CN116930093A - Error calibration method of double-vortex wave plate Mueller matrix ellipsometer - Google Patents
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Abstract
The invention provides an error calibration method of a double-vortex wave plate Mueller matrix ellipsometer, which integrally considers modulation vectors of a polarization modulation unit and an polarization analysis modulation unit, and can finish the calibration of an optical system through a series of simple measurements. The method does not depend on a system model, avoids system errors caused by modeling deviation, greatly reduces the difficulty of error calibration and improves the calibration precision of the system. Compared with the traditional parameter calibration method and the characteristic value calibration method, the invention does not need any standard sample, does not need any prior information of the system, can complete the system calibration by using the linear polaroid and the circular polaroid, and has convenient operation and stable calculation result. Experiments prove that the calibration method of the double-vortex wave plate Mueller matrix ellipsometer can effectively reduce the influence of various error factors of a system and remarkably improve the measurement accuracy of the Mueller matrix of a sample to be measured.
Description
Technical Field
The invention relates to the technical field of optics, in particular to an error calibration method of a double-vortex wave plate Mueller matrix ellipsometer.
Background
The Mueller matrix ellipsometer can realize all 16 Mueller matrix elements m of a sample to be measured st And (s, t=1, 2,3, 4), so that the richer optical characteristics such as anisotropy, depolarization effect and the like of the sample to be measured can be obtained, and the application field is wide. However, the traditional Mueller matrix ellipsometer has the defects of low measurement speed, poor mechanical stability, complex system structure and the like. In order to solve the defects of the traditional Mueller matrix ellipsometer, the double-vortex wave plate Mueller matrix ellipsometer is provided, and the single-shot image analysis of the scheme can realize the measurement of all Mueller matrix elements of a sample to be measured, and has the advantages of simple light path, convenient operation, good system stability and high measurement speed.
The schematic diagram of the optical path of the double vortex wave plate Mueller matrix ellipsometer is shown in fig. 1, and a polarization modulation unit 1, a sample stage 2, an polarization analysis modulation unit 3 and an image processing unit 4 are sequentially arranged side by side from left to right. The polarization modulation unit comprises a light source 101, a polarizer 102 and a first vortex quarter wave plate 103; placing a sample 201 to be tested on the sample stage 2; the polarization-analysis modulation unit comprises a second vortex quarter wave plate 301 and a polarization analyzer 302; the image processing unit includes an image sensor 401 and a computer 402. The core device of the instrument is two vortex quarter wave plates with a certain order ratio, and the modulation of the Mueller matrix of the sample to be detected is realized. Its physical model can be described as: s is S out ＝M A ·M V2 ·M s ·M V1 ·M P ·S in . M in the above A For the Mueller matrix of analyzer 302, M V2 Mueller matrix, M, of the second vortex quarter wave plate s For the Mueller matrix of the sample 201 to be measured, M V1 Mueller matrix, M, of the first vortex quarter wave plate P For the mueller matrix of polarizer 102, S in Representing the stokes vector of the incident light. Since the image sensor can only sense the light intensity information, the above formula can be further expressed as: i= [ 100 0 ]]·M A ·M V2 ·M s ·M V1 ·M P ·S in ＝a·M s P. Wherein p= [ p ] 1 p 2 p 3 p 4 ] T ＝M V1 ·M P ·S in P is defined as a modulation vector of the polarizing modulation unit 1, and is a stokes vector of the light wave emitted by the light source after passing through the polarizing modulation unit 1; a= [ a ] 1 a 2 a 3 a 4 ]＝[1 0 0 0]·M A ·M V2 Defined as the modulation vector of the polarization-preserving modulation unit 3, a being the first row of the overall muller matrix of the polarization-preserving modulation unit 3. In order to realize accurate measurement of the Mueller matrix of the sample to be measured, all optical components in the system are required to be placed according to a certain azimuth angle, the fast axis of the vortex quarter wave plate uniformly and continuously rotates in space according to a preset rule, the phase delay of each wave plate is ensured to be pi/2, and in addition, environmental stray light and noise of an image sensor are required to be kept at lower levels. However, in actual measurement, the above conditions are generally difficult to meet, resulting in measurement errors.
The existing error calibration method of the Mueller matrix ellipsometer can be divided into a parameter calibration method based on a system model and a characteristic value calibration method not based on the system model. The parameter calibration method needs to establish an optical system model containing various error factors, researches the influence of the error factors on a measurement result, carries out measurement on a standard sample, brings the measurement result into the error model for fitting, further calculates the error parameters, and completes error calibration; the characteristic value calibration rule is to integrally consider the polarizer and the analyzer, and measure the standard sample to calculate the real modulation matrix and analysis matrix of the polarizer and the analyzer, thereby completing the error calibration. Compared with a parameter calibration method, the characteristic value calibration method omits complicated physical model calculation, and can effectively simplify the error calibration process. However, the above two methods are only aimed at each fixed error factor in the traditional mueller matrix ellipsometer system, such as azimuth error and phase delay error of an optical element, and cannot meet the calibration of the errors of the light source light intensity spatial distribution in the double vortex wave plate mueller matrix ellipsometer system, the fast axis rotation of the vortex wave plate is uneven, and the like along with the change of azimuth angle, so that the two traditional error calibration methods are greatly limited in the double vortex wave plate mueller matrix ellipsometer system.
In summary, it is necessary to study an error calibration method suitable for a double vortex wave plate mueller matrix ellipsometer system and having a simple resolving process.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides an error calibration method of a double-vortex wave plate Mueller matrix ellipsometer, system modeling is not needed in the whole calibration process, modulation vectors of a polarization modulation unit and an polarization analysis modulation unit are considered integrally, and the calibration of the system can be completed through a series of simple measurements.
