CN115436025A - Method for measuring numerical aperture of optical system based on grating shearing interference - Google Patents
Method for measuring numerical aperture of optical system based on grating shearing interference Download PDFInfo
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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
Technical Field
The invention relates to the technical field of optical measurement, in particular to a method for measuring Numerical Aperture (NA) of an optical system based on grating shearing interference, which is suitable for measuring the numerical aperture of a photoetching machine projection objective or other optical imaging systems based on a grating shearing interferometer.
Background
Ronchi grating shearing interference is a shearing interferometer which adopts an extended light source and adopts grating to modulate the coherence of the light source on an object plane, and has the advantages of common optical path, large dynamic range, no need of an independent ideal reference wave surface, high precision, simple structure and the like. For example, in prior art 1 (Lu Yunjun, tang Feng, wang Xiangchao, grating shearing interference optical imaging system wave aberration detection method, chinese patent of the invention, patent No. 109900201B), a differential wavefront extraction algorithm of a Ronchi shearing interferometer is proposed, which can process a phase-shift interferogram to obtain a differential wavefront, and then obtain the wave aberration of a system to be measured by wavefront reconstruction on the basis.
The Numerical Aperture (NA) is used as an important parameter of the optical system, the imaging resolution of the optical system is determined, and when the double-grating Ronchi shearing interferometer is used for measuring the wave aberration of the optical system to be measured, the NA needs to be accurately calibrated in advance. In addition, for developing a high-NA shearing interferometer system, the NA also needs to be calibrated to establish a shearing quantity model with non-uniform distribution so as to realize high-precision measurement of wave aberration.
Conventional NA measurement methods require calibration of the focal length and 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. An f-number measuring method based on Ronchi shearing is provided in the prior art 2 (Sukmock Lee, direct determination of f-number by using Ronchi test, optics Express,17 (7), 5107-5111). The method can establish the relationship between the defocusing item and f in the reconstructed wavefront through the wave aberration at two different positions. And obtaining the numerical aperture of the objective lens to be measured through conversion of the f number. At that time, the method needs to measure the shearing phases in the x direction and the y direction at the same time, and then performs wavefront reconstruction to obtain a reconstructed wavefront, the test flow and data processing are complex, and the gratings in the x direction and the y direction need to be switched for many times in the measurement process, so that errors are easily introduced in the wavefront reconstruction process, and the precision of NA calibration is reduced.
At present, no numerical aperture detection method based on a grating shearing interferometer has the advantages of simple measurement process and high precision.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a numerical aperture measuring method of an optical system, which has a simpler process and higher measurement precision.
In order to achieve the above object, the technical solution of the present invention is as follows:
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, an illumination system, an object plane diffraction grating plate, a first three-dimensional displacement table, an image plane diffraction grating plate, a second three-dimensional displacement table, a two-dimensional photoelectric sensor and a calculation processing unit, wherein the light source and the illumination system output spatial incoherent light, the object plane diffraction grating plate is fixed on the first three-dimensional displacement table, the image plane diffraction grating plate is fixed on the second three-dimensional displacement table, the object plane diffraction grating plate is fixed on the second three-dimensional displacement table and comprises two groups of one-dimensional gratings with vertical grating directions, the image plane diffraction grating plate comprises one group of chessboard gratings or two groups of one-dimensional gratings with vertical grating line directions, the output end of the two-dimensional photoelectric sensor is connected with the calculation processing unit to establish an xyz coordinate system, the z-axis direction is along the direction of a system optical axis, the x-axis is along the direction of a second grating line on the object plane diffraction grating plate, the y-axis is along the direction of a first grating line on the object plane diffraction grating plate, and the movement axes of the first three-dimensional displacement table and the second three-dimensional displacement table are respectively an x-axis, a y-axis and a z-axis; the included angle between the diagonal direction of the chessboard grating and the x axis (or the y axis) is 45 degrees; the method is characterized by comprising the following steps:
(1) Placing the optical system to be measured in the grating shearing interferometer, enabling the light source and the illumination system to be located at the object space of the optical system to be measured, enabling the image plane diffraction grating plate to be located at the image space of the optical system to be measured, adjusting the first three-dimensional displacement table, enabling the object plane diffraction grating plate to be located at the object plane of the optical system to be measured, adjusting the second three-dimensional displacement table, and enabling the image plane diffraction grating plate to be located at the image plane of the optical system to be measured;
(2) And adjusting the first three-dimensional displacement platform to enable the second grating or the first grating on the object plane diffraction grating plate to enter the view field of the optical system to be measured, and adjusting the second three-dimensional displacement platform to enable the chessboard grating on the image plane diffraction grating plate or the one-dimensional grating in the corresponding direction to enter the view field and to be conjugated with the position of the second grating on the object plane diffraction grating plate. Recording the position of the image plane grating at the moment, and recording as P 1 ；
(3) Defining N positions (N) of the second stage along the z-direction with P1 as the starting point>= 2) as axial scanning position, denoted as P i Wherein i =1,2,3 … N;
(4) If the second grating 102 enters the field of view of the optical system 3 to be measured, a series of shearing interferograms in the x-axis direction are obtained through phase shift of the object plane or image plane grating by utilizing the prior art 1, and the difference wavefront in the x-axis direction is obtained through measurement
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 by utilizing the prior art 1, and the difference wavefront in the y-axis direction is obtained through measurement
To pair
Performing Zernike fitting, and extracting Z3 coefficient c 3,i Wherein i =1,2,3 … N;
(5) If the second displacement table is at the current z-direction position P i Is P N Then go to step 6)Otherwise, the second mobile station moves to the next position P i+1 Let P stand in i ＝P i+1 And returning to the step 4);
(6) If the second grating 102 enters the field of view of the optical system 3 under test, the Z2 coefficient c will be determined 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; calculating the numerical aperture NA of the N-1 groups of optical systems to be measured according to the formula (1):
if the first grating 101 enters the field of view of the optical system 3 under test, 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 to be measured (3) is calculated according to the formula (2):
(7) The numerical aperture of the final optical system (3) to be measured is the mean value of the N-1 groups of NA.
