CN114047101B - Optical simulation system and method for representing irregularity degree of particulate matter - Google Patents

Optical simulation system and method for representing irregularity degree of particulate matter Download PDF

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CN114047101B
CN114047101B CN202110786218.4A CN202110786218A CN114047101B CN 114047101 B CN114047101 B CN 114047101B CN 202110786218 A CN202110786218 A CN 202110786218A CN 114047101 B CN114047101 B CN 114047101B
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潘小乐
田雨
王自发
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Abstract

The invention provides an optical simulation system and method for representing the degree of irregularity of particulate matter, which relate to the technical field of atmospheric monitoring and comprise an incident light module, a scattering measurement cavity and an intensity detection module; the incident light module, the scattering measurement cavity and the intensity detection module are coaxially arranged; the scattering measurement intracavity is provided with forward scattering light measurement module and backscattered light and moves back partial ratio measurement module, forward scattering light measurement module with backscattered light moves back partial ratio measurement module and laser emission direction and is the angle setting. The invention designs the position of the optical lens reasonably distributed through strict T-Matrix optical model calculation, and ensures higher instrument signal-to-noise ratio through repeated measurement and calculation in a laboratory. Through establishing reasonable lens group arrangement order, adopt collimating lens and condensing lens's combination, reach real-time, effectively survey the design target of environmental particulate matter irregularity degree to transmit data into remote monitoring center in real time, improved atmospheric pollutants irregularity degree detection level to a certain extent.

Description

Optical simulation system and method for representing degree of irregularity of particulate matter
Technical Field
The invention relates to the technical field of atmospheric environment real-time monitoring, in particular to an optical simulation system and method for representing the irregularity degree of particulate matters.
Background
At present, the monitoring on air pollution particles mainly focuses on properties such as concentration, chemical components and the like. The real-time monitoring of the depolarization property of the single particulate matter is less, the irregularity degree of the environmental particulate matter is difficult to detect, and the judgment and judgment of the environmental pollutants are inaccurate. At present, related commercial instruments are lacked, and instruments and equipment for representing the irregularity degree of particles at present have great deviation on finally obtained data due to the lack of scientific guidance for selecting the detection angle of scattered light. Therefore, the angle of the incident laser line deviation is adjusted according to the particle characteristics with different regularity in the current urgent need, the optimal incident angle and position are determined according to the information such as the focal length of the lens system, and then the light intensity information of different vibration directions in the backscattering laser of the particles is obtained by the high-light-transmittance optical splitter, so that the precise calibration work of the lens system and the laser is carried out.
Disclosure of Invention
The invention aims to provide an optical simulation system and method for representing the irregularity degree of particulate matters, so as to solve the problems in the prior art.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
an optical simulation system for representing the irregularity degree of particulate matter comprises an incident light module, a scattering measurement cavity and an intensity detection module; the incident light module, the scattering measurement cavity and the intensity detection module are coaxially arranged;
the scattering measurement intracavity is provided with forward scattering light measurement module and backscattered light and moves back partial ratio measurement module, forward scattering light measurement module with backscattered light moves back partial ratio measurement module and laser emission direction and is the angle setting.
Preferably, the arrangement direction of the forward scattering light measurement module forms an included angle of 45 degrees with the laser emission direction;
the setting direction of the backward scattering light depolarization ratio measuring module and the laser emission direction form an included angle of 135 degrees.
Preferably, an aerosol particle beam inlet is further arranged in the scatterometry cavity, and the inlet is arranged between the forward scattered light measurement module and the backward scattered light depolarization ratio measurement module and is used for placing an aerosol particle beam to be measured into the scatterometry cavity.
Preferably, the optical simulation system further comprises a data acquisition processor, a remote monitoring center and a power module, wherein the power module is respectively connected with the incident light module, the forward scattering light measuring module, the backward scattering light depolarization ratio measuring module and the laser intensity detecting module, and the data acquisition processor is respectively connected with the forward scattering light measuring module, the backward scattering light depolarization ratio measuring module and the laser intensity detecting module;
the remote monitoring center is in communication with the data acquisition processor.
Preferably, the forward scattering light measuring module is connected with the data acquisition processor through a deconcentrator, and the backward scattering light depolarization ratio measuring module is connected with the laser intensity detecting module.