The invention provides an error calibration method of a double-vortex wave plate Mueller matrix ellipsometer, which comprises the following steps of: s0, providing a double-vortex wave plate Mueller matrix ellipsometer, wherein the double-vortex wave plate Mueller matrix ellipsometer comprises: the device comprises a polarization modulation unit, a sample stage, an polarization analysis modulation unit and an image processing unit which are sequentially arranged side by side; the polarization modulation unit comprises a light source, a polarizer and a first vortex quarter wave plate which are sequentially arranged; the sample table is suitable for placing a sample to be tested; the polarization analysis modulation unit comprises a second vortex quarter wave plate and a polarization analyzer which are sequentially arranged; the first vortex quarter wave plate is positioned between the polarizer and the second vortex quarter wave plate; step S1: removing the polarization analysis modulation unit from the double vortex wave plate Mueller matrix ellipsometer; step S2: turning on a light source, respectively and independently placing a 0-degree linear polaroid, a 135-degree linear polaroid, a right-hand circular polaroid and a left-hand circular polaroid on a sample stage between a polarization modulation unit and an image sensor, and sampling corresponding emergent light beams by using the image sensor to obtain corresponding first light intensity modulation images, second light intensity modulation images, third light intensity modulation images, fourth light intensity modulation images, fifth light intensity modulation images and sixth light intensity modulation images; the jth light intensity modulation image is changed in brightness and darkness alternately along with the azimuth angle of the jth light intensity modulation image; j is an integer of 1 or more and 6 or less; step S3, processing the first light intensity modulation image, the second light intensity modulation image, the third light intensity modulation image, the fourth light intensity modulation image, the fifth light intensity modulation image and the sixth light intensity modulation image respectively to obtain corresponding first light intensity modulation functionsNumber of digitsSecond light intensity modulation function->Third light intensity modulation function->Fourth light intensity modulation function->Fifth light intensity modulation function->And a sixth light intensity modulation function->The j-th light intensity modulation function->Modulating the light intensity in the image with azimuth angle for the jth light intensity>A function of the change; first light intensity modulation function->Second light intensity modulation function->Third light intensity modulation function->Fourth light intensity modulation function->Fifth light intensity modulation function->And a sixth light intensity modulation function->The first matrix equation is satisfied:
p＝[p 1 p 2 p 3 p 4 ] T the method comprises the steps of carrying out a first treatment on the surface of the p is the modulation vector of the polarization modulation unit;
step S4: solving the first matrix equation set to obtain a modulation vector p of a polarization modulation unit; step S5: the polarization-analysis modulation unit is installed back into the double-vortex wave plate Mueller matrix ellipsometer, the second vortex quarter wave plate is positioned between the polarization analyzer and the polarization-analysis modulation unit, and then the polarization analyzer and the first vortex quarter wave plate are removed from the polarization-analysis modulation unit; step S6: the method comprises the steps that a 0-degree linear polaroid, a 45-degree linear polaroid, a 90-degree linear polaroid, a 135-degree linear polaroid, a right-handed circular polaroid and a left-handed circular polaroid are respectively and independently arranged on a sample table between an analysis modulation unit and a light source, and an image sensor is utilized to sample outgoing light beams of the analysis modulation unit so as to obtain a seventh light intensity modulation image, an eighth light intensity modulation image, a ninth light intensity modulation image, a tenth light intensity modulation image, an eleventh light intensity modulation image and a twelfth light intensity modulation image which correspond to each other; the ith light intensity modulation image is changed in brightness and darkness alternately along with the azimuth angle of the ith light intensity modulation image; i is an integer of 7 or more and 12 or less; step S7: the seventh light intensity modulation image, the eighth light intensity modulation image, the ninth light intensity modulation image, the tenth light intensity modulation image, the eleventh light intensity modulation image and the twelfth light intensity modulation image are respectively processed to obtain corresponding seventh light intensity modulation functionsEighth light intensity modulation function->Ninth light intensity modulation function->Tenth light intensity modulation functionEleventh light intensity modulation function->And a twelfth light intensity modulation function->Ith light intensity modulation functionModulating the light intensity in the image with azimuth angle for the ith light intensity +.>A function of the change; seventh light intensity modulation function->Eighth light intensity modulation function->Ninth light intensity modulation function->Tenth light intensity modulation function->Eleventh light intensity modulation function->And a twelfth light intensity modulation function->The second matrix equation is satisfied:
a＝[a 1 a 2 a 3 a 4 ]a is a modulation vector of the polarization-analysis modulation unit;
step S8: solving a second matrix equation set to obtain a modulation vector a of the polarization-analysis modulation unit; step S9: and installing the polarizer and the first vortex quarter wave plate back into the double vortex wave plate Mueller matrix ellipsometer, wherein the polarizer is positioned between the first vortex quarter wave plate and the light source, and completing calibration.
Optionally, the method further comprises: a in modulation vector a 1 Normalization.
Optionally, the method further comprises: p in modulation vector p 1 Normalization.
Optionally, the method further comprises: step S10: removing the 0-degree linear polaroid, the 45-degree linear polaroid, the 90-degree linear polaroid, the 135-degree linear polaroid, the right-handed circular polaroid and the left-handed circular polaroid from the double-vortex wave plate Mueller matrix ellipsometer, and placing a sample to be detected on a sample table; sampling the emergent light beam of the polarization-analysis modulation unit by using an image sensor to obtain a light intensity function I; step S11: and acquiring a Mueller matrix M of the sample to be detected according to the light intensity function I, the modulation vector a of the polarization-analysis modulation unit and the modulation vector p of the polarization-analysis modulation unit, wherein I=a×M×p.
