CN109990736A - A kind of roll angle measurement method and device based on Stokes vector - Google Patents
A kind of roll angle measurement method and device based on Stokes vector Download PDFInfo
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Abstract
The invention belongs to Photoelectric Detections and fields of measurement, and specifically disclose a kind of roll angle measurement method and device based on Stokes vector, it generates linearly polarized light by linearly polarized light generation module, incident linearly polarized light is modulated to elliptically polarized light using the wave plate being connected with object under test, and the polarization state of elliptically polarized light is determined by the roll angle of object under test, the polarization state of elliptically polarized light is measured by complete Stokes polarimeter, the stokes parameter measured from Stokes polarimeter obtains the roll angle of rotating object.Compared with existing roll angle measurement method and device, the rolling angle measurement realizes the super large range absolute type measurement of roll angle, it can satisfy the application that Precision Machining and measurement, industrial robot, spacecraft automatic butt etc. are big to rolling angle measurement requirement range, precision is high and absolute type measures, and have the advantages that succinct, compact, high speed and low cost.
Description
Technical field
The invention belongs to Photoelectric Detections and fields of measurement, more particularly, to a kind of rolling based on Stokes vector
Angle measuring method and device.
Background technique
Precise motion pair is the inertia motion component of modern precision engineering, is widely used in numerically-controlled machine tool, space flight military project, same
The high-tech areas such as step radiation.The movement of object can be parallel to rectangular axes with three in dimensional Cartesian rectangular coordinate system
One-movement-freedom-degree and three around reference axis rotational freedom characterize, an object can be determined based on this six-freedom degree completely
The position of body in three dimensions.Roll angle is the displacement of its longitudinal axis of Objects around A as one of six-freedom degree, with yaw angle,
Pitch angle constitutes the angular errors of the three degree of freedom of object of which movement.Rolling angle measurement as accurate measurement key technology it
One, it has a wide range of applications in fields such as lathe, coordinate measuring machine and robot navigations.It is existing compared to yaw angle and pitch angle
Some roll angle measurement methods are difficult to meet the measurement demand of high-precision large-range, and mainly the angular displacement of roll angle is perpendicular to fortune
Dynamic direction causes the mature angular instrument of the high-precision such as two-frequency laser interferometer, autocollimator to be difficult to be directly used in rolling angle measurement.
Currently, mainly there are following three kinds to the measurement method of roll angle in research both at home and abroad:
Laser interferance method is that the parameter converted rolling angle measurement in interferometry measures, such as using specific
Optical device or structure make roll angle variation be optical path difference variation or phase difference variation.Such as US3790284A proposes one kind
The interferometry of double wollaston prisms is converted roll angle variation to symmetrical double wollaston prisms and symmetrical reflecting mirror
The variation of optical path difference, it is required that the adjustment alignment of reflecting mirror and double wollaston prisms, equipment cost is higher, thus application by
Limit；US2010141957A1 and CN101650166A proposes a kind of roll angle interferometer measuration system, is replaced using prism wedge
Wollaston prism is rotated together as sensing element with object to be measured, makes system it reduce cost but because increasing phasometer
Structure becomes complicated, and symmetry to prism wedge and face shape are more demanding.
Laser auto-collimation method is measured using the good spatial stability of laser, as passed through survey in parallel reference beam method
The straightness of two differences is on amount mobile platform to obtain roll angle size.Such as CN101846506A proposes a kind of base
In the roll angle measurement method of common path parallel beams, based on laser auto-collimation principle using symmetrical beam rood to two directional lights
Line converts roll angle variation to the optical path difference of total light, and altogether although light channel structure improves anti-interference, but this method structure
It is relative complex, increase and adjust difficulty, and is influenced vulnerable to straightness；CN104535019A proposes double diffraction grating heterodyne in one
Roll angle measurement method, uses that convert polarization phase for rolling angle information poor, realizes high-resolution and high-precision, but survey
It is small to measure range, and measuring system is complicated.
Rolling is measured on the basis of plane of polarization using laser polarization in face of the sensibility of rotation based on polarization characteristic method
Corner.Such as CN105222726A proposes a kind of photon flux method rolling angle measurement device based on multipass half wave plate
And method, cooperate prism array using 1/2 wave plate, to the superposability of polarization light action when use, places it in two sets of ribs
In lens array, the variation of the light intensity difference due to caused by array prism is converted by roll angle, improves the resolution ratio of rolling angle measurement,
But the light path system of this method is excessively complicated, optical path needs constantly to be reflected between half wave plate and two sets of prisms,
The collimation of optical path is required stringent.Shiguang Li et al. people is in document (Compact optical roll-angle
Sensor with large measurement range and high sensitivity, Optics letters, 2005
Year phase of volume 30 3,242-4 page) in propose detect the polarization state of light using Faraday rotor modulation come in ± 30 ° of work model
It encloses and carries out rolling angle measurement in the resolution ratio with 0.01 °, Steven R.Gillmer et al. improves this, uses acousto-optic modulation
Device has reached the rolling angle measurement of 43 ° of work measurement range and 0.002 ° of resolution ratio instead of Faraday rotor.
The above method is compared it is found that the system structure of laser interferance method is complicated, sensing element is at high cost to be unfavorable for promoting；Swash
It is big that light auto-collimation method adjusts difficulty, and influences vulnerable to straightness；Phase method based on polarization characteristic can realize high-resolution, but
Nonlinear response curve needs to demarcate, and reduces its precision and stability, and the light intensity based on polarization characteristic is sent out vulnerable to environment, light source etc.
