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Abstract
Environment variation is an important factor affecting the polarization propagation through the smoke. In this paper, we investigate the effects of the relative humidity and optical thickness on polarization transmission character, as well as the persistence of the linear and circular polarization of artificial smoke particles with simulations and experiments. We develop an environment modulation system to control the environment variation and measure the transmission degree of polarization (DOP). Correspondingly, by building the relation between the smoke filling time and optical thickness, as well as between the relative humidity and particle size and refractive index, we utilize the Monte Carlo program to track photon scattering process through varying the radius, refractive index and optical thickness. Both the simulation and the experimental results show that the DOP of both linear and circular polarizations are constantly decreased with the increasing of the optical thickness. However, at the same optical thickness, both the linear and circular polarization's persistence benefits with the increasing of the relative humidity. Moreover, circular polarization persists better than linear polarization in the larger optical thickness and the higher humidity environment under the wavelength of 532 nm. These works can verify the persistence of circular polarization and broaden the application range of polarized lights in a variable artificial smoke environment.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Polarization provides more information for the target recognition from the background, and for the increasing of the detection range in the underwater, fog and smoke environment [1–3]. The use of polarization has become an efficient measure in the research of target detection under the low contrast medium [4–6]. Therefore, studying the effects of the highly scattering environment on the polarization persistence is of significant importance for practical detection.
In the study of the polarization transmission characteristic, underwater, fog and smoke environment are usually considered as the highly scattering medium [7–9]. Previous research often has developed either experimental or theoretical solution for the polarization persistence measurement in these special environments [10–12]. For the underwater transmission environment, Xu et al. utilizes Monte Carlo algorithm to simulate the performance evaluation with polarization retrieve method for polarized light under different water types and transmission distances, this work should be very significant for underwater optical communication systems [13]. More recently, Zhang et al. measured the linearly polarized light scattering of pure water and seawater at various salinities and estimated the depolarization ratio using five different methods of data analysis, and achieved almost consistent results with these different methods [14]. Zhang and Wang et al. presented simulation results showing the effect of suspended particles on underwater optical communication links and laser polarization characteristics based on a combination of Mie scattering theory and Monte Carlo numerical simulation. They found that circularly polarized light maintains good polarization characteristic in the underwater laser transmission process [15]. To gain the knowledge of the polarized light propagation within gaseous medium, several researchers have developed the characteristic features of the polarization under the air, fog and smoke environment with either models or measurements. Li et al. developed a multi-angle optical scattering measurement system based on theoretical simulations to identify and classify different types of aerosols in the air [16]. For multi-scattering, due to the uncontrollability of the gas as the light propagates, most of these previously published works are simulation methods, utilizing Monte Carlo simulations [17–21]. Vander Laan et al. showed that the persistence of circular and linear polarization in transmission through several fog and dust environments over broad wavelength ranges from the visible to the infrared, and their works helped explain how circularly polarized light persists through these highly scattering environments [22–24]. Zeng et al. qualitatively analyzed the transmission characteristic of circularly and linearly polarized light in both radiation and advection fog environments, and showed circular polarization maintains a higher degree of polarization in some detection ranges [25].
Different environment variations of particles can generate effects on the persistence of polarization in gaseous media, this leads to the motivation of our study. In this paper, we combine Monte Carlo modeling with controlled experiments for polarization persistence in variable concentration and humidity environment, rather than limiting to the theory research for the multiple scattering in gaseous medium. To research the effects of environment variation of glycerol smoke particles on the persistence of linear and circular polarization, we firstly prepare the artificial smoke environment utilizing ultrasonic atomization of the glycerol. Then for experimental measurement, we test the transmission DOP of circular and linear polarization under the different concentrations and relative humidity in the glycerol smoke environment (described in Section 2). For a deeper understanding, we use the Monte Carlo algorithm to simulate the experiment process and verify experiment results (described in Section 3). Finally, we compare the simulated results with the experimental results in variable concentration and relative humidity environments, and analyze the percent agreement between the simulation and the experiment (described in Section 4). These works provide the experimental and theoretical basis for propagation of linearly and circularly polarized light in the glycerol smoke particles.