The technical scheme of the invention has the following beneficial effects:
according to the error calibration method of the double-vortex-wave-plate Mueller matrix ellipsometer, provided by the technical scheme of the invention, the modulation vectors of the polarization modulation unit and the polarization analysis modulation unit are considered on the whole, and the calibration of an optical system can be completed through a series of simple measurements. The method does not depend on a system model, avoids system errors caused by modeling deviation, greatly reduces the difficulty of error calibration and improves the calibration precision of the system. Compared with the traditional parameter calibration method and the characteristic value calibration method, the invention does not need any standard sample, does not need any prior information of the system, can complete the system calibration by using the linear polaroid and the circular polaroid, and has convenient operation and stable calculation result. Experiments prove that the calibration method of the double-vortex wave plate Mueller matrix ellipsometer can effectively reduce the influence of various error factors of a system and remarkably improve the measurement accuracy of the Mueller matrix of a sample to be measured.
The calibration method of the double vortex wave plate Mueller matrix ellipsometer can effectively reduce the influence of factors such as uneven light source intensity distribution, azimuth angle error of optical components, wave plate phase delay error, vortex wave plate fast axis direction error and the like, so that the maximum measurement error of the Mueller matrix of a sample to be measured is reduced from 0.1416 to 0.0352, and the root mean square of the error is reduced from within 0.0604 to within 0.0148.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the description of the embodiments or the prior art will be briefly described, and it is obvious that the drawings in the description below are some embodiments of the present invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic diagram of a double vortex wave plate Mueller matrix ellipsometer;
FIG. 2 is a flow chart of an error calibration method of a double vortex wave plate Mueller matrix ellipsometer according to the present invention;
FIG. 3 (a) is a first light intensity modulation image acquired when a 0 degree linear polarizer is placed after a polarization modulation unit;
FIG. 3 (b) is a second light intensity modulated image acquired when a 45 degree linear polarizer is placed after the polarizing modulation cell;
FIG. 3 (c) is a third light intensity modulated image acquired when a 90 degree linear polarizer is placed after the polarizing modulation cell;
FIG. 3 (d) is a fourth light intensity modulated image acquired when a 135 degree linear polarizer is placed after the polarizing modulation cell;
FIG. 3 (e) is a fifth light intensity modulation image acquired when a right-handed circular polarizer is placed after the polarizing modulation unit;
FIG. 3 (f) is a sixth intensity modulated image acquired when a left-handed circular polarizer is placed after the polarizing modulation cell;
FIG. 4 (a) is a first light intensity modulation function;
FIG. 4 (b) is a second light intensity modulation function;
FIG. 4 (c) is a third light intensity modulation function;
FIG. 4 (d) is a fourth light intensity modulation function;
FIG. 4 (e) is a fifth light intensity modulation function;
FIG. 4 (f) is a sixth light intensity modulation function;
FIG. 5 (a) shows a second parameter p of the modulation vector p of the polarizing modulation unit 2 (p to 1 Normalized) theoretical (solid line) and measured (dashed line);
FIG. 5 (b) shows a third parameter p of the modulation vector p of the polarizing modulation unit 3 (p to 1 Normalized) theoretical (solid line) and measured (dashed line);
FIG. 5 (c) is a fourth parameter p of the modulation vector p of the polarizing modulation unit 4 (p to 1 Normalized) theoretical (solid line) and measured (dashed line);
FIG. 6 (a) is a seventh light intensity modulation image acquired when a 0 degree linear polarizer is placed in front of the polarization-preserving modulation unit;
FIG. 6 (b) is an eighth light intensity modulation image acquired when a 45 degree linear polarizer is placed in front of the polarization analyzer unit;
FIG. 6 (c) is a ninth light intensity modulation image acquired when a 90 degree linear polarizer is placed in front of the polarization analyzer unit;
FIG. 6 (d) is a tenth intensity modulated image acquired when a 135 degree linear polarizer is placed in front of the polarization analyzer unit;
FIG. 6 (e) is an eleventh light intensity modulation image acquired when a right-handed circular polarizer is placed in front of the polarization-preserving modulation unit;
FIG. 6 (f) is a twelfth light intensity modulation image acquired when a left-handed circular polarizer is placed in front of an analyzer modulation cell;
FIG. 7 (a) is a seventh light intensity modulation function;
FIG. 7 (b) is an eighth light intensity modulation function;
FIG. 7 (c) is a ninth light intensity modulation function;
FIG. 7 (d) is a tenth light intensity modulation function;
FIG. 7 (e) is an eleventh light intensity modulation function;
FIG. 7 (f) is a twelfth light intensity modulation function;
FIG. 8 (a) shows a second parameter a of the modulation vector a of the polarization-maintaining modulation unit 2 (pair a) 1 Normalized) theoretical (solid line) and measured (dashed line);
FIG. 8 (b) shows a third parameter a of the modulation vector a of the polarization-maintaining modulation unit 3 (pair a) 1 Normalized) theoretical (solid line) and measured (dashed line);
FIG. 8 (c) is a fourth parameter a of the modulation vector a of the polarization-maintaining modulation unit 4 (pair a) 1 Normalized) theoretical (solid line) and measured (dashed line);
FIG. 9 (a) is a light intensity modulated image of an air sample;
FIG. 9 (b) is a light intensity modulated image of a 45 degree linear polarizer;
FIG. 9 (c) is a light intensity modulated image of a 60 degree linear polarizer;
FIG. 9 (d) is a light intensity modulated image of a 90 degree linear polarizer;
FIG. 9 (e) is a light intensity modulated image of a 135 degree linear polarizer;
FIG. 9 (f) is a light intensity modulated image of a 0 degree quarter wave plate;
FIG. 9 (g) is a light intensity modulated image of a 60 degree quarter wave plate;
fig. 9 (h) is a light intensity modulated image of a 90 degree quarter wave plate.
