CN103837476A - Mueller matrix self calibration measurement method - Google Patents

Abstract

The present invention relates to a Mueller matrix self calibration measurement method, the biggest characteristic of a Mueller matrix measurement method in the prior art is the need of precision calibration of an optical system of a measuring device, and the difficulty of precision measurement of a Mueller matrix is increased. According to the Mueller matrix self calibration measurement method, Stokes parameters of output polarization states before and after a to-be-test sample is put in are measured, a formula of the functional relationship between measured output light intensity and unknown parameters of a system and a Mueller matrix of a measured sample is established, and the Mueller matrix of the to-be-test sample is obtained by solution with a multiple-parameter nonlinear fitting method. The Mueller matrix self calibration measurement method needs no precision calibration of the measurement system, and realizes the self calibration measurement of the Mueller matrix, and the measurement method is simple and easy to operate, and can be widely used in Mueller matrix measurement of various polarization components and optical systems.

Description

A kind of self calibration measuring method of Mueller matrix

Technical field

The invention belongs to polarization optics detection technique field, the self calibration measuring method that particularly a kind of Mueller matrix that is applicable to polarizer and optical system detects.

Background technology

The measurement of Mueller matrix is one of important means of Polarization Detection, all polarization characteristics that Mueller matrix has comprised measured medium (except total phase place), are widely used in determining the polarization characterisitic parameter such as birefringence effect, loss or enhancement effect, fevering sodium effect of the media such as optical device, optical system.

The basic device of Mueller matrix measuring method is mainly made up of polarization generator, sample, polaroid analyze.Polarization generator and polaroid analyze can be respectively the polarizer and wave plate combined, light ball modulator combination, the combination of liquid crystal adjustable phase retarder etc., and reference is with Publication about Document [1-8].

These method measuring principles that exist are at present basic identical, all to produce at least 4 independently modulating polarization states at the input end of sample by polarization generator, again at output terminal by independently polarization state of at least 4 of polaroid analyze demodulation, finally by detector receiving light power.If modulating polarization state and demodulation polarization state are known, can be derived the relation of the Mueller matrix of surveying light intensity and modulating polarization state, demodulation polarization state and sample by Mueller matrix theory, and then solve the Mueller matrix of sample.The difficulty of these method maximums needs precise calibration modulating polarization state and demodulation polarization state before being to measure sample.Or by inserting standard model, or by using empty matrix scaling system to determine modulating polarization state and the demodulation polarization state document [9-10] that sees reference.The former, the performance of standard model directly affects the measuring accuracy of Mueller matrix; The latter, empty matrix calibration belongs to first approximation and solves, and measuring accuracy is limited.All there is defect in two kinds of calibrating methods, and all needs complicated calibrating method demonstration and calibration process.

The present invention puts into the Stokes parameter of testing sample front and back output polarization state by measurement, set up by the functional relation between the Mueller matrix of the output polarization state parameter recording, system unknown parameter and sample, use the nonlinear least square fitting of multiparameter to solve the Mueller matrix that obtains testing sample.Use the present invention without to the accurate calibration of measuring system, realized the self calibration of Mueller matrix and measured, measuring method is simple, and the Mueller matrix that can be widely used in various polarizers and optical system detects.

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Summary of the invention

The object of the invention is the deficiency existing for prior art, a kind of self calibration measuring method of Mueller matrix is provided, utilize it can precision measurement Mueller matrix, and without to measuring system calibration, made up existing methodical defect.

For achieving the above object, the present invention takes following design proposal:

A self calibration measuring method for Mueller matrix, measures structure and mainly comprises light source 1, polarization generator 2, sample 3, polaroid analyze 4, detector 5 and computing machine 6.Described light source 1 can be the light sources such as bromine tungsten filament lamp, xenon lamp, LED light source, laser; Described polarization generator 2 is made up of the rotation polarizer 7 and rotating wave plate 8; Described polaroid analyze 4 can be rotating wave plate and analyzer combination, light ball modulator and analyzer combination, liquid crystal phase delay device and analyzer combination etc.The testing procedure of realizing the measurement of Mueller matrix is as follows:

1) do not put into testing sample 3, for each modulating polarization state of polarization generator 2, polaroid analyze 4 demodulation obtain four independently polarization state received by detector 5.The polarizer 7 and wave plate 8 rotate a circle separately and obtain 4 × (360/ Δ θ) ²individual detection light intensity, is designated as vector I ₁.Known by inference I by Mueller matrix theory ₁it is the normalization Stokes vector S of incident light _in=[1 Q U V], phase delay δ, the initial orientation angle θ of rotating wave plate 8 ₀and dichroic angle Ψ, the polarization response matrix X nonlinear function of totally 22 unknown parameters of system transmittance τ and polaroid analyze 4.Utilize the non-linear fitting method of multiparameter to solve and obtain above-mentioned all unknown parameters including X;

2) put into sample, measuring process 1) identical, obtain equally 4 × (360/ Δ θ) ²individual detection light intensity, is designated as vector I ₂.Now, I ₂it is the normalization Stokes vector S of incident light _in=[I Q U V], phase delay δ, initial orientation angle θ 0 and dichroic angle Ψ, the polarization response matrix X of polaroid analyze 4 and the Mueller matrix M of testing sample 3 of rotating wave plate 8 _sthe long-pending A nonlinear function of the nonlinear function of totally 22 unknown parameters.Utilize the non-linear fitting method of multiparameter to solve and obtain above-mentioned all unknown parameters including A;

3) by A=XM _scan try to achieve the Mueller matrix M of testing sample _s=X ^-1a.

In the self calibration measuring method of above-mentioned a kind of Mueller matrix, described step 1) I ₁with the funtcional relationship of all unknown parameters as shown in formula (1).Wherein θ ₁and θ ₂be respectively the gyrobearing angle of the polarizer 7 and wave plate 8; R is rotation matrix; M _p, M _wPbeing respectively position angle is the polarizer 7 of 0 degree and the Mueller matrix of wave plate 8; R, M _p, M _wP, X matrix description as shown in formula (2).

I ₁(θ ₁，θ ₂)＝τXR(θ ₂)M _WPR(-θ ₂)R(θ ₁)M _PR(-θ ₁)S _in＝f(Q，U，V，δ，θ ₀，ψ，τ，X)θ ₁，θ ₂＝kΔθ，k＝0，1，...，360/Δθ (1)

$M_P=\frac{1}{2}\left[\begin{array}{cccc}1& 1& 0& 0\\ 1& 1& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 0& 0\end{array}\right]$ $R\left({\mathrm{\θ}}_{\mathrm{\α}}\right)=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& {\cos 2\mathrm{\θ}}_{\mathrm{\α}}& -{\sin 2\mathrm{\θ}}_{\mathrm{\α}}& 0\\ 0& {\sin 2\mathrm{\θ}}_{\mathrm{\α}}& {\cos 2\mathrm{\θ}}_{\mathrm{\α}}& 0\\ 0& 0& 0& 1\end{array}\right]\mathrm{\α}=\mathrm{1,2}$ (2)

$X=\left[\begin{array}{cccc}1& q_1& u_1& v_1\\ i_2& q_2& u_2& v_2\\ i_3& q_3& u_3& v_3\\ i_4& q_4& u_4& v_4\end{array}\right]$ $M_{\mathrm{WP}}=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& \cos \mathrm{\δ}& \sin \mathrm{\δ}\\ 0& 0& -\sin \mathrm{\δ}& \cos \mathrm{\δ}\end{array}\right]$

In the self calibration measuring method of above-mentioned a kind of Mueller matrix, described step 2) I ₂with the funtcional relationship of all unknown parameters as shown in formula (3).Wherein, M _sfor the Mueller matrix of testing sample 3, A, M _swith relation between X is as shown in formula (4).

I ₁(θ ₁，θ ₂)＝τXM _SR(θ ₂)M _WPR(-θ ₂)R(θ ₁)M _PR(-θ ₁)S _in＝f(Q，U，V，δ，θ ₀，ψ，τ，A)θ ₁，θ ₂＝kΔθ，k＝0，1，...，360/Δθ (3)

$A={\mathrm{XM}}_S=\left[\begin{array}{cccc}1& q_1& u_1& v_1\\ i_2& q_2& u_2& v_2\\ i_3& q_3& u_3& v_3\\ i_4& q_4& u_4& v_4\end{array}\right]\left[\begin{array}{cccc}{m}_{11}& m_{12}& m_{13}& m_{14}\\ m_{21}& m_{22}& m_{23}& m_{24}\\ m_{31}& m_{32}& m_{33}& m_{34}\\ m_{41}& m_{42}& m_{43}& m_{44}\end{array}\right]---\left(4\right)$

In the self calibration measuring method of above-mentioned a kind of Mueller matrix, the extinction ratio of the described polarizer 7 is greater than 10000: 1.

