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Abstract
Underwater active polarization imaging is a promising imaging method, however, it is ineffective in some scenarios. In this work, the influence of the particle size from isotropic (Rayleigh regime) to forward-scattering on polarization imaging is investigated by both Monte Carlo simulation and quantitative experiments. The results show the non-monotonic law of imaging contrast with the particle size of scatterers. Furthermore, through polarization-tracking program, the polarization evolution of backscattered light and target diffuse light are detailed quantitatively with Poincaré sphere. The findings indicate that the noise light’s polarization and intensity scattering field change significantly with the particle size. Based on this, the influence mechanism of the particle size on underwater active polarization imaging of reflective targets is revealed for the first time. Moreover, the adapted principle of scatterer particle scale is also provided for different polarization imaging methods.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Since underwater optical imaging technology has unique advantages of high sensitivity, fast imaging speed, and high spatial resolution, it has been widely used in marine scientific research, underwater rescue, seabed resource exploration, target monitoring, and other fields [1]. Due to the absorption of turbid water and scattering from micro-suspended particles, the target image is prone to be suffered and is even completely submerged in noise [2]. With regard to reducing the effect, numerous imaging methods based on space, time, polarization, deep learning, dark channel prior, and quantum correlation effect have been developed [3–8]. Active polarization imaging shows excellent application potential due to simple system structure and remarkable improvement [9,10], and the core of imaging is mining the uniqueness of the polarization information of the scattered light field. Currently, polarization imaging approaches include computational polarization imaging based on the physical degradation model [5,11–13] and physical imaging methods based on polarization differences between target light and backscattered light [14–16]. For turbid water, there are various shapes and particle sizes inside the micro-suspended particles. The stability of active polarization imaging is insufficient in practical applications, and the optimum imaging quality is only suitable for specific scattering environments and targets. For this reason, it is essential to research the evolution mechanism of polarized light in the imaging process.
From polarization imaging technology proposed, numerous vital findings have been developed. Alfano et al. experimentally studied the perpendicular polarizations of background light and target light by two polystyrene microsphere solutions with two particle sizes [17]. Kartazayeva et al. compared the target contrast with linearly and circularly polarized light as an incident beam in the medium of large and small particle sizes [18]. John et al. quantified the polarization persistence and memory of circularly polarized light in forward-scattering and isotropic (Rayleigh region) environments and detailed the evolution of both circularly and linearly polarized states for the first time [19]. Shukla et al. analyzed the relationship between the polarization-gated imaging effect and refractive index at specific scatterer scales [14]. Meanwhile, by employing the Monte Carlo simulation method, Bartel et al. obtained the backscattering Mueller matrix of high scattering medium composed of different particle sizes [20]. Guo et al. established a scattering model composed of a variety of particles that obeyed the log-normal distribution and explored the relationship between the degree of polarization of the polarized light and the particle distribution [21]. Ren et al. investigated the principle of polarization-difference imaging in optically scattering environments [22]. In general, the depolarization effect of circular and linear polarization is a research focus. In addition, the developed findings about the particle size affecting polarization imaging contrast mainly apply to typical environments consisting of large particles and small particles. However, the imaging laws of different active polarization methods in the case of continuous particle size variation have not yet been given. Besides, The variation in the particle size results in the polarization evolution, and the influence process of noise on imaging has not been explored in terms of backscattered light and target diffuse light.
Based on the transmission model of polarized light in turbid media, for the particle sizes of scatterers ranging from isotropic (Rayleigh regime) to forward-scattering (0.1µm∼3.0µm) at intervals of 0.1µm, a modified active polarization imaging model for highly reflective target is constructed. Polarization Monte Carlo program is used to analyze the contrast variation of three typical active polarization imaging methods. Furthermore, the optimal application range of the particle size for imaging methods is given and verified by quantitative experiments. Meanwhile, we quantitatively detail the polarization evolution of the noise information with Poincaré sphere, including target diffuse light and backscattered light, and abstain the intensity and polarization scattering field with various scatterer scales. Finally, the influence mechanism of the particle size on active polarization imaging is revealed. This work presents an original, efficient, and complete scheme for the influence mechanism of noise light and makes a significant contribution to the efficient application of active polarization technologies.