Factor influences, and Measurement Resolution is restricted.Simultaneously it can be found that in above-mentioned rolling angle transducer, the sensing of Polarization Method is utilized
The available wide range of device, the measurement range maximum of roll angle can reach 43 °, however measure in robot navigation, machine coordinates
Generally require to realize the application of super large range in the application fields such as machine, in current existing roll angle measurement method there has been no 0 °~
The rolling angle measurement sensor and method of 180 ° of ranges.
Summary of the invention
To overcome the shortcomings of existing rolling angle measurement device, under the precondition for guaranteeing measurement accuracy, the present invention is provided
A kind of roll angle measurement method and device based on Stokes vector, it is by the wave plate being connected with object under test that line is inclined
Vibration light modulation is elliptically polarized light, and measures the polarization state of elliptically polarized light by complete Stokes polarimeter to obtain Si Tuo
Gram this vector, to obtain the roll angle of rotating object based on Stokes vector, it can be achieved that within the scope of 0 °~180 ° of roll angle
Super large range absolute type measurement, suitable for required in super large range high measurement accuracy, high-resolution and absolute type measurement
The case where.
To achieve the above object, according to the invention in a first aspect, providing a kind of rolling based on Stokes vector
Angle measuring method, the linearly polarized light generated by linearly polarized light generation module enter after the wave plate modulation through being connected with object under test
Stokes vector is obtained in complete Stokes polarimeter, the rolling for obtaining object under test is calculated based on Stokes vector
Angle.
As it is further preferred that the measurement method includes transmission-type mensuration and reflective measurement.
As it is further preferred that roll angle calculates acquisition in the following way when transmission-type measures:
Judge S2It whether is 0, if so, θ ' is 0 ° or 90 °；If it is not, then being calculated using following formula:
If S2> 0, S3≥0
If S2< 0, S3> 0
If S2> 0, S3< 0
If S2< 0, S3< 0
Wherein, θ ' is roll angle to be measured, S1、S2And S3Respectively the second to four Xiang Yuansu of Stokes vector, Ps
For the initial azimuth of the polarizer in linearly polarized light generation module, δ is the phase-delay quantity of wave plate.
As it is further preferred that roll angle is calculated using following formula and is obtained when reflective measurement:
Judge whether S2 is 0, if so, θ ' is 0 ° or 90 °；If it is not, then being calculated using following formula:
If S2< 0, S3≥0
If S2> 0, S3> 0
If S2< 0, S3< 0
If S2> 0, S3< 0
Wherein, θ ' is roll angle to be measured, S1、S2And S3Respectively the second to four Xiang Yuansu of Stokes vector, Ps
For the initial azimuth of the polarizer in linearly polarized light generation module, δ is the phase-delay quantity of wave plate.
Second aspect according to the invention provides a kind of rolling angle measurement device based on Stokes vector, packet
Include linearly polarized light generation module, sensing module and analyzing module, wherein the linearly polarized light generation module includes light source and polarization
Device, the sensing module include wave plate, which is connected and rotates synchronously with rotating element to be measured as polarization-sensitive element, with
The roll angle variation of rotating element to be measured is converted to the polarization variations of detection light beam, the analyzing module is complete Stokes
Polarimeter；It first passes around polarizer by the collimated monochromatic light that light source issues when measurement to be polarized as linearly polarized light, then through wave plate tune
It is made as elliptically polarized light, finally enters in complete Stokes polarimeter and obtains Stokes vector.
The third aspect according to the invention provides a kind of rolling angle measurement device based on Stokes vector, packet
Include linearly polarized light generation module, sensing module, splitter module and analyzing module, wherein the line polarisation generation module includes
Light source and polarizer, the sensing module include plane mirror and wave plate, and the wave plate is as polarization-sensitive element and rotation to be measured
Turn element to be connected and rotate synchronously, the roll angle of element under test is changed and is converted into the polarization variations for detecting light beam, described point
Beam device module includes beam splitter, and the analyzing module is complete Stokes polarimeter；The collimation list issued when measurement by light source
Coloured light first passes around polarizer and is polarized as linearly polarized light, and wave plate is then impinged perpendicularly on after beam splitter, then impinges perpendicularly on flat
It is again incident in wave plate after the reflecting mirror of face, is most incident in complete Stokes polarimeter through beam splitter afterwards and obtains Stokes
Vector.
As it is further preferred that analyzing module includes the rotating wave plate, analyzer and detector set gradually along optical path.
As it is further preferred that light source is white light source, laser light source or LED source.
As it is further preferred that measuring device before measuring, using single rotation calibrated in situ method to measuring device into
Row is calibrated to obtain the system initial value of measuring device.
As it is further preferred that beam splitter is preferably unpolarized type beam splitter.
In general, through the invention it is contemplated above technical scheme is compared with the prior art, mainly have below
Technological merit:
1. can be realized the invention proposes the method for realizing rolling angle measurement based on Stokes vector by this method
The absolute type of the super large range of 180 ° of measurement ranges measures, and has widened rolling angle measurement range, can sit in robot navigation, lathe
Realize application in the fields such as co-ordinate measuring machine.
2. the present invention, on the basis of proposing above-mentioned measurement method, the also matched specific calculating for having studied roll angle is public
Formula is measured convenient and efficient with quickly calculating the roll angle for obtaining object to be measured by measurement known parameters.
