CN113281267A - Method for calibrating system parameters of dual-rotation compensator type Mueller matrix ellipsometer - Google Patents

Method for calibrating system parameters of dual-rotation compensator type Mueller matrix ellipsometer Download PDF

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CN113281267A
CN113281267A CN202110530232.8A CN202110530232A CN113281267A CN 113281267 A CN113281267 A CN 113281267A CN 202110530232 A CN202110530232 A CN 202110530232A CN 113281267 A CN113281267 A CN 113281267A
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陈修国
盛胜
庄锦峰
刘世元
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Abstract

The invention discloses a method for calibrating system parameters of a double-rotation compensator type Mueller matrix ellipsometer, which belongs to the field of system calibration of precise optical measuring instruments, and comprises the steps of sequentially placing a plurality of calibration samples on a calibration plane between a first rotation compensator and a second rotation compensator, and collecting light intensity information of the plurality of calibration samples; carrying out Fourier analysis on the light intensity information to obtain Fourier coefficients of the light intensity information, and establishing a matrix form function of the light intensity information by combining the Fourier coefficients; and solving a matrix form function of the light intensity information by using an eigenvalue calibration method to obtain a modulation matrix of the polarizing arm and an analysis matrix of the analyzing arm after calibration, thereby completing the calibration of system parameters. The calibration method for the system parameters of the double-rotation compensator type Mueller matrix ellipsometer provided by the invention does not need to model the system, can avoid system errors caused by modeling deviation, greatly reduces the difficulty of system calibration and greatly improves the calibration precision of the system.

Description

Method for calibrating system parameters of dual-rotation compensator type Mueller matrix ellipsometer
Technical Field
The invention belongs to the field of system parameter calibration of precise optical measuring instruments, and particularly relates to a method for calibrating system parameters of a double-rotation compensator type Mueller matrix ellipsometer.
Background
Compared with the traditional ellipsometer which can only measure the amplitude ratio angle and the phase difference angle of a sample, the double-rotation compensator type muller matrix ellipsometer can measure the full muller matrix information of the sample, and can represent more complex optical characteristics such as anisotropy, depolarization and the like of the sample. The ellipsometer can obtain the Mueller matrix of the sample under the conditions of corresponding wavelength and incident angle by controlling the two compensators to synchronously rotate at a certain rotation speed ratio, and has the advantages of simple modulation, high measurement precision, wide coverage spectrum range, good system stability and the like.
Conventional calibration methods typically require modeling the system and then fitting system parameters from the measured signals. The accuracy of this calibration method depends largely on the accuracy of the system modeling, and is also affected by the degree of alignment of the polarizer mounting. When the LM algorithm is used for fitting, a fitting result is influenced by an initial fitting value, and the initial value deviation is too large, so that a calibration result cannot be solved. The eigenvalue calibration method is only suitable for discrete measurement processes, such as a four-liquid-crystal mueller matrix measurement system.
Therefore, it is necessary to expand the eigenvalue calibration method so that it is suitable for the dual-rotation mueller matrix ellipsometer measurement system.
Disclosure of Invention
Aiming at the defects or improvement requirements of the prior art, the invention provides a method for calibrating system parameters of a dual-rotation compensator type Mueller matrix ellipsometer, the whole calibration method does not need to model the system, a modulation matrix of an analyzing arm and an analysis matrix of a polarizing arm are considered integrally, and the in-situ calibration of the system can be realized by measuring a series of calibration samples.
To achieve the above object, according to one aspect of the present invention, there is provided a method for calibrating parameters of a dual-rotation compensator type muller matrix ellipsometer, the method including the steps of:
s1, sequentially placing a plurality of calibration samples on a calibration plane between a first rotary compensator and a second rotary compensator, and collecting light intensity information of the plurality of calibration samples;
s2, providing a basis vector combination related to the rotating speed, converting continuously-changed light intensity into a discrete matrix form, carrying out Fourier analysis on the continuous light intensity signal to obtain a Fourier coefficient of the light intensity information, and solving each element in the matrix form of the light intensity information by combining the Fourier coefficient;
and S3, solving a matrix form function of the light intensity information by using a characteristic value calibration method to obtain a calibrated modulation matrix of the polarizing arm and an analysis matrix of the analyzing arm, thereby completing the calibration of the system parameters.
