阅读说明：本技术 一种光栅横向剪切干涉波前重建过程中的补偿方法 (Compensation method in grating transverse shearing interference wavefront reconstruction process ) 是由 李鹏 唐锋 王向朝 卢云君 刘洋 于 2021-06-28 设计创作，主要内容包括：一种光栅横向剪切干涉波前重建过程中光瞳坐标畸变和剪切量变化的同时补偿方法。波前经过光栅衍射后各级次衍射波前的形状及光路均不相同,使得一方面探测器平面检测到的坐标系相对光瞳坐标系存在畸变,另一方面剪切量随着坐标位置发生变化。该方法通过追迹各级次衍射波前的光路,计算得出待测波前在光瞳面内的坐标系与各级次衍射波前在探测器面内的坐标系之间的变换关系；由该坐标系变换关系可以得知探测器面上各个位置处检测到的剪切相位与待测波前中相位的对应关系,进而可以构建对应的波前多项式集合,并通过拟合的方式得到待测波前的多项式拟合结果,同时补偿光瞳坐标系畸变和剪切量变化。(A method for compensating pupil coordinate distortion and shearing amount change in a grating transverse shearing interference wavefront reconstruction process simultaneously. The shapes and the optical paths of the diffracted wavefronts of all levels are different after the wavefronts are diffracted by the grating, so that on one hand, a coordinate system detected by a detector plane has distortion relative to a pupil coordinate system, and on the other hand, the shearing quantity changes along with the coordinate position. Calculating to obtain a transformation relation between a coordinate system of the wavefront to be measured in a pupil plane and a coordinate system of each level of diffraction wavefront in a detector plane by tracing light paths of each level of diffraction wavefront; the coordinate system transformation relation can obtain the corresponding relation between the shearing phase detected at each position on the detector surface and the phase in the wavefront to be detected, so that a corresponding wavefront polynomial set can be constructed, a polynomial fitting result of the wavefront to be detected is obtained in a fitting mode, and the distortion and the shearing amount change of a pupil coordinate system are compensated.)

1. A method for simultaneously compensating pupil coordinate distortion and shearing quantity change in a grating transverse shearing interference wavefront reconstruction process is characterized by comprising the following steps:

1) utilizing a grating lateral shearing interferometer to generate a differential wavefront interference pattern of an optical system to be detected in the direction X, Y, and using a two-dimensional photoelectric sensor to receive the differential wavefront interference pattern I_x(x_d,y_d) And I_y(x_d,y_d) Wherein (x)_d,y_d) A pixel position coordinate system on the two-dimensional photoelectric sensor;

2) x, Y direction n is extracted from the obtained differential wavefront interferogram₁Stage and n₂Order diffracted wavefront, differential phase S_x(x_d,y_d) And S_y(x_d,y_d) Wherein n is₁≠n₂And are integers;

3) in the case of shearing in the X and Y directions, respectively, in the n-th direction₁、n₂The position coordinates of light rays received by different pixels on the plane of the two-dimensional photoelectric sensor in the pupil plane are reversely solved by the order diffraction light path, and the position coordinate obtained when the light rays are sheared in the X direction is (X)_n1x,y_n1x)、(x_n2x,y_n2x) The position coordinate obtained in the Y-direction shearing is (x)_n1y,y_n1y)、(x_n2y,y_n2y)；

4) Selecting the first m items (m)>1) Polynomial in the resulting coordinate system (x)_n1x,y_n1x)、(x_n2x,y_n2x)、(x_n1y,y_n1y)、(x_n2y,y_n2y) Constructing an equation set, and solving to obtain coefficients C corresponding to each polynomial when the wavefront to be measured is expressed by the selected polynomial_i(i＝1，2，…，m)；

5) Reconstructed wave front W_FThe formula is as follows:

wherein Z is_iRepresenting the ith term polynomial.

2. The method for simultaneously compensating for pupil coordinate distortion and shearing amount variation in a grating lateral shearing interference wavefront reconstruction process as claimed in claim 1, wherein the grating lateral shearing interferometer is a four-wave grating shearing interferometer, a Talbot grating shearing interferometer or a Ronchi grating shearing interferometer.

