CN109990736B - Method and device for measuring roll angle based on Stokes vector - Google Patents
Method and device for measuring roll angle based on Stokes vector Download PDFInfo
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- CN109990736B CN109990736B CN201910240923.7A CN201910240923A CN109990736B CN 109990736 B CN109990736 B CN 109990736B CN 201910240923 A CN201910240923 A CN 201910240923A CN 109990736 B CN109990736 B CN 109990736B
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Abstract
The invention belongs to the field of photoelectric detection and measurement, and particularly discloses a method and a device for measuring a roll angle based on a Stokes vector. Compared with the existing roll angle measuring method and device, the roll angle measuring method and device realize the ultra-large range absolute type roll angle measurement, can meet the application occasions of large range, high precision and absolute type roll angle measurement required by precision machining and measurement, automatic butt joint of industrial robots and spacecrafts, and the like, and have the advantages of simplicity, compactness, high speed, low cost and the like.
Description
Technical Field
The invention belongs to the field of photoelectric detection and measurement, and particularly relates to a method and a device for measuring a roll angle based on a Stokes vector.
Background
The precision kinematic pair is an inertia motion part of modern precision engineering, and is widely applied to high-tech fields such as numerical control machine tools, aerospace military industry, synchrotron radiation and the like. The motion of the object can be characterized by three degrees of freedom of movement parallel to a rectangular coordinate axis and three degrees of freedom of rotation around the coordinate axis in a space Cartesian rectangular coordinate system, and the position of the object in a three-dimensional space can be completely determined based on the six degrees of freedom. The roll angle is one of six degrees of freedom, is the displacement of the object around the longitudinal axis of the object, and forms the rotation angle error of three degrees of freedom of the motion of the object with the yaw angle and the pitch angle. Roll angle measurement is one of key technologies of precision measurement, and is widely applied to the fields of machine tools, coordinate measuring machines, robot navigation and the like. Compared with a yaw angle and a pitch angle, the existing roll angle measuring method cannot meet the requirements of high-precision and large-range measurement easily, and mainly the angular displacement of the roll angle is perpendicular to the motion direction, so that high-precision mature goniometers such as a dual-frequency laser interferometer and an autocollimator cannot be directly used for roll angle measurement.
Currently, there are three main methods for measuring the roll angle in domestic and foreign research:
laser interferometry, which converts roll angle measurements into interferometric parameters for measurement, such as changes in roll angle to optical path difference or phase difference using specific optics or structures. For example, US3790284A proposes an interferometric method using double wollaston prisms, in which a symmetrical double wollaston prism and a symmetrical mirror are used to convert a roll angle change into an optical path difference change, which requires alignment of the mirror and the double wollaston prism, resulting in higher equipment cost and limited application occasions; US2010141957a1 and CN101650166A propose a roll angle interferometry system using a wedge prism as a sensing element instead of a wollaston prism to rotate with the object to be measured, which reduces the cost but complicates the system structure by adding a phase meter and has high requirements on the symmetry and surface shape of the wedge prism.
The laser auto-collimation method utilizes the good spatial stability of laser to measure, for example, in the parallel double-beam method, the roll angle is obtained by measuring the straightness of two different points on a moving platform. For example, CN101846506A proposes a common-path parallel light-based roll angle measurement method, which obtains two parallel light beams by using a symmetric light path based on the laser auto-collimation principle, and converts the roll angle change into the optical path difference of the common light beam, and although the common-path structure improves the anti-interference performance, the method has a relatively complex structure, increases the adjustment difficulty, and is easily affected by the linearity; CN104535019A proposes a roll angle measuring method of double diffraction grating heterodyne, which adopts the method of converting roll angle information into polarization phase difference, thus realizing high resolution and high precision, but the measuring range is small and the measuring system is complex.
The roll angle is measured with the polarization plane as a reference based on the polarization characteristic method, which utilizes the sensitivity of the laser polarization plane to rotation. For example, CN105222726A proposes a light intensity method roll angle measurement device and method based on multiple passes through a half-wave plate, which utilizes 1/2 wave plate in cooperation with prism array, and places the prism array in two sets of prism arrays for converting the roll angle into the light intensity difference change caused by the array prisms, thereby improving the resolution of roll angle measurement. Shiguang Li et al, in the literature (Compact optical-roller with large measurement range and high sensitivity, Optics letters, vol. 30, 2005, 3, pages 242-4) proposed to modulate the polarization state of the probe light with a faraday rotator to perform roll angle measurements in the working range of ± 30 ° and resolution of 0.01 °, improved by Steven r.
Compared with the method, the laser interferometry has the advantages that the system structure is complex, the cost of the sensing element is high, and the popularization is not facilitated; the laser auto-collimation method has high adjustment difficulty and is easily influenced by straightness; the phase method based on the polarization characteristic can realize high resolution, but a nonlinear response curve needs to be calibrated, so that the precision and the stability of the phase method are reduced, the light intensity based on the polarization characteristic is easily influenced by factors such as environment, a light source and the like, and the measurement resolution is limited. Meanwhile, the sensor utilizing the polarization method can obtain a large range in the roll angle sensor, the measurement range of the roll angle can reach 43 degrees at most, however, the sensor is often required to be applied in the application fields of robot navigation, machine tool coordinate measuring machines and the like, and the roll angle measurement sensor and method with the range of 0-180 degrees are not available in the existing roll angle measurement method at present.