Preferably, step S1 further includes performing blank test on the system and acquiring light intensity information.
Preferably, step S2 specifically includes the following steps,
s21, calculating a theoretical Fourier coefficient of theoretical light intensity information;
s22, two kinds of basic vectors related to the rotating speed are defined, the Fourier function corresponding to the light intensity is expanded into a combined function of the basic vectors, and a matrix form function of the light intensity information is established by comparing Fourier coefficients of terms of the same frequency.
Preferably, in step S22, the rotation speed ratio of the first compensation rotary compensator and the second compensation rotary compensator is set to be in a relatively prime relationship, and the rotation speed of the first rotary compensator is greater than that of the second rotary compensator, and the obtained light intensity information is subjected to fourier analysis.
Preferably, the fourier analysis of the obtained light intensity information includes all frequencies of [0, 2p, 2q, 4p, 4q, (2p-2q), (2p +2q), (4p-2q), (4p +2q), (2p-4q), (2p +4q), (4p-4q), (4p +4q) ], and the corresponding light intensity information has at most 25 non-zero fourier coefficients, wherein p: q is the rotation speed ratio of the first compensation rotation compensator and the second rotation compensator, and p and q are in a cross-prime relationship.
Preferably, the signals collected over a plurality of cycles are averaged to obtain the light intensity information of the calibration sample.
Preferably, the plurality of calibration samples includes a polarizer having an azimuth angle of 0 °, a polarizer having an azimuth angle of about 90 °, and a quarter-wave plate having an azimuth angle of about 30 °.
Preferably, the step S3 specifically includes,
s31, analyzing the characteristic value of the Mueller matrix of the calibration sample according to the matrix form function of the light intensity information, and reversely deducing the Mueller matrix without azimuth angle information of the calibration sample by combining the Mueller matrix form of the calibration sample;
and S32, traversing the azimuth angle of the Mueller matrix of the calibration sample to enable the constructed semi-positive definite matrix to have a unique zero eigenvalue, rearranging zero eigenvector elements corresponding to the unique zero eigenvalue to obtain a modulation matrix of a polarizing arm and an analysis matrix of a polarization analyzing arm, and matching the result with a theoretical result to finish calibration.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
1. the calibration method for the system parameters of the double-rotation compensator type Mueller matrix ellipsometer provided by the invention does not need to model the system, can avoid system errors caused by modeling deviation, greatly reduces the difficulty of system calibration and greatly improves the calibration precision of the system.
2. The method for calibrating the parameters of the dual-rotation compensator type Mueller matrix ellipsometer system, provided by the invention, is used for solving the numerical solution of the calibration parameters by combining the characteristic value calibration method, and compared with the traditional fitting method, the method is free of any prior information, better in algorithm robustness and more stable in calculation result.
3. The calibration method for the system parameters of the dual-rotation compensator type Mueller matrix ellipsometer, provided by the invention, can realize the calibration of the system parameters by only measuring a plurality of calibration samples, and is high in calibration speed and convenient to operate.
4. According to the calibration method for the system parameters of the double-rotation compensator type muller matrix ellipsometer, disclosed by the invention, the in-situ calibration of the system can be realized by measuring a series of standard samples, and the final calibration precision can reach six thousandths.
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FIG. 1 is a schematic diagram of a reflection-type system of a dual-rotation compensator type Mueller matrix ellipsometer according to the present invention;
FIG. 2 is a schematic diagram of a transmission-type system of a dual-rotation compensator type Mueller matrix ellipsometer according to the present invention;
FIG. 3 is a flow chart of the calibration algorithm principle of the present invention;
FIG. 4 is a graph comparing measured air values and theoretical values after calibration of an embodiment of the present invention using a system with a 5:3 speed ratio of the first and second rotational compensators.
