CN113790873B - High NA objective lens wave aberration detection method - Google Patents
High NA objective lens wave aberration detection method Download PDFInfo
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Abstract
The invention provides a high NA objective wave aberration detection method, which comprises the following steps: s1, obtaining light intensity signals of interference light which is irradiated on area array CCD pixel points, wherein the area array CCD comprises a plurality of pixel points, every four pixel points which are adjacent to each other in pairs form a pixel group, and the pixel groups correspond to the view field points of the high NA objective lens one by one; s2, acquiring a phase difference value at the position of the pixel group based on the light intensity signal of the interference light which is irradiated on the area array CCD pixel point; s3, performing unwrapping operation based on the phase difference value at the pixel group position to obtain a corrected phase difference value at the pixel group position; and S4, acquiring a wave aberration value of a view field point of the high NA objective lens corresponding to the pixel group based on the corrected phase difference value at the position of the pixel group. The method for detecting the wave aberration of the high-NA objective lens solves the problem that the transmitted wave aberration of the high-NA objective lens is difficult to test, and has important significance for manufacturing the high-performance objective lens.
Description
Technical Field
The invention relates to the technical field of optical wave detection of lenses, in particular to a method for detecting wave aberration of a high NA objective lens.
Background
High numerical aperture objectives are core components in lithographic and semiconductor inspection equipment, and numerical aperture, which characterizes the light gathering capability of the objective, is one of the important properties of the objective, usually denoted by "NA". The numerical aperture of the objective lens determines the resolving power and effective magnification of the objective lens.
The transmitted wave aberration of the high NA objective lens is an important index for representing the imaging performance of the high NA objective lens, and the smaller the wave aberration of the objective lens is, the clearer the image obtained by the system is; the larger the wave aberration of the objective lens, the more blurred the image quality, which can seriously affect the performance of the system. Therefore, achieving transmitted wave aberration detection for high NA objectives is of great significance for manufacturing high performance objectives. At present, the transmitted wave aberration of a high-NA objective lens is difficult to detect, and the Modulation Transfer Function (MTF) of the objective lens is usually used to evaluate the imaging quality of the objective lens, however, the MTF test result cannot satisfy the performance of the high-precision high-NA objective lens.
Disclosure of Invention
The invention provides a high NA objective lens wave aberration detection method aiming at the current situation that the prior art is difficult to detect the transmitted wave aberration of the high NA objective lens.
The invention provides a high NA objective wave aberration detection method, which comprises the following steps:
s1, obtaining light intensity signals of interference light which is irradiated on area array CCD pixel points, wherein the area array CCD comprises a plurality of pixel points, every four pixel points which are adjacent to each other in pairs form a pixel group, and the pixel groups correspond to the view field points of the high NA objective lens one by one;
s2, acquiring a phase difference value at the position of the pixel group based on the light intensity signal of the interference light which is irradiated on the area array CCD pixel point;
s3, performing unwrapping operation based on the phase difference value at the pixel group position to obtain a corrected phase difference value at the pixel group position;
and S4, acquiring a wave aberration value of a view field point of the high NA objective lens corresponding to the pixel group based on the corrected phase difference value at the position of the pixel group.
According to the wave aberration detection method of the high NA objective lens, interference light which is emitted to the pixel point of the area array CCD is formed by interference of reference light and detection light on the surface of the area array CCD after the reference light and the detection light pass through the imaging lens and the polarization phase plate.
According to the high NA objective lens wave aberration detection method provided by the invention, the reference light is a light beam directly reflected back by the rear surface of the standard plane lens; and the detection light is a light beam which is formed by continuously transmitting the incident light through the high NA objective lens after transmitting the standard plane lens, continuously transmitting the incident light through the high NA objective lens after being reflected back by the original path of the spherical reflector, and continuously transmitting the incident light through the high NA objective lens and the standard plane lens again.
According to the high NA objective lens wave aberration detection method provided by the invention, the small hole is arranged between the imaging lens and the polarization phase plate, and is arranged at the focus of the imaging lens.