Preferably, the forward scattering light measurement module comprises two sets of symmetrically arranged forward scattering measurement optical paths, each measurement optical path comprises a lens group and a photomultiplier, and the lens groups and the photomultiplier are sequentially arranged to measure the intensity of forward scattering light caused by particles.
Preferably, the backscattered light depolarization ratio measuring module comprises a backscattered light measuring light path which is symmetrically arranged, the backscattered light measuring light path comprises a first plano-convex lens, a second plano-convex lens, a third plano-convex lens, a polarized light splitter, a first photomultiplier and a second photomultiplier, the first plano-convex lens, the polarized light splitter, the second plano-convex lens and the first photomultiplier are sequentially arranged, the third plano-convex lens is arranged between the second photomultiplier and the polarized light splitter, and the two groups of photomultipliers are arranged along the vertical direction.
Another object of the present invention is to provide an optical simulation method for characterizing the irregularity degree of particles, which is characterized by comprising the following steps:
s1, the incident light module emits laser, enters the measurement cavity module, and is intersected with the aerosol particle beam in the measurement cavity module to generate scattering;
s2, allowing the scattered forward scattered light to enter a forward scattered light measuring module for light intensity measurement, allowing the backward scattered light to enter a backward scattered light depolarization ratio measuring module, calculating a depolarization ratio, and representing the irregular degree of the particle shape;
and S3, the data acquisition processor acquires the test results of the forward scattering light measurement module and the backward scattering light depolarization ratio measurement module and transmits the results to a remote control center.
Preferably, the specific calculation process in step S2 is as follows:
s21, according to the key parameter of particle swarm scattering, namely Stokes scattering matrix, considering a small volume element dvThe inner particle group, each randomly oriented and rotationally symmetric, is capable of independent scattering, and has optical properties such as extinction cross section (C) averaged with all the individual particlesext) Scattering cross section (C)sca) And dimensionless Stokes scattering matrix representation, namely:
Figure BDA0003158900000000031
where Θ is the scattering angle, i.e. the angle between the incident light and the scattered beam; assuming the Stokes vector I of the incident lightincAnd Stokes vector I of scattered lightscaAre both defined relative to the scattering plane (the plane defined by the incident and scattered light), the total scattered light intensity IscaCan be expressed as:
Figure BDA0003158900000000032
wherein n is0Is the density of the particles, R is the small volume element dvDistance to a viewpoint; the Stokes vector I is defined as a (4 × 1) column function containing four Stokes parameters I, Q, U and V:
Figure BDA0003158900000000033
of these 8 parameters, 8 are non-zero, and 6 of these 8 parameters are independent parameters, and there is a special relationship between these 6 parameters at scattering angles of 0 and π, as follows:
a2(0)=a3(0),a2(π)=-a3(π),
b1(0)=b2(0)=b1(π)=b2(π)=0,
a4(π)=a1(π)-2a2(π)
f in Stokes scattering matrix11I.e. a1(Θ), a well-known phase function in particle scattering optics, satisfies the following equation:
Figure BDA0003158900000000034
the parameter g is the symmetry factor of the phase function, positive for forward-scattering particles, negative for backward-scattering particles, 0 for forward-backward symmetric particles of the phase function:
Figure BDA0003158900000000041
the average absorption cross-section of each particle is defined as the difference between the extinction cross-section and the scattering cross-section,
Cabs=Cext-Csca
for a small volume element, the single scattering albedo is defined as the ratio of the scattering cross-section to the extinction cross-section:
ω=Csca/Cext
s22, solving key parameters in the Stokes matrix by adopting a T-matrix:
considering the case where a planar electromagnetic wave is scattered by a non-spherical particle, the incident field E isincAnd a scattered field EscaUsing spherical vector functions M, respectivelymnAnd NmnUnfolding into the following steps:
Figure BDA0003158900000000042
Figure BDA0003158900000000043
wherein R is the radius of the outer spherical surface of the scattering particles; g is gravity acceleration; k is a correction coefficient and has no specific meaning; m and n are the arguments of the spherical function.