Detailed Description
The following description of the embodiments of the present invention will be made apparent and fully in view of the accompanying drawings, in which some, but not all embodiments of the invention are shown. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
In the description of the present invention, it should be noted that the directions or positional relationships indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. are based on the directions or positional relationships shown in the drawings, are merely for convenience of describing the present invention and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a specific orientation, be configured and operated in a specific orientation, and thus should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description of the present invention, it should be noted that, unless explicitly specified and limited otherwise, the terms "mounted," "connected," and "connected" are to be construed broadly, and may be either fixedly connected, detachably connected, or integrally connected, for example; can be mechanically or electrically connected; the two components can be directly connected or indirectly connected through an intermediate medium, or can be communicated inside the two components, or can be connected wirelessly or in a wired way. The specific meaning of the above terms in the present invention will be understood in specific cases by those of ordinary skill in the art.
In addition, the technical features of the different embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
The embodiment of the invention provides an error calibration method of a double-vortex wave plate Mueller matrix ellipsometer. The error calibration method of the double vortex wave plate Mueller matrix ellipsometer comprises the following steps: referring to fig. 1, a dual vortex wave plate mueller matrix ellipsometer is provided, the dual vortex wave plate mueller matrix ellipsometer comprising: a polarization modulation unit 1, a sample stage 2, an polarization analysis modulation unit 3 and an image processing unit 4 which are arranged in parallel in sequence. The polarization modulation unit comprises a light source 101, a polarizer 102 and a first vortex quarter wave plate 103 which are sequentially arranged. The sample stage 2 is adapted to hold a sample 201 to be measured. The polarization analyzer modulation unit 3 comprises a second vortex quarter wave plate 301 and a polarization analyzer 302 which are sequentially arranged; the image processing unit includes an image sensor 401 and a computer 402. The first vortex quarter wave plate 103 is located between the polarizer 102 and the second vortex quarter wave plate 301.
The sample 201 to be measured is a transmissive sample. The thickness direction of the sample 201 to be measured is parallel to the surface of the sample stage 2. The arrangement direction of the light source 101, the polarizer 102 and the first vortex quarter wave plate 103, and the arrangement direction of the second vortex quarter wave plate 301 and the analyzer 302 are all parallel to the surface of the sample stage 2.
The light source 101 emits a collimated light beam having a uniform light intensity distribution. The light source 101 may be a laser light source. The polarizer 102 and the first vortex quarter wave plate 103 are sequentially arranged along the propagation direction of the light emitted by the light source 101. The light emitted from the light source 101 passes through the polarizer 102 and becomes horizontally linearly polarized light. The light exiting through the first vortex quarter wave plate 103 is a vector polarized light field with the polarization state regularly changing along with the azimuth angle. The second vortex quarter wave plate 301 and the analyzer 302 are sequentially arranged along the propagation direction of the light transmitted by the sample 201 to be measured.
In one embodiment, the order d1 of the first vortex quarter wave plate 103 and the order d2 of the second vortex quarter wave plate 301 satisfy that d1 and d2 are both positive integers, d2 is greater than 2d1, and d1 and d2 are mutually prime.
The sample stage 2 has a stage central axis perpendicular to the surface of the sample stage 2; the arrangement direction of the light source 101, the polarizer 102 and the first vortex quarter wave plate 103 in the polarization modulation unit 1 and the arrangement direction of the second vortex quarter wave plate 301 and the polarization analyzer 302 in the polarization modulation unit 3 are symmetrical relative to the central axis of the table top. The intensity of the outgoing beam of the analyzer 302 alternates with the azimuthal brightness. The outgoing beam of the analyzer 302 is captured by an image sensor 401, and the image sensor 401 samples the outgoing beam of the analyzer 302 to obtain a light intensity modulation image, where the light intensity modulation image changes in brightness and darkness alternately along with the azimuth angle of the light intensity modulation image.
Referring to fig. 2, the error calibration method of the double vortex wave plate mueller matrix ellipsometer includes:
step S1: the polarization-analysis modulation unit 3 is removed from the double vortex wave plate mueller matrix ellipsometer.
Step S2: turning on the light source 101, placing a 0 degree linear polarizer, a 45 degree linear polarizer, a 90 degree linear polarizer, a 135 degree linear polarizer, a right-handed circular polarizer and a left-handed circular polarizer on a sample stage between the polarization modulation unit 1 and the image sensor 401, respectively, and sampling corresponding outgoing light beams by using the image sensor 401 to obtain corresponding first light intensity modulation images (refer to fig. 3 a), second light intensity modulation images (refer to fig. 3 b), third light intensity modulation images (refer to fig. 3 c), fourth light intensity modulation images (refer to fig. 3 d), fifth light intensity modulation images (refer to fig. 3 e) and sixth light intensity modulation images (refer to fig. 3 f); the jth light intensity modulation image is changed in brightness and darkness alternately along with the azimuth angle of the jth light intensity modulation image; j is an integer greater than or equal to 1 and less than or equal to 6.
Step S3, processing the first light intensity modulation image, the second light intensity modulation image, the third light intensity modulation image, the fourth light intensity modulation image, the fifth light intensity modulation image and the sixth light intensity modulation image respectively to obtain corresponding first light intensity modulation functions(see FIG. 4 a), second light intensity modulation function +.> (see FIG. 4 b), third light intensity modulation function(see FIG. 4 c), fourth light intensity modulation function +.>(see FIG. 4 d), fifth light intensity modulation function +.>(refer to FIG. 4 e) and sixthLight intensity modulation function->(refer to fig. 4 f); the j-th light intensity modulation function->Modulating the light intensity in the image with azimuth angle for the jth light intensity>A function of the change; the j-th light intensity modulation function->The azimuth angle of the jth light intensity modulation image is taken as an independent variable, and the light intensity value of the jth light intensity modulation image is taken as a dependent variable.
