Obtaining clear images of a target embedded in a turbid medium by means of optical techniques has potential applications in atmospheric remote sensing, underwater imaging, and biomedical diagnostics. The main difficulty encountered in optical imaging is the fact that scattered light leads to image blurring. There has been a growing interest in developing novel approaches to improve the contrast and resolution in optical scattering environment. For instance, time gating,^[1] coherence gating,^[2] and frequency domain gating^[3] have been proposed to extract unscattered or weakly scattered photons based on the parameters of photon such as propagation time and phase. Recently, polarization imaging has been widely utilized to detect the target embedded in the turbid medium^[4–10] because of the simplicity of experimental setup such as polarimeter^[11] and the capability to reject unwanted photons. The feasibility of polarization imaging is sensitively influenced by the difference in the polarization state of light experiencing different scattering events, which depends upon a variety of optical properties of the turbid medium, including the scattering coefficient, the absorption coefficient, the anisotropy factor, the size of scatterer, and the refractive index.^[12] The relationship between the polarization characteristics of scattered light and the optical properties of turbid medium is quite complicated. Thus, investigating the influence of the variations in optical properties of turbid medium on the validity of polarization imaging is required for its implementation and several studies have been carried out by means of theoretical analysis, Monte Carlo simulation, and experimental investigation.^[13–17]

Generally, birefringence is a prevalent phenomenon exhibited in a turbid medium, especially in biological tissue.^[18] Detailed analyses of the evolution of polarized light in a birefringent medium has also been made. In Ref. [19], the authors developed Monte Carlo algorithm to investigate the spatial distribution of the polarization state of the light backscattered from the birefringent turbid medium for the cases of linearly and circularly polarized incident light. They also presented the dependence of the polarization characteristics of light on the birefringent parameters.^[20] Otsuki proposed a double-scattering model that represents the geometry of photon propagating in turbid infinite plane medium to study the multiple scattering of polarized light in a birefringent turbid medium.^[21] Baravian et al. focused both experimentally and theoretically on the relationship between the backscattered Mueller matrices and the birefringence of turbid medium.^[22] Through simulation and experiment, Alali et al. examined the symmetry properties of the transmission Mueller matrix in the bilayered medium with different uniaxial orientation in each layer. These research results will be of benefit to the applications of polarization imaging.^[23]

Polarization-based range-gated imaging (PR), which is the combination of polarization–difference imaging and range-gated technology, has been developed to further enhance the visibility of target by suppressing the background photons.^[24] When PR is utilized for target detection in turbid medium, additional background photons could be filtered out by polarization–difference imaging after partial background photons being filtered out with the aid of range-gated technology.^[25] The optical parameter of turbid medium also affects the feasibility of PR. Consequently, it is necessary to make the systematic analysis of the influence of these parameters on the image quality using PR. We have concluded that PR is significantly affected by the particle size and the polarization state of incident light for the isotropic medium in previous studies.^[26] In this work, we present a quantitative study of the relation between the size parameter of scatterer and the image quality obtained by PR in the birefringent medium though Monte Carlo method so that a better understanding of the effective method for target detection could be exhibited, which may provide useful insights for using PR.

The rest of this paper is organized as follows. In Section 2, we briefly describe the main process that the polarized light undergoes in the birefringent scattering medium. Section 3 contains the observed dependence of contrast of PR on the birefringence of the medium, the polarization state of incident light, and the size of scatterer. Plausible explanations for this dependence obtained from the measured distribution of degree of polarization (DoP) or degree of depolarization (DP) of the polarized light in the scattering medium are also presented in this section. The conclusions are presented in Section 4.

In our simulation, from the respect of the reliability of the results and the efficiency of the simulation process, the photon number was set to 5×10⁷. Each result was written in the form of matrix whose size is 300 × 300 and presented as a two-dimensional image with 2 cm on each side.

In Fig. 2, we show the simulated results of the target embedded inside the birefringent medium comprising smaller-size scatterers of 0.11 μm in diameter when the value of reduced-scattering coefficient ( was 0.39 and the value of optical thickness τ was 1.50 (the product of the imaging distance and the scattering coefficient). Figure 2(a) shows the intensity image and the image obtained by PR using linearly polarized photons (L-PR) is shown in Fig. 2(b). The intensities of both the intensity image and the image obtained by L-PR (L-PR image) are normalized. From Fig. 2, it can be seen that there is no distinct difference between the background and the target in the intensity image so that it cannot discriminate the target from the background, while the target is significantly brighter than the background in the L-PR image. From this, the target could be retrieved by means of L-PR.

Fig. 2.

	Figure Option ViewDownloadNew Window
	Fig. 2. (color online) Images obtained by intensity imaging (a) and L-PR (b) in the birefringent medium composed of 0.11-μm diameter scatterers having a value of τ = 1.50.