The same reference numbers will be used throughout the drawings to refer to the same or like elements or structures, wherein: a light source 101; a collimating lens 102; a polarizer 103; a first rotation compensator 104; a first calibration plane 105; a sample stage 106; a second calibration plane 107; a second rotation compensator 108; an analyzer 109; a collecting lens 110; a detector 111; a third calibration plane 502.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Fig. 1 shows a schematic diagram of an optical path of a reflective system of a dual-rotation compensator type muller matrix ellipsometer according to the present invention. The dual-rotation compensator type muller matrix ellipsometer system comprises a light source 101, a collimating lens 102, a polarizer 103, a first rotation compensator 104, a first calibration plane 105, a sample stage 106, a second calibration plane 107, a second rotation compensator 108, an analyzer 109, a collecting lens 110 and a detector 111. The light source 101 and the collimating lens 102 constitute a light source module, which is used for providing a parallel illumination beam to the system; the polarizer 103 and the first rotary compensator 104 form a polarizing arm for modulating the polarization state of the light beam incident on the sample; the second rotary compensator 108 and the analyzer 109 form an analyzer arm for analyzing the polarization state of the emergent light after passing through the sample. The first rotation compensator 104 and the second rotation compensator 108 are controlled by a servo motor to rotate at a constant rotation speed ratio, and the detector 111 is controlled to acquire a synchronization signal.
Fig. 2 shows a schematic diagram of an optical path of a transmission-type system of a dual-rotation compensator type muller matrix ellipsometer to be calibrated in the present invention. The dual-rotation compensator type muller matrix ellipsometer system comprises a light source 101, a collimating lens 102, a polarizer 103, a first rotation compensator 104, a third calibration plane 502, a second rotation compensator 108, an analyzer 109, a collecting lens 110 and a detector 111. Compared with the reflection type system, the transmission type system does not have a sample stage, and the equivalent sample stage is equivalent to air and does not need calibration, so that the reflection type system is taken as an example during calibration, and the calibration principle is also suitable for the transmission type system. The calibration process of the present invention is further described below in conjunction with specific embodiments.
The calibration method provided by the invention expands the characteristic value calibration method, so that the calibration method is suitable for a dual-rotation Mueller matrix ellipsometer measurement system, and mainly considers the following calibration parameters: (1) combining base vectors under different rotation speed ratios; (2) a light intensity matrix of the continuous sampling signal of the detector under the corresponding base vector; (3) a modulation matrix of the polarizing arm under the corresponding base vector; (4) and analyzing the matrix of the analyzing arm under the corresponding base vector.
The parameter to be measured is calibrated in two steps, the first step is used for calibrating a modulation matrix W of a polarizing arm, and the second step is used for calibrating an analysis matrix A of a polarization analyzing arm.
Example one
In an embodiment of the present invention, the calibration sample includes a polarizer with an azimuth angle of 0 °, a polarizer with an azimuth angle of about 90 °, and a quarter-wave plate with an azimuth angle of about 30 °, and the test method is as shown in fig. 3:
step one, the three calibration samples are sequentially placed on the first calibration plane 105, the light path is aligned, the data acquisition of the light intensity information is completed, and the result is recorded as If i(t), wherein i is 1,2,3, correspond different calibration samples in proper order and can gather the signal of a plurality of cycles, average again in order to reduce in the system along with followingThe effect of machine error on the measurement results.
Step two, the three calibration samples are sequentially placed at the second calibration plane 107 to align the light path, the data acquisition of the light intensity information is completed, and the result is recorded as Ib iAnd (t), wherein i is 1,2 and 3, signals of a plurality of periods can be collected corresponding to different calibration samples in sequence, and then averaging is carried out to reduce the influence of random errors in the system on the measurement result.
Taking down all the calibration samples, performing empty measurement on the system, completing data acquisition of light intensity information of the system in the air, and recording the result as I0(t)。
And step four, carrying out Fourier analysis on the acquired light intensity information to obtain a Fourier coefficient. Taking an appropriate basis vector in combination with the rotation speed ratio of the first rotation compensator 104 and the second rotation compensator 108, writing the measured light intensity signal i (t) into a 5 × 5 matrix form:
I(t)＝SA(t)·B·SW(t)
wherein SA(t) is a 1 × 5 vector, SW(t) is a 5 × 1 vector, B is a 5 × 5 matrix form, and the basis vectors of the measurement signals of different samples are consistent, and B can be understood as a discrete form of I (t).