In the formula, the scattered wave coefficient pmnAnd QmnCoefficient of incident wave amnAnd bmnLinear correlation, which can be expressed as:
Figure BDA0003158900000000044
Figure BDA0003158900000000045
written in matrix form as follows:
Figure BDA0003158900000000046
a is obtained by solving T matrixmnAnd bmnAnd further calculating the extinction cross section, the scattering cross section, the absorption cross section and the single scattering albedo of the non-spherical particle swarm as follows:
Figure BDA0003158900000000051
Figure BDA0003158900000000052
Cabs=Cett-Cxa
Figure BDA0003158900000000053
the invention has the beneficial effects that:
the optical simulation system is reasonable in structure, the detection angles of 45 degrees in the forward direction and 135 degrees in the backward direction are selected by utilizing the T-maxtrix theory for calculation, the linear relation between the scattering light intensity and the depolarization ratio and the particle size of the particles is observed to be more obvious, and therefore the particle size and the morphology of the particles can be more accurately estimated. Through establishing the combination of reasonable collimating lens and condensing lens, reach the purpose of effectively surveying the irregular degree of environmental particulate matter to transmit data in real time to the remote monitoring center, effectively improved the detection level of atmospheric pollutants physicochemical property.
Drawings
Fig. 1 is a schematic diagram of a basic principle of an optical simulation system in embodiment 1 of the present invention;
FIG. 2 is a schematic view of an external configuration of an optical simulation system in embodiment 1 of the present invention;
FIG. 3 is a graph of the calculated grain depolarization ratio as a function of its aspect ratio and scattering light angle based on a T-matrix optical model according to the present invention;
FIG. 4 is a graph of particle depolarization ratio versus particle aspect ratio at 135 deg. for different complex refractive indices calculated based on the T-matrix optical model of the present invention. (ii) a
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings. It should be understood that the detailed description and specific examples, while indicating the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention.
Example 1
An optical simulation system for representing the irregularity degree of particulate matter comprises an incident light module, a scattering measurement cavity and an intensity detection module; the incident light module, the scattering measurement cavity and the intensity detection module are coaxially arranged;
the scattering measurement intracavity is provided with forward scattering light measurement module and backscattered light and moves back partial ratio measurement module, forward scattering light measurement module with backscattered light moves back partial ratio measurement module and laser emission direction and is the angle setting.
In the embodiment, the arrangement direction of the forward scattering light measurement module forms an included angle of 45 degrees with the laser emission direction;
the setting direction of the backward scattering light depolarization ratio measuring module and the laser emission direction form an included angle of 135 degrees.
And an aerosol particle beam inlet is also arranged in the scattering measurement cavity, and the inlet is arranged between the forward scattering light measurement module and the backward scattering light depolarization ratio measurement module and is used for placing an aerosol particle beam to be measured into the scattering measurement cavity.
The optical simulation system in this embodiment further includes a data acquisition processor, a remote monitoring center, and a power module, where the power module is connected to the incident light module, the forward scattered light measurement module, the backward scattered light depolarization ratio measurement module, and the laser intensity detection module, respectively, and the data acquisition processor is connected to the forward scattered light measurement module, the backward scattered light depolarization ratio measurement module, and the laser intensity detection module, respectively;
the remote monitoring center is in communication with the data acquisition processor.
The device is connected with the forward scattering light measuring module, the backward scattering light depolarization ratio measuring module and the laser intensity detecting module through a data acquisition processor and a deconcentrator.
The forward scattering light measurement module in this embodiment includes two sets of forward scattering measurement optical paths that the symmetry set up, the measurement optical path includes a lens group and photomultiplier, lens group and photomultiplier set up in order, measure the forward scattering light intensity that is aroused by the particulate matter.
The backscatter depolarization ratio measuring module in this embodiment includes the backscatter measurement light path that the symmetry set up, the backscatter measurement light path includes first plano-convex lens, second plano-convex lens, third plano-convex lens, polarisation beam splitter, first photomultiplier and second photomultiplier, first plano-convex lens the polarisation beam splitter the second plano-convex lens with first photomultiplier sets up in order, the third plano-convex lens sets up the second photomultiplier with between the polarisation beam splitter, and two sets of photomultiplier sets up along the vertical direction.
