Comparative study of differential polarization imaging using linear and circular polarization in different scattering medium

TIAN Heng， WU Yelin， TIAN Jingjing， ZHANG Bo， ZHU Jingping

(1. School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, China；2. Shaanxi Key Lab of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049, China)

Abstract： Differential polarization imaging has been widely used to selectively probe the target embedded in turbid medium. A thorough understanding of image quality involved in differential polarization imaging is essential for practical use. Using polarized light Monte Carlo simulations, it has been investigated how the state of polarization of incident light and the optical properties of scattering medium affect the image contrast. The contrast for linear polarization is similar to that for circular polarization in the isotropic medium comprising small-particles. The image quality is more pronounced for circular polarization in the isotropic medium containing large-particles and the birefringent medium. Furthermore, differential polarization imaging provides better image quality for the birefringent medium compared with isotropic medium. The effect of particle-size and birefringence on the polarization characteristics of target light and backscattered light is investigated. With the help of numerical results, the polarization characteristics of target light and backscattered light, the image quality is well explained in the turbid medium mentioned above.

Key words： polarization imaging； target detection； Monte Carlo simulation； scattering； birefringence

0 Introduction

Clear image of target embedded in turbid medium, such as ocean and biological tissue, plays a pivotal role in scientific research. The image quality could be significantly degraded due to absorbing and scattering caused by the particle present in the turbid medium[1]. In order to eliminate such negative influence on target detection, various optical methods for image recovery, such as time gating[2], coherence gating[3]and frequency domain gating[4], have been introduced to extract the light that contains the target information called effective light from the background illumination. The investigation has demonstrated that polarization information could provide a powerful tool to reveal the target hidden in a turbid medium, and polarization imaging technique has been well developed and widely applied[5-11]. Differential polarization imaging, a valid, simple and inexpensive method, has been proposed to accomplish the enhancement of visibility of the target in the turbid medium[12-13]. The configuration for active illumination consists of illuminating the scene with a totally polarized beam and acquiring two images： the first one, called the co-polarized component, is formed with the fraction of light having the same state of polarization as the incident illumination; and the second one, called the cross-polarized component, is formed with the fraction of the light in the orthogonal state. From the two images, the differential polarization image could be obtained.

Differential polarization imaging has been well documented as an effective method for medical diagnosis of skin diseases[14], discrimination of targets[15], ghost imaging[16]. However, the feasibility of this approach would depend upon the dissimilar of polarization properties between the target light and backscattered light which, in turn, are influenced by a number of parameters such as the state of polarization of incident light, type of target, size, concentration, and refractive index of scatterer present in a turbid medium. Several investigations have been conducted in the past to interpret the relations between the polarization properties and these parameters. Ni and Alfano reported on the effect of particle size on the state of polarization of the backscattered light for linear and circular polarization[17]. Yao demonstrated that the type of target affects the polarization image[18]. Shukla revealed that the refractive index of the scatterer on the polarization imaging through turbid media[19-20]. These researches contribute to our understanding of differential polarization imaging. In order to understand the effective imaging method adequately, it is rather nontrivial to explore the factor that affects differential polarization technology by carrying out studies on the evolution of scattered light in detail.

In this work, the effects of particle size on the effectiveness of differential polarization imaging have been investigated through Monte Carlo simulation with linearly and circularly polarized light[21-23]. The depolarization behavior of target light and backscattered light was investigated to show the plausible explanations for the image quality. In addition, birefringence was considered in the simulation experiment. The investigation might be beneficial to the implementation of differential polarization imaging.