3. The method of claim 1, wherein n is a number of n that can be used to compensate for the simultaneous distortion of pupil coordinates and the change in shear during the reconstruction of a wavefront with interference from lateral shearing of a grating₁Stage and n₂The order diffraction wavefront differential phase is between 0 order and the differential phase of + -1 order diffraction wavefront or + -1 order diffraction wavefrontThe differential phase of (2).

4. The method of claim 1, wherein the inverse solution is ray tracing or iterative, and the method is used to compensate for pupil coordinate distortion and shear variation during reconstruction of a wavefront with grating lateral shear interference.

5. The method of claim 1, wherein the polynomial is a Zernike polynomial, a differential Taylor polynomial, or a Seidel aberration expression.

6. The method for simultaneously compensating for pupil coordinate distortion and shear variation in a grating lateral shear interference wavefront reconstruction process according to claim 1, wherein the coefficient C in step 4) is_iThe solving process of (2) is specifically as follows:

for X, Y direction differential phase S detected on the k-th pixel on the two-dimensional photoelectric sensor_xkAnd S_ykAnd constructing an equation set:

wherein the upper right corner labels n1x, n2x, n1y, n2y of Z respectively indicate that the value of the term is the coordinate system (x)_n1x,y_n1x)、(x_n2x,y_n2x)、(x_n1y,y_n1y)、(x_n2y,y_n2y) The kth coordinate point is obtained by substituting the selected ith polynomial expression; the lower right subscript i represents the ith term polynomial, and k represents the value of the term as the value corresponding to the kth coordinate in the selected coordinate system;

the data detected by all pixels on the two-dimensional photoelectric sensor are processed to obtain the following equation set:

solving the least squares solution of the above system of equations, i.e. coefficient C_i。

Technical Field

The invention belongs to the technical field of optical testing, relates to a wavefront reconstruction method, and particularly relates to a method for simultaneously compensating pupil coordinate distortion and shearing amount change in a grating transverse shearing interference wavefront reconstruction process.

Background

In the grating transverse shearing interference technology, the wavefront to be measured is diffracted by the grating and then is transmitted along different diffraction directions to form different orders of diffraction wavefronts. The projection shapes of different diffraction wavefronts on the detection device are not consistent, and when any two diffraction wavefronts are subjected to shearing interference, the shearing quantities corresponding to the shearing interference phases at different positions are different. This phenomenon is particularly significant in large NA optical system wavefront aberration detection applications, which need to be compensated for to obtain correct detection results.

Wavefront reconstruction algorithms are mainly classified into two categories, namely region methods and mode methods. When the two algorithms are used for reconstructing the wavefront phase to be measured by using the shearing phase, the shearing amount of the system is required to be a certain value. For example, a typical least square Wave front reconstruction algorithm of the area method (see prior art 1, Southwell, William h. "Wave-front estimation from Wave-front slope measures." JOSA 70.8(1980):998-1006.) when constructing the constraint equation set, it is necessary to ensure that the shearing amount is constant, so as to serially connect the obtained discrete data into different sub-grids and solve the sub-grids; for the typical representative FFT reconstruction algorithm of the pattern method (see prior art 2, C.Elster and I.Weingrtner, "Exact wave-front reconstruction from two linear reconstruction algorithms," J.Opt.Soc.Am.A. 16, 2281-2285 (1999)), the algorithm logic is established on the premise that the shearing amount is not changed, which also results in that the algorithm cannot be used when the shearing amount is not uniformly distributed.

In order to deal with the influence of the change of the shear amount distribution with the position during the detection of the wave aberration of the large NA optical system, a least square wave front reconstruction algorithm (see prior art 3, Miyakawa, ryan. Although the method solves the principle problem of the least square wave front reconstruction algorithm, the method comprises a large amount of linear estimation operations, so that the operation amount is increased, and the accuracy of the result is limited.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provide a method for simultaneously compensating pupil coordinate distortion and shearing amount change in the process of reconstructing a grating transverse shearing interference wavefront. The method uses a reverse solving algorithm to establish the coordinate corresponding relation between the shearing interference phase and the wave front phase to be detected, further uses the relation to establish a polynomial fitting matrix, and can directly obtain the fitting result of expressing the wave front to be detected by using a polynomial in a least square solving mode.