According to the wave aberration detection method of the high NA objective lens, provided by the invention, the polarization phase plate comprises a plurality of linear polaroids, and each linear polaroid has a corresponding polarization direction; and the linear polaroid is correspondingly arranged in front of each pixel point of the area array CCD.
According to the wave aberration detection method of the high NA objective lens, the four linear polaroids corresponding to the pixel group comprise four different polarization directions which are respectively a 0-degree polarization direction, a 90-degree polarization direction, a 180-degree polarization direction and a 270-degree polarization direction.
According to the method for detecting the wave aberration of the high NA objective lens provided by the present invention, the formula for calculating the phase difference value at the pixel group position in step S2 is:
where φ (x, y) is the phase difference value of the pixel group at physical position (x, y), I 1 、I 2 、I 3 、I 4 The light intensity values corresponding to four pixel points in the pixel group with the physical position (x, y) are obtained.
According to the method for detecting the wave aberration of the high NA objective lens provided by the present invention, the unwrapping operation in the step S3 specifically includes: solving to obtain the sine value and the cosine value corresponding to the phi (x, y), and further obtaining the correction phase difference value phi at the position of the pixel group 1 (x, y) to extend the range of values of phi (x, y) from (-pi/2, pi/2) to (0,2 pi).
According to the method for detecting the wave aberration of the high NA objective lens provided by the present invention, in step S4, the formula for calculating the wave aberration value of the field point of the high NA objective lens corresponding to the pixel group is as follows:
wherein Δ w (x, y) is a wave aberration value, Φ, of a field point of the high-NA objective lens corresponding to the pixel group at which the physical position is (x, y) 1 (x, y) is a corrected phase difference value of the pixel group at a physical position of (x, y), and λ is a wavelength of the incident light.
The invention provides a wave aberration detection method of a high NA objective based on a detection light path comprising a spherical reflector, a polarization phase plate and an area array CCD (charge coupled device), which solves the problem of difficult detection of transmitted wave aberration of the high NA objective by specially designing the detection light path and a detection algorithm.
Drawings
In order to more clearly illustrate the technical solutions of the present invention or the prior art, the following will briefly introduce some drawings needed to be used in the description of the embodiments or the prior art, and it is obvious that the drawings in the following description are some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a flow chart of a method for detecting wave aberration of a high NA objective lens according to the present invention;
FIG. 2 is a schematic diagram of the wave aberration detection path of a high NA objective lens of the present invention;
FIG. 3 is a schematic diagram of a pixel group and the corresponding relationship between the pixel points and a linear polarizer in the pixel group according to the present invention;
FIG. 4 is a diagram of the light intensity resolved phase difference versus abscissa of the present invention;
fig. 5 is a schematic diagram of the relationship between the corrected phase difference value processed by the unwrapping algorithm and the abscissa.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Fig. 1 is a flowchart of a method for detecting wave aberration of a high NA objective lens according to the present invention, and as shown in fig. 1, the method includes four steps S1-S4:
s1, obtaining light intensity signals of interference light which is irradiated on area array CCD pixel points, wherein the area array CCD comprises a plurality of pixel points, every four pixel points which are adjacent to each other in pairs form a pixel group, and the pixel groups correspond to the view field points of the high NA objective lens one by one;
s2, acquiring a phase difference value at the position of the pixel group based on the light intensity signal of the interference light which is irradiated on the area array CCD pixel point;
s3, performing unwrapping operation based on the phase difference value at the pixel group position to obtain a corrected phase difference value at the pixel group position;
and S4, acquiring a wave aberration value of a view field point of the high NA objective lens corresponding to the pixel group based on the corrected phase difference value at the position of the pixel group.
The interference light emitted to the area array CCD pixel point is formed by interference of reference light and detection light on the surface of the area array CCD after passing through the imaging lens and the polarization phase plate.
The reference light is a light beam of incident light directly reflected back through the rear surface of the standard planar lens; and the detection light is a light beam which is formed by continuously transmitting the incident light through the high NA objective lens after transmitting the standard plane lens, continuously transmitting the incident light through the high NA objective lens after being reflected back by the original path of the spherical reflector, and continuously transmitting the incident light through the high NA objective lens and the standard plane lens again.