1 Parameter setting

The propagation of polarized light in turbid medium has been simulated by using Monte Carlo method with Stokes Mueller formalism[21]. A target, a reflective parallelepiped whose size is 0.2 cm×0.2 cm×0.1 cm, was placed in the semi-infinite turbid medium simulated by the suspension of monodispersed polystyrene microspheres in water. The refractive indexs of particle and surrounding were 1.59 and 1.333. According to the criteria of particle size[19], particles of 0.11 μm and 2.00 μm in diameters were selected as small-particle and large-particle, respectively[20,24-26]. The polarized light with a wavelength of 632.8 nm was injected into the turbid medium vertically from the upper boundary of medium. The polarization state of linearly polarized light is [1 1 0 0]T, and the polarization state of circularly polarized light is [1 0 0 1]T. After undergoing series of scattering events and collision behaviors in the turbid medium, the incident light emerged from the turbid medium through the upper boundary carrying the target information. The number of photon was 5×107in the simulation to enhance the precision of simulation and reduce the time consuming.

2 Results and discussion

2.1 Effect of isotropic medium on image quality

In Fig.1(a) and (b), the target images are shown for the isotropic medium prepared by using polystyrene microspheres of 0.11 μm in diameter (the anisotropy parametergis 0.092) with the optical thicknessτof 1.00 (τ=μs×l, whereμsis the scattering coefficient of turbid medium, andlis the image distance defined as the distance between the top surface of target and the upper boundary of turbid medium). The simulated result of the target embedded inside the turbid medium is shown in Fig.1(c) and (d), containing polystyrene microspheres of 2.00 μm in diameter (g=0.914) having a value ofτ=2.50. From Fig.1, it can be seen that the background illumination of the intensity images is significantly brighter than that of images acquired by differential polarization imaging. The results fully indicate that compared with intensity imaging, both differential polarization imaging with the use of linearly polarized (L-PD) light and differential polarization imaging with the use of circularly polarized (C-PD) light could eliminate the background illumination and extract the effective light to improve the quality of vision in turbid medium.

Fig.1 Intensity image (color online) (a) and L-PD image (b) in isotropic medium with particle diameter of 0.11 μm. Intensity image (c) and C-PD image (d) in isotropic medium with particle diameter of 2.00 μm

To investigate the evolution of image quality in the turbid medium with small-particles or large-particles, the images obtained by L-PD and C-PD were recorded respectively. Image contrast calculated by (Imax-Imin)/(Imax+Imin) provides a quantitative criterion to evaluate the imaging quality. Here,Imaxis the average intensity of the black square, andIminis the average intensity of the four white rectangles in the image. According to this method, a high value of image contrast corresponds to the target image with better visibility.

The contrast curves are obtained by L-PD and C-PD versus the value ofτin the isotropic medium (Fig.2). The optical thickness is as a function ofμsbecause the image distance keeps constant in all the simulations. From the contrast curves, it can be concluded that the visibility by using L-PD is equivalent to that using C-PD in the medium containing small-particles while the image quality is better for C-PD in the medium containing large-particles.

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Degree of polarization (DoP) of backscattered light and target light calculated by (I‖-I⊥)/(I‖+I⊥) could provide a possible detailed explanation for the contrast profiles in terms of polarization characteristics because they form the effective light and background illumination.I‖is the intensity of the light having the same polarization state as the incident light, andI⊥is the intensity of the light having the opposite polarization state as the incident light. For the sample prepared by using small-particles, the variations of DoP for linear and circular polarization at 2.00 optical thickness is shown in Fig.3.

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The curve presented here is the average value of five distribution curves along the vertical direction. The measurements of target light for the two kinds of incident light are similar in the target region, whose average value is 0.98. Outside the target region, the value for linearly polarized light is 0.05 greater than that for circularly polarized light. The backscattered light exhibits slightly high degree of depolarization for linear polarization in the entire region and the difference is 0.04. The effective light containing the target information consists of the target light in the target region. The results show that the same amount of effective light has been retained by L-PD and C-PD. Furthermore, the forward-scattered light, namely the target light with multiple forward scattering events, is also an important component of background illumination. The elimination of forward-scattered light would be slightly efficient for C-PD while L-PD could suppress slightly more backscattered light. DoP shows that the amount of background illumination caused from forward-scattered light is qualitatively similar to that caused from backscattered light by using L-PD and C-PD. As a result, the capacity of L-PD in enhancing image quality is consistent with that of C-PD.