Converting the acquired light intensity signals into a discrete form, solving by using an over-determined equation set of a characteristic value calibration method to obtain a calibrated modulation matrix W of the polarizing arm and an analysis matrix A of the analyzing arm, and enabling the measurement signals to meet the following requirements:
I(t)＝SA(t)·B·SW(t)＝SA(t)·A·Mi·W·SW(t) (1)
wherein M isiIs the Mueller matrix of the sample to be tested.
For a single measurement sample, the theoretical calculation model of the measurement signal i (t) acquired by the detector is as follows:
Figure BDA0003067370260000061
wherein S isinStokes vector, M, representing the light emitted by the light sourceA、MC2、MC1、MP、MSRespectively representing a polarization analyzer, a second compensator, a first compensator, a polarizer and a Mueller matrix in a measured sample; r (theta)A)、R(θC2)、R(θC1)、R(θP) Is the rotation matrix of the corresponding device. Assuming that the rotation speed ratio of a wave plate of the double-rotation compensator type muller matrix ellipsometer is p: q, analyzing the temporal change of the Stokes vector of the light incident on the surface of the sample according to formula (2) as follows:
SPSG(t)＝R(-θC1)MC1R(θC1)R(-θP)MPSin (3)
and (4) carrying out analysis on the formula (3), memorizing the initial azimuth angle of the polarizer as P and the initial azimuth angle of the first compensator as CS1The first compensator has a delay delta1It is possible to obtain:
Figure BDA0003067370260000071
wherein Γ ═ 4p ω t-4CS1. In order to facilitate the subsequent use of the characteristic value calibration method, components in s (t) with the rotation speed p ω and the time t need to be separated, and equation (4) is further simplified:
Figure BDA0003067370260000072
Figure BDA0003067370260000073
at this time, SPSG(t) writing a 4 × 5 matrix W and a 5 × polarizing arm vector SWWherein the modulation matrix W is related to the polarization parameters of the polarizing arm system components, vector SWOnly with respect to the first compensator rotational speed p omega and the time t. Similarly, the analyzer arm system model can be simplified as follows:
Figure BDA0003067370260000081
Figure BDA0003067370260000082
Figure BDA0003067370260000083
A25＝sinδ2sin(2Cs2+2A)(6.2)
similarly, SPSA(t) writing a 1 × 5 matrix analyzer arm vector SAIn the form of a product with a 5 x 4 analysis matrix A, where the analysis matrix A is related to polarization parameters of the components of the analyzer arm system, vector SAOnly with the second compensator rotational speed q omega and the time t. Analyzing the sampling signal of the final detector by combining the formulas (5.1), (5.2), (6.1) and (6.2) can obtain:
I(t)＝SA·A·M·W·SW＝SA·D·SW (7.1)
SW(t)＝[1cos2pωt sin2pωt cos4pωt sin4pωt]T (7.2)
SA(t)＝[1cos2qωt sin2qωt cos4qωt sin4qωt] (7.3)
Figure BDA0003067370260000084
wherein, W is a modulation matrix in the formula (5.1), A is an analysis matrix in the formula (6.1), M is a Mueller matrix of the sample to be detected, and D is recorded as a light intensity matrix of the detector. In order to analyze the specific form of the light intensity matrix, i (t) is a continuous periodic signal whose spectrogram must be discrete, and fourier analysis is performed on i (t) by:
Figure BDA0003067370260000091
expanding the formula (7.1) and simplifying by using an integral sum difference formula, comparing coefficients with the light intensity Fourier expansion form of the formula (8), and establishing a coefficient equation by setting the coefficients of the same frequency components to be equal to each otherij(i, j ═ 1,2,3,4,5) is solved, and the general equation form is as follows:
Figure BDA0003067370260000092
and the rotating speed ratio p: q of the compensator is in a prime relationship, p is more than q, Fourier analysis is carried out on the obtained light intensity signals, all frequencies are [0, 2p, 2q, 4p, 4q, (2p-2q), (2p +2q), (4p-2q), (4p +2q), (2p-4q), (2p +4q), (4p-4q) and (4p +4q) ], and the corresponding signals have 25 non-zero Fourier coefficients at most. When p + q is more than or equal to 6, 25 corresponding coefficient equations can be directly solved, when p + q is less than 6, 25 nonzero Fourier transforms are less than 25, 25 coefficient equations are less than 25, constraint conditions need to be artificially added at the moment, appropriate constraint conditions can be added according to the specific form of the equations by aiming at simplifying calculation, for example, 0 is directly taken for partial elements, so that the number of equation sets reaches 25, and then the corresponding light intensity matrix is solved.