Example 2
The embodiment provides an optical simulation method for characterizing the irregularity degree of particulate matter, which adopts the optical simulation system described in embodiment 1, and includes the following steps:
s1, the incident light module emits laser, enters the measurement cavity module, and is intersected with the aerosol particle beam in the measurement cavity module to generate scattering;
s2, allowing the scattered forward scattered light to enter a forward scattered light measuring module for light intensity measurement, allowing the backward scattered light to enter a backward scattered light depolarization ratio measuring module, calculating a depolarization ratio, and representing the irregular degree of the particle shape;
and S3, the data acquisition processor acquires the test results of the forward scattering light measurement module and the backward scattering light depolarization ratio measurement module and transmits the results to a remote control center.
In this embodiment, the specific calculation process in step S2 is as follows:
the specific calculation process in step S2 is as follows:
s21, according to the key parameter of particle swarm scattering, namely Stokes scattering matrix, considering a small volume element dvThe inner particle group, each randomly oriented and rotationally symmetric, is capable of independent scattering, and has optical properties such as extinction cross section (C) averaged with all the individual particlesext) Scattering cross section (C)sca) And dimensionless Stokes scattering matrix representation, namely:
Figure BDA0003158900000000071
where Θ is the scattering angle, i.e. the angle between the incident light and the scattered beam; assuming the Stokes vector I of the incident lightincAnd Stokes vector I of scattered lightscaAre both defined relative to the scattering plane (the plane defined by the incident and scattered light), the total scattered light intensity IscaCan be expressed as:
Figure BDA0003158900000000072
wherein n is0Is the density of the particles, R is the small volume element dvDistance to a viewpoint; the Stokes vector I is defined as a (4 × 1) column function containing four Stokes parameters I, Q, U and V:
Figure BDA0003158900000000081
of these 8 parameters, 8 are non-zero, and 6 of these 8 parameters are independent parameters, and there is a special relationship between these 6 parameters at scattering angles of 0 and π, as follows:
a2(0)=a3(0),a2(π)=-a3(π),
b1(0)=b2(0)=b1(π)=b2(π)=0,
a4(π)=a1(π)-2a2(π)
f in Stokes scattering matrix11I.e. a1(Θ), a well-known phase function in particle scattering optics, satisfies the following equation:
Figure BDA0003158900000000082
the parameter g is the symmetry factor of the phase function, positive for forward-scattering particles, negative for backward-scattering particles, 0 for forward-backward symmetric particles of the phase function:
Figure BDA0003158900000000083
the average absorption cross-section of each particle is defined as the difference between the extinction cross-section and the scattering cross-section,
Cabs=Cext-Csca
for a small volume element, the single scattering albedo is defined as the ratio of the scattering cross-section to the extinction cross-section:
ω=Csca/Cext
solving key parameters in the Stokes matrix by adopting a T-matrix:
considering the case where a planar electromagnetic wave is scattered by a non-spherical particle, the incident field E isincAnd a scattered field EscaUsing spherical vector functions M, respectivelymnAnd NmnUnfolding into the following steps:
Figure BDA0003158900000000091
Figure BDA0003158900000000092
wherein R is the radius of the outer spherical surface of the scattering particles; g is gravity acceleration; k is a correction coefficient and has no specific meaning; m and n are the arguments of the spherical function.
In the formula, the scattered wave coefficient pmnAnd QmnCoefficient of incident wave amnAnd bmnLinear correlation, which can be expressed as:
Figure BDA0003158900000000093
Figure BDA0003158900000000094
written in matrix form as follows:
Figure BDA0003158900000000095
after the T matrix is solved, parameters such as an extinction cross section, a scattering cross section, an absorption cross section, a single scattering albedo and the like of the non-spherical particles can be calculated, so that the irregular degree of the particle morphology is represented;
Figure BDA0003158900000000096
Figure BDA0003158900000000097
Cabs=Cett-Cxa
Figure BDA0003158900000000098
the irregular particles are detected by the system and the method, irregular parameters are obtained through T-maxtrix theoretical calculation, and the results are shown in fig. 3 and fig. 4, wherein in fig. 3, the depolarization ratio (delta) of the scattered light of the particles is obtained when infrared light (1024nm) irradiates the particles with different shapes at different scattering angles. Obviously, although the polarization degree of each particle is different, the distribution of the patterns is approximately similar, and the depolarization ratio (delta) is almost 0 within the scattering angle of 0 DEG to 90 DEG, taking the scattering result of 10 mu m particles as an example; in the range of 90 degrees to 180 degrees, the depolarization ratio increases and then decreases along with the increase of the irregularity of the particles, and the aspect ratio (lambda) when the depolarization ratio (delta) reaches the peak value decreases along with the increase of the scattering angle, which is more obvious for large particles (the particle size is more than 2.5 mu m). From this, we conclude that: the depolarization ratio (delta) shows great difference when different particle shapes exist, the scattering polarization characteristic of single non-spherical particles is not eliminated by the random effect of particle groups, and therefore, the particle scattering polarization distribution is influenced by the shapes of the particles and can be used as a detection index of the particle morphology in atmospheric detection.