Disclosure of Invention
In order to overcome the defects of the existing roll angle measuring device and under the premise of ensuring the measuring precision, the invention provides a roll angle measuring method and device based on Stokes vectors, which modulate linearly polarized light into elliptically polarized light through a wave plate connected with an object to be measured and measure the polarization state of the elliptically polarized light through a complete Stokes polarizer to obtain the Stokes vectors, thereby obtaining the roll angle of a rotating object based on the Stokes vectors, realizing the absolute measurement of the ultra-large range of the roll angle within the range of 0-180 degrees, and being suitable for the conditions that high measuring precision, high resolution and absolute measurement are required within the ultra-large range.
In order to achieve the above object, according to a first aspect of the present invention, a method for measuring a roll angle based on a stokes vector is provided, in which linearly polarized light generated by a linearly polarized light generating module enters a complete stokes polarizer after being modulated by a wave plate fixedly connected to an object to be measured to obtain the stokes vector, and a roll angle of the object to be measured is obtained based on a stokes vector calculation.
Further preferably, the measurement method includes a transmission measurement method and a reflection measurement method.
Further preferably, in the transmission measurement, the roll angle is calculated as follows:
judgment S2Whether the angle is 0 or not, if yes, the angle theta' is 0 degree or 90 degrees; if not, calculating by adopting the following formula:
Where θ' is the roll angle to be measured, S1、S2And S3And Ps are initial azimuth angles of the polarizers in the linearly polarized light generation module and phase retardation of the wave plates.
More preferably, in the case of reflection measurement, the roll angle is calculated by the following formula:
judging whether S2 is 0 or not, if yes, theta' is 0 degree or 90 degrees; if not, calculating by adopting the following formula:
Where θ' is the roll angle to be measured, S1、S2And S3And Ps are initial azimuth angles of the polarizers in the linearly polarized light generation module and phase retardation of the wave plates.
According to a second aspect of the invention, a rolling angle measuring device based on a stokes vector is provided, which comprises a linearly polarized light generating module, a sensing module and an analyzing module, wherein the linearly polarized light generating module comprises a light source and a polarizer, the sensing module comprises a wave plate which is used as a polarization sensitive element and is connected with a rotating element to be detected and synchronously rotates so as to convert the rolling angle change of the rotating element to be detected into the polarization change of a detection light beam, and the analyzing module is a complete stokes polarimeter; during measurement, collimated monochromatic light emitted by a light source is polarized into linearly polarized light through a polarizer, then is modulated into elliptically polarized light through a wave plate, and finally enters a complete Stokes polarizer to obtain a Stokes vector.
According to a third aspect of the invention, a rolling angle measuring device based on a stokes vector is provided, which comprises a linearly polarized light generating module, a sensing module, a beam splitter module and an analyzing module, wherein the linearly polarized light generating module comprises a light source and a polarizer, the sensing module comprises a plane mirror and a wave plate, the wave plate is used as a polarization sensitive element and is connected with a rotating element to be detected and synchronously rotates to convert the rolling angle change of the rotating element to be detected into the polarization change of a detection light beam, the beam splitter module comprises a beam splitter, and the analyzing module is a complete stokes polarizer; during measurement, collimated monochromatic light emitted by a light source is polarized into linearly polarized light through a polarizer, then vertically enters a wave plate through a beam splitter, then vertically enters a plane mirror and then enters the wave plate again, and finally enters a complete Stokes polarizer through the beam splitter to obtain a Stokes vector.
As a further preferred, the polarization analyzing module comprises a rotating wave plate, an analyzer and a detector which are arranged in sequence along the optical path.
Further preferably, the light source is a white light source, a laser light source or a light emitting diode light source.
It is further preferable that the measuring device is calibrated by a single-rotation in-situ calibration method before measurement to obtain a system initial value of the measuring device.
Further preferably, the beam splitter is preferably a non-polarizing beam splitter.
Generally, compared with the prior art, the above technical solution conceived by the present invention mainly has the following technical advantages:
1. the invention provides a method for realizing roll angle measurement based on Stokes vectors, which can realize absolute measurement of ultra-large range in a 180-degree measurement range, broaden the roll angle measurement range and can be applied to the fields of robot navigation, machine tool coordinate measuring machines and the like.
2. On the basis of the measurement method, the invention also researches a specific calculation formula of the roll angle in a matched manner so as to quickly calculate and obtain the roll angle of the object to be measured by measuring the known parameters, and the measurement is convenient and quick.
3. The invention also designs a measuring device for realizing the method in a matching way, and designs a transmission type measuring device and a reflection type measuring device in a pertinence way according to different measuring modes, and can effectively realize the rolling angle measurement based on the Stokes vector through the research and design of the specific structure and the specific assembly mode of the device, and greatly simplifies the optical path system, and has accurate and rapid measurement and super-large range.