2. Active polarization imaging theory
Firstly, based on the process of Monte Carlo simulation of polarized light transmission in medium [23,24], we established a full-link model including polarized light emission, absorption, scattering, colliding boundary, colliding target, and finally captured by detection surface. A laboratory coordinate system (x, y, z) is defined in Fig. 1(a), the perpendicular electric field vector and the parallel electric field vector are set along the x-axes and y-axes, respectively, the photon propagation direction u is set along the z-axis. Thus, ${{\boldsymbol e}_r}$(0, 1, 0), ${{\boldsymbol e}_l}$(1, 0, 0), and u (0, 0, 1) construct the initial local coordinate frame utilized to express the initial Stoke vector of the incident light beam.
Fig. 1. Active polarization imaging model of Monte Carlo simulation and imaging results. (a) Active detection model. (b) Imaging results under different scattering medium.
Under the premise that the detection optical thickness is certain [2], the scattering coefficient ${\mu _s}$ is set to 0.61 cm-1[17], and the absorption coefficient ${\mu _a}$ is set to 0.047 cm-1. A semi-infinite turbid medium, modeled as a suspension of uniformly monodispersed polystyrene microspheres in water, has a slab structure and is used in the simulation. A flat light beam of 0.30 cm in diameter is orthogonally injected into the turbid medium; the incident wavelength was 532 nm, the initial polarization Stokes vector is $\boldsymbol S = {[1\textrm{ 1 0 0]}^\textrm{T}}$, representing linear horizontally polarized light; a smooth square thin aluminum sheet is chosen as a target due to polarization-maintaining; the detection distance is l = 4 cm; the acquisition plane is $2cm \times 2cm $; the acquisition grid density is $\textrm{300} \times \textrm{300}$. Scattering particles are modeled as homogenous refractive index (n = 1.597 for polystyrene) spheres, rigorous Mie scattering theory is utilized for each simulated scattering event. As shown in Fig. 1(b), the examples of intensity imaging in different scattering mediums are obtained by simulation. Under highly scattering, a large amount of backscattering is around the square target in strong scattering, and the imaging contrast is seriously degraded.
Differences in the characteristics of polarized light in the medium originate from the absorption attenuation, multiple scattering, and the role of the target, which changes the polarization and propagation direction. According to the transmission paths, BB, BS, and BD are used to represent background ballistic light, background snake light, and background diffuse light. TB, TS, and TD are used to describe target ballistic light, target snake light, and target diffuse light separately. As shown in Fig. 2 is shrouded in a layer of “mist”, oceans of different types of noise light are distributed in target and background areas.
As a result, the Stokes vector images received by the detection surface are expressed as Eq. (1). The main noise signal affecting the imaging contrast comes from the backscattered light from the medium and the diffuse light from the target [25]. The Stokes vector of target and backscattered information can be described as Eq. (2) and Eq. (3).
In the simulation of active polarization imaging process, we set polarization state generator (PSG) and polarization state analyzer (PSA) to modulate the incident and emergent beams with different polarization directions, respectively. Meanwhile, laser range gating is achieved by adjusting the time threshold ($\textrm{t} > 2\boldsymbol l{n_{\boldsymbol m}}/c$) of the emergent photon package, where ${n_m}$ is the refractive index of the medium, and c is the speed of light in vacuum.
Regarding polarized transmission modeling, the Stokes vectors of the incident polarized beam is denote as ${\boldsymbol S_{\boldsymbol {in}}}\textrm{ = [}\boldsymbol {I Q U V}{\textrm{]}^\textrm{T}}$ and the Mueller matrix ${\boldsymbol {M_p}}$ of the polarizer in angular form with different directions is as Eq. (4), where $\gamma$ is the polarization angle.
The polarization of photons after passing through polarizers with different directions is ${\boldsymbol {S_f}}$, which is expressed as Eq. (5), representing the Stokes vector before being recorded.