3. the present invention goes back the measuring device that Aided design realizes the above method, and presses the difference of measurement method, specific aim
Devise transmission-type measuring device and reflective measuring device, pass through specific structure to above-mentioned apparatus and specific assembly method
Research and design, can effectively realize the rolling angle measurement based on Stokes vector, and greatly simplify light path system, measure
It is accurate quick, and there is super large range.
4. the present invention can get four Stokes' parameters of description light polarization state by complete Stokes polarimeter,
Compared to traditional interferometer or laser measurement, complete Stokes polarimeter can be inherited easily in optical system, and
And the polarization state information more horn of plenty of the light obtained by polarimeter, thus inherently simplify optical measuring device, promotes light
Learn the microminiaturization of measuring device.
5. in addition, carrying out school to measuring device using single rotation calibrated in situ method the invention also provides before measuring
Standard guarantees the accuracy of system initial value, to obtain the system initial value of measuring device convenient for the accurate calculating of subsequent roll angle.
Detailed description of the invention
Fig. 1 is optics Stokes rolling angle transducer transmission-type measuring principle figure；
Fig. 2 is roll angle and Stokes symbol decision schematic diagram in rolling angle transducer；
Fig. 3 is the calculated value of roll angle and the theory relation curve graph of roll angle input value,
Fig. 4 is rolling angle transducer transmission-type calibrating principle figure；
Fig. 5 is the schematic diagram of the fixed analyzer formula polarimeter of rotation retarder；
Fig. 6 is the schematic diagram of divide amplitude four-way polarimeter；
Fig. 7 is the reflective measuring principle figure of optics Stokes rolling angle transducer；
Fig. 8 is the reflective calibrating principle figure of rolling angle transducer；
Fig. 9 is the measurement result figure that rolling angle transducer transmission-type measures 0 °~360 °；
Figure 10 is the measurement accuracy result figure that rolling angle transducer transmission-type measures 0 °~360 °；
Figure 11 is that rolling angle transducer transmission-type measures 0.03 ° of resolution ratio result figure；
Figure 12 is that rolling angle transducer transmission-type measures 0.02 ° of resolution ratio result figure.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.As long as in addition, technical characteristic involved in the various embodiments of the present invention described below
Not constituting a conflict with each other can be combined with each other.
The present invention provides a kind of roll angle measurement methods based on Stokes vector, by linearly polarized light generation module
The linearly polarized light of generation enters polarimeter after the wave plate modulation through being connected with object under test and obtains Stokes vector, based on this support
Gram this vector calculates the roll angle for obtaining object under test, specifically includes the following steps:
(1) linearly polarized light is obtained by linearly polarized light generation module；
(2) linearly polarized light passes through the sensing module being connected with rotating object to be measured and modulates, and polarization state changes；
(3) polarised light modulated through sensing module obtains one group of Stokes vector by complete Stokes polarimeter；
(4) it is rotated by rotating object to be measured drive sensing module, wave plate one angle of every rotation, complete Stokes is inclined
Vibration Meter records one group of Stokes vector；
(5) according to obtaining the corresponding multiple roll angles of testee after the multiple groups Stokes vector data processing of measurement
Size.
Method of the invention (is sweared roll angle sensing element (wave plate i.e. in sensing module) with polarization state by Stokes
Scale sign) combine the measurement for realizing super large range roll angle.Above-mentioned measurement method includes transmission-type mensuration and reflective survey
Amount method utilizes reflective rolling angle sensor device wherein realizing that transmission-type measures using transmission-type rolling angle sensor device
Realize reflective measurement.
Two kinds of devices are described in detail separately below.As shown in Figure 1, being a kind of transmission provided in an embodiment of the present invention
Formula rolling angle sensor device, is with reference to the accompanying drawing explained in detail it.The device includes: linearly polarized light generation module
1, sensing module 2, analyzing module 3, wherein line polarisation generation module includes light source 101 and polarizer 102, and light source need to generate list
Laser or light emitting diode etc. of the white light source in conjunction with filter plate, with certain wavelength can be used in the collimated light beam of wavelength,
And the optical source wavelength is within the operating wavelength range of polarizer, wave plate and detector, and the retardation that should meet wave plate is wanted
It asks, the light modulation that light source is emitted by polarizer is linearly polarized light, can also directly adopt the laser of built-in polarizer.Sensing module
2 include wave plate 103 and fixing element 104, and analyzing module 3 is specially complete Stokes polarimeter comprising is set gradually
Rotating wave plate 105, analyzer 106 and detector 107.
The collimated monochromatic light issued from light source 101, which first passes around polarizer 102, becomes linearly polarized light, which passes through
Ellipse inclined polarised light is modulated to after wave plate 103, which passes through fixing element as polarization-sensitive element and rotating element to be measured
104 connections, and convert the variation of the roll angle of element under test to the polarization variations for detecting light beam, wave plate is around the rotation side of its fast axle
Parallactic angle is roll angle to be measured；The ellipse inclined polarised light that modulation obtains can measure stoke after complete Stokes polarimeter
This vector can calculate the roll angle for obtaining rotating element to be measured according to Stokes vector.The standard that light source 101 issues in the device
Straight monochromatic light impinges perpendicularly on polarizer 102, quarter-wave plate 103 and impinges perpendicularly in complete Stokes polarimeter.