4. The invention can obtain four Stokes parameters describing the light polarization state through the complete Stokes polarization instrument, compared with the traditional interferometer or laser measurement, the complete Stokes polarization instrument can be easily inherited into an optical system, and the polarization state information of light obtained through the polarization instrument is richer, thereby essentially simplifying the optical measurement device and promoting the miniaturization of the optical measurement device.
5. In addition, the invention also provides a method for calibrating the measuring device by adopting a single-rotation in-situ calibration method before measurement so as to obtain the system initial value of the measuring device, thereby ensuring the accuracy of the system initial value and facilitating the accurate calculation of the subsequent roll angle.
Drawings
FIG. 1 is a schematic diagram of an optical Stokes roll angle sensor transmission measurement;
FIG. 2 is a schematic diagram of the determination of the roll angle and Stokes sign in a roll angle sensor;
figure 3 is a theoretical plot of calculated roll angle versus input roll angle,
FIG. 4 is a schematic diagram of roll angle sensor transmission calibration;
FIG. 5 is a schematic diagram of a rotating retarder fixed analyzer type polarizer;
FIG. 6 is a schematic diagram of a four-channel polarimeter using partial amplitude method;
FIG. 7 is a schematic diagram of an optical Stokes roll angle sensor reflectometry;
FIG. 8 is a schematic diagram of roll angle sensor reflective calibration;
FIG. 9 is a graph of the measurement results of roll angle sensor transmission measurements from 0 to 360;
FIG. 10 is a graph of the measurement accuracy of the roll angle sensor for transmission measurements from 0 to 360;
FIG. 11 is a graph of roll angle sensor transmission measurement 0.03 resolution results;
FIG. 12 is a graph of roll angle sensor transmission measurement 0.02 resolution results.
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.
The invention provides a method for measuring a roll angle based on a Stokes vector, which comprises the following steps that linearly polarized light generated by a linearly polarized light generation module enters a polarizer after being modulated by a wave plate fixedly connected with an object to be measured to obtain the Stokes vector, and the roll angle of the object to be measured is calculated and obtained based on the Stokes vector:
(1) linearly polarized light is obtained by a linearly polarized light generating module;
(2) the linearly polarized light is modulated by a sensing module fixedly connected with a rotating object to be measured, and the polarization state is changed;
(3) polarized light modulated by the sensing module passes through a complete Stokes polarimeter to obtain a group of Stokes vectors;
(4) the sensing module is driven to rotate by a rotating object to be detected, and a complete Stokes polarization instrument records a group of Stokes vectors when the wave plate rotates for an angle;
(5) and processing the measured multiple groups of Stokes vector data to obtain the sizes of multiple roll angles corresponding to the measured object.
The method of the invention combines a roll angle sensitive element (namely a wave plate in a sensing module) and a polarization state (characterized by a Stokes vector) to realize the measurement of the roll angle with ultra-large range. The measuring method comprises a transmission type measuring method and a reflection type measuring method, wherein the transmission type measuring method is realized by using a transmission type roll angle sensor device, and the reflection type measuring method is realized by using a reflection type roll angle sensor device.
The two devices are described in detail below. Referring to fig. 1, a transmission-type roll angle sensor device according to an embodiment of the present invention is described in detail below with reference to the accompanying drawings. The device includes: the linear polarization light generation module comprises a light source 101 and a polarizer 102, the light source needs to generate a collimated light beam with a single wavelength, a white light source can be combined with a filter, a laser or a light emitting diode with a certain wavelength can be adopted, the wavelength of the light source is within the working wavelength range of the polarizer, a wave plate and a detector, the requirement of the retardation of the wave plate is met, the polarizer modulates the light emitted by the light source into linear polarization light, and the laser with the built-in polarizer can also be directly adopted. The sensing module 2 comprises a wave plate 103 and a fixed element 104, and the polarization analyzing module 3 is specifically a full stokes polarization meter, and comprises a rotating wave plate 105, an analyzer 106 and a detector 107 which are arranged in sequence.
The collimated monochromatic light emitted by the light source 101 is firstly converted into linearly polarized light through the polarizer 102, the linearly polarized light is modulated into elliptically polarized light after passing through the wave plate 103, the wave plate 103 is used as a polarization sensitive element and is connected with a rotating element to be detected through the fixed element 104, the change of the roll angle of the element to be detected is converted into the polarization change of the detection light beam, and the rotating azimuth angle of the wave plate around the fast axis of the wave plate is the roll angle to be detected; the Stokes vector can be measured after the modulated ellipsometric light passes through the complete Stokes polarizer, and the roll angle of the rotating element to be measured can be calculated according to the Stokes vector. In the device, collimated monochromatic light emitted by a light source 101 is perpendicularly incident on a polarizer 102, a quarter-wave plate 103 and a full stokes polarizer.