2. Experimental materials and methods
2.1 Experimental setup
The polarization persistence measurement setup is shown in Fig. 1. The light source is a 532 nm laser with 83.06 mW output power and 0.378% stability. A variable attenuator (ATT) controls the illumination power. The incident polarization state of the collimated light is controlled by the polarization state generator (PSG). It is composed of a rotatable linear polarizer (P, LPVISC050-MP2, Thorlabs, US) and a quarter-wave plate (W, AQWP10M-580, Thorlabs, US). The P and W are used to generate the needed polarization states during the measurement. The artificial smoke particles are contained in an environment modulation system (EMS) and stirred by a smoke mixer at the bottom of the EMS. The scattering light passing through the EMS is then received by polarimeter (PM, PAX5710VIS, made by Thorlabs, US) to measure its polarization states. The personal computer (PC) connects with the EMS and PM, which controls the environment variation in EMS and receives information from PM, respectively.
Fig. 1. Schematic of the measurement setup of polarization state (a) and light power (b). S, light source; ATT, attenuator; PSG, polarization state generator; P, linear polarizer; W, quarter wave-plate; EMS, environment modulation system; PM, polarimeter; PC, personal computer; LPM, light power meter.
In this study, we take the ultrasonic atomization of the glycerol (refractive index 1.47 for visible light supplied by Antari Company, Taiwan) as the artificial smoke environment. In the EMS, we use smoke filling time of 0.5-4s (intervals of 0.5s) and relative humidity to control environment variation in the glycerol smoke particles. Due to the concentration of the smoke environment is uncontrollable during the smoke filling, the light power of scattering light is measured by a light power meter (LPM, PM100D, made by Thorlabs, US) in real time to represent the optical thickness, as described in Section 2.2 and shown in Fig. 1(b). In the meantime, the ultrasonic humidifier (ZS-10Z, supplied by Hangzhou Zhengdao Electrical Equipment Co., Ltd, China) is used to control the humidity in the EMS, and the effect of relative humidity on glycerol smoke particles is presented in Section 2.3.
2.2 Measurement of concentration variation
Because the limitations in the measurement of the concentration, the exact relationship between the transmission characteristics of the polarization and the smoke concentration cannot be completely matched. The optical thickness, $\tau$, is a function of particle concentration $\rho$, extinction cross-section ${C_e}$ and distance L, which is
in which, the distance is invariable in EMS. So there is a proportional relationship between the optical thickness and the particle concentration.Before the measurement of the optical thickness, we need to define the stability of the artificial smoke environment during the smoke filling. Figure 2 features the intensity variations of emergent light under the sampling time of 6 min for the smoke filling time of 2s. The emergent light result shows that the stabilization phenomenon of the glycerol smoke particles occurs during the period of 2 min - 6 min. Therefore, we obtain measurement results of the polarization state and optical thickness in this interval to avoid smoke interference.
For the homogeneous and isotropic particles, if the transmittance is between 2% and 90%, the absorption and scattering of the particles are not affected by the surrounding particles [26]. We can use Beer’s law to define the optical thickness based on light intensity, which can be expressed as
in which, ${I_o}$ and I are intensity of the incident light and the emergent light, respectively. During the optical thickness measurement, ${I_o}$ and I can be measured by LPM before and after glycerol smoke filling in the EMS, which is shown in Fig. 1(b).The optical thickness under the different smoke filling time in the period of the glycerol smoke stabilization is shown in Fig. 3. When the smoke filling time is from 0.5s to 4s, the transmittance of the glycerol smoke environment is approximately between 2% and 82%, which can meet the Beer's law. Correspondingly, the minimum and maximum values of the optical thickness are 0.2 and 4.
2.3 Effect of relative humidity on glycerol smoke particles
Because of the hygroscopicity of the glycerol [27], condensation of water vapor on glycerol smoke particles causes the size and refractive index of these particles to change with the increasing of the relative humidity. To calculate the effect of relative humidity on the persistence of linear and circular polarization, it is necessary to describe the dependence of particle size and index of refraction on relative humidity.
As the water absorption of the single particle cannot be measured, according to a great deal of observed data, the mixture rule approximation which is due to Hanel [28] is employed to describe increased particle size and reduced mean refractive index. At thermodynamic equilibrium, Hanel’s empirical growth function of particle size is shown as
where ${r_h}$ and ${r_0}$ are the wet and dry particle radius, and ƒ is the relative humidity. The mean index is the volume-weighted average of the indices of the dry particle (${m_0} = {m_{r0}} + i{m_{i0}}$) and of water (${m_w} = {m_{rw}} + i{m_{iw}}$), which can be written as [28] where ${m_{re}}$ and ${m_{ie}}$ are the real and imaginary parts of the index of refraction of hygroscopic particles. For artificial smoke particles in this paper, the imaginary part of the refractive index is not considered here.In our previous works, we have measured the cumulative volume of glycerol particles with Malvern spraytec (STP5311, made by Malvern instrument limited, Britain), and converted the volume distribution to the number distribution of the particle size according to the volumes of the particles and the total light beam [29]. Since the mean radius of the smoke particles for the smoke filling time 0.5-4s has a small difference, we use the mean radius 0.75 μm for the initial radius of the smoke particles for simplification of the simulation, and the refractive index of the smoke particle is 1.47. The size parameter ${{2\pi {r_h}} / \lambda }$(wavelength $\lambda = 0.532$ μm) and real part of refractive index of glycerol smoke particle as a function of relative humidity are shown in Fig. 4.