Specifically, traditional Glan Taylor (Glan-Taylor) prism can be selected in polarizer 102, also can be selected novel
Film class polarizer and structure class polarizer.The polarizer of different type different materials has different preparation process and performance, because
This meets the polarizer that the present apparatus is compact, micromation requires and be polarized function and can be applied in apparatus of the present invention.Polarizer 102
It is preferred that reducing the volume of whole device in the case where guaranteeing High Extinction Ratio using Glan polarizer.Wave plate 103 can be selected
Quarter-wave plate, material can use mica, quartz and liquid crystal etc., it is preferred to use a quarter zero-th order waveplates reduce phase and prolong
The error measured late.The injection light that the retardation of wave plate is emitted with light source it is Wavelength matched, and the retardation of wave plate is in transmission-type
With it is reflective under should all meet its requirement about measurement range, and the retardation of rotating wave plate can be selected after optimization
It selects.Therefore the wave plate for meeting retardation requirement can be applied in apparatus of the present invention.
Transmission-type measurement model is as shown in Figure 1, shown in its system model such as formula (1):
S=R (- θ ') MCR(θ′)R(-Ps)MPSin (1)
Wherein, R (θ '), R (Ps) it is wave plate 103, the corresponding spin matrix of polarizer 102, θ ' is to be connected with wave plate 103
The roll angle of rotating element to be measured, PsFor the initial azimuth of polarizer, MC、MP、SinThe respectively Muller matrix of wave plate, polarization
The Stokes vector of the Muller matrix of device, incident light.
Fig. 2 is with the variation Stokes vector element of roll angle and the relationship of roll angle, according to fig. 2 available rolling
The calculation formula of corner is as follows:
Wherein, θ ' is roll angle to be measured, S1、S2And S3Respectively the second to four Xiang Yuansu of Stokes vector, Ps
For the initial azimuth (can determine in advance or obtain by calibration) of polarizer, δ is that the phase-delay quantity of wave plate 103 (can be preparatory
Determine or obtained by calibration), second due to Stokes vector depends on wave plate to the symbol of element of Section 4 always
The azimuth of rotation and the azimuth of polarizer, work as S3When=0, S2Consistently greater than it is equal to 0, so being not in S2< 0, S3=0
The case where.
Work as Ps=0 °, result when δ=90 ° are as follows:
Enable S2=0, then available sin (2Ps)=sin (2Ps- 4 θ '), i.e. θ ' is only 0 ° or 90 °, so, 0 °~
Within the scope of 180 °, if S2=0, then θ ' is 0 ° or 90 ° (180 ° are considered as 0 °).So being added in the beginning of judgement to S2It whether is 0
Judgement, i.e. S2=0, then θ ' is 0 ° or 90 °, if S2It ≠ 0 °, is then calculated using above-mentioned formula (2)-(5).In the first of polarizer
Under the premise of beginning azimuth is known, S can use3Symbol (i.e. positive and negative) judge roll angle for 0 ° or 90 °, PsAt > 0 °, if
S3< 0 θ '=0 °, if S3> 0 θ '=90 °；PsAt < 0 °, if S3> 0 θ '=0 °, if S3< 0 θ '=90 °；If Ps=0 ° or
S3When=0, θ '=0 ° or 90 ° can not be judged.
Fig. 3 is PsAt=4 °, the result of system emulation.Wherein, it inputs for wave plate within the scope of 0 °~180 °, every 10 °
Constantly variation, and obtain corresponding stoke vector.According to the symbol decision system of obtained Stokes vector and setting and
Calculation formula seeks the value of the roll angle of the wave plate of input.It can be seen that in no introducing error, input value and output valve energy
It is enough to agree with well, and PsThe value that the roll angle of each wave plate still can be effectively judged within the scope of=± 4 °, due to wave plate
Muller matrix information in 0 ° and 180 ° be overlapped, therefore think 0 ° with 180 ° be as.
Need to calibrate the initial azimuth of each component before measuring.Due to that in actual measurement, can only be polarized
The approximate range of the initial azimuth of component and can not accurately determine its value, also, initial azimuth can not be such as inclined
All in ideal situation described in Vibration Meter part, need to take into account initial azimuth when calculating Stokes vector element.
Existing many calibration methods can be used for the calibration of measuring device to calibrate, it is for example inclined to obtain system initial value
The initial azimuth P of vibration devices, wave plate initial azimuth Cs1, wave plate phase-delay quantity δ1, rotating wave plate initial azimuth
Cs2, rotating wave plate phase-delay quantity δ2, analyzer initial azimuth As.Calibrated in situ method is rotated present invention preferably employs single
Calibrated, system be added in rotating wave plate, obtained and multi-group data and calibrated by rotating wave plate, and wave plate 103 from
0 ° starts to be spaced 20 ° of discrete rotations of angle, until going to 180 °.