The technical solution of the invention is as follows:

1. a method for simultaneously compensating pupil coordinate distortion and shearing amount change in a grating transverse shearing interference wavefront reconstruction process is characterized by comprising the following steps:

1) using a grating lateral shearing interferometer to generate a differential wavefront interference pattern of an optical system to be measured in the direction X, Y, and using a two-dimensional photoelectric sensor to receive the interference pattern I_x(x_d,y_d) And I_y(x_d,y_d) Wherein (x)_d,y_d) A pixel position coordinate system on the two-dimensional photoelectric sensor;

2) x, Y direction n is extracted from the obtained interference pattern₁Stage and n₂Order diffracted wavefront (n)₁≠n₂And are all integers) differential phase S_x(x_d,y_d) And S_y(x_d,y_d)；

3) Respectively in the n-th direction in the case of shearing in the direction X, Y₁、n₂The position coordinates of light rays received by different pixels on the plane of the two-dimensional photoelectric sensor in the pupil plane are reversely solved by the order diffraction light path, and the position coordinate obtained when the light rays are sheared in the X direction is (X)_n1x,y_n1x)、(x_n2x,y_n2x) The position coordinate obtained in the Y-direction shearing is (x)_n1y,y_n1y)、(x_n2y,y_n2y)；

4) Before selectionm term (m)>1) Polynomial in the resulting coordinate system (x)_n1x,y_n1x)、(x_n2x,y_n2x)、(x_n1y,y_n1y)、(x_n2y,y_n2y) Constructing an equation set, and solving to obtain coefficients C corresponding to each polynomial when the wavefront to be measured is expressed by the selected polynomial_i(i＝1，2，…，m)；

5) Solving C by coefficient_iObtaining a reconstructed wavefront W_FComprises the following steps:

wherein Z_iRepresenting the ith term polynomial.

6) Outputting a reconstruction result W_F。

2. The method for simultaneous compensation of pupil coordinate distortion and shearing quantity variation in grating lateral shearing interference wavefront reconstruction as claimed in claim 1, wherein the grating lateral shearing interferometer is a four-wave grating shearing interferometer, a Talbot grating shearing interferometer or a Ronchi grating shearing interferometer.

3. The method of claim 1 for simultaneous compensation of pupil coordinate distortion and shear variation during grating lateral shear interference wavefront reconstruction, n₁Stage and n₂The order-diffracted wavefront differential phase is the differential phase between the 0 order and the ± 1 order diffracted wavefronts, or the ± 1 order diffracted wavefronts, respectively.

4. The method of claim 1, wherein the inverse solution is ray tracing or iterative, and the method is used to compensate for pupil coordinate distortion and shear variation during reconstruction of a wavefront with grating lateral shear interference.

5. The method of claim 1, wherein the polynomial is Zernike polynomial, differential Taylor polynomial, or Seidel aberration expression.

6. The coefficient C in the step 4)_iThe solution process of (2) is as follows:

for X, Y direction differential phase S detected on the k-th pixel on the two-dimensional photoelectric sensor_xkAnd S_ykAnd constructing an equation set:

the upper right hand corner markers n1x, n2x, n1y, n2y for Z respectively indicate that the value of the term is the coordinate system (x)_n1x,y_n1x)、(x_n2x,y_n2x)、(x_n1y,y_n1y)、(x_n2y,y_n2y) The kth coordinate point is obtained by substituting the selected ith polynomial expression; the lower right subscript i indicates that the term is the ith term polynomial and k indicates that the value of the term is the value corresponding to the kth coordinate in the selected coordinate system. The data detected by all pixels on the two-dimensional photoelectric sensor are arranged to obtain an equation set:

solving the least squares solution of the above equation set to obtain the coefficient C_i。

Compared with the prior art, the invention has the following advantages:

1. compared with the prior art, the method can be applied to the situation of the change of the shearing quantity;

2. compared with the prior art, the method can simultaneously compensate the shearing amount change and the coordinate distortion;

3. compared with the prior art, the method only needs to calculate the coordinate transformation relation once under the condition that the parameters of the detection system are not changed, so that the method has the advantages of less calculation amount and higher wavefront reconstruction speed.