When the incident linearly polarized light reaches the target surface, most of specular reflected signal is the same polarization as incident light for highly reflective target [17]. While scattered signal from diffuse target is converted into partially polarized light, and the propagation direction is random [26]. To simplify the influence from the target and focus more on the analysis of the scattering medium, the highly reflective target is the focus in this paper.
A detailed description of the update of the polarization state of the photon resulting from the scattering, collision, and detection in the propagation process is presented in previous studies [23]. A polarization-tracking Monte Carlo program is applied to capture the changes in spatial location, scattering events, and polarization parameters about different transmission light, which are the data basis for analyzing influence mechanism.
3. Influence of the particle size on the contrast of active polarization imaging
3.1 Monte Carlo simulation results
It is generally accepted that the average particle size of the scatterer in the open sea is approximately 0.1 µm, while the particle size range of marine sediment and debris is usually on the micron scale [27]. Consequently, the particle size range of scatterers is from 0.1 µm to 3.0 µm in simulation, which corresponds to the scale parameter range of 0.78∼23.56 ($\alpha \textrm{ = }\pi \boldsymbol d\textrm{/}\lambda$), covering from the Rayleigh region to the large particle Mie region. We choose polarization gate imaging (P-G) [14], polarization difference imaging (P-D) [15], and polarization difference range-gated imaging (P-D range-gated) [16] as comparisons, the reason for this is that these methods achieve noise filtering with different polarization imaging dimensions and are representative. The simulated imaging results with typical particle sizes d = 1.5 µm and d = 2.5 µm are shown in Fig. 3.
Fig. 3. Comparison of active polarization imaging with four methods at two typical particle sizes of scatterers, the scattering coefficient ${\mu _s}$ = 0.61 cm-1 [16], and the absorption coefficient ${\mu _a}$ = 0.047 cm-1.
The image Contrast (C) [15] is calculated as Eq. (6), the average intensity retrieved from pixels corresponding to the object center in the image is ${\boldsymbol I_{\max }}$, and the background average intensity of the four equivalent areas across the four sides outside the object is ${\boldsymbol I_{\min }}$. The requirements for target area are in the center of the object, and the selection area is square. The principles for background area are the four equivalent areas across the four sides outside the object, and the selection area is a rectangle with a long side as wide as the target area, as shown in Fig. 3.
As shown in Fig. 3, it is evident that the improvement of the three polarization imaging methods exhibits a significant difference. The contrast of intensity imaging at particle sizes of d = 1.5 µm is higher than d = 2.5 µm. On the contrary, the improvement of contrast with P-D imaging and the P-D range-gated at d = 2.5 µm is more than five times at d = 1.5 µm, and the maximum value comes to 156.52%, which indicates that polarization scattering field of noise light is influenced by the scatterer scale. There is a huge difference in imaging contrast for three polarization imaging methods.
To further discover this phenomenon, we simulated the imaging contrast of the four imaging methods under continuous particle size varying from 0.1 µm to 3.0 µm at 0.1 µm intervals. As shown in Fig. 4, for thin aluminum sheet, the contrast in descending order is P-D range-gated imaging, P-D imaging, P-G imaging, and intensity imaging. Regarding intensity imaging as a comparison reference, for a particle size of d < 0.6 µm, as the particle size increase, the imaging contrast except P-D range-gated imaging rises significantly due to backscattering being weakened. On the contrary, the maximum improvement of contrast by P-D range-gated imaging is more than ten times, while the improvement via other approaches is weak. When the particle size of d varies from 0.6 µm to 1.5 µm, the contrast through all active polarization imaging methods decreases, and the improvement is insensitive to the change in particle size, only achieving approximately 25% by P-D range-gated imaging. As the particle size of d increases from 1.5 µm to 2.5 µm, it can be seen that the interval of the bar curves gradually increases, which means the better effect is significant by P-D imaging and P-D range-gated imaging, especially when d = 2.5 µm, the enhancement of P-D imaging is more than 1.0 times, and the P-D range-gated is 1.5 times. With the particle size of d gradually rising to 3 µm, all three polarization imaging methods are not practical due to the increase in the forward diffuse light. The result indicates that the contrast of different polarization imaging methods is closely related to scatterer scale parameters for highly reflective target under a certain optical thickness.