And solving a corresponding light intensity matrix for the signal I (t) measured each time, recording the measurement result at the first calibration plane as D, recording the measurement result at the second calibration plane as B, and then solving the modulation matrix W and the analysis matrix A through an eigenvalue calibration algorithm. The traditional eigenvalue calibration method can only be used for solving a modulation matrix and an analysis matrix in a 4 × 4 form, and the eigenvalue calibration method can be popularized to the method for solving a modulation matrix W in an n × 4 form and an analysis matrix A in a 4 × m form. The Mueller matrix of a plurality of calibration samples used in calibration is recorded as Mi. When the air is subjected to the space measurement, the Mueller matrix of the air is an identity matrix I, and the Mueller matrix of the sample platform is M0And then, respectively placing the three calibration samples on two different calibration planes for measurement to obtain a light intensity matrix measured each time:
D0＝AM0W (10.1)
Di＝AM0MiW (10.2)
Bi＝AMiM0W (10.3)
because A is a column full rank matrix and W is a row full rank matrix, the inversion of non-square matrixes is considered as that the inverse of the full rank is decomposed and then Moore-Penrose generalized inverse matrix is taken, and then
Ci＝D0 +Di＝W+M0 +A+AM0MiW＝W+MiW (11.1)
C′i＝BiD0 -1＝AMiM0WW+M0 +A+＝AMiA+ (11.2)
Wherein alpha isi、βiAre each a 4 x 1 column vector and,
αi＝k1α1+k2α2+k3α3+k4α4(i＝1,2,3,...,n) (12)
according to
Figure BDA0003067370260000101
Then there is
Figure BDA0003067370260000111
When n is 4, the equation
Figure BDA0003067370260000112
Is an appropriate set of equations, and C4×4And M4×4Similarly, all are full rank matrices, and C4×4Is Cn×n(n>4) A fourth order of formula, then r (C)n×n)≥4；
From alphai＝k1α1+k2α2+k3α3+k4α4(i ═ 1,2, 3.., n) can indicate Cn×nLine 5-n, each of which can be represented as a linear combination of the first four lines, namely: cn×nAny quintic determinant value of (a) is 0. Thereby determining r (C)n×n) 4. According to the definition of the characteristic value,
Cn×nXn×1＝λXn×1 (14)
if there is a non-zero n-dimensional vector X and a corresponding number λ such that the above equation holds, λ is its eigenvalue and X is the corresponding eigenvector. Cn×nOf 4, then there must be an n-4 th order 0 eigenvalue, and 4 non-0 eigenvalues. Under the measurement model of the defined equation, there are
Figure BDA0003067370260000113
C4×4Similar to the calibration sample mueller matrix M, and is a full rank matrix, there are four non-0 eigenvalues. To obtain equation Cn×nXn×1＝λXn×1Non-zero solution of medium λ, r (C)n×n) 4, and the elementary transformation of the line does not influence the equation solution, and C is transformed by the linen×nAll of the 5 th row to the nth row of the vector X are converted into 0 rows, and the 5 th row to the nth row of the vector X are correspondingly converted for being completely equivalent to the converted equation. At this time have
Cn×nXn×1＝λXn×1 (16.1)
Figure BDA0003067370260000121
X 'to make equation true'(n-4)×1For a vector of 0, the equation is further simplified as:
Figure BDA0003067370260000122
when equation (17.2) is equivalent to C4×4X4×1＝λX4×1And obviously there are four non-zero eigenvalues λbiIts corresponding feature vector is marked as Xbi(4×1)(i＝1,2,3,4；Xbi(4×1)A non-zero vector). Then for equation (17.1)) Then, there are:
Figure BDA0003067370260000123
according to definition, there is Cn×nIs λbiThe corresponding feature vector is [ X ]bi(4×1) 0(n-4)×1]T。
In summary, Cn×nThere are n-4 eigenvalues of 0, and 4 non-0 eigenvalues, with 4 non-0 eigenvalues and C in any combination4×4Or 4 eigenvalues of the Mueller matrix of the calibration sample are kept consistent. From equations (11.1) and (11.2), equation Ci，C’i4 non-zero eigenvalues and the calibration sample mueller matrix MiAre equal, the mueller matrix for the calibration sample can be found.