First light intensity modulation functionSecond light intensity modulation function->Third light intensity modulation functionFourth light intensity modulation function->Fifth light intensity modulation function->And a sixth light intensity modulation functionThe first matrix equation is satisfied:
p＝[p 1 p 2 px p 4 ] T the method comprises the steps of carrying out a first treatment on the surface of the p is the modulation vector of the polarization modulation unit 1.
Step S4: the first system of matrix equations is solved to obtain the modulation vector p of the polarization modulation unit 1.
Step S5: the polarization-detecting modulation unit 3 is installed back into the double-vortex-wave-plate mueller matrix ellipsometer, the second vortex quarter-wave plate 301 is located between the polarization detector 302 and the polarization-detecting modulation unit, and then the polarizer 102 and the first vortex quarter-wave plate 103 are removed from the polarization-detecting modulation unit 1.
Step S6: the 0 degree linear polaroid, the 45 degree linear polaroid, the 90 degree linear polaroid, the 135 degree linear polaroid, the right-hand circular polaroid and the left-hand circular polaroid are respectively and independently arranged on a sample stage between the polarization-analysis modulation unit 3 and the light source 101, and the image sensor 401 is used for sampling the emergent light beam of the polarization-analysis modulation unit 3 to obtain a seventh light intensity modulation image (refer to fig. 6 a), an eighth light intensity modulation image (refer to fig. 6 b), a ninth light intensity modulation image (refer to fig. 6 c), a tenth light intensity modulation image (refer to fig. 6 d), an eleventh light intensity modulation image (refer to fig. 6 e) and a twelfth light intensity modulation image (refer to fig. 6 f); the ith light intensity modulation image is changed in brightness and darkness alternately along with the azimuth angle of the ith light intensity modulation image; i is an integer of 7 or more and 12 or less.
Step S7: the seventh light intensity modulation image, the eighth light intensity modulation image, the ninth light intensity modulation image, the tenth light intensity modulation image, the eleventh light intensity modulation image and the twelfth light intensity modulation image are respectively processed to obtain corresponding seventh light intensity modulation functions(refer to FIG. 7 a), eighth light intensity modulation function +.>(see FIG. 7 b), ninth light intensity modulation function(refer to FIG. 7 c), tenth light intensity modulation function +.>(refer to FIG. 7 d), eleventh light intensity modulation function +.>(refer to FIG. 7 e) and a twelfth light intensity modulation function +.>(refer to fig. 7 f); ith light intensity modulation function->Modulating the light intensity in the image with azimuth angle for the ith light intensity +.>A function of the change; ith light intensity modulation function->The azimuth angle of the ith light intensity modulation image is taken as an independent variable, and the light intensity value of the ith light intensity modulation image is taken as a dependent variable.
Seventh light intensity modulation functionEighth light intensity modulation function->Ninth light intensity modulation functionTenth light intensity modulation function->Eleventh light intensity modulation function->And a twelfth light intensity modulation functionThe second matrix equation is satisfied:
a＝[a 1 a 2 a 3 a 4 ]a is a modulation vector of the polarization-analyzing modulation section 3.
Step S8: the second system of matrix equations is solved to obtain the modulation vector a of the polarization-analyzing modulation unit 3.
Step S9: the polarizer 102 and the first vortex quarter wave plate 103 are installed back into the double vortex wave plate mueller matrix ellipsometer, and the polarizer 102 is positioned between the first vortex quarter wave plate 103 and the light source 101, so that calibration is completed.
The polarizer 102 in step S9 is the same as the polarizer 102 in step S2, and the first vortex quarter wave plate 103 in step S9 is the same as the first vortex quarter wave plate 103 in step S2.
In one embodiment, the light source 101 is a collimator with an outgoing wavelength of 633nm, the polarizer 102 and the analyzer 302 are LPVISE100-a polarizers manufactured by Thorlabs (cable Lei Bo), the first vortex quarter wave plate 103 is a VR1-633Q-SP type first-order vortex quarter wave plate manufactured by yubang technology (LBTEK), the second vortex quarter wave plate 301 is a VR5-633Q-SP type fifth-order vortex quarter wave plate manufactured by yubang technology (LBTEK), and the image sensor 401 is a dhiana 95 type scientific CMOS image sensor of a photo-electric (Tucsen).
In step S2, a 0 degree linear polarizer is placed on the sample stage between the polarizing modulation unit 1 and the image sensor 401, and the light beam emitted from the image sensor 401 is sampled to obtain a first light intensity modulation image I 10 The method comprises the steps of carrying out a first treatment on the surface of the A 45-degree linear polaroid is arranged between the polarization modulation unit 1 and the image sensor 401, and the light beam emitted by the image sensor 401 is used for sampling to obtain a second light intensity modulation image I 20 The method comprises the steps of carrying out a first treatment on the surface of the A 90-degree linear polarizer is placed between the polarizing modulation unit 1 and the image sensor 401, and an image is usedThe light beam emitted by the sensor 401 is sampled to obtain a third light intensity modulation image I 30 The method comprises the steps of carrying out a first treatment on the surface of the A 135-degree linear polaroid is arranged between the polarization modulation unit 1 and the image sensor 401, and the light beam emitted by the image sensor 401 is used for sampling to obtain a fourth light intensity modulation image I 40 The method comprises the steps of carrying out a first treatment on the surface of the A right-hand circular polaroid is arranged between the polarization modulation unit 1 and the image sensor 401, and the light beam emitted by the image sensor 401 is used for sampling to obtain a fifth light intensity modulation image I 50 The method comprises the steps of carrying out a first treatment on the surface of the A left-hand circular polaroid is arranged between the polarization modulation unit 1 and the image sensor 401, and the light beam emitted by the image sensor 401 is used for sampling to obtain a sixth light intensity modulation image I 60 . First light intensity modulation image I 10 (see FIG. 3 a) modulating the image I with the first light intensity 10 The azimuth angle of (2) is alternately changed in brightness and darkness. Second light intensity modulated image I 20 (see FIG. 3 b) modulating image I with second light intensity 20 The azimuth angle of (2) is alternately changed in brightness and darkness. Third light intensity modulated image I 30 (see FIG. 3 c) modulating image I with third light intensity 30 The azimuth angle of (2) is alternately changed in brightness and darkness. Fourth light intensity modulated image I 40 (see FIG. 3 d) modulating image I with fourth light intensity 40 The azimuth angle of (2) is alternately changed in brightness and darkness. Fifth light intensity modulation image I 50 (see FIG. 3 e) modulating image I with fifth light intensity 50 The azimuth angle of (2) is alternately changed in brightness and darkness. Sixth light intensity modulated image I 60 (refer to FIG. 3 f) modulating image I with sixth light intensity 60 The azimuth angle of (2) is alternately changed in brightness and darkness.