An aperture is provided between the imaging lens and the polarization phase plate and arranged at a focal point of the imaging lens.
Fig. 2 is a schematic diagram of a transmitted wave aberration detection optical path of a high NA objective lens, as shown in fig. 2, incident light emitted by a laser is collimated and reaches a beam splitter, and the incident light transmitted through the beam splitter is transmitted to a standard planar lens, where a rear surface of the standard planar lens is a standard plane and has a reflectivity of 4% and a transmittance of 96%. 4% of light rays are reflected back along the original path through the rear surface of the standard plane lens and then reach the imaging lens after being reflected by the beam splitter, and the light beams reflected back by the rear surface of the standard plane lens are called as reference light; in addition, 96% of light rays continuously pass through the high-NA objective lens after being transmitted through the standard plane lens and then are focused at the focus of the high-NA objective lens; placing a spherical reflector to ensure that the spherical center of the spherical reflector is superposed with the focus of the high-NA objective lens, wherein the light focused on the focus of the high-NA objective lens enters the surface of the spherical reflector along the normal direction of the spherical reflector and then returns along the original path, the returning light sequentially passes through the high-NA objective lens, the standard plane lens and the beam splitter and then reaches an imaging lens, and the light of the beam passing through the high-NA objective lens is called as detection light; after passing through the imaging lens and the polarization phase plate, the reference light and the detection light form an interference phenomenon on the surface of the area array CCD, and each pixel point of the CCD can obtain corresponding interference light intensity.
Furthermore, in order to prevent extra light from entering pixel points on the area array CCD, a small hole can be arranged between the imaging lens and the polarization phase plate, and the small hole is arranged at the focus of the imaging lens to filter stray light and improve the signal-to-noise ratio.
The polarization phase plate comprises a plurality of linear polaroids, and each linear polaroid has a corresponding polarization direction; and the linear polaroid is correspondingly arranged in front of each pixel point of the area array CCD.
The four linear polarizing plates corresponding to the pixel group comprise four different polarization directions, namely a 0-degree polarization direction, a 90-degree polarization direction, a 180-degree polarization direction and a 270-degree polarization direction.
Fig. 3 shows the correspondence between the linear polarizer on the polarization phase plate and the pixel on the area array CCD in fig. 2. The polarization phase plate comprises a plurality of linear polaroids, one linear polaroid is arranged in front of each pixel point of the area array CCD, and the polarization direction corresponding to each linear polaroid is different. As can be seen from fig. 3, the serial number of each linear polarizer is composed of a number and a letter, the number represents the corresponding pixel group number during subsequent phase calculation, for example, for number 1, the number corresponds to the coordinates of four physical pixel points, the coordinates of each physical pixel point all obtain a light intensity signal during detection, but during phase calculation, the pixel group 1 with number 1 only obtains a phase difference value through calculation. In short, only one phase difference value can be obtained by resolving every four physical pixel points with the same number. The letters in each linear polarizer number in fig. 3 represent the polarization direction, and it can be seen from fig. 3 that there are four different letter designations, a, b, c, d, which represent the polarization directions of 0 °, 90 °, 180 °, 270 °, respectively.
The formula for calculating the phase difference value at the pixel group position in step S2 is:
where φ (x, y) is the phase difference value of the pixel group at physical position (x, y), I 1 、I 2 、I 3 、I 4 The light intensity values corresponding to four pixel points in the pixel group with the physical position (x, y) are obtained.
The unwrapping operation in step S3 is specifically: solving to obtain the sine value and the cosine value corresponding to the phi (x, y), and further obtaining the correction phase difference value phi at the position of the pixel group 1 (x, y) to expand the range of phi (x, y) from (-pi/2, pi/2) to (0,2 pi).
In step S4, the formula for calculating the wave aberration value of the field point of the high NA objective lens corresponding to the pixel group is:
wherein Δ w (x, y) is a wave aberration value, Φ, of a field point of the high-NA objective lens corresponding to the pixel group at which the physical position is (x, y) 1 (x, y) is a corrected phase difference value of the pixel group at which the physical position is (x, y), and λ is a wavelength of the incident light.