The curves of DoP of target light and backscattered light under the condition ofτ=2.00 in the isotropic medium containing large-particles are shown in Fig.4.

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Linear polarization could achieve higher DoP of target light than circular polarization in the target area. The greater depolarization of linearly polarized light is shown in the Fig.4, which indicates that circular polarization has a better ability in reserving effective light by using differential polarization imaging. DoP of target light outside the target area for linear polarization is equivalent to that for circular polarization. This result indicates that the contribution of effective light on image quality for C-PD is noticeable. DoP of backscattered light under the condition of linear polarization is noticeable lower than that for circular polarization. The measurement indicates that L-PD takes dominant role in attenuating the degradation of imaging quality caused by backscattered light. However, due to the main scattering behavior the photons undergoing in the medium containing large-particles is forward-scattering, backscattered light has limited attenuation on the image quality[21]. Consequently, even though L-PD leads to elimination of backscattered light, the better contrast could be obtained by C-PD thanks to the better reserve of the effective light.

2.2 Effect of birefringent medium on image quality

Generally, turbid medium, such as biological tissue, exhibits attractive birefringence properties. It is necessary to make systematic analysis of the image quality in the birefringent medium for real-world applications. In accordance with the characteristic of biological tissue, the positive birefringent medium with Δn(the birefringent value) of 1.0 × 10-4is set in the simulation process[27]. The birefringence has a slow axis along the incident direction of light. The image quality for L-PD and C-PD in the birefringent mediums consisting of large-particles and small-particles is illustrated in Fig.5. It should be noted that the image quality of C-PD is better than that of L-PD. The comparison demonstrates that C-PD could suppress the effect of background illumination and enhance the image quality adequately.

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DoP of target light and backscattered light in the birefringent medium with particle diameter of 0.11 μm is illustrated in the Fig.6.

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In the target area, linear polarization provides slightly higher DoP of target light than circular polarization. Outside the target area, at this value ofτ=2.00, the difference in the average value of DoP for linear and circular polarization is 0.25. The results demonstrate that the forward-scattered light for linear polarization could maintain polarization state better as compared with circular polarization. The average value of DoP of backscattered light for linear polarization 0.37, is greater than the value for circular polarization which is 0.07. The superiority in depolarization for circular polarization is presented here. The fact that the similar distribution of DoP of target light in the target area leads to that the nearly same amount of effective photons could be recorded by L-PD and C-PD. Whereas, circular polarization could filter out 2 times as much forward-scattered light and 3 times as much backscattered light as linear polarization approximately. Consequently, C-PD gives better image quality in the birefringent medium with particle diameter of 0.11 μm.

DoP of target light and backscattered light for the birefringent medium containing large-particles is shown in the Fig.7. In the entire area, DoP of both target light and backscattered light for linear polarization is greater than that for circular polarization. The difference of target light in the average value of DoP between linear and circular polarization is 0.1 in the target area and in the range of 0.2 to 0.5 outside the target area. For backscattered light, the value was worked out to be 0.25. It implies that the backscattered light preserves its polarization better for linearly polarized light. From the profiles, L-PD could retain more target light than C-PD. However, comparing with the retention of target light, the rejection of background illumination would be done more efficiently by using C-PD because of the effect of background illumination caused by forward scattering. What’s more, C-PD provides a significant improvement in the elimination of backscattered light. The image contrast with C-PD is significantly pronounced due to the contributions of target light and backscattered light.

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2.3 Comparison of image quality between isotropic and birefringent media

For purpose of presenting the difference of the image quality obtained by PD in the isotropic medium and birefringent medium, the contrast of L-PD and C-PD image in the medium containing small-particles is shown in Fig.8. The better detection for birefringent medium is observed by differential polarization imaging. Furthermore, the superiority in enhancing image quality for circularly polarized light is more distinguishable.