Fig. 4. The contrast of four imaging methods with continuous scattering particle sizes of scatterers, the scattering coefficient ${\mu _s}$ = 0.61 cm-1, and the absorption coefficient ${\mu _a}$ = 0.047 cm-1.
3.2 Experiment and results
To further elucidate the results, an experimental system is established, as shown in Fig. 5. An LD (Thorlabs) laser with a central wavelength of 532 nm Lasers and beam expanders are composed as light source; the PSG system is composed of a set of polarizers, and the PSA system is similar; a Dyna 400D back-illuminated SCMOS camera is used as the detector. To quantify the grey value difference in the target area and background area, a smooth and uniform aluminum sheet after polishing is chosen as a target and placed in a square high transmittance quartz cuvette. The incident beam vertically illuminates the target and the detector is in the same direction at a slight angle, the other conditions are the same as in the simulation. We intentionally select the polystyrene microspheres at the particle sizes of d = 0.1 µm, 0.6 µm, 1.0 µm, 1.5 µm, 2.0 µm, 2.5 µm, and 3.0 µm in the curve variation in Fig. 4, and further add deionized water without impurities to configure the turbid medium solution.
By adjusting concentration of the polystyrene microspheres, the scattering coefficient ${\mu _s}$ of the turbid water is determined. It is known well that Indian ink with different concentrations is used as an absorber, which can eliminate multiple scattered photons that constitute the major part of long-path photons. For this reason, the radiation intensity detected with different concentrations of Indian ink can be obtained by subtracting the detected radiation intensity without Indian ink, and the tail component is consequently acquired in the range-gated technology. A range of orthogonal polarization image groups is necessary for all three polarization imaging, obtained by adjusting the angles of PSA. The twenty-eight groups experiment results by four imaging methods, performed in Fig. 6.
Fig. 6. The experimental results with intensity imaging, P-G, P-D, and P-D range-gated, at particle sizes of d = 0.1 µm, 0.6 µm, 1.1 µm, 1.5 µm, 2.0 µm, 2.5 µm, and 3.0 µm, the ${\mu _s}$ = 0.61 cm-1 and ${\mu _a}$ = 0.047 cm-1.
It can be seen from Fig. 6 that strong scattering would cause intensity imaging to wrap in mist, but parts of backscattered light can be filtered out via active polarization imaging methods. The grey value difference in the target and background area is maximum for P-D range-gated, and P-D imaging comes second, indicating more imaging dimensions can better improve the imaging contrast, which is reflected in attenuating background gray. More importantly, the enhancement of active polarization imaging methods shows a correlation with particle sizes, such as the particle sizes of d = 0.1 µm, 1.5 µm, and 2.5 µm. Here, five areas marked by the red and white outline in upper left corner of Fig. 6 are specifically selected to calculate contrast to avoid the influence of illumination nonuniformity. It can be found and the curves trend in Fig. 7(a) is the same as the simulation result in Fig. 4. For a particle size of d = 0.1 µm, only the contrast C = 0.75 with P-D range-gated imaging is the highest, and others are close to intensity imaging. When the particle size of d varies from 1.1 µm to 2.5 µm, only the contrast of intensity imaging decreases, however, the other three methods are remarkably effective. For a particle size of d = 3.0 µm, the result with all polarization imaging methods degrades.
Fig. 7. The contrast and improvement of intensity imaging, P-G, P-D, and P-D range-gated at various particle sizes (d = 0.1 µm, 0.6 µm, 1.1 µm, 1.5 µm, 2.0 µm, 2.5 µm, and 3.0 µm). (a) Contrast, (b) cumulative bar chart. The heights of the three colors bars represent the contrast enhancement of different methods relative to intensity imaging.