PC1CrThe system model of SA type ellipsometer can be indicated with following formula:
S=MAR(As)R(-Cs2)MC(δ2)R(Cs2)R(-Cs1)MC(δ1)R(Cs1)R(-Ps)MPSin
Wherein, SinPC is respectively indicated with S1CrThe Stokes Vector of SA type ellipsometer incident light and emergent light, C1For wave
Piece, CrFor rotating wave plate；Incident light is natural light, and M (δ) indicates the Muller matrix of the wave plate, MP、MC(δ1)、MC(δ2)、MARespectively
For polarizer 102, wave plate 103, rotating wave plate 105, analyzer 106 Muller matrix, R (Ps)、R(Cs1)、R(Cs2)、R(As) be
Polarizer 102, wave plate 103, rotating wave plate 105, analyzer 106 rotate Muller matrix, δ1、δ2Respectively wave plate 103, rotation wave
The phase-delay quantity of piece 105, Cs1For the initial azimuth of wave plate 103, Cs2For the initial azimuth of rotating wave plate 105, PsIt is inclined
The initial azimuth of vibration device, AsFor 106 initial azimuth of analyzer, then have:
Sin=[I0,0,0,0]T (12)
The expression formula of each Muller matrix is as follows:
Wherein, θ can indicate the initial azimuth P of polarizer Ps, wave plate C1Initial azimuth Cs1, rotating wave plate Cr's
Initial azimuth Cs2, the initial azimuth A of analyzer As。
The theoretical light intensity signal of single rotation compensation type ellipsometer can be indicated with Fourier expansion formula:
In the rotation of transmission-type list, referential is established with the fast axle of polarizer P, so unknown quantity has Ps、Cs1、δ1、Cs2、
δ2、As, due to the presence singly rotated, only there are four Fourier coefficient, α for spectrum4、β4、α2、β2It is C respectivelys1、δ1、Cs2、δ2、AsDeng
Parameter combination.
The calibration process and principle of single rotation calibrated in situ method is described below:
(1) wave plate 103 is located at its initial azimuth Cs1Under, one group of light intensity data I is acquired using detector0And calculating pair
The Fourier coefficient α answered41、β41、α21、β21, according to α21And β21Calculate Cs2+AsThe sum of；
(2) wave plate 103 is rotated into a fixed known angle Cs, wave plate is rotated 20 ° under normal conditions, measures one
Group light intensity ICs, and duplicate measurements is multiple, needs to obtain (I under theoretical condition0、ICs、I2Cs) at least three groups of data, and seek three groups of phases
Fourier coefficient (the α answered4i、β4i、α2i、β2i), P is sought according to Fourier coefficients、Cs1、δ1、Cs2、δ2、AsValue；
(3) preliminary system initial value, i.e. P are obtained in two steps in fronts、Cs1、δ1、Cs2、δ2、AsValue, but by
In single measurement there may be error, the initial value acquired according to single measurement can also have an error accordingly, therefore by wave plate 103
It is acquired within its optical cycle every 20 ° and obtains ten groups of practical Fourier coefficient (α4i、β4i、α2i、β2i)。
It is previously noted that PC1CrThe system model of SA type ellipsometer can be indicated with following formula:
S=MAR(As)R(-Cs2)MC(δ2)R(Cs2)R(-Cs1)MC(δ1)R(Cs1)R(-Ps)MPSin
Wherein, Cs1Indicate the initial azimuth of wave plate 103.
It needs to generate the emulation light intensity for meeting actual measurement on theoretical model, even Cr=ωcT, ωcFor actual measurement
When rotating wave plate angular frequency, Sin=(1,0,0,0)TIndicate that incident light is natural light.Specific fit procedure is as follows:
It is fitted analysis using lsqcurvefit function in matlab program, the input of function is actually measured Fourier coefficient
(α4i、β4i、α2i、β2i) and system initial value Ps、Cs1、δ1、Cs2、δ2、As, the output of function is the system P after accurate calibrations、
Cs1、δ1、Cs2、δ2、AsValue.The P that will be calculated in (2) steps、Cs1、δ1、Cs2、δ2、AsInitial value is as lsqcurvefit
The initial value of function iteration, and this initial value is substituted into PC1CrTen groups of emulation light intensity S are generated in SA type ellipsometer system modeli, and root
Ten groups of theoretic Fourier coefficient (α are obtained according to emulation light intensity4i′、β4i′、α2i′、β2i'), compare actually measured Fourier system
Number (α4i、β4i、α2i、β2i) and theoretic Fourier coefficient (α4i′、β4i′、α2i′、β2i') and to calculate corresponding residual sum square
Difference, when residual sum mean square deviation excessive (specific value and range can be defined according to actual needs), the system that adjusts input
Value Ps、Cs1、δ1、Cs2、δ2、As, until the residual sum for obtaining meeting condition (i.e. residual sum mean square deviation within a preset range) is square
System value P at this time is exported after differences、Cs1、δ1、Cs2、δ2、As, that is, pass through lsqcurvefit function more new system Ps、Cs1、δ1、
Cs2、δ2、AsValue, then by updated Ps、Cs1、δ1、Cs2、δ2、AsValue substitutes into PC1CrIt is generated in SA type ellipsometer system model
Ten groups of emulation light intensity SiTo obtain new theoretic Fourier coefficient, then pass through new theoretic Fourier coefficient and reality
The Fourier coefficient that border measures is compared to be judged, continues iteration if residual sum mean square deviation is excessive, if meeting
Condition then exports system value P at this times、Cs1、δ1、Cs2、δ2、As, it is the initial value of system after calibrating, accordingly, the school of system
Quasi- process is completed.