The image quality could be quantitatively evaluated by the image contrast defined as (I_max–I_min)/(I_max+I_min). Here, I_max and I_min represent the intensities of target and background calculated by averaging the intensity of the target center area marked by the black square containing 100 pixels and the intensities of the four designated areas containing 50 pixels, respectively, marked by the white rectangles outside the target area in Fig. 2(a). The image quality will be better when the image contrast has a greater value. To facilitate the comparison process, the regions selected to calculate the image contrast were kept unchanged under different conditions. In Fig. 3(a), we present the measured contrast profiles versus the optical thickness for intensity imaging and L-PR in the birefringent medium prepared using 0.11-μm diameter microspheres. The location of the target is fixed in the turbid medium so that the variation of optical thickness is caused by changing the scattering coefficient resulted from the variation of scatterer concentration. By comparing the contrast profiles, it should be noted that the contrast for L-PR is marginally higher than that obtained by intensity imaging in the entire range of optical thickness. The comparison demonstrates the superiority of the combination of polarization information and range-gated technology in the elimination of the background light and the enhancement of the contrast in the birefringent medium adequately.

Fig. 3.

	Figure Option ViewDownloadNew Window
	Fig. 3. (color online) Variation of contrast with optical thickness acquired using intensity imaging (I), L-PR, and C-PR in the birefringent medium composed of 0.11-μm diameter scatterers.

Linearly and circularly polarized light, which are two types of incident light, are commonly utilized for active polarization imaging. In order to present their evolution in the birefringent medium, the images obtained by PR using circularly polarized photons (C-PR) were also recorded for the two samples with small-particle as well as large-particle respectively at each optical thickness and compared with the L-PR images under the same condition. The comparison of the contrast profiles for L-PR image and the image obtained by C-PR (C-PR image) in the birefringent medium containing 0.11-μm diameter scatterers is displayed in Fig. 3(b). We observe the variation in image contrast depends on the optical thickness. At lower values of τ (= 0.25–3.50), the contrast is observed to be marginally better for C-PR. On the contrary, beyond a value of τ = 3.50, the improvement of contrast is less pronounced for C-PR as compared with L-PR. Furthermore, there is only a marginal difference in contrast between the cases of linearly and circularly polarized light.

Investigating the distributions of DoP and DP could provide an easy and effective way for accounting for the trend in distribution of image contrast. DoP is calculated by (I_∥–I_⊥)/(I_∥+I_⊥).^[7] I_∥ and I_⊥ are the intensities of the light parallel and perpendicular to incident polarization for the case of linear polarization and the intensities of the light of the same and opposite helicity as the incident light for the case of circular polarization. DP is calculated by 1–DoP.^[27] It is pertinent to note that the amount of backscattered light (the light entering the detector before colliding with target due to the backscattering behaviors and making up the main part of background light) filtered out by range-gated technology because the propagation time relies on the photon path and propagation speed, is not related to the polarization state of incident light. As a result, it is polarization–difference imaging that determines the image quality obtained by PR. Note that, in PR, polarization–difference imaging is implemented after the implementation of range-gated technology in PR. Therefore, the polarization characteristic expressed in the form of the images and profiles of DoP and DP should be measured after the implementation of range-gated technology to analyze the image quality.

For the case of lower optical thickness, was set to 0.39. In Fig. 4(a), we show the variations in value of DP of backscattered photons for incident linearly and circularly polarized light at the optical thickness τ = 1.50. Our observation of DP for circularly polarized photons (the mean value is 0.85) is higher than that for linearly polarized photons (the mean value is 0.79) for the entire range of pixel. The greater depolarization of circularly polarized light is presented here. According to the scattering number, the backscattered light could be simplified as two types: the highly scattered light and the weakly scattered light including the single scattered light and the light experiencing a limited number of scattering event.^[7,26] The measured results indicate that polarization–difference technology of C-PR plays a greater role in reducing the effect of backscattered light undergoing multiple scattering events on the image quality after the weakly scattered light being eliminated by range-gated technology. Consequently, the capacity in elimination of backscattered light of L-PR is inferior to that of C-PR.

Fig. 4.

	Figure Option ViewDownloadNew Window
	Fig. 4. (color online) Images and profiles of DP of backscattered light (a) and images and profiles of DoP of target light (b) acquired using linearly and circularly polarized light at the optical thickness τ = 1.50 for the birefringent medium composed of 0.11-μm diameter scatterers.