In step S2, the light emitted from the light source 101 sequentially passes through the polarizer 102, the first vortex quarter wave plate 103, and a wave plate (0 degree linear polarizer, 45 degree linear polarizer, 90 degree linear polarizer, 135 degree linear polarizer, right-handed circular polarizer, or left-handed circular polarizer) on the sample stage, and is received by the image sensor 401.
In step S2, the second vortex quarter wave plate 301 and the analyzer 302 are not in the double vortex wave plate muller matrix ellipsometer. In step S2, when the 0-degree linear polarizer is placed between the polarization modulation unit 1 and the image sensor 401, the 45-degree linear polarizer, the 90-degree linear polarizer, the 135-degree linear polarizer, the right-handed circular polarizer, and the left-handed circular polarizer are not in the double vortex wave plate mueller matrix ellipsometer; when the 45-degree linear polarizer is placed between the polarization modulation unit 1 and the image sensor 401, the 0-degree linear polarizer, the 90-degree linear polarizer, the 135-degree linear polarizer, the right-handed circular polarizer and the left-handed circular polarizer are not in the double-vortex wave plate mueller matrix ellipsometer; when the 90-degree linear polarizer is placed between the polarization modulation unit 1 and the image sensor 401, the 0-degree linear polarizer, the 45-degree linear polarizer, the 135-degree linear polarizer, the right-handed circular polarizer and the left-handed circular polarizer are not in the double-vortex wave plate mueller matrix ellipsometer; when the 135-degree linear polarizer is placed between the polarization modulation unit 1 and the image sensor 401, the 0-degree linear polarizer, the 45-degree linear polarizer, the 90-degree linear polarizer, the right-handed circular polarizer and the left-handed circular polarizer are not in the double vortex wave plate mueller matrix ellipsometer; when the right-hand circular polarizer is placed between the polarization modulation unit 1 and the image sensor 401, the 0-degree linear polarizer, the 45-degree linear polarizer, the 90-degree linear polarizer, the 135-degree linear polarizer and the left-hand circular polarizer are not in the double vortex wave plate mueller matrix ellipsometer; when the left-hand circular polarizer is placed between the polarization modulation unit 1 and the image sensor 401, the 0-degree linear polarizer, 45-degree linear polarizer, 90-degree linear polarizer, 135-degree linear polarizer and right-hand circular polarizer are not in the double vortex wave plate mueller matrix ellipsometer.
In this embodiment, the method further includes: p in modulation vector p 1 Normalization.
In step S6, a 0-degree linear polarizer is placed between the polarization-analyzing modulation unit 3 and the light source 101, and the outgoing light beam is sampled by the image sensor 401 to obtain a seventh light intensity-modulated image I 70 The method comprises the steps of carrying out a first treatment on the surface of the A 45-degree linear polarizer is arranged between the polarization-detecting modulation unit 3 and the light source 101, and the emergent light beam is sampled by the image sensor 401 to obtain an eighth light intensity modulation image I 80 The method comprises the steps of carrying out a first treatment on the surface of the A 90-degree linear polarizer is arranged between the polarization-detecting modulation unit 3 and the light source 101, and the emergent light beam is sampled by the image sensor 401 to obtain a ninth light intensity modulation image I 90 The method comprises the steps of carrying out a first treatment on the surface of the A 135 degree linear polarizer is arranged between the polarization-detecting modulation unit 3 and the light source 101, and the emergent light beam is sampled by the image sensor 401 to obtain a tenth light intensity modulation image I 100 The method comprises the steps of carrying out a first treatment on the surface of the Placing the right-handed circular polaroid on the polarization analyzerBetween the modulation unit 3 and the light source 101, and the outgoing light beam is sampled by the image sensor 401 to obtain an eleventh light intensity modulated image I 110 The method comprises the steps of carrying out a first treatment on the surface of the A left-hand circular polarizer is arranged between the polarization-detecting modulation unit 3 and the light source 101, and the emergent light beam is sampled by the image sensor 401 to obtain a twelfth light intensity modulation image I 120 . Seventh light intensity modulated image I 70 (refer to FIG. 6 a) modulating image I with seventh light intensity 70 The azimuth angle of (2) is alternately changed in brightness and darkness. Eighth light intensity modulation image I 80 (refer to FIG. 6 b) modulating image I with eighth light intensity 80 The azimuth angle of (2) is alternately changed in brightness and darkness. Ninth light intensity modulated image I 90 (refer to FIG. 6 c) modulating image I with ninth light intensity 90 The azimuth angle of (2) is alternately changed in brightness and darkness. Tenth light intensity modulated image I 100 (refer to FIG. 6 d) modulating image I with tenth light intensity 100 The azimuth angle of (2) is alternately changed in brightness and darkness. Eleventh light intensity modulated image I 110 (refer to FIG. 6 e) modulating image I with eleventh light intensity 110 The azimuth angle of (2) is alternately changed in brightness and darkness. Twelfth light intensity modulated image I 120 (refer to fig. 6 f) alternately changing brightness and darkness with the azimuth angle of the twelfth light intensity modulation image.