For solving the modulation matrix W and the analysis matrix A, constructing:
Ti＝MiW-WCi (18.1)
Ti′＝AMi-C′iA (18.2)
since the experimental data inevitably introduce errors, the equation T is not necessarily solved when being equal to 0, and therefore a least square solution is adopted as an approximate solution of the equation. For convenient calculation, matrix orientation quantization operators are
vec(Ti)＝vec(MiW-WCi)＝Hi×vec(W) (19.1)
vec(Ti′)＝vec(AMi-C′iA)＝H′i×vec(A) (19.2)
|vec(Ti)|2＝vec(W)THi THivec(W)＝vec(W)TKivec(W) (19.3)
|vec(Ti′)|2＝vec(A)TH′i TH′ivec(A)＝vec(A)TK′ivec(A) (19.4)
Ktot＝∑Ki (20.5)
K′tot＝∑K′i (20.6)
A more robust solution can be obtained by summing the measurements from a plurality of different calibration samples. The Mueller matrix M of the calibration samples is now calibrated in equations (19.1) and (19.2)iWithout including its azimuth information, to solve for a specific azimuth, it can be determined by equations (20.5) and (20.6), a semi-positive definite matrix KtotAnd K'totThere are 16 eigenvalues, the minimum eigenvalue of which is 0 and unique, assuming that the 16 eigenvalues are denoted λ 1, λ 2, λ 3, · λ 16 in order from large to small. And traversing the azimuth angle of the Mueller matrix of the calibration sample, so that the lambda 16/lambda 15 is the minimum value, and the corresponding azimuth angle is the azimuth angle of the calibration sample. Constructed matrix KtotAnd K'totThe matrix is a semi-positive definite matrix, the minimum eigenvalue is 0, and the modulation matrix W and the analysis matrix A can be obtained after the eigenvector elements corresponding to the zero eigenvalue are rearranged.
Example two
An embodiment of the invention is directed to a 5:3 dual-rotation compensator type muller matrix ellipsometer, and a specific calibration method is implemented as follows:
and step 100, obtaining sampling signals according to formulas (7.1), (7.2), (7.3), (7.4), (8) and (9), performing Fourier analysis to obtain Fourier coefficients, selecting corresponding basis vector values and solving a 5 x 5 form light intensity matrix D.
Figure BDA0003067370260000131
SW(t)＝[1cos10ωt sin10ωt cos20ωt sin20ωt]T (20.2)
SA(t)＝[1cos6ωt sin6ωt cos12ωt sin12ωt] (20.3)
Figure BDA0003067370260000141
Wherein alpha isi、βjAre the fourier coefficients of the sampled signal.
200, after obtaining the light intensity matrix corresponding to each group of sampling signals, analyzing the characteristic value of the Mueller matrix of the calibration sample according to the formulas (11.1) and (11.2), reversely deducing the Mueller matrix without the azimuth angle of the calibration sample by combining the Mueller matrix form of the calibration sample, subsequently solving the azimuth angles of the polarizer and the wave plate by using a traversal method, and solving the modulation matrix W and the analysis matrix A by combining the equations (20.1) to (20.6), wherein the result is identical with the theoretical result of the formulas (5.1) and (6.1).