Specifically, the polarizer 102 may be a conventional Glan-Taylor prism, or a novel thin-film polarizer or a structural polarizer. The polarizers made of different materials have different preparation processes and performances, so that the polarizer meeting the requirements of compactness, miniaturization and polarizing function of the device can be applied to the device. The polarizer 102 is preferably a Glan polarizer, which reduces the overall device size while ensuring a high extinction ratio. The wave plate 103 can be a quarter wave plate, the material of which can be mica, quartz, liquid crystal and the like, and a quarter zero-order wave plate is preferably adopted to reduce the error of the phase retardation. The retardation of the wave plate is matched with the wavelength of the single-ray emitted by the light source, the retardation of the wave plate should meet the requirements of the measurement range in both a transmission type and a reflection type, and the retardation of the rotating wave plate can be selected after optimization. Therefore, any wave plate satisfying the retardation requirement can be applied to the device of the present invention.
The transmission measurement model is shown in fig. 1, and the system model is shown in formula (1):
S＝R(-θ′)MCR(θ′)R(-Ps)MPSin(1)
wherein R (theta'), R (P)s) Is a rotation matrix corresponding to the wave plate 103 and the polarizer 102, theta' is a roll angle of the rotation element to be measured fixedly connected with the wave plate 103, and PsIs the initial azimuth angle of the polarizer, MC、MP、SinThe polarization state of the light is controlled by the polarization controller, and the polarization state of the light is controlled by the polarization controller.
FIG. 2 is a relationship between Stokes vector elements and a roll angle along with changes of the roll angle, and a roll angle calculation formula can be obtained according to FIG. 2 as follows:
where θ' is the roll angle to be measured, S1、S2And S3Respectively second to of the Stokes vectorFour elements, Ps being the initial azimuth angle of the polarizer (either pre-determined or calibrated), and the phase retardation of the plate 103 (either pre-determined or calibrated), since the signs of the elements of the second to fourth terms of the Stokes vector always depend on the azimuth angle of the plate rotation and the azimuth angle of the polarizer, when S is3When equal to 0, S2Is always greater than or equal to 0, so S does not appear2＜0,S3Case 0.
When P is presentsThe results at 0 ° and 90 ° are:
order S2If 0, sin (2P) can be obtaineds)＝sin(2Ps-4 θ '), i.e., θ' can only be 0 ° or 90 °, so in the range of 0 ° to 180 °, if S2When 0, θ' is 0 ° or 90 ° (180 ° is regarded as 0 °). Therefore, at the beginning of the judgment, the pair S is added2Determination of whether or not 0, i.e. S2When 0, θ' is 0 ° or 90 °, and S is not less than S2Not equal to 0 °, the calculation is performed using the above equations (2) - (5). S can be used with the initial azimuthal angle of the polarizer known3The sign (i.e., positive or negative) of (A) determines whether the roll angle is 0 DEG or 90 DEG, Ps>At 0 deg. if S3<0 then θ' is 0 °, if S3>0 then θ' is 90 °; ps<At 0 deg. if S3>0 then θ' is 0 °, if S3<0 then θ' is 90 °; if P s0 ° or S3When θ 'is 0, it cannot be determined whether θ' is 0 ° or 90 °.
FIG. 3 is P s4 degrees, the result of system simulation. Wherein, the input is that the wave plate is constantly changed at intervals of 10 degrees within the range of 0-180 degrees, and corresponding Stokes vectors are obtained. And solving the value of the roll angle of the input wave plate according to the obtained Stokes vector, a set symbol judgment system and a calculation formula. It can be seen that the input and output values fit well without introducing errors, and PsThe roll angle of each wave plate can still be effectively judged within the range of +/-4 degrees, and the mueller matrix information of the wave plates at 0 degrees and 180 degrees is overlapped, so that the 0 degrees and the 180 degrees are considered to be the same.
The initial orientation angles of the individual components are calibrated prior to measurement. In actual measurement, only an approximate range of the initial azimuth angle of the polarization component can be obtained, so that the value of the initial azimuth angle cannot be accurately determined, and the initial azimuth angle cannot be in an ideal condition as described in the polarimeter part, so that the initial azimuth angle needs to be taken into account when calculating the stokes vector elements.
The calibration of the measuring device can be performed by using various existing calibration methods to obtain the initial system value such as the initial azimuth angle P of the polarizersInitial azimuth angle C of wave plates1Phase retardation of wave plate1Initial azimuth angle C of rotating wave plates2Phase retardation of rotating wave plate2Initial azimuth angle A of analyzers. The invention preferably adopts a single-rotation in-situ calibration method for calibration, wherein a rotating wave plate is added into the system, a plurality of groups of data are obtained through the rotating wave plate and are calibrated, and the wave plate 103 is discretely rotated at an angle of 20 degrees from 0 degree until the angle is rotated to 180 degrees.