The 0 degree linear polarizer, 45 degree linear polarizer, 90 degree linear polarizer, 135 degree linear polarizer, right-handed circular polarizer and left-handed circular polarizer are respectively and independently arranged between the polarization analyzer unit 3 and the light source 101, which means that when one wave plate of the 0 degree linear polarizer, 45 degree linear polarizer, 90 degree linear polarizer, 135 degree linear polarizer, right-handed circular polarizer and left-handed circular polarizer is arranged between the polarization analyzer unit 3 and the light source 101, the other wave plates of the 0 degree linear polarizer, 45 degree linear polarizer, 90 degree linear polarizer, 135 degree linear polarizer, right-handed circular polarizer and left-handed circular polarizer are not arranged in the double wave plate mueller matrix ellipsometer.
In step S6, the light emitted from the light source 101 sequentially passes through a wave plate (0 degree linear polarizer, 45 degree linear polarizer, 90 degree linear polarizer, 135 degree linear polarizer, right-handed circular polarizer, or left-handed circular polarizer), a second vortex quarter wave plate 301, and an analyzer 302 on the sample stage, and is received by the image sensor 401. In step S6, the polarizer 102 and the first vortex quarter wave plate 103 are not in the double vortex wave plate muller matrix ellipsometer.
In this embodiment, the method further includes: a in modulation vector a 1 Normalization.
In this embodiment, the method further includes: step S10: removing the 0-degree linear polaroid, the 45-degree linear polaroid, the 90-degree linear polaroid, the 135-degree linear polaroid, the right-handed circular polaroid and the left-handed circular polaroid from the double-vortex wave plate Mueller matrix ellipsometer, and placing a sample to be detected on a sample table; sampling the emergent light beam of the polarization-analysis modulation unit by using an image sensor to obtain a light intensity function I; step S11: and acquiring a Mueller matrix M of the sample to be detected according to the light intensity function I, the modulation vector a of the polarization-analysis modulation unit and the modulation vector p of the polarization-analysis modulation unit, wherein I=a×M×p.
The matrix elements in M are denoted as M ij I is an integer of 1 or more and 4 or less, and j is an integer of 1 or more and 4 or less. m is m ij Is the matrix element of the ith row and jth column in M.
In this embodiment, the method further includes: for m 11 Normalization was performed.
In one embodiment, the information of the light emitted by the light source in step S2, step S6 and step S10 is consistent.
In steps S1 to S9, the sample to be measured is not in the double vortex wave plate muller matrix ellipsometer.
The mueller matrix ellipsometer with double vortex wave plates is used for measuring the mueller matrix of the sample 201 to be measured, which is an air, 45-degree, 60-degree, 90-degree, 135-degree linear polarizer and a 0-degree, 60-degree and 90-degree quarter wave plate. The light intensity modulation images acquired by the image sensor are shown in fig. 9 (a) to (h), respectively. Directly analyzing the 8 light intensity modulation images to obtain 8 samples of uncorrected Mueller matrices (m in the Mueller matrix 11 Normalized) is shown in table 1. From the table, it can be seen that: the deviation between the directly measured Mueller matrix elements and the theoretical value is larger, the maximum value of the root mean square of the error of each Mueller matrix reaches 0.0604, and the maximum measurement error of the Mueller matrix elements reaches 0.1416.
Table 1 Mueller matrix direct measurements and errors for each sample
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Next, calibrating the measurement result by using the calculated modulation vectors of the polarization-increasing modulation unit and the polarization-analyzing modulation unit to obtain 8 kinds of sample-calibrated Mueller matrices (for m in the Mueller matrix 11 Normalized) is shown in table 2. As can be seen from table 2: the calibrated Mueller matrix elements are well matched with the theoretical values, the measurement error is obviously reduced, the maximum value of the root mean square of the error of each Mueller matrix is reduced from 0.0604 to 0.0180, and the maximum measurement error of the Mueller matrix elements is reduced from 0.1416 to 0.0352, so that the feasibility and the accuracy of the error calibration method of the double vortex wave plate Mueller matrix ellipsometer are proved.
TABLE 2 Mueller matrix calibration results for each sample and errors after calibration
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The calibration method of the double vortex wave plate Mueller matrix ellipsometer provided by the invention integrally considers the modulation vectors of the polarization modulation unit and the polarization analysis modulation unit, and can finish the calibration of an optical system through a series of simple measurements. The method does not depend on a system model, avoids system errors caused by modeling deviation, greatly reduces the difficulty of error calibration and improves the calibration precision of the system. Compared with the traditional parameter calibration method and the characteristic value calibration method, the invention does not need any standard sample, does not need any prior information of the system, can complete the system calibration by using the linear polaroid and the circular polaroid, and has convenient operation and stable calculation result. Experiments prove that the calibration method of the double-vortex wave plate Mueller matrix ellipsometer can effectively reduce the influence of various error factors of a system and remarkably improve the measurement accuracy of the Mueller matrix of a sample to be measured.
It is apparent that the above examples are given by way of illustration only and are not limiting of the embodiments. Other variations or modifications of the above teachings will be apparent to those of ordinary skill in the art. It is not necessary here nor is it exhaustive of all embodiments. While still being apparent from variations or modifications that may be made by those skilled in the art are within the scope of the invention.