Calibration method is illustrated in conjunction with Fig. 4, the step of transmission-type calibrated in situ is as follows:
(1) according to the step of Fig. 4 by light source 101, polarizer 102, wave plate 103, rotating wave plate 105, analyzer 106 and visit
It surveys device 107 and is successively aligned optical path, guarantee that the collimated light beam come out from light source impinges perpendicularly in each element；
(2) light source 101 and detector 107 are opened, and the suitable intensity collection time is set；
(3) start the motor of wave plate 103 and the motor of rotating wave plate 105, and the motor of rotating wave plate is made to be in continuous rotation
Turn state；
(4) wave plate is spaced to 20 ° of discrete rotations of angle since 0 °, detector 107 is acquired under each angle, directly
Until going to 180 °, ten groups of spectrum are obtained；
(5) it is analyzed according to the light intensity of acquisition, calculates the initial side for obtaining polarizer, wave plate, rotating wave plate, analyzer
The phase-delay quantity of parallactic angle and wave plate.
Specifically, detector simultaneously measures the light intensity of two-beam, photodiode array, Charged Couple can be selected
Device (Charge Coupled Device, CCD) imaging sensor, spectrometer, camera, photomultiplier tube etc..Different detectors
Have the characteristics that respective, therefore the present apparatus can be made compact, while the detector that can be realized light intensity real-time measurement can be applied to
In apparatus of the present invention.
After obtaining system initial value, it can be calculated according to the intensity signal of measurement and be sweared by the Stokes of the light after wave plate
Amount.It is described below and how to seek Stokes vector, the Stokes vector of light describes the element of the polarization state of light by four
Composition, measurement process can be described as:
I=AS (17)
Wherein, I is the luminous flux vector obtained by detector measurement, and A is the survey determined by pendulous frequency and optical system
Moment matrix (it is known parameters), S=[S0,S1,S2,S3]TIt is incident Stokes vector；
Therefore, available Stokes vector:
S=A+I (18)
Complete Stokes polarimeter is all four elements for referring to complete measurement Stokes, and this incomplete support
The Stokes element of gram this polarimeter measurement is less than 4.The polarimeter of measurement Stokes vector is broadly divided into four classes: machine
Tool modulation method, electro-optic modulation method, wavefront dividing method, amplitude dividing method, the Stokes vector that distinct methods measure are consistent.
The present embodiment illustrates one of the machinery modulation method of the complete Stokes vector of measurement as used in the present invention.
The complete Stokes vector polarimeter of Fig. 5 is the fixed analyzer polarization of rotation retarder in machinery modulation method
Instrument, wherein rotating wave plate 105 (i.e. rotation retarder), analyzer 106, detector 107 are in same optical path.Fig. 6 is amplitude point
The four-way polarimeter in method is cut, wave plate 602,604 plays a point amplitude, and light beam is divided by beam splitter 601,605,608
Multi beam optical path, detector 603,606,607,609 detect light intensity.
The acquisition process of Stokes vector is specifically described by taking the fixed analyzer of rotation retarder as an example below.
The fixed analyzer polarimeter of rotation retarder is common Stokes polarimeter completely, detection in machinery modulation method
Device only observes a kind of polarization state.Modulated signal is made of two kinds of frequencies, and modulated signal can be represented as following Fourier system
Number:
Wherein, β is the azimuth of rotating wave plate, if rotating wave plate is quarter-wave plate, and detector acquires number
According to start position be the initial azimuth of rotating wave plate be zero and the initial azimuth of analyzer is zero, then Stokes vector
It can be represented as:
The Stokes after passing through wave plate is detected in value calibration at the beginning of completion system and by optics Stokes polarimeter
After vector, using optics Stokes measurement roll angle transmission-type device measurement method the following steps are included:
(1) as shown in Figure 1, then assembly rolling angle transducer opens light source 101 and complete Stokes polarimeter, and sets
Set suitable acquisition time；
(2) object under test is connect by fixing element 104 with wave plate 103；
(3) object under test is rotated, and light intensity signal is acquired by complete Stokes polarimeter in real time；
(4) signal of complete Stokes polarimeter acquisition is analyzed, calculates the roll angle of object under test.
As shown in fig. 7, being a kind of reflective rolling angle sensor device provided in this embodiment, it is carried out below in detail
Elaboration.The device includes: linearly polarized light generation module 1, sensing module 2, splitter module 3, analyzing module 4.Wherein, line is inclined
Light generation module 1 include light source 701 and polarizer 702, light source it is available including have good stability white light source, have
The laser light source or LED source of specific wavelength can also directly adopt the laser of built-in polarizer.Sensing module 2
Including plane mirror 703, wave plate 705 and fixing element 704.Splitter module 3 includes beam splitter 706, and analyzing module 4 is specific
For complete Stokes polarimeter, which includes rotating wave plate 707, analyzer 708 and detector
709.First passing around polarizer 702 by the collimated monochromatic light that light source 701 issues is linearly polarized light, which passes through beam splitter
Wave plate 705 is impinged perpendicularly on after 706, is again incident in wave plate 705 after impinging perpendicularly on plane mirror 703 later, is passed through
It is incident on after beam splitter 706 in the complete Stokes polarimeter of analyzing module, the roll angle of rotating element to be measured can be measured.
The wave plate 705 passes through fixing element 704 as polarization-sensitive element and rotating element to be measured and connect, and by the rolling of element under test
Angle variation is converted into the polarization variations of detection light beam.
Specifically, beam splitter has polarization beam apparatus and two kinds of non-polarizing beamsplitter, polarization beam apparatus can be by S and P polarization
Light is divided into two different directions, and non-polarizing beamsplitter can at the same rate separate incident light.In the present invention, beam splitting
Device uses non-polarizing beamsplitter, and incident light is separated according to certain ratio, changes incident light beam strikes direction to play and goes out
Penetrate the effect in direction.