Drawings

FIG. 1 is an experimental optical path diagram relating to example 1 of the present invention;

FIG. 2 is an X-direction shearing interferogram obtained in example 1 of the present invention;

FIG. 3 is a Y-direction shearing interferogram obtained in example 1 of the present invention;

FIG. 4 shows the X-direction shear phase in example 1 of the present invention;

FIG. 5 shows the Y-direction shear phase in example 1 of the present invention;

FIG. 6 shows the fitting coefficients calculated in example 1 of the present invention;

fig. 7 shows the phase to be measured reconstructed in embodiment 1 of the present invention;

FIG. 8 is an experimental optical path diagram relating to example 1 of the present invention;

Detailed Description

The present invention will be further described with reference to the following examples and drawings, but the scope of the present invention should not be limited by these examples.

Example 1:

the method comprises the steps of measuring the wave aberration of a projection objective system by using a Ronchi grating shearing interferometer shown in FIG. 1, sequentially arranging a focusing lens, an object plane grating (the period T is 20 μm), a projection objective system to be measured (NA is 0.9), an image plane grating (the period T is 5 μm) and a two-dimensional photoelectric sensor along the light beam propagation direction of a light source (the wavelength λ is 532 nm); the object plane grating is positioned in the back focal plane of the focusing mirror; the front focal plane of the projection objective system to be measured is superposed with the back focal plane of the focusing lens; the image surface grating is positioned on the back focal plane of the projection objective system to be measured; the two-dimensional photoelectric sensor is parallel to the image plane grating, and the distance between the two-dimensional photoelectric sensor and the image plane grating meets the requirement that the sampling number of 0-order diffraction light is 256 multiplied by 256 pixels. The measurement steps are as follows:

1) using a grating lateral shearing interferometer to generate a differential wavefront interference pattern of the wave aberration of the projection objective system to be measured in the X, Y direction, and using a two-dimensional photoelectric sensor to receive the interference pattern I_x(x_d,y_d) And I_y(x_d,y_d) As shown in fig. 2-3;

2) the interference obtained was extracted from the sample using prior art 4 (wu bin, phase extraction method based on lang-qi shearing interferometer, shanghai city, shanghai institute of optical precision mechanics, china academy of sciences, 2017-05-01.CN104111120B)The X, Y direction-1 order and +1 order diffraction wavefront differential phase S is extracted from the diagram_x(x_d,y_d) And S_y(x_d,y_d) As shown in fig. 4 and 5;

3) the intersection points of paths through which light rays emitted from different positions on the pupil plane pass and the detector plane are traced along the-1 st and +1 st order diffraction optical paths respectively under the condition of X, Y th direction shearing, and the positions on the selected pupil plane are continuously adjusted so that the intersection points of the light rays and the detector plane fall on a specified pixel, thereby obtaining the position coordinates of the light rays received by different pixels on the two-dimensional photoelectric sensor plane corresponding to the positions in the pupil plane. The position coordinate obtained when the cutting is carried out in the X direction is (X)_-1x,y_-1x)、(x_+1x,y_+1x) The position coordinate obtained in the Y-direction shearing is (x)_-1y,y_-1y)、(x_+1y,y_+1y)；

4) Selecting the coordinate system (x) obtained by the Zernike polynomials of the first 100 items_-1x,y_-1x)、(x_+1x,y_+1x)、(x_-1y,y_-1y)、(x_+1y,y_+1y) An equation set is constructed, and the Zernike coefficients C corresponding to the Zernike polynomials when the wavefront to be measured is expressed by the selected Zernike polynomials are obtained through solution_i(i＝1，2，…，100)；

Specifically, the method comprises the following steps:

for X, Y direction differential phase S detected on the k-th pixel on the two-dimensional photoelectric sensor_xkAnd S_ykAnd constructing an equation set:

wherein the upper right hand corner of Z is marked +1x, -1x, +1y, -1y respectively to indicate that the value of the term is a coordinate system (x)_-1x,y_-1x)、(x_+1x,y_+1x)、(x_-1y,y_-1y)、(x_+1y,y_+1y) The kth coordinate is obtained by calculation after being substituted into the selected ith Zernike polynomial expression; the lower right-hand index i indicates that the term is an i-th Zernike polynomial and k indicates that the value of the term is the value corresponding to the kth coordinate in the selected coordinate system. The data detected by all pixels on the two-dimensional photoelectric sensor are arranged to obtain an equation set:

solving the least squares solution of the above equation set to obtain the coefficient C_iAs shown in fig. 6.

