阅读说明：本技术 一种偏振态检测系统中偏振态分析器的选择方法 (Selection method of polarization state analyzer in polarization state detection system ) 是由 李艳秋 宁天磊 李建慧 周国栋 于 2019-11-11 设计创作，主要内容包括：本发明公开了一种偏振态检测系统中偏振态分析器的选择方法,该检测系统在测量装置中添加了空间变化的相位延迟器,从多次测量简化到一次测量,进一步的,为了此系统能普适到任意的空间变化的相位延迟器,在偏振态分析器的选择和控制上,进行了优化,优化步骤包括需要设定相位延迟器和偏振态分析器的穆勒矩阵信息；建立探测面强度分布模型以及建立强度分布模型和偏振几率密度模型的关系,并通过选取偏振几率密度的最大值对应的偏振态作为待测光偏振态,通过上述方法选定合适的偏振态分析器,与给选定的空间变化的相位延迟器匹配,以达到准确的偏振几率密度及偏振态测量结果。(The invention discloses a selection method of a polarization state analyzer in a polarization state detection system, wherein the detection system is additionally provided with a phase retarder with spatial variation in a measuring device, the measurement is simplified from multiple times to one time, furthermore, in order to ensure that the system can be universally applied to the phase retarder with any spatial variation, optimization is carried out on the selection and control of the polarization state analyzer, and the optimization step comprises the step of setting the Mueller matrix information of the phase retarder and the polarization state analyzer; establishing a detection surface intensity distribution model and a relation between the intensity distribution model and a polarization probability density model, selecting a polarization state corresponding to the maximum value of the polarization probability density as a polarization state of light to be measured, selecting a proper polarization state analyzer by the method, and matching the polarization state analyzer with the phase retarder with the selected space variation to achieve accurate measurement results of the polarization probability density and the polarization state.)

1. A method for selecting a polarization analyzer in a polarization detection system, comprising:

step one, because the established detection intensity distribution model is based on the relationship between a Mueller matrix and an incident light Stokes vector, the Mueller matrix information of a phase retarder and a polarization state analyzer needs to be set;

mapping the polarization state of the light to be measured to a detection light intensity distribution, and further obtaining the polarization state of incident light by measuring the intensity distribution; establishing a detection surface intensity distribution model;

thirdly, to measure the polarization state of the incident light, establishing a relation between an intensity distribution model and a polarization probability density model, and selecting the polarization state corresponding to the maximum value of the polarization probability density as the polarization state of the light to be measured;

and (3) only when the partial derivative in the third step obtains a unique zero point, the polarization probability density can obtain a unique maximum value, namely, the polarization state analyzer under the condition is selected as the polarization state analyzer adopted by the method and is matched with the selected phase delayer with space change, so that the polarization probability density and the polarization state measurement result are obtained.

2. The method of claim 1, comprising a light source module, a polarization generator, a spatial filter, a collimating lens, a spatially varying phase modulator, a polarization analyzer, a focusing lens, a detector, and a data processing module.

3. The method for selecting a polarization analyzer in a polarization detection system according to claim 1 or 2, wherein in the step one, mueller matrix information of the phase retarder and the polarization analyzer is set;

i.e. the mueller matrix of an arbitrary spatially varying phase retarder is expressed as:

the mueller matrix of the waveplate variable fast axis azimuth polarization analyzer is expressed as:

wherein θ represents the variable fast axis azimuth of the polarization analyzer waveplate, M_PSAA mueller matrix representing a polarization state analyzer.