Reflective incident light is natural light, converts line polarisation for natural light by the polarizer, then make by beam splitter
Obtaining incident light can impinge perpendicularly on wave plate to be measured, and light beam, will again by the vertical reflection after wave plate to be measured by plane mirror
Secondary to impinge perpendicularly on wave plate to be measured, later again by beam splitter, the polarization state of light beam at this time is to pass twice through wave to be measured
Polarization state after piece uses the polarization state of polarimeter detection light beam after beam splitter.
Reflective measurement model is as shown in fig. 7, its test system model is as follows:
S=BSbMCbMmirrorMCfBsfMPSin (21)
It is to simplify system model, and the spin matrix in above system model is all contained in corresponding module, wherein Sin
The Stokes Vector of incident light and emergent light, M are respectively indicated with SPFor the Muller matrix of polarizer, BSf、BSbRespectively twice
Muller matrix after beam splitter, MmirrorFor the Muller matrix that plane mirror vertically reflects, MCf、MCbTo pass through wave twice
The Muller matrix of piece.
The calculation formula of its roll angle is as follows:
Wherein, θ ' is roll angle to be measured, S1、S2And S3Respectively the second to four Xiang Yuansu of Stokes vector, Ps
For the initial azimuth (can determine in advance or obtain by calibration) of polarizer, δ is that the phase-delay quantity of wave plate 705 (can be preparatory
Determine or obtained by calibration), second due to Stokes vector depends on wave plate to the symbol of element of Section 4 always
The azimuth of rotation and the azimuth of polarizer, work as S3When=0, S2Consistently greater than it is equal to 0, so being not in S2< 0, S3=0
The case where.
Reflective similar with transmission-type in the judgement of 0 ° or 90 ° for θ ', so it will not be repeated.
Reflective single rotation calibrated in situ method is illustrated in conjunction with Fig. 8.
The step of reflective calibration, is as follows:
(1) according to Fig. 8 by light source 701, polarizer 702, wave plate 705, plane mirror 703, beam splitter 706, rotation wave
Piece 707, analyzer 708 and detector 709 are successively aligned optical path, and it is each to guarantee that the collimated light beam come out from light source impinges perpendicularly on
In element；
(2) light source 701 and detector 709 are opened, and the suitable intensity collection time is set；
(3) start the motor of wave plate 705 and the motor of rotating wave plate 707, and the motor of rotating wave plate is made to be in continuous rotation
Turn state；
(4) wave plate is spaced to 20 ° of discrete rotations of angle since 0 °, and is acquired under each angle, until going to
Until 180 °, ten groups of spectrum are obtained；
(5) it is analyzed according to the light of acquisition, calculates the initial orientation for obtaining polarizer, wave plate, rotating wave plate, analyzer
The phase-delay quantity at angle and wave plate.
The above-mentioned device using optics Stokes measurement roll angle, the measurement method of reflective system includes following step
It is rapid:
(1) as shown in Figure 7, when assembling rolling angle transducer and then open light 701 and detector, and suitable acquire being set
Between；
(2) object under test is connect by fixing element 704 with wave plate 705；
(3) object under test is rotated, and signal is acquired by Stokes polarimeter in real time；
(4) signal of Stokes polarimeter acquisition is analyzed, calculates the roll angle of object under test.
It is learnt in theory analysis in front, after completing above-mentioned simulation analysis, the present invention has carried out a series of experiment
Measurement is analyzed with data.Using quarter-wave plate in transmission-type experiment, calibration method is that the rotation of transmission-type list is in situ
Calibration, complete Stokes polarimeter are the fixed analyzer formula polarimeter of rotation retarder.It can be reached to embody measurement range
To 0 °~180 ° but actually due to the limitation of wave plate, 180 ° can not be actually measured, therefore measurement range of the present invention is at 0 °~179 °
Between, and totally ten class value is measured every 20 ° according to wave plate in the section.Simultaneously in order to embody quarter-wave plate 0 °~
There is repeatability, measurement period is amplified to 0 °~359 ° by the present invention, and is obtained in 180 ° of sections and 180 °~360 ° sections
The experiment curv of Fig. 9.The measurement range of wave plate is expanded to 0 °~360 ° by the present invention, and the method for use is to utilize physical means
Two duplicate periods are distinguished, coat one layer of light source sensitive materials on 0 °~180 ° surfaces of wave plate, and 180 ° of wave plate~
360 ° without any processing, is able to detect which wave plate be located in period in end of probe in this way, to realize wave plate at 0 °
Detection within the scope of~360 °.The result of Fig. 9 has confirmed initial setting well, i.e., measurement result show wave plate 0 °~
179 ° of ranges can be measured accurately.The measurement accuracy of Figure 10 is the accuracy comparison of measured value and expected given value, wherein being expected
Given value derives from calibration result.
Resolution test is carried out below.So-called resolution ratio refers to that such measurement method can identify that wave plate rotates through most
Small angle value, i.e., when wave plate rotates through a small angle, can sensor be distinguished the angle value of rotation front and back.
Measurement wave plate is loaded on the motor that an encoder is 360 °/288000, i.e. the resolution ratio of motor theoretically can reach
0.00125 °, in actual software operating process, the coding of motor always has the bounce of 3~4 codings, therefore, it is considered that motor
Actual precision is at 0.005 °.Figure 11 and Figure 12 is actual measured results, and measurement scheme is in each angle duplicate measurements five times
To reduce randomness, and incremental units resolution ratio every time.As can be seen that rotating 0.03 ° and 0.02 °, this hair every time for wave plate
Bright measurement method can be very good to tell.