To quantify the enhancement effect of different methods compared with intensity imaging, In Fig. 7(b), the relative improvement is given by cumulative bar chart, it can be seen the height of the blue column and orange column are higher than other colors at d = 0.1 µm and d = 2.5 µm, which indicates the significance with P-D imaging and P-D range-gated imaging. Besides, P-G imaging and P-D imaging all presented a trend that first increases and then decrease. In the experiments, the actual polystyrene microsphere scatterer particle size distribution cannot meet the rational value, and there is an inevitable error in the selection of Indian ink in the control time gate. These factors result in a lower experimental contrast improvement than the theoretical value.
4. Influence mechanism
In previous sections, the non-monotonic law between the particle size of scatterer and polarization imaging contrast is given and proved. The influence mechanism needs to be discussed with regard to noise, including backscattered light and target diffuse light.
4.1 Intensity analysis of noise light
Under independent scattering conditions, the backscattered and forward scattered light fields are formed by the superposition of single particle scattering. It is important to note that the Stokes vectors of individual photons in the Monte Carlo simulation are single instantaneous “independent light streams” [19,28], the ensemble of the individual photons’ Stokes parameters is called the cumulative Stokes vector. Consequently, we calculate the cumulative weight I of target diffuse light and backscattered light within different scattering particle sizes through polarization-tracking Monte Carlo program. As shown in Fig. 8(a), the cumulative weight I of backscattered light shows a trend from decreasing to increasing and then falling as the particle size increases, while target diffuse light is inverse, which shows the intensity component of noise is non-monotonic with particle size. Meanwhile, to determine the composition of noise light, the intensity weight of backscattered light in the total noise is analyzed. It is well known that the anisotropy parameter (g) is used to characterize the distribution of the scattering field, which is added as a comparative reference. Referring to the imaging contrast curve in Fig. 4 at different particle sizes, it can be found that only the contrast with P-D range-gated imaging is entirely negatively correlated with g and proportional with the weight proportion of backscattering, both indicating this method depends more on the intensity influence of backscattered light; for other methods, when the particle size of d < 0.6 µm, the contrast enhancement is positively correlated with g, while it shows a strong negative correlation when d > 0.6 µm. It is suggested that P-G and P-D imaging are affected not only by the intensity field of the two types of noise signal but also by the polarization field.
Fig. 8. Influence mechanism in terms of the intensity of target diffuse light and backscattered light. (a) The total cumulative weight I of noise light. (b) Correlation between the weight proportion of backscattering and anisotropy parameters. The total number of incident photon packets is 106, and the weight of the incident packet is w = 1.
4.2 Polarization analysis of noise light
With regard to the evolution of polarized light, the location and polarization state of each photon packet are tracked through Monte Carlo simulation. Here, linearly polarized photons (one million of each polarization state for each simulation) are propagated perpendicular to the face of a slab of scattering media, and an initial Stokes vector is used to express the photon’s initial polarization state. The polarization of each photon needs to be constantly corrected, and Stokes vector is updated after each event. As shown in Fig. 9(a) and (b), with Poincaré sphere, the sizeable yellow sphere on the right represents the polarization state of the incident light, which is located on the east side of the equatorial circle. Each photon polarization state with target diffuse light and backscattered light is plotted on the surface of Poincaré sphere. To more intuitively show the evolution trend of different polarizations, the photons when the Stokes vector Q < 0 are colored by red, and others when Q$\ge $0 are colored by blue in the following Fig. 9. Meanwhile, the end view and front view of Poincaré sphere are given, which helps us understand point distributions with 0°, 45°, 90°, and 135° linear polarization and circular polarization.
Fig. 9. The description of polarization states of two types of noise light with Poincaré sphere. (a) Backscattered light. (b) Target diffuse light. The total number of incident photon packets is 106, and the initial weight is w = 1. When the Stokes $\boldsymbol Q < 0$ are colored by red, and others when $\boldsymbol Q \ge 0$ are colored by blue.