4. The method for selecting a polarization analyzer in a polarization state detection system according to claim 1 or 2, wherein in step two, a detection plane intensity distribution model is established; the method specifically comprises the following steps: according to the first two mueller matrices M, M_PSASetting the total number of pixel points of the detection surface to be K; obtaining the ith (i belongs to [1, K ] of the detection surface]) The intensity distribution of the pixel points is as follows:

wherein

further simplifying equation (4) is:

wherein v is₁＝m₀₀+m₁₀cos²(2θ)+m₂₀sin(2θ)cos(2θ)-m₃₀sin(2θ)

v₂＝m₀₁+m₁₁cos²(2θ)+m₂₁sin(2θ)cos(2θ)-m₃₁sin(2θ)

v₃＝m₀₂+m₁₂cos²(2θ)+m₂₂sin(2θ)cos(2θ)-m₃₂sin(2θ)

v₄＝m₀₃+m₁₃cos²(2θ)+m₂₃sin(2θ)cos(2θ)-m₃₃sin(2θ)；

Further, a relation between the photon polarization probability density and any spatially-variable phase modulation Mueller matrix, the incident light polarization state and the fast axis azimuth angle of the polarization state analyzer wave plate is established.

5. The method for selecting the polarization analyzer in the polarization state detection system according to claim 1 or 2, wherein in step three, the polarization state corresponding to the maximum value of the polarization probability density is selected as the polarization state of the light to be measured;

(1) the polarization probability density model is built as follows, giving the polarization state of the incident light

when the intensity received by each pixel point of the detection surface is I₁,I₂...I_i,...I_KThe number of photons each point falls into is N₁,N₂,...N_i,...N_K(ii) a The formula is expressed as:

wherein the content of the first and second substances,the light source omega to be measured with uniform polarization is a constant;

wherein the content of the first and second substances,

logarithm of formula (7) is

(2) respectively for the Stokes component s₂、s₃、s₄Partial derivatives are calculated as follows:

wherein v of the above formula₁、v₂、v₃、v₄See the notes below equation (5)

Wherein

Only when the above partial derivative obtains a unique zero point, the polarization probability density can obtain a unique maximum value, that is, the polarization state analyzer under the condition is selected as the polarization state analyzer adopted by the method and matched with the selected phase retarder with spatial variation, so that accurate polarization probability density and polarization state measurement results are achieved.

6. A method of selecting a polarization analyzer in a polarization state detection system according to claim 1 or 2, wherein the system is constrained by: the wave plate of the polarization state analyzer is selected to change the azimuth angle of the fast axis, and the transmission axis direction of the polaroid is fixed to be the horizontal direction.

Technical Field

The invention belongs to the technical field of polarization measurement, and particularly relates to a method and a system for measuring polarization probability density and polarization state.

Background

Polarization is an important property of light, and polarized light is very sensitive to microstructure characteristics in samples such as optical elements, materials, biological tissues and the like. The interaction of light with the sample can cause refraction, reflection, scattering, etc. to change the polarization state of the incident light. The change capability of the sample on the polarization state of light is represented by a Mueller matrix, the Mueller matrix contains all polarization information of the sample, can be further decomposed into polarization parameters which are closely related to the microstructure of the sample, have practical physical significance, can be quantized, such as depolarization, phase retardation, dichroism, fast axis direction angle, optical rotation and the like, and can be used for obtaining the polarization characteristics and the structural parameters of the sample. Polarization measurement is an important tool for analyzing polarization characteristics of light and samples, and has been widely applied to the fields of biomedicine, quantum communication, laser radar and the like.

The conventional polarization measurement methods mainly include: time-sharing polarization measurement, amplitude-sharing polarization measurement, aperture-sharing polarization measurement and focus plane polarization measurement. The document "stokes parameter detection and precision analysis based on rotating wave plate" [ J ], spectroscopy and spectral analysis, 2016, 36(8) discloses a time-sharing polarization measurement method. The time-sharing polarization measurement obtains a plurality of light field intensity graphs by rotating the polarization element for a plurality of times, and then calculates the polarization state to be measured. This method introduces additional rotational errors due to the multiple rotation of the device and it does not enable real-time polarization measurements. Patent document CN103017908A discloses an amplitude-splitting polarization measurement method based on four-way light splitting, which further resolves four stokes components to be measured by collecting intensity distribution of four-way detectors. Patent document CN108731810A discloses a method for measuring polarization of a focusing plane, which reconstructs polarization information of incident light by using a microwave sheet array constructed by a pixilated cell. Patent document CN208060025U discloses a method for measuring the polarization state of an arbitrary light beam, which includes interfering a reference light beam and a measuring light beam, and calculating the polarization state of incident light by using the obtained interference pattern. The above method uses a complex multi-optical path system or a precisely machined grating device to realize real-time polarization measurement. Most polarization measurement methods are not widely used due to the complexity of the system and the expensive device processing. In addition, the conventional polarization measurement technology is only suitable for polarization measurement under strong light, and the polarization measurement method is not suitable for environments with weak light or a small number of photons. With the further development of science and technology, a detection system which is simple in structure and can realize rapid polarization probability density and polarization state needs to be developed in the fields of biomedicine, quantum communication, laser radar and the like. In fact, another chinese patent CN201810749870.7 discloses a method for calibrating a polarization measurement system by an eigenvalue calibration method, in which a polarization probability density distribution model is established, and a polarization state of a light field to be measured is further obtained by obtaining a target stokes parameter corresponding to a maximum value of a polarization probability, thereby completing a measurement task; however, since the method is established for a combination of a spatially varying phase retarder (SEO) and a left-handed polarization analyzer, the method cannot be applied to any spatially varying phase retarder.