5) Solving C by coefficient_iObtaining a reconstructed wavefront W_FComprises the following steps:

wherein Z_iDenotes the i-th Zernike polynomial.

6) Outputting a reconstruction result W_FAs shown in fig. 7.

Example 2:

the grating four-wave shearing interferometer shown in fig. 8 is used to measure the wave aberration of an optical system to be measured. A focusing mirror, a small filtering hole, an optical system to be measured, a two-dimensional grating (with the period of 36 μm and the same direction of X, Y) and a two-dimensional photoelectric sensor are arranged in sequence along the light beam propagation direction of a light source (with the wavelength λ being 532 nm); the center of the filtering small hole is superposed with the back focus of the focusing lens and the object space field point to be measured of the optical system to be measured; the two-dimensional grating is positioned near the back focal plane of the optical system to be measured and is parallel to the back focal plane; the two-dimensional photoelectric sensor is positioned behind the two-dimensional grating and is parallel to the two-dimensional grating, and the distance between the two-dimensional photoelectric sensor and the image plane grating meets the requirement that the sampling number of 0-order diffraction light is 256 multiplied by 256 pixels. The measurement steps are as follows:

1) using a grating four-wave shearing interferometer to generate a differential wavefront interference pattern of the wave aberration of the projection objective system to be measured in the X, Y direction, and using a two-dimensional photoelectric sensor to receive the interference pattern I_x(x_d,y_d) And I_y(x_d,y_d)；

2) FFT (fast Fourier transform) is carried out on the interferogram to obtain a corresponding spectrogram, a first-order frequency spectrum in the X, Y direction in the spectrogram is filtered out, the first-order frequency spectrum is translated to the center to carry out inverse FFT (fast Fourier transform) and phase unwrapping, and a X, Y direction-1-order and + 1-order diffraction wavefront differential phase S is obtained_x(x_d,y_d) And S_y(x_d,y_d)；

3) The-1 st order diffraction light paths and the +1 st order diffraction light paths in the case of cutting in the direction of X, Y are approximately regarded as originating from different point sources, and corresponding pupil plane coordinates are directly and reversely calculated according to the pixel coordinates of the detector, so that the position coordinates, corresponding to the light rays received by different pixels on the plane of the two-dimensional photoelectric sensor, in the pupil plane are obtained. The position coordinate obtained when the cutting is carried out in the X direction is (X)_-1x,y_-1x)、(x_+1x,y_+1x) The position coordinate obtained in the Y-direction shearing is (x)_-1y,y_-1y)、(x_+1y,y_+1y)；

4) Selecting the first 100 Taylor polynomials according to the obtained coordinate system (x)_-1x,y_-1x)、(x_+1x,y_+1x)、(x_-1y,y_-1y)、(x_+1y,y_+1y) An equation set is constructed, and the Taylor coefficient C corresponding to each Taylor polynomial when the wavefront to be measured is expressed by the selected Taylor polynomial is obtained through solving_i(i＝1，2，…，100)；

Specifically, the method comprises the following steps:

for X, Y direction differential phase S detected on the k-th pixel on the two-dimensional photoelectric sensor_xkAnd S_ykAnd constructing an equation set:

wherein the upper right hand corner of Z is marked +1x, -1x, +1y, -1yThe values representing the terms are respectively coordinate systems (x)_-1x,y_-1x)、(x_+1x,y_+1x)、(x_-1y,y_-1y)、(x_+1y,y_+1y) The k coordinate in the (b) is substituted into the selected i-th Taylor polynomial expression to obtain the result; the lower right subscript i indicates that the term is the i-th term Taylor polynomial, and k indicates that the value of the term is the value corresponding to the k-th coordinate in the selected coordinate system. The data detected by all pixels on the two-dimensional photoelectric sensor are arranged to obtain an equation set:

solving the least squares solution of the above equation set to obtain the coefficient C_i。

5) Solving C by coefficient_iObtaining a reconstructed wavefront W_FComprises the following steps:

wherein Z_iRepresenting the Taylor polynomial of the i-th term.

6) Outputting a reconstruction result W_F。