Claims (4)
1. The error calibration method of the double vortex wave plate Mueller matrix ellipsometer is characterized by comprising the following steps of:
s0, providing a double-vortex wave plate Mueller matrix ellipsometer, wherein the double-vortex wave plate Mueller matrix ellipsometer comprises: the device comprises a polarization modulation unit, a sample stage, an polarization analysis modulation unit and an image processing unit which are sequentially arranged side by side; the polarization modulation unit comprises a light source, a polarizer and a first vortex quarter wave plate which are sequentially arranged; the sample table is suitable for placing a sample to be tested; the polarization analysis modulation unit comprises a second vortex quarter wave plate and a polarization analyzer which are sequentially arranged; the first vortex quarter wave plate is positioned between the polarizer and the second vortex quarter wave plate;
step S1: removing the polarization analysis modulation unit from the double vortex wave plate Mueller matrix ellipsometer;
step S2: turning on a light source, respectively and independently placing a 0-degree linear polaroid, a 135-degree linear polaroid, a right-hand circular polaroid and a left-hand circular polaroid on a sample stage between a polarization modulation unit and an image sensor, and sampling corresponding emergent light beams by using the image sensor to obtain corresponding first light intensity modulation images, second light intensity modulation images, third light intensity modulation images, fourth light intensity modulation images, fifth light intensity modulation images and sixth light intensity modulation images; the jth light intensity modulation image is changed in brightness and darkness alternately along with the azimuth angle of the jth light intensity modulation image; j is an integer of 1 or more and 6 or less;
step S3, processing the first light intensity modulation image, the second light intensity modulation image, the third light intensity modulation image, the fourth light intensity modulation image, the fifth light intensity modulation image and the sixth light intensity modulation image respectively to obtain corresponding first light intensity modulation functionsSecond light intensity modulation function->Third light intensity modulation function->Fourth light intensity modulation functionFifth light intensity modulation function->And a sixth light intensity modulation function->The j-th light intensity modulation function->Modulating the light intensity in the image with azimuth angle for the jth light intensity>A function of the change;
first light intensity modulation functionSecond light intensity modulation function->Third light intensity modulation function->Fourth light intensity modulation function->Fifth light intensity modulation function->And a sixth light intensity modulation function->The first matrix equation is satisfied:
p＝[p 1 p 2 p 3 p 4 ] T the method comprises the steps of carrying out a first treatment on the surface of the p is the modulation vector of the polarization modulation unit;
step S4: solving the first matrix equation set to obtain a modulation vector p of a polarization modulation unit;
step S5: the polarization-analysis modulation unit is installed back into the double-vortex wave plate Mueller matrix ellipsometer, the second vortex quarter wave plate is positioned between the polarization analyzer and the polarization-analysis modulation unit, and then the polarization analyzer and the first vortex quarter wave plate are removed from the polarization-analysis modulation unit;
step S6: the method comprises the steps that a 0-degree linear polaroid, a 45-degree linear polaroid, a 90-degree linear polaroid, a 135-degree linear polaroid, a right-handed circular polaroid and a left-handed circular polaroid are respectively and independently arranged on a sample table between an analysis modulation unit and a light source, and an image sensor is utilized to sample outgoing light beams of the analysis modulation unit so as to obtain a seventh light intensity modulation image, an eighth light intensity modulation image, a ninth light intensity modulation image, a tenth light intensity modulation image, an eleventh light intensity modulation image and a twelfth light intensity modulation image which correspond to each other; the ith light intensity modulation image is changed in brightness and darkness alternately along with the azimuth angle of the ith light intensity modulation image; i is an integer of 7 or more and 12 or less;
step S7: the seventh light intensity modulation image, the eighth light intensity modulation image, the ninth light intensity modulation image, the tenth light intensity modulation image, the eleventh light intensity modulation image and the twelfth light intensity modulation image are respectively processed to obtain corresponding seventh light intensity modulation functionsEighth light intensity modulation function->Ninth light intensity modulation function->Tenth light intensity modulation functionEleventh light intensity modulation function->And a twelfth light intensity modulation function->Ith light intensity modulation functionModulating the light intensity in the image with azimuth angle for the ith light intensity +.>A function of the change;
seventh light intensity modulation functionEighth light intensity modulation function->Ninth light intensity modulation function->Tenth light intensity modulation function->Eleventh light intensity modulation function->And a twelfth light intensity modulation function->The second matrix equation is satisfied:
a＝[a 1 a 2 a 3 a 4 ]a is a modulation vector of the polarization-analysis modulation unit;
step S8: solving a second matrix equation set to obtain a modulation vector a of the polarization-analysis modulation unit;
step S9: and installing the polarizer and the first vortex quarter wave plate back into the double vortex wave plate Mueller matrix ellipsometer, wherein the polarizer is positioned between the first vortex quarter wave plate and the light source, and completing calibration.
2. The method for calibrating an error of a double vortex wave plate mueller matrix ellipsometer according to claim 1, further comprising: a in modulation vector a 1 Normalization.
3. The method for calibrating errors of a double vortex wave plate mueller matrix ellipsometer according to claim 1, wherein the method comprises the following steps ofAnd further comprises: p in modulation vector p 1 Normalization.
4. The method for calibrating an error of a double vortex wave plate mueller matrix ellipsometer according to claim 1, further comprising:
step S10: removing the 0-degree linear polaroid, the 45-degree linear polaroid, the 90-degree linear polaroid, the 135-degree linear polaroid, the right-handed circular polaroid and the left-handed circular polaroid from the double-vortex wave plate Mueller matrix ellipsometer, and placing a sample to be detected on a sample table; sampling the emergent light beam of the polarization-analysis modulation unit by using an image sensor to obtain a light intensity function I;
step S11: and acquiring a Mueller matrix M of the sample to be detected according to the light intensity function I, the modulation vector a of the polarization-analysis modulation unit and the modulation vector p of the polarization-analysis modulation unit, wherein I=a×M×p.
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