Disclosure of Invention

In view of this, the invention provides a method for selecting a polarization state analyzer in a polarization state detection system, which is a method for selecting a polarization state analyzer by establishing a relationship between a photon polarization probability density and a phase modulation mueller matrix with arbitrary spatial variation, an incident light polarization state and a fast axis azimuth angle of a wave plate of the polarization state analyzer, and matches a selected spatially varying phase retarder by changing the fast axis azimuth angle of the wave plate of the polarization state analyzer, thereby achieving the purpose of accurately measuring the polarization information of a light field to be measured.

The technical scheme for realizing the invention is as follows:

a polarization state detection system comprises a polarization state analyzer, a spatial light filter, a collimating lens, a spatially varying phase retarder, a polarization state analyzer, a focusing lens and a detector; the light beam to be measured sequentially penetrates through the polarization state generator, the spatial light filter, the collimating lens, the spatially-variable phase retarder and the polarization state analyzer, and then the light beam is imaged to the detector by the focusing lens; the detector receives the intensity distribution of the light to be measured, sends the obtained intensity map to the data processing module for data processing, and further provides the polarization information of the light to be measured.

The spatial optical filter is composed of a small hole with the diameter of 5 μm and a microscope objective, and the phase delay of the spatial variable phase retarder satisfies the spatial variation in the light transmission range, so the method is not limited to use of a specific phase retarder, and the phase retarder satisfying the spatial variation can be used.

The polarization state analyzer consists of a quarter-wave plate controlled by the electric turntable and a fixed linear polarizer;

the key points of the invention are as follows: a spatially varying phase retarder is added to a measuring device which measures a plurality of times and measures one time, and further, the method is optimized in the selection and control of a polarization state analyzer so that the method can be universally applied to any spatially varying phase retarder.

A method of selecting a polarization analyzer in a polarization state detection system, comprising the steps of:

constraint conditions are as follows: selecting a variable fast axis azimuth angle of a wave plate of the polarization state analyzer, wherein the transmission axis direction of a polaroid is fixed in the horizontal direction;

the wave plate of the polarization state analyzer is controlled by the electric turntable, and the method for selecting the variable fast axis azimuth angle is as follows:

step one, because the established detection intensity distribution model is based on the relationship between the Mueller matrix and the Stokes vector of the incident light, the Mueller matrix information of the phase retarder and the polarization state analyzer needs to be set,

i.e. the mueller matrix of an arbitrary spatially varying phase retarder is expressed as:

the mueller matrix of the waveplate variable fast axis azimuth polarization analyzer is expressed as:

wherein θ represents the waveplate of the polarization analyzerVariable fast axis azimuth, M_PSAA mueller matrix representing a polarization state analyzer;

mapping the polarization state of the light to be measured to a detection light intensity distribution, and further obtaining the polarization state of incident light by measuring the intensity distribution; establishing a detection surface intensity distribution model, which specifically comprises the following steps: according to the first two mueller matrices M, M_PSASetting the total number of pixel points of the detection surface to be K; obtaining the ith (i belongs to [1, K ] of the detection surface]) The intensity distribution of the pixel points is as follows:

wherein

Representing the polarization state of the light to be measuredAnd further substituting the formulas (1) and (2) into the formula (3) to obtain an intensity distribution model of the detection surface:

further simplifying equation (4) is:

wherein v is₁＝m₀₀+m₁₀cos²(2θ)+m₂₀sin(2θ)cos(2θ)-m₃₀sin(2θ)

v₂＝m₀₁+m₁₁cos²(2θ)+m₂₁sin(2θ)cos(2θ)-m₃₁sin(2θ)

v₃＝m₀₂+m₁₂cos²(2θ)+m₂₂sin(2θ)cos(2θ)-m₃₂sin(2θ)

v₄＝m₀₃+m₁₃cos²(2θ)+m₂₃sin(2θ)cos(2θ)-m₃₃sin(2θ)；

Further, establishing a relation between the photon polarization probability density and any spatially-variable phase modulation Mueller matrix, the polarization state of incident light and the fast axis azimuth angle of a wave plate of the polarization state analyzer;

and step three, establishing a relation between an intensity distribution model and a polarization probability density model when measuring the polarization state of the incident light, and selecting the polarization state corresponding to the maximum value of the polarization probability density as the polarization state of the light to be measured. The polarization probability density model was established as follows:

given polarization state of incident light

One photon falls on the ith (i is E [1, K ] of the detection surface]) The probability density of the pixel points is:

when the intensity received by each pixel point of the detection surface is I₁,I₂...I_i,...I_KThe number of photons each point falls into is N₁,N₂,...N_i,...N_K。

WhereinAnd omega is constant for the uniformly polarized light source to be measured.

Wherein

The probability of obtaining a certain polarization state is represented, and P (i) the probability that the photon can hit the ith pixel point is represented;

logarithm of formula (7) is

Only Q varies with the Stokes parameter of incident light, ln omega is constantA number of, whereinThe polarization probability density is denoted as Q.

(2) Respectively for the Stokes component s₂、s₃、s₄Partial derivatives are calculated as follows:

wherein v of the above formula₁、v₂、v₃、v₄See the annotation below in equation (5),

wherein

Only when the above partial derivative obtains a unique zero point, the polarization probability density can obtain a unique maximum value, that is, the polarization state analyzer under the condition is selected as the polarization state analyzer adopted by the method and matched with the selected phase retarder with spatial variation, so that accurate polarization probability density and polarization state measurement results are achieved.

It is worth noting that: the control is preferably controlled by an electric turntable, and the control precision is higher than that of manual operation.

Has the advantages that:

1. the spatial optical filter of the present invention is composed of an aperture with a diameter of 5 μm and a microscope objective lens, and the phase delay of the spatially varying phase retarder satisfies the spatial variation in the light transmission range, so that the method is not limited to use of a specific phase retarder and can be used as long as the phase retarder satisfies the spatial variation.

2. The invention also provides a method for selecting a proper polarization state analyzer to match with the selected space variation phase modulator through the formula (8-10) and the following contents, which gets rid of the dependence on a single phase retarder, and the proper polarization state analyzer selected through the method is matched with the phase retarder giving the selected space variation so as to achieve accurate polarization probability density and polarization state measurement results.

3. The polarization state measuring system comprises a polarization state analyzer, a spatial optical filter, a collimating lens, a spatially-variable phase retarder, a polarization state analyzer, a focusing lens and a detector; all the components are connected in series, so that the system only comprises one optical path system, has a simple structure and high stability, and reduces polarization measurement errors introduced in the optical transmission process; high-precision real-time dynamic measurement can be realized.

4. The invention introduces statistical knowledge (as shown in formula (6-10)) in polarization measurement, and meanwhile, the established intensity distribution model can be obtained through experiments, so that the method is not easily influenced by light source fluctuation and is more suitable for polarization measurement under weak light.

Drawings

FIG. 1 is a schematic diagram of a fast polarization probability density and polarization state measurement system.

FIG. 2 is a graph showing the variation of polarization probability density with Stokes' parameters when different polarization state analyzers are selected.