To quantitatively characterize the evolution of the polarization state of noise light, the density numbers of the red polarized photon packets R-N and the blue polarized photon packets B-N are calculated, and then the cumulative Stokes Q are analyzed, which can be expressed as Eq. (7) and Eq. (8), ${Q_i}$ and ${w_i}$ represents the final obtained Stokes vector and weight of a detected photon packet respectively.
At the same time, according to the theory of active polarization imaging, the proportion of negative cumulative Q in the total cumulative is analyzed to measure the degree of conversion of polarized light converted into cross-polarization, which is defined as Eq. (9)
For backscattered light, the point distribution state of Poincaré sphere at five particle sizes can be seen in Fig. 9(a), and the data is shown in Table 1. With a particle size of d = 0.1 µm under the Rayleigh regime, the point density on the entire sphere is the highest. From the Poincaré-End viewer, the photon packets remain along the equator of Poincaré sphere, and the point density in the left red hemisphere is quarter of that in the right blue hemisphere, which indicates that it is a medium with an absolute dominance of backscattering, and backscattered light is only converted to linear polarization directions. The proportion of negative cumulative Q in the total cumulative is only 10.68%, which characterizes the predominance of backscattering parallel to the direction of polarization of the incident light, for a result, the enhancement of polarization gating and polarization difference is extremely poor. When the particle size d is larger than the incident wavelength, the point density on the entire sphere decreases, which proves that backscattering is gradually attenuated. Meanwhile, we can see that backscattered light is distributed over the whole sphere and the trend gradually intensifies as the particle size increases. As shown in Fig. 9(a) Poincaré-End, the red points in the left hemisphere approach the center of the circle, which explains backscattered light is transformed into other linear polarization. It can be seen that the proportion of negative cumulative Q in the total increases from 19.85% at d = 0.6 µm to 41.79% at d = 2.5 µm, as shown in Table 1, which indicates that cross-polarization part of backscattering increased significantly. While further analyzing the Fig. 9(a) sphere-front viewer, oceans of points are distributed near the north and south poles of the sphere, and the red points located in the left hemisphere are closer to the poles compared with the blue points in the right hemisphere, this trend demonstrates that the conversion of backscattered light to circular polarization is gradually enhanced, and there are more cross-polarization converted to circular polarization. Under this particle range, P-G imaging and P-D imaging to suppress the scattering noise are the most effective. When the particle size is close to large particle Mie region, the proportion of negative cumulative Q is more than 39%. Due to the intensification of forward scattering, more target diffused light constrains the improvement of imaging contrast.
Table 1. Statistical analysis of the polarization states of backscattered light
For target diffused light, the point distribution state of Poincaré sphere with different particle sizes is shown in Fig. 9(b) and Table 2. At the particle size of d = 0.1µm, the point density in the sphere is the lowest, and the forward scattering is approximately ignored. However, the proportion of negative cumulative Q in the total cumulative is the highest at 30.78%, it can be found that the conversion of forward scattered light to the orthogonal polarization is strong. As the particle size d further increases, all of the points are concentrated near the large yellow sphere of the incident polarization, while the red points located in the left hemisphere are almost absent. It is worth noting that the point density of the target diffused light when d = 1.5 µm is the highest, but the proportion of negative cumulative Q is minimum, only 0.04%, which illustrates that almost all of the target diffuse light maintains the same polarization as the incident light. Overall, the effect of eliminating target diffuse light is approximately negligible for three polarization imaging methods.
Table 2. Statistical analysis of the polarization states of target diffuse light
4.3 Summary of influence mechanism
As shown in the experimental results in Fig. 7, There is a non-monotonic law between the active polarization imaging contrast and the particle size of scatterers. As has been previously analyzed in sections 4.1 and 4.2, the influence mechanism is not only closely related to the intensity of noise signal but also polarization. In the Rayleigh region, the target diffused light intensity can be almost ignored, and backscattered light is uniformly transformed to other linear polarizations, which substantially weakens the enhancement with P-D and P-G imaging. While P-D range-gated imaging is in the optimal working conditions because of the time feature of backscattered signal; in the small particle Mie region, as more backscattered light is evolved to other linear, circular, elliptical, and partial polarizations, the noise suppression is gradually strengthened for all active polarization methods; in the large particle Mie region, despite small amounts of backscattered light is transformed into others inconsistent polarization, more target diffused light, whose polarization and optical path are similar to target ballistic light, finally results in no obvious effect for three active polarization imaging methods.