Illustratively, the phase difference value at the position of the corresponding pixel group can be calculated by four light intensity values measured by four physical pixel points with the same number.
For a measured light intensity value at a physical pixel point, it can be expressed as:
wherein (x, y) represents the horizontal and vertical coordinates of the physical position of the pixel point, I c Represents the reference light (i.e. the light beam reflected from the rear surface of the standard planar lens in the optical path of FIG. 2) inThe light intensity value generated at the position of the pixel point; i is j Representing the light intensity value generated by the detection light (i.e. the return light beam after passing through the high NA objective lens and the spherical reflector) at the position of the pixel point; phi is the phase difference value generated by the transmission distance between the reference light and the detection light (the transmitted wave aberration information of the high NA objective lens is included); delta is the initial phase difference between the reference light and the detection light;
defining the fringe contrast as gamma, which is defined as shown in formula (4):
then equation (3) can be written as:
I(x,y)＝I 0 (1+γcos(φ(x,y)+δ)) (5)
wherein, I 0 ＝I c +I j The intermediate transition parameter can be simultaneously reduced on the numerator and denominator during calculation, and has no influence on the calculation result.
For equation (5), it is expanded as follows:
I(x,y)＝I 0 +I 0 γcosδcos(φ(x,y))-I 0 γsinδsin(φ(x,y)) (6)
the parameter variables in formula (6) are replaced as in formula (7),
the result of equation (6) can be written as equation (8):
I(x,y)＝a 0 +a 1 cosδ+a 2 sinδ (8)
by comparing the formula (7), the relationships of the formulae (9) and (10) can be obtained.
For the transmitted wave aberration value of the high NA objective lens, the following relationship exists between the transmitted wave aberration value and the phase difference value calculated by the formula (9):
Δ w (x, y) is a wave aberration value to be solved, and as can be seen from equation (11), after the phase difference value Φ (x, y) is obtained, the wave aberration value Δ w (x, y) can be obtained.
The phase difference value phi (x, y) at each pixel group position can be obtained by the following method.
For circularly polarized light emergent laser, linear polarizers in different polarization directions are placed in front of each physical pixel point position of the polarization phase plate, and different initial phase differences delta are given to the pixel points in different positions.
For the four areas a, b, c, and d, the corresponding initial phase differences are 0 °, 90 °, 180 °, and 270 °, respectively, and then for the position of the pixel group 1, the intensity values of the light intensity signals obtained at the four physical pixel points 1a, 1b, 1c, and 1d are as shown in formula (10). Wherein the intensity value of the light intensity signal obtained at 1a is I 1 The intensity value of the light intensity signal obtained at 1b is I 2 And the intensity value of the light intensity signal obtained at 1c is I 3 And the intensity value of the light intensity signal obtained at the position 1d is I 4 。
From equation (12):
the phase difference value at the position of the pixel group 1 can be obtained by substituting formula (13) into formula (9):
and substituting the result of the formula (14) into the formula (11) to obtain the transmission wave aberration value of the field point of the high NA objective lens corresponding to the position of the pixel group 1. In the same way, the corresponding phase difference value of the positions of other pixel groups can be obtained, and the whole transmitted wave aberration detection result of the high-NA objective lens can be obtained.
The phase difference results at each pixel group position obtained in the above-described manner are generally shown in fig. 4. As can be seen from fig. 4, the obtained phase difference value (or the obtained high NA objective lens transmitted wave aberration result, both of which are linear relations as shown in formula (9)) is a stepwise discontinuous distribution, which is not in accordance with the actual situation. The reason for this is that the range of the phase difference obtained by using arctan in the formula (14) is (-pi/2, pi/2), and therefore, it is necessary to perform further unwrapping operation on the phase difference obtained by solving the formula (14), and a obtained by solving the formula (13) 1 And a 2 Substituting the numerical value into the formula (7), solving to obtain a sine value and a cosine value corresponding to the phase difference value phi (x, y), and recalculating by using the sine value or the cosine value to obtain a corrected phase difference value phi 1 (x, y) to expand the range of the phase difference value from (-pi/2, pi/2) to (0,2 pi), as shown in the following table.