Fig. 4. Effect of relative humidity on (a) size parameter and (b) real part of refractive index of particle.
During experiments, we set the glycerol smoke environment as the dry, low, moderate and high humidity environment at the same optical thickness. The effects of other particle size distributions from the ultrasonic humidifier, such as the water particles, are neglected, as well as the glycerol smoke particles after moisture absorption regard as the homogeneous and isotropic particles with equivalent method to obey the Beer’s law. To keep the same optical thickness in humidity environments as the dry particles, we measure the emergent light by LPM during the glycerol smoke filling in the EMS, once the optical thickness meets the test requirement, we will terminate the glycerol smoke filling and starts the DOP tests. Note that, for the testing condition of the same optical thickness, when there is water spray in the EMS, the extinction cross-section ${C_e}$ in Eq. (1) is increasing with the larger particle size so that the concentration of particles is decreasing.
3. Simulations
Due to the ignorance of the effects of the atmospheric molecules and the impurities during Mie scattering, the transmission of polarization in EMS is completely affected by glycerol smoke particles. To compare the transmission characteristic measurements of linear and circular polarization during environment variation more comprehensively, the Monte Carlo method for isotropic, homogeneous and spherical particles is applied here to analyze the behavior of the polarizations propagating in the glycerol smoke environment.
For each environment in EMS, one million purely polarized photons with either linear or circular polarization are launched into the glycerol smoke medium. The incident polarization state can be expressed by the Stokes vectors ${S_0} = {[\begin{array}{cccc} {{I_0}}&{{Q_0}}&{{U_0}}&{{V_0}} \end{array}]^T}$, in which ${I_0}$ represents the total light intensity, ${Q_0}$ and ${U_0}$ are linear polarization in two directions, and ${V_0}$ denotes the circular polarization. Our previous study has shown that the linear polarizations in different directions after propagation have almost the same degree of polarization (DOP) [29]. So in this work, we only set the polarization state of the horizontal linear polarization state ($[\begin{array}{cccc} {{I_0}}&{{Q_0}}&{{U_0}}&{{V_0}} \end{array}] = \left[ {\begin{array}{cccc} 1&1&0&0 \end{array}} \right]$) and right-hand circular polarization state ($[\begin{array}{cccc} {{I_0}}&{{Q_0}}&{{U_0}}&{{V_0}} \end{array}] = \left[ {\begin{array}{cccc} 1&0&0&1 \end{array}} \right]$) for the illumination lights. The Monte Carlo simulation based on Ramella-Roman et al. [17] tracks the polarization state of each photon as it scatters through the particles and the then arrives at a given receiving area. The scattering events of homogeneous spherical particles can be described as
After scattering at different time, the cumulated Stokes vector components can be expressed as $S = \left[ {\begin{array}{cccc} I&Q&U&V \end{array}} \right]$, so the DOP after the overall scattering can be written as
For each simulation, the polarization character of the emergent light based on Mie scattering theory is related to the particle size, the refractive index of the particles, wavelength of the incident light, as well as the concentration and the relative humidity of the environment. In this study, our goal is to investigate the persistence of linear and circular polarization in the different glycerol smoke environments: a) For the effect of environment concentration on the transmission characteristic, the concentration of the glycerol smoke is determined by the optical thickness measuring in Section 2.2; b) For the relative humidity variation, the radius and the refractive index of the glycerol smoke particles are defined by different relative humidity on the basis of Eqs. (3) - (5). From these inputs, we utilize the simulation results to verify our measurement outputs.4. Results and discussion
For each environment, one million photons of 0 degree linear and right-hand circular polarization states were launched under the wavelength of 532 nm. To change the concentration in EMS, eight glycerol smoke filling samples with filling time from 0.5s to 4s corresponds to eight different optical thickness, the experiments were completed in a stable glycerol smoke environment. For variable humidity environment, on the basis of Eqs. (3) - (5), the relative humidity is related to the size and refractive index of the particle. The variable size and refractive index of the particles, as well as the optical thickness under the corresponding smoke filling time are selected in the simulations, therefore we can verify the polarization character under different glycerol smoke environments with both measurements and simulations. For each measurement, we recorded data five times for the mean value to remove the error effects.