Figure BDA0003067370260000142
Figure BDA0003067370260000143
The method is based on a characteristic value calibration method, popularizes the characteristic value solution of the over-determined equation set in the form, and is used for the system calibration of the double-rotation compensator type Mueller matrix ellipsometer. The whole calibration algorithm does not need to model the system, integrally considers the modulation matrix of the polarization detection arm and the analysis matrix of the polarization arm, and can realize the in-situ calibration of the system by measuring a series of standard samples, the final calibration precision can reach six thousandths, and the air measurement result is shown in figure 4.
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 (8)

1. A method for calibrating system parameters of a dual-rotation compensator type Mueller matrix ellipsometer is characterized by comprising the following steps:
s1, sequentially placing a plurality of calibration samples on a calibration plane between a first rotary compensator and a second rotary compensator, and collecting light intensity information of the plurality of calibration samples;
s2, providing a basis vector combination related to the rotating speed, converting continuously-changed light intensity into a discrete matrix form, carrying out Fourier analysis on the continuous light intensity signal to obtain a Fourier coefficient of the light intensity information, and solving each element in the matrix form of the light intensity information by combining the Fourier coefficient;
and S3, solving a matrix form function of the light intensity information by using a characteristic value calibration method to obtain a calibrated modulation matrix of the polarizing arm and an analysis matrix of the analyzing arm, thereby completing the calibration of the system parameters.
2. The method for calibrating the system parameters of the dual-rotation compensator-type muller matrix ellipsometer according to claim 1, wherein the step S1 further includes performing aerial survey on the system and collecting light intensity information.
3. The method as claimed in claim 1, wherein the step S2 comprises the following steps,
s21, calculating a theoretical Fourier coefficient of theoretical light intensity information;
s22, two kinds of basic vectors related to the rotating speed are defined, the Fourier function corresponding to the light intensity is expanded into a combined function of the basic vectors, and a matrix form function of the light intensity information is established by comparing Fourier coefficients of terms of the same frequency.
4. The method as claimed in claim 3, wherein the rotation speed ratio of the first compensation rotary compensator to the second compensation rotary compensator is set to be relatively prime and the rotation speed of the first compensation rotary compensator is greater than that of the second compensation rotary compensator in step S22, and the fourier analysis is performed on the obtained light intensity information.
5. The method for calibrating the system parameters of the dual-rotation compensator type muller matrix ellipsometer according to claim 4, wherein the fourier analysis of the obtained light intensity information includes all frequencies [0, 2p, 2q, 4p, 4q, (2p-2q), (2p +2q), (4p-2q), (4p +2q), (2p-4q), (4p +4q) ], and the corresponding light intensity information has at most 25 non-zero fourier coefficients, wherein p: q is a rotation speed ratio of the first compensation rotation compensator to the second rotation compensator, and p and q are in a cross-prime relationship.
6. The method as claimed in claim 1, wherein the signals collected over a plurality of periods are averaged to obtain the light intensity information of the calibration sample.
7. The method as claimed in any one of claims 1 to 6, wherein the plurality of calibration samples comprise a polarizer having an azimuth angle of 0 °, a polarizer having an azimuth angle of about 90 °, and a quarter-wave plate having an azimuth angle of about 30 °.
8. The method as claimed in claim 7, wherein the step S3 specifically includes,
s31, analyzing the characteristic value of the Mueller matrix of the calibration sample according to the matrix form function of the light intensity information, and reversely deducing the Mueller matrix without azimuth angle information of the calibration sample by combining the Mueller matrix form of the calibration sample;
and S32, traversing the azimuth angle of the Mueller matrix of the calibration sample to enable the constructed semi-positive definite matrix to have a unique zero eigenvalue, rearranging zero eigenvector elements corresponding to the unique zero eigenvalue to obtain a modulation matrix of a polarizing arm and an analysis matrix of a polarization analyzing arm, and matching the result with a theoretical result to finish calibration.
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