5. Discussion
Considering the realistic underwater environment, the particle size of scatterers is in polydisperse scattering distribution. Researchers measured the particle-size distribution (PSD) from coastal water and the open ocean, and the two-component model was proved to be an adequate PSD model for use in backscattering calculations providing satisfactory results [29]. Therefore, to better explore the influence laws of the particle size on underwater polarization imaging, a polydisperse medium consisting of two scatterers is modeled for Monte Carlo simulation, the particle sizes of polydisperse scatterers correspond to the large particle d = 3.0 µm (Mie forward-scattering regime) and the small particle d = 0.1 µm (Rayleigh regime), respectively. The heterogeneity of environment can be adjusted by changing the weight of different particle sizes in the total scattering. We set the number ratio of large particle (d = 0.1 µm) in total scatterers be k, varying from 0% to 100% in intervals of 10%, and simulate the imaging contrast of the four polarization imaging methods, as shown in Fig. 10.
Fig. 10. The contrast of four imaging methods with the number ratio w of large particle in total scatterers, the large particle d = 3.0 µm (Mie forward-scattering regime), and the small particle d = 0.1 µm (Rayleigh regime), the scattering coefficient ${\mu _s}$ = 0.61 cm-1, and the absorption coefficient ${\mu _a}$ = 0.047 cm-1.
As one notices in the figure, the best imaging contrast is still achieved through P-D range-gated method, and the contrast of P-D imaging is the second highest. As the number ratio k rises, by comparing the longitudinal spacing between different curves, the improvement with P-D imaging in image contrast becomes more apparent. On the contrary, the effect of P-D range-gated is attenuating. This opposite trend occurs since more large scattering particles result in more scattered light with other linear, circular, elliptical, and partial polarizations, on the other hand, with the accumulation of forward scattering due to more large scattering particles, reduced transmission difference between noise and useful signal limits the imaging effect.
Overall, P-G imaging, P-D imaging, and P-D range-gated imaging are more feasible and applicable for environments satisfying two optical characteristics: the incident beam is strongly backscattered and is converted to an inconsistent polarization. However, the actual environment consisting of multi-size scatterers is complex and diverse, in addition, the observation target usually has rich detailed information. Therefore, establishing polarization detection model that is more in line with practical application scenarios is worth exploring.
6. Conclusion
In highly scattering underwater, the intensity and polarization field of backscattered light and target diffuse light are the critical factors affecting active polarization imaging. Due to the coupling effect of scattering, the cumulative scattering field can be approximately equivalent to the superposition of a single scattering field and finally results in the evolution of noise light. On the one hand, it is reflected in the intensity component of noise light, and the other is performed in the polarization. The experiments and simulations results in this paper indicate that polarization difference range-gated imaging is suitable for an environment where the particle size is sub-wavelength. On the contrary, polarization gate imaging and polarization difference imaging are more effective in approximately 3∼5 times incident wavelength environment, and the effect depends not only on the relative intensity of two noise signals but also on the conversion to cross-polarization, elliptical polarization, and partial polarization. With forward scattering dominating, separating and deconstructing target diffuse light is the cornerstone to improving imaging distance and imaging clarity.
We hope the findings will maximize the effectiveness of existing active polarization imaging methods and provide new theoretical support for the innovation of polarization imaging technologies. In the future, various polydisperse mediums closer to turbid water and targets with more elements are worth considering, besides, more image evaluation parameters will be used to measure image quality more accurately.
Funding
National Natural Science Foundation of China (61890961, 62127813, 62001382); Natural Science Basic Research Program of Shaanxi Province (2018JM6008).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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