4.1 Effect of optical thickness
Figure 5 presents the polarization characteristics of linear and circular polarizations under wavelength of 532 nm with different optical thicknesses for simulations. When the optical thickness is increasing, the concentration of the glycerol smoke environment is increasing, so the transmission DOP of both the linearly and circularly polarized light all decrease for the increasing of the scattering number. By comparing linearly and circularly polarized light, it can be seen that the linear polarization is more affected by transmission concentration than circular polarization. The key to the increasing depolarization of linear polarization is the larger scattering number of glycerol smoke environment. Overall, for eight kinds of glycerol smoke filling samples circular polarization maintains its DOP better than linear polarization except for the optical thickness of 0.2 under the wavelength of 532 nm.
Fig. 5. Influence of optical thickness on DOP of linear and circular polarization for dry glycerol smoke particles under the wavelength of 532 nm in simulations.
For a better understanding, we carried out the transmission experiments recorded by the PM to compare the Monte Carlo simulation results. Figure 6 illustrates the relationship between the optical thickness and the transmission DOP for dry glycerol smoke particles under the wavelength of 532 nm in experiments. By observing Fig. 6, the experimental results are basically as predicted by the simulations, but there are still some oscillations in the experimental results. For both the linear and circular polarizations, the polarization degree will decrease with the increasing optical thickness, and the circular polarization always outperforms linear polarization except for the first sample under the wavelength of 532 nm. Among these eight glycerol smoke filling samples, the transmission DOP of linear polarization increasing from the optical thickness 3.49 to 4 is less nearly in according with the simulations, probably due to disturbance of some other particles with larger sizes in the air and the limitation of the optimum transmittance of Beer's law. However, the transmission still shows a similarly changing tendency with the theory and simulations.
Fig. 6. Influence of optical thickness on DOP of linear and circular polarization for dry glycerol smoke particles under the wavelength of 532 nm in experiments.
More concretely, we use percent agreement between experiments and simulations discussed in our previous paper [29], which is
4.2 Effect of relative humidity at the same optical thickness
In the scattering of glycerol smoke particles under different relative humidity, to research the effect of relative humidity on the particle scattering, we applied scattering phase function ${P_{11}}$ of the scattering matrix in Eq. (6) to describe the scattering properties [30]. Mie scattering phase function of glycerol smoke particle with different relative humidity is shown in Fig. 7. It is apparent that the scattering lights are concentrated at small scattering angles and the values under the scattering angle from ${0^\textrm{o}}$ to ${10^\textrm{o}}$ are higher three orders of magnitudes than that at other lager scattering angles (shown as a larger version of Fig. 7 for details). When the relative humidity is increasing, the scattering effects of the glycerol smoke particle become more forward-scattering.
Figure 8 shows the influence of relative humidity on DOP of linear and circular polarization in simulations. Three kinds of relative humidity of 20%, 50% and 80% are selected as the low, moderate and high humidity environment. Figure 8 illustrates that under different relative humidity both the linearly and circularly polarized lights cause the depolarization phenomenon with the increasing of the optical thickness. However, with the increasing of the relative humidity the overall DOP of the linear and circular polarization increase at the same optical thickness, and the difference between the polarization states is larger at the higher humidity environment. For comparison, Fig. 8(a) shows a preference for linear polarization during all samples of the optical thickness for relative humidity of 20%, and Figs. 8(b) and 8(c) illustrate that, in the moderate and high humidity environment circularly polarized light outperforms linear polarized light. For quantitative analysis of the transmission performance in variable relative humidity, we calculate the reducing DOP of linearly and circularly polarized light under the optical thickness from 0.2 to 4. When the relative humidity is 20%, 50% and 80%, the corresponding reducing values of DOP are 0.6541, 0.6454 and 0.5727 for linear polarization, as well as 0.6548, 0.5910 and 0.5008 for circular polarization. These happen because the effects of relative humidity on both the radius and the complex refractive index of the particle, described in Section 2.3. When the humidity in the glycerol smoke environment increases, the particle radius increases, and the real part of the complex refractive index decreases (shown in Fig. 4). In addition, the change of the radius is more significant than refractive index as the relative humidity is larger than 50% [31]. For this case, particle size made more contribution to the transmission character variation of the polarizations. According to the theory of the forward-peaked scattering of polarized light [32–34], the persistence of polarization states is prominent with the forward-scattering environment, the more forward-scattering effects, the larger DOP of polarizations and the better persistence of circular polarization [23]. The forward-scattering is related to the particle size and the refractive index, and the larger particle size leads to more forward-scattering environment, so the increasing relative humidity medium with larger particles generates the better persistence of circular polarization. This can also be verified by Mie scattering phase function of glycerol smoke particle with different relative humidity shown in Fig. 7. By comparing the relative humidity of 20% with the dry glycerol smoke environment [shown in Fig. 8(a) and Fig. 5], this phenomenon does not occur because of the joint effect of both the radius and refractive index when the scattering particles are in a low humidity environment.