101-light source, 102-polarization state generator, 103-spatial light filter, 104-collimating lens, 105-spatially varying phase retarder, 106-polarization state analyzer, 107-focusing lens, 108-detector, 109-data processing module.

Detailed Description

The invention is described in detail below by way of example with reference to the accompanying drawings.

For example, the spatially varying phase retarder of choice in the present invention is a vortex half-wave plate with a left-handed polarization analyzer and a horizontal polarization analyzer and to detect s₄The parameters are used as an example to show how to select a more suitable polarization analyzer using the above method.

The fast axis azimuth angle of the wave plate of the horizontal polarization analyzer is 0 °, i.e., θ is 0 °. The above formula (4) is thus expressed as:

and substituting the formula (11) into the formula (7), and further analyzing the change condition of the polarization probability density along with the Stokes parameters of the light to be detected. As shown in the figure (b) of the specification.

Similarly, the fast axis azimuth angle of the wave plate of the left-handed polarization analyzer is-45 °, i.e., θ is-45 °, and the equation (4) is expressed as:

substituting the formula (12) into the formula (7), and further analyzing the polarization probability density along with the Stokes parameters s of the light to be measured₄The variation of (2). As shown in the attached figure (a) of the specification.

By observing (a) in the attached drawing (3) of the specification, it can be seen that the formula (10) cannot obtain a unique zero point by using the left polarization state analyzer, that is, the polarization probability density Q cannot obtain a unique maximum value by using the left polarization state analyzer. When a horizontal polarization state analyzer is used, the polarization probability density Q can take a unique maximum value as shown in (b) of fig. 3 in the specification. Equation (10) has a unique zero. Therefore, a suitable polarization analyzer can be selected by the method, and the measurement of the polarization state can be completed by the following steps.

The method comprises the following specific steps:

the light beam to be detected sequentially passes through the spatial light filter 103, the collimating lens 104, the spatially varying phase retarder 105 and the polarization state analyzer 106, and the emergent light beam is converged to the detection surface 208 through the focusing lens 107.

Step one, establishing an intensity distribution model, wherein the normalized polarization state of the light to be measured can be expressed as

Driven deviceThe polarization characteristics of the light beam to be measured are represented by a mueller matrix, and the light beam to be measured sequentially passes through a phase retarder with spatial variation, a polarization state analyzer 106 (the transmission axis direction of a polarizing plate is fixed in the horizontal direction), and a focusing lens and is finally received by a detector 108. Taking a first parameter of the stokes vector of the outgoing light beam as the total intensity of the outgoing light beam, the following formula is satisfied:

wherein m is_i,jThe mueller matrix of the spatially varying phase retarder is represented, and θ represents the angle between the fast axis direction of the polarization analyzer wave plate and the horizontal direction (i.e., the fast axis azimuth angle). For example, the polarization analyzer used in this patent is a horizontal polarization analyzer, in which the fast axis direction θ of the polarization analyzer wave plate is 0 °. The intensity distribution of the detection area should therefore satisfy:

and step two, establishing the relation between the polarization probability density and the random space change phase retarder, the fast axis azimuth angle of the wave plate of the polarization state analyzer and the polarization state of incident light, wherein photons received by each pixel point of the detection surface meet probability distribution. The probability of receiving photons at a certain pixel point should be equal to the ratio of the number of photons received at the point to the total number of photons received by the detection surface. Therefore, the invention establishes the relation between the polarization probability density and the random space variation phase retarder:

logarithm of the above formula is obtained

WhereinReferred to as polarization probability density.

Step (ii) ofThirdly, obtaining a light intensity distribution to be measured, and extracting the photon number N of each pixel area_iAnd the data is led to the photon polarization probability density and photon polarization state data processing module 109.

And step four, a sample space of incident light Stokes is given, the polarization probability density corresponding to each Stokes is calculated in a value taking mode in the sample space, so that the method can obtain the polarization probability density corresponding to different incident light Stokes vectors, and the Stokes corresponding to the maximum value of the polarization probability is taken as the measured value of the polarization state of the light to be measured.

In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.