PC1CrThe system model for a SA ellipsometer can be represented by the following equation:
S＝MAR(As)R(-Cs2)MC(2)R(Cs2)R(-Cs1)MC(1)R(Cs1)R(-Ps)MPSin
wherein S isinAnd S respectively represents PC1CrIncident light of SA ellipsometerStokes vector of the emitted light, C1Is a wave plate, CrIs a rotating wave plate; incident light is natural light, M () represents the Mueller matrix of the wave plate, MP、MC(1)、MC(2)、MAMueller matrix, R (P), of polarizer 102, wave plate 103, rotating wave plate 105, and analyzer 106, respectivelys)、R(Cs1)、R(Cs2)、R(As) A polarizer 102, a wave plate 103, a rotating wave plate 105 and an analyzer 106 rotate the Mueller matrix,1、2the phase retardation amounts, C, of the wave plate 103 and the rotary wave plate 105, respectivelys1Is the initial azimuth angle, C, of the wave plate 103s2Is the initial azimuth angle, P, of the rotating wave plate 105sIs the initial azimuth angle of the polarizer, AsFor the initial azimuth angle of the analyzer 106, there are:
Sin＝[I0,0,0,0]T(12)
the expression for each mueller matrix is as follows:
wherein θ may represent an initial azimuth angle P of the polarizer PsWave plate C1Initial azimuth angle C ofs1Rotating wave plate CrInitial azimuth angle C ofs2Initial azimuth angle A of analyzer As。
The theoretical light intensity signal of a single rotation compensator ellipsometer can be represented by a fourier expansion equation:
in the case of a single rotation in the transmissive mode,the fast axis of the polarizer P is used to establish the reference frame, so that the unknown quantity has Ps、Cs1、1、Cs2、2、AsThe spectrum has only four fourier coefficients due to the presence of a single rotation, α4、β4、α2、β2Are respectively Cs1、1、Cs2、2、AsAnd (4) combining the parameters.
The calibration process and principle of the single-rotation in-situ calibration method are described below:
(1) positioning the wave plate 103 at its initial azimuthal angle Cs1Then, a set of light intensity data I is collected by a detector0And calculates corresponding fourier coefficients α41、β41、α21、β21According to α21And β21Calculate Cs2+AsSumming;
(2) rotating the wave plate 103 by a fixed, known angle CsTypically, the wave plate is rotated by 20 DEG to measure a set of intensities ICsAnd repeating the measurement for many times, and obtaining (I) under theoretical conditions0、ICs、I2Cs) At least three sets of data, and three corresponding sets of Fourier coefficients (α) are determined4i、β4i、α2i、β2i) Calculating P from the Fourier coefficients、Cs1、1、Cs2、2、AsA value of (d);
(3) in the previous two steps, a preliminary system initial value, P, is obtaineds、Cs1、1、Cs2、2、AsBecause of the possible errors in the single measurements, and the corresponding errors in the initial values obtained from the single measurements, the acquisition of the waveplate 103 at 20 ° intervals in its optical cycle yields ten sets of actual fourier coefficients (α)4i、β4i、α2i、β2i)。
As mentioned above, PC1CrThe system model for a SA ellipsometer can be represented by the following equation:
S＝MAR(As)R(-Cs2)MC(2)R(Cs2)R(-Cs1)MC(1)R(Cs1)R(-Ps)MPSin
wherein, Cs1Representing the initial azimuth of the waveplate 103.
The simulated light intensity conforming to the actual measurement needs to be generated on a theoretical model, namely Cr＝ωct，ωcFor rotating the angular frequency of the wave plate during actual measurement, Sin＝(1,0,0,0)TThe specific fitting procedure is as follows, the fitting analysis is carried out in matlab program using lsqcurvefit function, the input of which is the actually measured fourier coefficient (α)4i、β4i、α2i、β2i) And a system initial value Ps、Cs1、1、Cs2、2、AsThe output of the function is the accurately calibrated system Ps、Cs1、1、Cs2、2、AsThe value of (c). P calculated in the step (2) is addeds、Cs1、1、Cs2、2、AsThe initial value is used as the initial value of the lsqcurvefit function iteration and substituted into PC1CrTen groups of simulated light intensities S generated in SA-type ellipsometer system modeliAnd obtaining ten sets of theoretical Fourier coefficients (α) according to the simulated light intensity4i′、β4i′、α2i′、β2i') comparing the actually measured Fourier coefficients (α)4i、β4i、α2i、β2i) And theoretical fourier coefficients (α)4i′、β4i′、α2i′、β2i') and calculating corresponding residual error and mean square error, and when the residual error and mean square error are too large (the specific numerical value and range can be defined according to actual requirements), adjusting the input system value Ps、Cs1、1、Cs2、2、AsUntil a residual error and a mean square error which meet the condition (namely the residual error and the mean square error are both in a preset range) are obtained, outputting the system value P at the moments、Cs1、1、Cs2、2、AsI.e. updating the system P by means of the lsqcurvefit functions、Cs1、1、Cs2、2、AsThen the updated Ps、Cs1、1、Cs2、2、AsSubstitution of value into PC1CrTen groups of simulated light intensities S generated in SA-type ellipsometer system modeliObtaining a new theoretical Fourier coefficient, comparing the new theoretical Fourier coefficient with the actually measured Fourier coefficient for judgment, continuing iteration if residual error and mean square error are too large, and outputting a system value P at the moment if a condition is mets、Cs1、1、Cs2、2、AsAnd the initial value is the initial value of the calibrated system, and accordingly, the calibration process of the system is completed.