According to the method for measuring the numerical aperture of the optical system based on the grating shearing interference, the ratio of the period of the one-dimensional grating on the object plane diffraction grating plate to the period of the chessboard grating or the one-dimensional grating on the image plane diffraction grating plate is equal to the magnification factor of the optical system to be measured.
According to the method for measuring the numerical aperture of the optical system based on the grating shearing interference, the grating duty ratio on the object plane diffraction grating plate and the grating duty ratio on the image plane diffraction grating plate are both 50%.
The method has the technical effects that based on the grating shearing interferometer, the differential wavefront at two or more axial positions is measured by an axial scanning method, the coefficient of the tilt term (Z2 of the differential wavefront in the x direction or Z3 of the differential wavefront in the y direction) of the differential wavefront is fitted, and the NA of the optical system to be measured is directly calculated by the difference between the distance between two adjacent positions and the coefficient of the tilt term of the differential wavefront. The method does not need to manufacture additional gratings, does not need to change the structure of the shearing interferometer, only needs to add one-time measurement of the shearing phase, and has the characteristics of simple measurement flow and simple output processing.
Drawings
FIG. 1 is a schematic diagram of a device for measuring the numerical aperture of an optical system based on grating shearing interference;
FIG. 2 is a schematic diagram of an object plane diffraction grating plate;
FIG. 3 is a schematic diagram of an image plane diffraction grating version checkerboard grating;
FIG. 4 is a diagram illustrating the optical path difference between the defocused gratings;
FIG. 5 is a schematic diagram showing the Z2 coefficient before the differential wavefront in the x direction, the Z3 coefficient before the differential wavefront in the y direction, and the position of the grating in the Z direction;
wherein, 1, object plane diffraction grating plate; 2. a first three-dimensional displacement stage; 3. an optical system to be tested; 4. an image plane diffraction grating plate; 5. a second three-dimensional displacement stage; 6. a two-dimensional photoelectric sensor; 7. a calculation processing unit; 8. light source and lighting system.
Detailed Description
For better understanding of the objects, technical solutions and advantages of the present invention, the following description is provided with reference to the accompanying drawings and examples, which should not be construed as limiting the scope of the present invention.
The invention discloses a method for measuring the numerical aperture of an optical system based on grating shearing interference, a grating shearing interferometer adopted by the method is shown in figure 1, and the system comprises: 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, and the output end of the two-dimensional photoelectric sensor 6 is connected with the calculation processing unit 7;
establishing an xyz coordinate system, wherein the direction of a z axis is along the direction of an optical axis of the shearing interferometer, the direction of an x axis is along the direction of grating lines of a second grating 102 on the object plane diffraction grating plate 1, the direction of a y axis is along the direction of grating lines of a first grating 101 on the object plane diffraction grating plate 1, and the motion axes of the first three-dimensional displacement table 2 and the second three-dimensional displacement table 5 are respectively set as the x axis, the y axis and the z axis;
the first three-dimensional displacement table 2 is used for moving the first grating 101 and the second grating 102 in the object plane diffraction grating plate 1 to the center of the object plane view field of the optical system 3 to be measured;
the second three-dimensional displacement table 5 is used for moving the chessboard grating in the image plane diffraction grating plate 4 to the image plane view field center of the optical system 3 to be detected, and carrying out specific periodic movement in the x-axis direction and the y-axis direction on the image plane diffraction grating plate 4;
the two-dimensional photoelectric sensor 6 can be a charge coupled device CCD or CMOS image sensor, and a detection surface receives shearing interference fringes generated by diffraction of a chessboard grating;
the calculation processing unit 7 is used for acquiring and storing the interference pattern, and processing and analyzing the interference pattern;
fig. 2 is a schematic diagram of the object plane diffraction grating plate 1, which includes two one-dimensional diffraction gratings, that is, a first grating 101 whose grating lines are along the y-axis direction and a second grating 102 whose grating lines are along the x-axis direction, where the period of the one-dimensional diffraction grating is P1 and the duty ratio 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 image plane diffraction grating plate 4 chessboard grating, which is a chessboard grating with a period of P2 and a duty ratio of 50%; the chessboard grating consists of square grids, and the diagonal direction of each square is along the x-axis direction or the y-axis direction;
the period P1 of the one-dimensional grating and the period P2 of the two-dimensional grating satisfy:
P1＝M·P2 (1)
wherein M is the magnification of the imaging optical system 3 to be measured.