The present invention generates linearly polarized light by linearly polarized light generation module, utilizes the polarization-sensitive element being connected with object under test
Incident linearly polarized light is modulated to elliptically polarized light by wave plate, and the polarization state of elliptically polarized light is determined by the roll angle of object under test
It is fixed, the polarization state of elliptically polarized light, the stoke measured from Stokes polarimeter are measured by complete Stokes polarimeter
This parameter obtains the roll angle of rotating object.Compared with existing roll angle measurement method and device, which is realized
The super large range absolute type measurement of roll angle, can satisfy Precision Machining and measurement, industrial robot, spacecraft automatic butt
Range is big, precision is high and the application of absolute type measurement Deng requiring rolling angle measurement, and have succinct, compact, high speed and
The advantages that inexpensive.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to
The limitation present invention, any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should all include
Within protection scope of the present invention.
Claims (10)
1. a kind of roll angle measurement method based on Stokes vector, which is characterized in that generated by linearly polarized light generation module
Linearly polarized light through with object under test be connected wave plate modulation after enter complete Stokes polarimeter in obtain Stokes arrow
Amount calculates the roll angle for obtaining object under test based on Stokes vector.
2. as described in claim 1 based on the roll angle measurement method of Stokes vector, which is characterized in that the measurement side
Method includes transmission-type mensuration and reflective measurement.
3. as claimed in claim 2 based on the roll angle measurement method of Stokes vector, which is characterized in that transmission-type measurement
When, roll angle calculates acquisition in the following way:
Judge S2It whether is 0, if so, θ ' is 0 ° or 90 °；
If it is not, then being calculated using following formula:
If S2> 0, S3≥0
If S2< 0, S3> 0
If S2> 0, S3< 0
If S2< 0, S3< 0
Wherein, θ ' is roll angle to be measured, S1、S2And S3Respectively the second to four Xiang Yuansu of Stokes vector, Ps are line
The initial azimuth of polarizer in polarised light generation module, δ are the phase-delay quantity of wave plate.
4. as claimed in claim 2 based on the roll angle measurement method of Stokes vector, which is characterized in that reflective measurement
When, roll angle is calculated using following formula and is obtained:
Judge whether S2 is 0, if so, θ ' is 0 ° or 90 °；
If it is not, then being calculated using following formula:
If S2< 0, S3≥0
If S2> 0, S3> 0
If S2< 0, S3< 0
If S2> 0, S3< 0
Wherein, θ ' is roll angle to be measured, S1、S2And S3Respectively the second to four Xiang Yuansu of Stokes vector, Ps are line
The initial azimuth of polarizer in polarised light generation module, δ are the phase-delay quantity of wave plate.
5. a kind of for realizing the roll angle measurement method according to any one of claims 1-4 based on Stokes vector
Measuring device, which is characterized in that including linearly polarized light generation module (1), sensing module (2) and analyzing module (3), wherein institute
Stating linearly polarized light generation module (1) includes light source (101) and polarizer (102), and the sensing module (2) includes wave plate (103),
The wave plate (103) is connected and rotates synchronously with rotating element to be measured as polarization-sensitive element, by the rolling of rotating element to be measured
Corner variation is converted to the polarization variations of detection light beam, and the analyzing module (3) is complete Stokes polarimeter；When measurement by
The collimated monochromatic light that light source (101) issues first passes around polarizer (102) and is polarized as linearly polarized light, then adjusts through wave plate (103)
It is made as elliptically polarized light, finally enters in complete Stokes polarimeter and obtains Stokes vector.
6. a kind of for realizing the roll angle measurement method according to any one of claims 1-4 based on Stokes vector
Measuring device, which is characterized in that including linearly polarized light generation module (1), sensing module (2), splitter module (3) and analyzing mould
Block (4), wherein the line polarisation generation module (1) includes light source (701) and polarizer (702), sensing module (2) packet
Plane mirror (703) and wave plate (705) are included, which is connected simultaneously as polarization-sensitive element with rotating element to be measured
It rotates synchronously, converts the roll angle variation of element under test to the polarization variations of detection light beam, splitter module (3) packet
It includes beam splitter (706), the analyzing module (4) is complete Stokes polarimeter；The collimation issued when measurement by light source (701)
Monochromatic light first passes around polarizer (702) and is polarized as linearly polarized light, then impinges perpendicularly on wave plate after beam splitter (706)
(705), it then after impinging perpendicularly on plane mirror (703) is again incident in wave plate (705), most enters afterwards through beam splitter (706)
It is mapped in complete Stokes polarimeter and obtains Stokes vector.
7. such as measuring device described in claim 5 or 6, which is characterized in that analyzing module includes the rotation set gradually along optical path
Turn wave plate, analyzer and detector.
8. such as measuring device described in claim 5 or 6, which is characterized in that light source is white light source, laser light source or luminous two
Pole pipe light source.
9. such as measuring device described in claim 5 or 6, which is characterized in that measuring device is before measuring, former using single rotation
Position calibration method is calibrated measuring device to obtain the system initial value of measuring device.
10. measuring device as claimed in claim 6, which is characterized in that beam splitter (506) is preferably unpolarized type beam splitter.
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