In the self calibration measuring method of above-mentioned a kind of Mueller matrix, the phase delay δ of described wave plate 8 is within the scope of 70 °-150 °.

In the self calibration measuring method of above-mentioned a kind of Mueller matrix, described step delta θ is within the scope of 1 °-50 °.

In the self calibration measuring method of above-mentioned a kind of Mueller matrix, the polarizer 7 of described polarization generator 2 and wave plate 8 must independently rotate with step delta θ separately.

In the self calibration measuring method of above-mentioned a kind of Mueller matrix, described polaroid analyze 4 has and can only modulate four independently output polarization states.

In sum, compared with the several method of the present invention and prior art, advantage is:

1. put into the Stokes parameter of testing sample front and back output polarization state by measurement, set up by the functional relation between the Mueller matrix of the output polarization state parameter recording, system unknown parameter and sample, use the non-linear fitting method of multiparameter to solve the Mueller matrix that obtains testing sample.Without to the accurate calibration of experimental system, simplify measuring process, realize the self calibration of Mueller matrix and measured;

2. use the nonlinear least square fitting method of multiparameter to solve all systematic parameters, without the accurate calibration of system component parameter, require low to the design accuracy of component parameter;

3. the method is without calibrating system is accurate, and all parameters are tried to achieve by approximating method, are more suitable for the Mueller matrix spectrum measurement of sample.Without as prior art, need to be at each wavelength place to system precise calibration;

4. measuring accuracy is high, not high, applied widely to experiment condition and environmental requirement.

Brief description of the drawings

Fig. 1 is the principle of compositionality figure of the self calibration measuring method of a kind of Mueller matrix of the present invention.

Fig. 2 is the pie graph of polarization generator.

Fig. 3 is the pie graph of polaroid analyze.

Embodiment

Embodiments of the invention accompanying drawings is as follows:

Referring to Fig. 1, the structure of the self calibration measuring method of Mueller matrix of the present invention is made up of light source 1, polarization generator 2, sample 3, polaroid analyze 4, detector 5 and computing machine 6.Polarization generator comprises the rotation polarizer 7 and rotating wave plate 8 (seeing Fig. 2).Polaroid analyze forms (seeing Fig. 3) by two ferroelectric liquid crystals wave plates 9,10 and analyzer 11, thereby ferroelectric liquid crystals 9 and 10 obtains four independently outgoing polarization states with modulation angle 45 degree conversion fast axis directions.The light beam that light source 1 produces enters polarization generator 2, and polarization generator 2 is controlled the polarizer 7 by computing machine 6 and wave plate 8 is spent freely and independently rotated a circle with step-length 40 respectively, obtains 81 modulating polarization states.Each polarization attitude output light after sample 3, enter polaroid analyze 4 demodulation obtain four independently polarization state be detected device 5 and receive, receiving light power reaches computing machine 6 and is recorded.

Adopt above-mentioned measurement structure, the self calibration measuring method step of Mueller matrix of the present invention is as follows:

First, take out sample 3, polarization generator 2 obtains 81 modulating polarization states by 8 modulation of the rotation polarizer 7 and rotating wave plate, and each polarization state polaroid analyze 4 demodulation obtain four independently outgoing polarization states and are detected device 5 and receive by computing machine 6 records, are designated as light intensity I ₁;

Secondly, put into sample 3, polarization generator 2 obtains 81 modulating polarization states by 8 modulation of the rotation polarizer 7 and rotating wave plate, and each polarization state polaroid analyze 4 demodulation obtain four independently outgoing polarization states and are detected device 5 and receive by computing machine 6 records, are designated as light intensity I ₂;

Finally, set up the funtcional relationship of surveying between light intensity and the Mueller matrix of each unknown parameter of system and sample 3 according to formula (1)-(4), solve all unknown parameters by nonlinear least square fitting, thereby obtain X and A.According to M _s=X ^-1a tries to achieve the Mueller matrix of testing sample 3.

The various embodiments described above can some variations in addition under not departing from the scope of the present invention, thus above explanation comprise should be considered as exemplary, but not in order to limit the protection domain of the present patent application patent.