Fig. 4 is a schematic diagram showing the optical path difference at any point M on the CCD when the image plane grating is out of focus. The distance from the image plane grating 4 to the focal plane is Δ Z, taking x-direction shearing as an example, the optical path difference introduced by +1 level light and-1 level light due to defocusing of the image plane grating is as follows:
wherein, P is the image surface grating period, NA is the numerical aperture of the optical system, and lambda is the wavelength. It can be seen that the main component of the optical path difference is a tilt term (Z2 term in Zernike polynomial). Similarly, if the y-direction shear is performed, the main component of the optical path difference is the tilt term (Z3 term).
Fig. 5 shows a relationship curve between the shear phase tilt term coefficient (Z2 term coefficient of the x-direction shear phase or Z3 term coefficient of the y-direction shear phase) and the defocus distance of the image plane grating.
Example 1:
the method for measuring the numerical aperture of the optical system based on the grating shearing interference is characterized by comprising the following steps of:
(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 at the object space of the optical system 3 to be measured, enabling an image plane diffraction grating plate 4 to be located at the image space of the optical system 3 to be measured, adjusting a first three-dimensional displacement table 2, enabling an object plane diffraction grating plate 1 to be located at the 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 at the image plane of the optical system 3 to be measured;
(2) And adjusting the first three-dimensional displacement platform 2 to enable the second grating 102 on the object plane diffraction grating plate 1 to enter the view field of the optical system 3 to be measured, and adjusting the second three-dimensional displacement platform 5 to enable the chessboard grating on the image plane diffraction grating plate 4 or the one-dimensional grating in the corresponding direction to enter the view field and conjugate with the position of the second grating 102 on the object plane diffraction grating plate 1. Record thisPosition of the hour plane grating, denoted as P 1 ；
(3) With P 1 As a starting point, N positions (N) of the second stage 5 along the z-direction are defined (N)>= 2) as axial scanning position, denoted P i Wherein i =1,2,3 … N;
(4) By utilizing the prior art 1, a series of shearing interferograms in the x-axis direction are obtained through phase shift of an object plane or an image plane grating, and the difference wavefront in the x-axis direction is obtained through measurement
For is to
Zernike fitting is carried out, and Z2 coefficient c is extracted 2,i Wherein i =1,2,3 … N;
(5) If the second displacement table 5 is in the current z-position P i Is P N 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);
(6) C is a Z2 coefficient 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 From 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;
(7) The numerical aperture NA of the N-1 groups of optical systems to be measured 3 is calculated according to the formula (1):
the numerical aperture of the final optical system (3) to be measured is the mean value of the N-1 groups of NA.
Example 2:
the method for measuring the numerical aperture of the optical system to be measured by using the Ronchi grating shearing interferometer comprises the following steps of:
(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 at the object space of the optical system 3 to be measured, enabling an image plane diffraction grating plate 4 to be located at the image space of the optical system 3 to be measured, adjusting a first three-dimensional displacement table 2, enabling an object plane diffraction grating plate 1 to be located at the 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 at the image plane of the optical system 3 to be measured;
(2) And adjusting the first three-dimensional displacement table 2 to enable the first grating 101 on the object plane diffraction grating plate 1 to enter the field of view of the optical system 3 to be measured, and adjusting the second three-dimensional displacement table 5 to enable the chessboard grating on the image plane diffraction grating plate 4 or the one-dimensional grating in the corresponding direction to enter the field of view and to be conjugated with the position of the first grating 101 on the object plane diffraction grating plate 1. Recording the position of the image plane grating at the moment, and recording as P 1 ；
(3) With P 1 As a starting point, N positions (N) of the second stage 5 along the z-direction scan are defined>= 2) as axial scanning position, denoted as P i Wherein i =1,2,3 … N;
(4) By utilizing the prior art 1, a series of shearing interferograms in the y-axis direction are obtained through the phase shift of an object plane or an image plane grating, and the differential wavefront in the y-axis direction is obtained through measurement
For is to
Zernike fitting is carried out, and Z3 coefficient c is extracted 3,i Wherein i =1,2,3 … N;
(5) If the second displacement table 5 is in the current z-position P i Is P N 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);
(6) C is a Z3 coefficient 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;
(7) The numerical aperture NA of the N-1 groups of optical systems to be measured 3 is calculated according to the formula (1):
the final numerical aperture of the optical system (3) to be measured is the N-1 groups NA i Is measured.
The method for measuring the numerical aperture of the optical system based on the grating shearing interference is characterized in that the numerical aperture of an objective to be measured is calculated by measuring the differential wavefronts at two or more axial positions, fitting the tilt terms of the differential wavefronts and combining the difference of the tilt term coefficients and the distance between adjacent positions. The method does not need to manufacture an additional grating, 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.
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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