) to be measured, adjusting a second three-dimensional displacement table (5), and enabling the image plane diffraction grating plate (4) to be located in an image plane of the optical system (3) to be measured;

step 2) adjusting the first three-dimensional displacement platform (2) to enable the second grating (102) or the first grating (101) on the object plane diffraction grating plate (1) to enter a view field of the optical system to be measured (3), adjusting the second three-dimensional displacement platform (5) to enable the chessboard grating or the one-dimensional grating in the corresponding direction on the image plane diffraction grating plate (4) to enter the view field and conjugate with the position of the second grating (102) on the object plane diffraction grating plate (1), recording the position of the image plane grating at the moment, and marking the position as P ₁ ；

Step 3) with P ₁ Defining N positions (N) of the second stage (5) scanned in the z-direction as starting points>= 2) as axial scanning position, denoted as P _i Wherein i =1,2,3 … N;

step 4) if the second grating (102) enters the field of view of the optical system (3) to be measured, obtaining a series of shearing interferograms in the x-axis direction through phase shift of the object plane or image plane grating, and measuring to obtain the differential wavefront in the x-axis direction

To pair

Zernike fitting is carried out, and Z2 coefficient c is extracted _2,i Wherein i =1,2,3 … N;

if the first grating (101) enters the field of view of the optical system (3) to be measured, a series of shearing interferograms in the y-axis direction are obtained through phase shift of the object plane or image plane grating, and differential waves in the y-axis direction are obtained through measurementFront side

To pair

Zernike fitting is carried out, and Z3 coefficient c is extracted _3,i Wherein i =1,2,3 … N;

step 5) if the current z-direction position P of the second displacement table (5) _i Is P _N Then step 6) is entered, otherwise the second displacement table (5) is moved to the next position P _i+1 Let P stand _i ＝P _i+1 And returning to the step 4);

step 6) if the second grating (102) enters the visual field of the optical system (3) to be measured, the Z2 coefficient c is calculated _2,i Z2 coefficient c from the previous position _2,i-1 Subtracting to obtain the difference deltac of N-1Z 2 coefficients _2,i At a position P _i And the previous position P _i-1 Subtracting to obtain the corresponding axial distance delta Z _i Wherein i =2,3 … N; at the moment, the numerical aperture NA of the N-1 groups of optical systems to be measured (3) is calculated according to the formula (1):

if the first grating (101) enters the field of view of the optical system (3) to be measured, the Z3 coefficient c is calculated _3,i Z3 coefficient c from the previous position _3,i-1 Subtracting to obtain the difference deltac of N-1Z 3 coefficients _3,i At a position P _i And the previous position P _i-1 Subtracting to obtain the corresponding axial distance delta Z _i Wherein i =2,3 … N, the numerical aperture NA of the N-1 sets of optical systems (3) to be measured is calculated according to the formula (2):

and 7) the final numerical aperture of the optical system (3) to be measured is the mean value of the N-1 groups of NA.

2. The method for measuring the numerical aperture of an optical system to be measured according to claim 1, wherein the ratio of the period of the one-dimensional grating on the object plane diffraction grating plate (1) to the period of the chessboard grating or the one-dimensional grating on the image plane diffraction grating plate (4) is equal to the magnification of the optical system to be measured (3).

3. The method as claimed in claim 1, wherein the duty cycle of the object plane diffraction grating and the image plane diffraction grating is 50%.

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