The calibration method is described with reference to fig. 4, and the steps of the transmissive in-situ calibration are as follows:
(1) aligning a light source 101, a polarizer 102, a wave plate 103, a rotating wave plate 105, an analyzer 106 and a detector 107 in turn to an optical path according to the steps of fig. 4, and ensuring that a collimated light beam from the light source is perpendicularly incident into each element;
(2) turning on the light source 101 and the detector 107, and setting a proper light intensity acquisition time;
(3) starting the motor for the wave plate 103 and the motor for rotating the wave plate 105, and enabling the motor for rotating the wave plate to be in a continuous rotation state;
(4) the wave plate is discretely rotated at an angle of 20 degrees from 0 degree, the detector 107 collects the signals at each angle until the signals are rotated to 180 degrees, and ten groups of spectrums are obtained;
(5) and analyzing according to the acquired light intensity, and calculating to obtain the initial azimuth angles of the polarizer, the wave plate, the rotating wave plate and the analyzer and the phase delay amount of the wave plate.
Specifically, the detector measures the light intensity of two beams of light simultaneously, and may select a photodiode array, a Charge Coupled Device (CCD) image sensor, a spectrometer, a camera, a photomultiplier tube, and the like. Different detectors have their own characteristics, so that the device can be compact, and simultaneously, the detectors capable of realizing the real-time measurement of the light intensity can be applied to the device.
After the initial value of the system is obtained, the Stokes vector of the light passing through the wave plate can be calculated according to the measured light intensity information. The following illustrates how to derive the stokes vector, which consists of four elements describing the polarization state of light, and the measurement process can be described as:
I＝AS (17)
where I is a luminous flux vector measured by a probe, a is a measurement matrix (which is a known parameter) determined by the number of measurements and an optical system, and S ═ S0,S1,S2,S3]TIs the incident stokes vector;
thus, the stokes vector can be obtained:
S＝A+I (18)
a complete stokes polarimeter refers to all four elements that are capable of completely measuring stokes, while a non-complete stokes polarimeter measures fewer than 4 stokes elements. Polarimeters that measure stokes vectors can be roughly classified into four categories: the Stokes vectors measured by different methods are consistent. This example illustrates one of the mechanical modulation methods used in the present invention to measure the full stokes vector.
The complete stokes vector polarimeter of fig. 5 is a rotating retarder fixed analyzer polarimeter in a mechanical modulation method, wherein a rotating wave plate 105 (i.e. a rotating retarder), an analyzer 106 and a detector 107 are on the same optical path. Fig. 6 shows a four-channel polarizer in the amplitude division method, wave plates 602 and 604 function to divide amplitude, beam splitters 601, 605 and 608 divide a beam into a plurality of optical paths, and detectors 603, 606, 607 and 609 detect light intensity.
The process of acquiring the stokes vector is specifically described below by taking a rotating retarder fixed analyzer as an example.
The polarization meter of the rotating retarder fixed analyzer is a complete Stokes polarization meter commonly used in a mechanical modulation method, and a detector only observes one polarization state. The modulation signal is composed of two frequencies, and can be expressed as the following fourier coefficients:
where β is the azimuth angle of the rotating wave plate, if the rotating wave plate is a quarter wave plate and the starting position of the data acquired by the detector is that the initial azimuth angle of the rotating wave plate is zero and the initial azimuth angle of the analyzer is zero, the stokes vector can be expressed as:
after the system initial value calibration is completed and the Stokes vector after passing through the wave plate is detected by the optical Stokes polarizer, the measuring method of the transmission type device for measuring the roll angle by using the optical Stokes comprises the following steps:
(1) as shown in fig. 1, the roll angle sensor is assembled and then the light source 101 and the full stokes polarizer are turned on and the appropriate acquisition time is set;
(2) connecting the object to be measured with a wave plate 103 through a fixing element 104;
(3) rotating an object to be detected, and acquiring a light intensity signal in real time through a complete Stokes polarimeter;
(4) and analyzing the signals acquired by the complete Stokes polarimeter, and calculating the roll angle of the object to be measured.
As shown in fig. 7, a reflective roll angle sensor device according to the present embodiment will be described in detail below. The device includes: the polarization detection device comprises a linearly polarized light generation module 1, a sensing module 2, a beam splitter module 3 and an analyzing module 4. The linearly polarized light generating module 1 includes a light source 701 and a polarizer 702, where the light source may be selected from a white light source with good stability, a laser light source with a specific wavelength, or a light emitting diode light source, and a laser with a built-in polarizer may also be directly used. The sensing block 2 comprises a plane mirror 703, a wave plate 705 and a fixed element 704. The beam splitter module 3 comprises a beam splitter 706 and the analyzer module 4 is embodied as a full stokes polarimeter comprising a rotating waveplate 707, an analyzer 708 and a detector 709. The collimated monochromatic light emitted by the light source 701 is first linearly polarized light through the polarizer 702, the linearly polarized light vertically enters the wave plate 705 after passing through the beam splitter 706, then vertically enters the plane mirror 703 and enters the wave plate 705 again, the collimated monochromatic light enters the complete stokes polarization instrument of the polarization analysis module after passing through the beam splitter 706, and the roll angle of the rotating element to be measured can be measured. The wave plate 705 is connected to the rotation element to be measured as a polarization sensitive element through the fixing element 704, and converts the roll angle change of the rotation element to be measured into the polarization change of the probe beam.