Claims (8)

1. a self calibration measuring method for Mueller matrix, is characterized in that: the measurement structure of the method is mainly made up of light source 1, polarization generator 2, testing sample 3, polaroid analyze 4, detector 5 and computing machine 6.Polarization generator 2 is made up of the polarizer 7 and wave plate 8, and the polarizer 7 and wave plate 8 rotate freely with certain step delta θ separately.Realize Mueller matrix self calibration measure step as follows:

1) do not put into testing sample 3, for each modulating polarization state of polarization generator 2, polaroid analyze 4 demodulation obtain four independently polarization state received by detector 5.The polarizer 7 and wave plate 8 rotate a circle separately and obtain 4 × (360/ Δ θ) ²individual detection light intensity, is designated as vector I ₁.Known by inference I by Mueller matrix theory ₁it is the normalization Stokes vector S of incident light _in=[1 Q U V], phase delay δ, initial orientation angle θ 0 and the dichroic angle Ψ of rotating wave plate 8, the polarization response matrix X nonlinear function of totally 22 unknown parameters of system transmittance τ and polaroid analyze 4.Utilize the non-linear fitting method of multiparameter to solve and obtain above-mentioned all unknown parameters including X;

2) put into sample, measuring process 1) identical, obtain equally 4 × (360/ Δ θ) ²individual detection light intensity, is designated as vector I ₂.Now, I ₂it is the normalization Stokes vector S of incident light _in=[I Q U V], phase delay δ, the initial orientation angle θ of rotating wave plate 8 ₀and dichroic angle Ψ, the polarization response matrix X of polaroid analyze 4 and the Mueller matrix M of testing sample 3 _sthe long-pending A nonlinear function of the nonlinear function of totally 22 unknown parameters.Utilize the non-linear fitting method of multiparameter to solve and obtain above-mentioned all unknown parameters including A;

3) by A=XM _scan try to achieve the Mueller matrix M of testing sample _s=X ^-1a.

2. the self calibration measuring method of a kind of Mueller matrix according to claim 1, is characterized in that: step 1) in, I ₁with the funtcional relationship of all unknown parameters as shown in formula (1).Wherein θ ₁and θ ₂be respectively the gyrobearing angle of the polarizer 7 and wave plate 8; R is rotation matrix; M _p, M _wPbeing respectively position angle is the polarizer 7 of 0 degree and the Mueller matrix of wave plate 8; R, M _p, M _wP, X matrix description as shown in formula (2).

I ₁(θ ₁，θ ₂)＝τXR(θ ₂)M _WPR(-θ ₂)R(θ ₁)M _PR(-θ ₁)S _in＝f(Q，U，V，δ，θ ₀，ψ，τ，X)θ ₁，θ ₂＝kΔθ，k＝0，1，...，360/Δθ (1)

(2)

。

3. the self calibration measuring method of a kind of Mueller matrix according to claim 1, is characterized in that: step 2) in, I ₂with the funtcional relationship of all unknown parameters as shown in formula (3).Wherein, M _sfor the Mueller matrix of testing sample 3, A, M _swith relation between X is as shown in formula (4).

I ₁(θ ₁，θ ₂)＝τXM _SR(θ ₂)M _WPR(-θ ₂)R(θ ₁)M _PR(-θ ₁)S _in＝f(Q，U，V，δ，θ ₀，ψ，τ，A)θ ₁，θ ₂＝kΔθ，k＝0，1，...，360/Δθ (3)

。

4. the self calibration measuring method of a kind of Mueller matrix according to claim 1, is characterized in that: the extinction ratio of the polarizer 7 is greater than 10000: 1.

5. the self calibration measuring method of a kind of Mueller matrix according to claim 1, is characterized in that: the phase delay δ of wave plate 8 is within the scope of 70 °-150 °.

6. the self calibration measuring method of a kind of Mueller matrix according to claim 1, is characterized in that: step delta θ range of choice is 1 °-50 °.

7. the self calibration measuring method of a kind of Mueller matrix according to claim 1, is characterized in that: the polarizer 7 of polarization generator 2 and wave plate 8 must independently rotate with step delta θ separately.

8. the self calibration measuring method of a kind of Mueller matrix according to claim 1, is characterized in that: polaroid analyze 4 has and can only modulate four independently output polarization states.

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