Fig. 4 is a graph of a relationship between a particle depolarization ratio and a particle aspect ratio at 135 ° when different complex refractive indexes are calculated based on a T-matrix optical model, where the abscissa in the graph is the depolarization ratio and the ordinate is an irregular parameter — the particle aspect ratio, and according to the graph, only the detected depolarization ratio value at a forward scattering angle of 45 ° is substituted, and the corresponding aspect ratio is found to obtain the degree of irregularity of the particles.
By adopting the technical scheme disclosed by the invention, the following beneficial effects are obtained:
the optical simulation system is reasonable in structure, the detection angles of 45 degrees in the forward direction and 135 degrees in the backward direction are selected by utilizing the T-maxtrix theory for calculation, the linear relation between the scattering light intensity and the depolarization ratio and the particle size of the particles is observed to be more obvious, and therefore the particle size and the morphology of the particles can be more accurately estimated. Through establishing the combination of reasonable collimating lens and condensing lens, reach the purpose of effectively surveying the irregular degree of environmental particulate matter to transmit data in real time to the remote monitoring center, effectively improved the detection level of atmospheric pollutants physicochemical property.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and improvements can be made without departing from the principle of the present invention, and such modifications and improvements should also be considered within the scope of the present invention.

Claims (7)

1. An optical simulation system for representing the irregularity degree of particulate matter is characterized by comprising an incident light module, a scattering measurement cavity, an intensity detection module, a data acquisition processor, a remote monitoring center and a power module; the incident light module, the scattering measurement cavity and the intensity detection module are coaxially arranged;
a forward scattering light measuring module and a backward scattering light depolarization ratio measuring module are arranged in the scattering measuring cavity, and the forward scattering light measuring module and the backward scattering light depolarization ratio measuring module are arranged at an angle with the laser emission direction;
the power supply module is respectively connected with the incident light module, the forward scattered light measuring module, the backward scattered light depolarization ratio measuring module and the laser intensity detecting module, and the data acquisition processor is respectively connected with the forward scattered light measuring module, the backward scattered light depolarization ratio measuring module and the laser intensity detecting module;
the remote monitoring center is in communication connection with the data acquisition processor;
the method for performing optical simulation of the particle irregularity characterization by using the optical simulation system comprises the following steps:
s1, the incident light module emits laser, enters the measurement cavity module, and is intersected with the aerosol particle beam in the measurement cavity module to generate scattering;
s2, enabling the forward scattered light after scattering to enter a forward scattered light measuring module, measuring the light intensity by the forward scattered light measuring module, enabling the backward scattered light to enter a backward scattered light depolarization ratio measuring module, calculating a depolarization ratio, and representing the irregular degree of the particle morphology;
s3, the data acquisition processor acquires the test results of the forward scattering light measurement module test and the backward scattering light depolarization ratio measurement module, and transmits the test results to a remote control center;
the specific calculation process in step S2 is as follows:
s21, according to the key parameter of particle swarm scattering, namely Stokes scattering matrix, considering a small volume element dvThe inner particle group, each of which is randomly oriented and rotationally symmetric, is capable of independent scattering, and the optical properties of which can be averaged by the extinction cross section C of all the individual particle groupsextScattering cross section CscaAnd dimensionless Stokes scattering matrix representation, namely:
Figure FDA0003565310560000021
where Θ is the scattering angle, i.e. the angle between the incident light and the scattered beam, assuming the Stokes vector I of the incident lightincAnd Stokes vector I of scattered lightscaAre all defined relative to the scattering plane, the total scattered light intensity IscaExpressed as:
Figure FDA0003565310560000022
wherein n is0Is the particle density and R is the small volume element dvThe Stokes vector I is defined as a 4 × 1 column function, including four Stokes parameters I, Q, U, and V:
Figure FDA0003565310560000023
of these 8 parameters, 8 are non-zero, and 6 of these 8 parameters are independent parameters, and there is a special relationship between these 6 parameters at scattering angles of 0 and π, as follows:
a2(0)=a3(0),a2(π)=-a3(π),
b1(0)=b2(0)=b1(π)=b2(π)=0,
a4(π)=a1(π)-2a2(π).