Specifically, the beam splitter has two types, a polarizing beam splitter that splits S and P polarized light into two different directions, and a non-polarizing beam splitter that splits incident light at the same rate. In the invention, the beam splitter adopts a non-polarization beam splitter to split incident light according to a certain ratio, thereby playing a role in changing the incident direction and the emergent direction of the incident light.
The reflective incident light is natural light, the natural light is converted into linearly polarized light through the polarizer, the incident light can vertically enter the wave plate to be detected through the beam splitter, the light beam passes through the wave plate to be detected and then vertically enters the wave plate to be detected through the vertical reflection of the plane mirror, and then passes through the beam splitter again, the polarization state of the light beam at the moment is the polarization state after passing through the wave plate to be detected twice, and the polarization state of the light beam is detected by using the polarization meter behind the beam splitter.
The reflection measurement model is shown in fig. 7, and the test system model is as follows:
S＝BSbMCbMmirrorMCfBsfMPSin(21)
in order to simplify the system model, the rotation matrix in the system model is contained in the corresponding module, wherein SinAnd S represents the Stokes vectors of incident and emergent light, respectively，MPMueller matrix being a polarizer, BSf、BSbRespectively, the Mueller matrix, M, passing through the beam splitter twicemirrorMueller matrix, M, being vertical reflection of plane mirrorsCf、MCbIs a mueller matrix passing twice through a waveplate.
The roll angle is calculated as follows:
where θ' is the roll angle to be measured, S1、S2And S3The second to fourth elements of the Stokes vector, respectively, Ps the initial azimuth angle of the polarizer (which may be predetermined or obtained through calibration), and the phase retardation of the wave plate 705 (which may be predetermined or obtained through calibration), since the signs of the elements of the second to fourth terms of the Stokes vector always depend on the azimuth angle of the wave plate rotation and the azimuth angle of the polarizer, when S is3When equal to 0, S2Is always greater than or equal to 0, so S does not appear2＜0,S3Case 0.
The determination of θ' at 0 ° or 90 ° in the reflective mode is similar to that in the transmissive mode, and therefore is not described again.
The reflective single-rotation in-situ calibration method is described with reference to fig. 8.
The reflective calibration procedure is as follows:
(1) according to fig. 8, a light source 701, a polarizer 702, a wave plate 705, a plane mirror 703, a beam splitter 706, a rotating wave plate 707, an analyzer 708 and a detector 709 are aligned to the optical path in sequence, so as to ensure that a collimated light beam from the light source is perpendicularly incident to each element;
(2) turning on the light source 701 and the detector 709, and setting a suitable light intensity acquisition time;
(3) starting a motor for the wave plate 705 and a motor for rotating the wave plate 707, and enabling the motors for rotating the wave plate to be in a continuous rotation state;
(4) discretely rotating the wave plate from 0 degrees at an angle of 20 degrees, collecting at each angle until the wave plate is rotated to 180 degrees, and acquiring ten groups of spectra;
(5) and analyzing according to the obtained light, and calculating to obtain the initial azimuth angles of the polarizer, the wave plate, the rotating wave plate and the analyzer and the phase retardation of the wave plate.
The measuring method of the reflection type system of the device for measuring the roll angle by using the optical Stokes comprises the following steps:
(1) as shown in fig. 7, the roll angle sensor is assembled and then the light 701 and detector are turned on and the appropriate acquisition time is set;
(2) connecting the object to be measured with a wave plate 705 through a fixing element 704;
(3) rotating an object to be detected, and acquiring signals in real time through a Stokes polarimeter;
(4) and analyzing the signals acquired by the Stokes polarimeter, and calculating the roll angle of the object to be measured.
In the theoretical analysis, it is known that after the simulation analysis is completed, a series of experimental measurements and data analysis are performed in the invention. The quarter-wave plate is adopted in the transmission type experiment, the calibration method is transmission type single-rotation in-situ calibration, and the complete Stokes polarization instrument is a polarization instrument with a rotating retarder and a fixed analyzer. In order to embody that the measurement range can reach 0-180 degrees, but in practice, 180 degrees cannot be actually measured due to the limitation of the wave plate, the measurement range of the present invention is between 0-179 degrees, and ten sets of values are measured at intervals of 20 degrees by the wave plate in this interval. Meanwhile, in order to show that the quarter-wave plate has repeatability in the interval of 0-180 degrees and the interval of 180-360 degrees, the measurement period is enlarged to 0-359 degrees, and the measurement curve of the graph 9 is obtained. The invention extends the measuring range of the wave plate to 0-360 degrees, adopts a method that two repeated cycles are distinguished by physical means, a layer of light source sensitive substance is coated on the surface of the wave plate from 0-180 degrees, and the wave plate from 180-360 degrees is not processed, so that the wave plate can be detected in which cycle at the detection end, thereby realizing the detection of the wave plate from 0-360 degrees. The results of fig. 9 are well documented for the initial setup, i.e., the measurements show that the wave plate can be measured accurately in the 0 to 179 range. The measurement accuracy of fig. 10 is a comparison of the accuracy of the measured value with the expected given value, which is derived from the calibration results.