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The distribution trend of contrast was considered according to DoP of target light and backscattered light, as shown in Fig.9.

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Obviously, the birefringence leads to that target light depolarizes faster. Furthermore, the difference of DoP of target light between the two samples is more pronounced for circular polarization, as compared to linear polarization. In agreement with the case of target light, DoP of backscattered light in the isotropic medium is greater than that in the birefringent medium for both linear and circular polarization and their difference are 0.3 and 0.6, respectively.

The distributions presented here demonstrate that the extraction in effective light in isotropic medium is less efficient while the elimination in backscattered light is more distinguishable in the birefringent medium for either linear or circular polarization.Considering DoP alone, the number of filtered backscattered light is 17.5 times that of linearly polarized reserved target and 23 times that of circular-polarized reserved target. What’s more, the advantage of birefringence in filtering out outside the target region entails better image quality for birefringent medium. Consequently, for small-particles, differential polarization imaging could yield noticeable improvement in contrast and the superiority for circular polarization is more pronounced.

The contrast profiles for L-PD and C-PD images in the isotropic medium and birefringent medium with particle diameter of 2.00 μm displayed in Fig.10 indicates that the contrast relies on the polarization state. For linear polarization, no appreciable difference is found in image quality between the isotropic and birefringent medium. On the contrary, for circular polarization, the image quality is less marked in the isotropic medium as compared with that in the birefringent medium. By comparing Figs.8 and 10, the insignificant difference in contrast between the isotropic and birefringent medium is observed for medium with large-particles using either linear or circular polarization.

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To understand the variation of image quality,the DoP of target light and backscattered light in isotropic birefringent medium with large particles of 2.00 optical thickness is shown in Fig.11. In the isotropic medium, DoP of target light remains nearly constant in the enter pixel and has a great value using both linearly and circularly polarized light. The corresponding values for the birefringent medium are 0.92 and 0.85 with linear and circular polarization in the target region. Further, outside the target region, DoP of target light for circular polarization destroyed faster than that for linear polarization. In contrast to the target light, the computed value of DoP of backscattered light is complex and relies on the polarization state. For linear polarization, the value in the isotropic medium is lower than the value in the birefringent medium. However, DoP is greater than that in the birefringent medium for circular polarization, and the difference is about 0.3. These results show that both L-PD and C-PD exhibit the significant advantages in retrieving image information and eliminating backscattered light in the isotropic medium. However, in the birefringent medium, L-PD could filter out more background illumination caused by forward-scattering. As discussed earlier, in the turbid medium with large-particles, forward-scattering is the main scattering behaviors that the photons undergo. This means that the forward-scattered light makes dominant contribution to reducing the image quality. As a result, L-PD resulted in improved contrast in the birefringent medium because of the superiority of eliminating the forward-scattered light. What’s more, in the birefringent medium, C-PD could eliminate more backscattered light in addition to the greater efficiency in removing the forward-scattered light. Considering comprehensively the contribution on image quality of target light and backscattered light, C-PD offers a better contrast in the birefringent medium.

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3 Conclusions

The effects of particle size, birefringence and polarization state on the imaging quality of differential polarization imaging are studied by Monte Carlo simulation. In the isotropic medium, the image quality with linear polarization is the same as that with circular polarization for smaller-sized light while circular polarization yields better image quality for larger-sized scatterer. For the birefringent medium composed of either larger-sized scatterer or smaller-sized scatterer, circularly polarized light leads to the marked enhancement of contrast as compared with linearly polarized light, which indicates the contrast being not related to the particle size. Differential polarization imaging leads to better image quality for both linear and circular polarization in the birefringent medium, as compared to the case with isotropic medium, without caring about the particle size. With the aid of the distribution of DoP of target light and backscattered light, a plausible reason for the simulated results was provided according to the amount of background illumination and effective light. The investigation makes clear the relationship between the image quality and the parameter of turbid medium as well as the polarization scheme, which gives useful guidance for the application of differential polarization imaging and the excellent imaging results could be obtained.