f in Stokes scattering matrix11I.e. a1(Θ), a well-known phase function in particle scattering optics, satisfies the following equation:
Figure FDA0003565310560000031
the parameter g is the symmetry factor of the phase function, positive for forward-scattering particles, negative for backward-scattering particles, 0 for forward-backward symmetric particles of the phase function:
Figure FDA0003565310560000032
the average absorption cross-section of each particle is defined as the difference between the extinction cross-section and the scattering cross-section,
Cabs=Cext-Csca
for a small volume element, the single scattering albedo is defined as the ratio of the scattering cross-section to the extinction cross-section:
ω=Csca/Cext
s22, calculating the T-matrix solving method of the key parameters in the Stokes matrix by adopting the T-matrix solving method:
considering the case where a planar electromagnetic wave is scattered by a non-spherical particle, the incident field (E) isinc) And a scattered field (E)sca) Using spherical vector functions M, respectivelymnAnd NmnUnfolding into the following steps:
Figure FDA0003565310560000033
Figure FDA0003565310560000034
wherein R is the radius of the outer spherical surface of the scattering particles; g is gravity acceleration; k is a correction coefficient and has no specific meaning; m and n are independent variables of the spherical function;
in the formula (1), the scattered wave coefficient pmnAnd QmnCoefficient of incident wave amnAnd bmnLinear correlation, which can be expressed as:
Figure FDA0003565310560000041
Figure FDA0003565310560000042
written in matrix form as follows:
Figure FDA0003565310560000043
a is obtained by solving T matrixmnAnd bmnAnd further calculating the extinction cross section, the scattering cross section, the absorption cross section and the single scattering albedo of the non-spherical particle swarm as follows:
Figure FDA0003565310560000044
Figure FDA0003565310560000045
Cabs=Cett-Cxa
Figure FDA0003565310560000046
2. the optical simulation system of claim 1, wherein the forward scattering light measurement module is disposed at an angle of 45 ° to the laser emission direction;
the setting direction of the backward scattering light depolarization ratio measuring module and the laser emission direction form an included angle of 135 degrees.
3. The optical simulation system of claim 1, wherein an aerosol particle beam inlet is further disposed in the scatterometry cavity, the inlet being disposed intermediate the forward scattered light measurement module and the backscattered light depolarization measurement module for introducing an aerosol particle beam to be measured into the scatterometry cavity.
4. The optical simulation system of claim 2, wherein the forward scattered light measurement module, the backward scattered light depolarization ratio measurement module and the laser intensity detection module are connected through a splitter by a data acquisition processor.
5. The optical simulation system of claim 1, wherein the forward scattering light measurement module comprises two symmetrically arranged sets of forward scattering measurement paths, the measurement paths comprising a lens set and a photomultiplier tube, the lens set and the photomultiplier tube being arranged in series to measure the intensity of forward scattering light caused by particulate matter.
6. The optical simulation system of claim 1, wherein the backscattered light depolarization ratio measurement module comprises a symmetrically arranged backscatter measurement optical path, the backscatter measurement optical path comprising a first plano-convex lens, a second plano-convex lens, a third plano-convex lens, a polarization beam splitter, a first photomultiplier tube, and a second photomultiplier tube, the first plano-convex lens, the polarization beam splitter, the second plano-convex lens, and the first photomultiplier tube being arranged in sequence, the third plano-convex lens being arranged between the second photomultiplier tube and the polarization beam splitter, and both sets of photomultiplier tubes being arranged in a vertical direction.
7. The optical simulation system of claim 1, wherein the final test result in step S3 is a depolarization ratio at a forward scattering angle of 45 °.
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