The resolution test is performed as follows. The resolution is that the measurement method can identify the minimum angle value of the wave plate rotated, that is, when the wave plate rotates by a tiny angle, the sensor can distinguish the angle values before and after the rotation. The measuring wave plate is loaded on a motor with an encoder of 360 degrees/288000 degrees, namely the resolution of the motor can reach 0.00125 degrees theoretically, in the actual software operation process, the code of the motor always has 3-4 code jumps, and therefore the actual precision of the motor is considered to be 0.005 degrees. Fig. 11 and 12 are actual measurement results, and the measurement scheme is to repeat the measurement five times at each angle to reduce randomness, and increment the unit resolution each time. It can be seen that the measurement method of the present invention can be well resolved for each rotation of the wave plate by 0.03 ° and 0.02 °.
The linearly polarized light generating module generates linearly polarized light, the polarization sensitive element wave plate fixedly connected with the object to be measured is utilized to modulate the incident linearly polarized light into elliptically polarized light, the polarization state of the elliptically polarized light is determined by the roll angle of the object to be measured, the polarization state of the elliptically polarized light is measured by the complete Stokes polarizer, and the roll angle of the rotating object is obtained from the Stokes parameters measured by the Stokes polarizer. Compared with the existing roll angle measuring method and device, the roll angle measuring method and device realize the ultra-large range absolute type roll angle measurement, can meet the application occasions of large range, high precision and absolute type roll angle measurement required by precision machining and measurement, automatic butt joint of industrial robots and spacecrafts, and the like, and have the advantages of simplicity, compactness, high speed, low cost and the like.
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 (7)
1. A method for measuring a roll angle based on a Stokes vector is characterized in that linearly polarized light generated by a linearly polarized light generating module enters a complete Stokes polarizer after being modulated by a wave plate fixedly connected with an object to be measured to obtain the Stokes vector of emergent light, and the roll angle of the object to be measured is obtained through calculation based on the Stokes vector of the emergent light;
the measurement method includes a transmission type measurement method or a reflection type measurement method,
in the transmission type measurement, the roll angle is calculated and obtained by adopting the following method:
judgment S2Whether the angle is 0 or not, if yes, the angle theta' is 0 degree or 90 degrees;
if not, calculating by adopting the following formula:
In the reflection type measurement, the roll angle is calculated and obtained by adopting the following formula:
judgment S2Whether the angle is 0 or not, if yes, the angle theta' is 0 degree or 90 degrees;
if not, calculating by adopting the following formula:
Where θ' is the roll angle to be measured, S1、S2And S3The second to fourth elements of the stokes vector of the emergent light are respectively, Ps is the initial azimuth angle of the polarizer in the linearly polarized light generation module, and is the phase retardation of the wave plate.
2. A measuring device for implementing the stokes vector-based roll angle measuring method according to claim 1, which comprises a linearly polarized light generating module (1), a sensing module (2) and an analyzing module, wherein the linearly polarized light generating module (1) comprises a light source (101) and a polarizer (102), the sensing module (2) comprises a wave plate (103), the wave plate (103) is used as a polarization sensitive element and is connected with a rotating element to be measured and synchronously rotates to convert the roll angle change of the rotating element to be measured into the polarization change of a detection light beam, and the analyzing module is a complete stokes polarimeter; during measurement, collimated monochromatic light emitted by a light source (101) is polarized into linearly polarized light through a polarizer (102), then is modulated into elliptically polarized light through a wave plate (103), and finally enters a complete Stokes polarizer to obtain a Stokes vector of emergent light.
3. A measuring device for implementing a stokes vector-based roll angle measuring method according to claim 1, which comprises a linearly polarized light generating module (1), a sensing module (2), a beam splitter module and an analyzing module, wherein the linearly polarized light generating module (1) comprises a light source (701) and a polarizer (702), the sensing module (2) comprises a plane mirror (703) and a wave plate (705), the wave plate (705) is used as a polarization sensitive element and is connected with a rotating element to be measured and synchronously rotates to convert the roll angle change of the rotating element to be measured into the polarization change of a detection light beam, the beam splitter module comprises a beam splitter (706), and the analyzing module is a complete stokes polarizer; during measurement, collimated monochromatic light emitted by a light source (701) is polarized into linearly polarized light through a polarizer (702), then vertically enters a wave plate (705) through a beam splitter (706), then vertically enters a plane mirror (703), enters the wave plate (705) again, and finally enters a complete Stokes polarizer through the beam splitter (706) to obtain a Stokes vector of emergent light.
4. A measurement device according to claim 2 or claim 3, wherein the polarization-analyzing module comprises a rotating wave plate, an analyzer and a detector arranged in series along the optical path.
5. A measuring device as claimed in claim 2 or 3, characterized in that the light source is a white light source, a laser light source or a light-emitting diode light source.
6. A measuring device as claimed in claim 2 or 3, characterized in that the measuring device is calibrated before the measurement by means of a single-rotation in-situ calibration method to obtain a system initial value of the measuring device.
7. A measuring device as claimed in claim 3, characterized in that the beam splitter (706) is a non-polarizing beam splitter.
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| CN111380501B (en) * | 2020-03-25 | 2021-03-26 | 华中科技大学 | Real-time attitude angle measuring method and device based on birefringent crystal field effect |
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