Fig. 8. Influence of optical thickness on DOP of linear and circular polarization for glycerol smoke particles under wavelength of 532 nm at the relative humidity of (a) 20%; (b) 50%; (c) 80% in simulations.
Figure 9 shows the transmission experiment results for glycerol smoke environments consisting of low, moderate and high humidity under the wavelength of 532 nm. We can summarize from Fig. 9 that: (1) only the low humidity environment shows a persistence benefit for linear polarization, circular polarization is preferred for both the moderate and high humidity glycerol smoke particles, which are basically corresponding to the simulation results; (2) compared with simulation results, the difference between the linear and circular polarization in experiments is larger than which in simulations at the low optical thickness environment, and there are some oscillations in the experiment results due to the disturbance of some other particles in the EMS, but the overall downward trend is invariable with the increasing of the optical thickness.
Fig. 9. Influence of optical thickness on DOP of linear and circular polarization for glycerol smoke particles under wavelength of 532 nm at the relative humidity of (a) 20%; (b) 50%; (c) 80% in experiments.
For further discussion, the percent agreement between simulation and experiment for glycerol smoke humidity environment is calculated in Table 1. We can see the maximum and the minimum values of the percent agreement are 91.24% and 84.19%.
Table 1. Percent agreement between simulation and experiment for glycerol smoke humidity environment.
By comparing the simulation and experiment of the polarization behaviors, we can see the simulation curves can be fitted as the addition of two terms of exponential functions for quantitative analysis, but there are more components in the relationship according to the experimental results. In real applications, in addition to the influence of disturbance phenomenon and size distribution variation of the glycerol smoke environment described in Section 4.1, there are still some effects from other particle size distributions from the ultrasonic humidifier in experiments with relative humidity, such as the water particles. These all can lead to the lower agreement between the simulation and the experiment.
5. Conclusions
In this paper, we present the simulation and experiment results showing that the effect of the concentration and relative humidity in the glycerol smoke environment on the linear and circular polarized light. An experimental setup is established to measure the polarization character after transmission in the artificial smoke particles and control the environment variation, such as the relative humidity and the glycerol smoke filling in EMS. For further study on the scattering process, using the relationship between the relative humidity and the particle property, we simulate polarization propagation with Monte Carlo program for varying input parameters of particle size, refractive index, wavelength and optical thickness. The experiments and corresponding simulations were performed for each glycerol smoke environment with optical thickness ranging from 0.2 to 4 for increasing relative humidity of 20%, 50% and 80%.
Experimental and simulation results show that with the increasing of the optical thickness the transmission DOP of the lasers will decrease, and the circular polarization persists better than linear polarization. Moreover, for glycerol smoke environment with increasing relative humidity at the same optical thickness, the transmission DOP of both the linear and circular polarizations will increase due to the variation of the particle size and refractive index. When the glycerol smoke particles are in a low humidity environment, linearly polarized light persists superiorly for all the glycerol smoke filling time samples under the wavelength of 532 nm. However, when the relative humidity is increasing, the circularly polarized light outperformed linearly polarized light in the moderate and high humidity environment. Therefore, circular polarization has the better performance in the variable glycerol smoke environment. The larger optical thickness and the higher relative humidity of glycerol smoke environment, the better persistence of circular polarization.
From the simulation and the experiment results, we can get a good agreement of the polarization propagation tendency, which confirms the effects of the environment variation on the linear and circular polarization and expands the application range of polarization under the variable glycerol smoke environment. The difference of DOP values between the experiment and simulations also demonstrates that we need improve more complete environment modulation and measurement system.
Funding
National Natural Science Foundation of China (61905025, 61890963, 61705017); Jilin Scientific and Technological Development Program (20200201261JC).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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