Then correcting the phase difference phi 1 The corrected wave aberration value of the field point of the high NA objective lens at the pixel group (x, y) can be obtained by substituting (x, y) into the expression (11), and as can be seen from fig. 5, the whole corrected phase difference value is continuous and is consistent with the actual situation.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (9)
1. A wave aberration detection method of a high NA objective lens is characterized by comprising the following steps:
s1, obtaining light intensity signals of interference light which is irradiated on area array CCD pixel points, wherein the area array CCD comprises a plurality of pixel points, every four pixel points which are adjacent to each other in pairs form a pixel group, and the pixel groups correspond to the view field points of the high NA objective lens one by one;
s2, acquiring a phase difference value at the position of the pixel group based on the light intensity signal of the interference light which is irradiated on the area array CCD pixel point;
s3, performing unwrapping operation based on the phase difference value at the pixel group position to obtain a corrected phase difference value at the pixel group position;
and S4, acquiring a wave aberration value of a view field point of the high NA objective lens corresponding to the pixel group based on the corrected phase difference value at the position of the pixel group.
2. The method as claimed in claim 1, wherein the interference light incident on the pixel of the area array CCD is formed by interference of the reference light and the detection light on the surface of the area array CCD after passing through the imaging lens and the polarization phase plate.
3. The method of claim 2, wherein the reference light is a beam of incident light directly reflected back through a back surface of a standard planar lens; and the detection light is a light beam which is formed by continuously transmitting the incident light through the high NA objective lens after transmitting the standard plane lens, continuously transmitting the incident light through the high NA objective lens after being reflected back by the original path of the spherical reflector, and continuously transmitting the incident light through the high NA objective lens and the standard plane lens again.
4. The method of claim 2, wherein an aperture is provided between the imaging lens and the polarization phase plate, and the aperture is disposed at a focal point of the imaging lens.
5. The method for detecting wave aberration of a high NA objective lens according to claim 2, wherein the polarization phase plate comprises a plurality of linear polarizers, each linear polarizer having a corresponding polarization direction; and the linear polaroid is correspondingly arranged in front of each pixel point of the area array CCD.
6. The method for detecting wave aberration of high-NA objective lens according to claim 5, wherein the four linear polarizers corresponding to the pixel group comprise four different polarization directions, namely 0 ° polarization direction, 90 ° polarization direction, 180 ° polarization direction and 270 ° polarization direction.
7. The method for detecting wave aberration of high NA objective lens according to claim 6, wherein the formula for calculating the phase difference value at the pixel group position in step S2 is as follows:
where φ (x, y) is the phase difference value of the pixel group at physical position (x, y), I 1 、I 2 、I 3 、I 4 The light intensity values corresponding to four pixel points in the pixel group with the physical position (x, y) are obtained.
8. The method for detecting wave aberration of a high NA objective lens according to claim 7, wherein the unwrapping operation in the step S3 is specifically: solving to obtain the sine value and cosine value corresponding to the phi (x, y), and further obtaining the correction phase difference value phi at the position of the pixel group 1 (x, y) to expand the range of phi (x, y) from (-pi/2, pi/2) to (0,2 pi).
9. The method for detecting the wave aberration of the high NA objective lens according to claim 8, wherein the formula for calculating the wave aberration value of the field point of the high NA objective lens corresponding to the pixel group in step S4 is as follows:
wherein Δ w (x, y) is a wave aberration value, Φ, of a field point of the high NA objective lens corresponding to the pixel group at the physical position (x, y) 1 (x, y) is a corrected phase difference value of the pixel group at the physical position (x, y), and λ is a wavelength of incident light.
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| GB0625775D0 (en) * | 2006-12-22 | 2007-02-07 | Isis Innovation | Focusing apparatus and method |
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| CN102073218A (en) * | 2009-11-20 | 2011-05-25 | 上海微电子装备有限公司 | Device for measuring projection objective wave aberration, and measurement method thereof |
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