In addition to the backscattered light, the light reflected from the target (target light) also has significant influence on the image quality. Thus, it is necessary to measure DoP of the target light, which is displayed in Fig. 4(b). In the target area (the range between the 136th pixel and the 165th pixel), the light consists mainly of the weakly scattered part of target light. We observe that the values of DoP for the two cases are in the range of 0.96–0.98. It means that at lower values of optical thickness, the birefringence effect has little influence on the depolarization capacity of the target light. The same extent of depolarization of the target light for linearly and circularly polarized light leads to the result that the amounts of the effective light for both L-PR and C-PR are nearly equal. However, outside the target area, the forward-scattered light (the part of target light which constitutes the background light due to series of forward scattering events) for linearly polarized light keeps polarization state better than that for circularly polarized light because of the multiple scattering. L-PR will not be that efficient to remove the forward-scattered light. Even though the amount of forward-scattered light is less for the case of smaller-sized scatterers,^[26] the trend in distribution of DoP of forward-scattered light is in favor of the better image quality for C-PR. Considering synthetically the polarization characteristics of backscattered light and target light, C-PR gives better image quality at lower values of optical thickness.

For the case of higher optical thickness, was set to 0.97. Figure 5(a) shows that at the optical thickness τ = 3.75, the distributions of DP of the backscattered light in the case of linearly and circularly polarized light are mainly in the range of 0.86 to 0.88. It means that the depolarization capacity of the diffusely backscattered photons retained by range-gated technology for circular polarization compares to that for linear polarization under the condition of larger value of optical thickness. A comparison between Fig. 4(a) and Fig. 5(a) reveals that the increase in the scattering number caused by the increased optical thickness results in the similar extent of depolarization of the backscattered light suffered multiple scattering for linearly and circularly polarized light. Accordingly, the contribution of backscattered photons obtained using linearly polarized light is the same as that obtained using circularly polarized light.

Fig. 5.

	Figure Option ViewDownloadNew Window
	Fig. 5. (color online) Images and profiles of DP of backscattered light (a) and images and profiles of DoP of target light (b) acquired using linear and circular polarized light at the optical thickness τ = 3.75 for the birefringent medium of 0.11-μm diameter scatterers.

Figure 5(b) shows the variations in DoP of the target light. In the target area, DoP of the target light consisting mainly of the light experiencing weakly scattering events for linear polarization is destroyed slower than that for circular polarization. The comparison between Fig. 4(b) and Fig. 5(b) indicates that with the optical thickness increasing, it is obvious that the birefringence effect causes that the target light is depolarized to a larger extent for circularly polarized light. Thus, the amount of the effective light extracted by L-PR is larger than that extracted by C-PR. As observed for the backscattered light, DoP of the forward-scattered light for circular polarization is seen to be similar to that for linear polarization. Consequently, the improvement of image contrast would be more efficient for L-PR as compared to that for C-PR in the birefringent medium made up of smaller-sized scatterers at larger values of optical thickness.

Figure 6 illustrates the variations of image contrast for L-PR and C-PR in the birefringent medium containing large size scatterers with diameter of 2.00 μm. By comparing Fig. 3(b) and Fig. 6, the remarkable difference in contrast for linearly and circularly polarized light is observed in the case of larger-sized scatterers as compared to the case with smaller-sized scatterers. In the entire range of optical thickness, the image quality is seen to be better for C-PR as compared with L-PR. As mentioned above, the image quality could be explained by the measurement of DoP and DP. For the sake of generality, the case of and τ = 3.00 was selected to acquire the measured distribution of DP of the backscattered photon, which is shown in Fig. 7(a). DP in the case of linearly polarized light is observed to be quantitatively similar with that in the case of circularly polarized light. This means that after the short-path backscattered light being filtered out by range-gated technology, the difference in the depolarization capacity of the residual backscattered photons that experience a sequence of small-angle scattering events in both cases is negligible. Consequently, polarization–difference imaging could suppress the equal amount of unwanted photons resulted from backscattering. Consequently, summing up the contributions of the backscattered photon, one can obtain that the target light becomes the key factor to determine the image quality using either L-PR or C-PR for the birefringent sample prepared using larger-sized scatterers.

Fig. 6.

	Figure Option ViewDownloadNew Window
	Fig. 6. (color online) Variation of contrast with optical thickness acquired using L-PR and C-PR (C-PR) in the birefringent medium composed of 2.00-μm diameter scatterers.

Fig. 7.

	Figure Option ViewDownloadNew Window
	Fig. 7. (color online) Images and profiles of DP of backscattered light (a) and images and profiles of DoP of target light (b) acquired using linear and circular polarized light at the optical thickness τ = 3.00 for the birefringent medium composed of 2.00-μm diameter scatterers.

Figure 7(b) shows the distribution of DoP of the target light for the turbid medium having 2.00-μm diameter scatterers. It can be seen that DoP for linearly polarized light is noticeable higher than that for circularly polarized light without the consideration of scattering number over the entire pixel area. The figure shows that depolarization of circularly polarized light is strong in the target area, which implies that linearly polarized light has a distinct advantage in reserving effective light using polarization–difference technology. DoP of the forward-scattered light outside the target area for the linearly polarized light is preserved up to a much higher extent than that for circularly polarized light. This result reveals that compared with L-PR, C-PR could reduce the contribution of forward-scattered light. It has been demonstrated that for the scattering sample prepared using larger-sized scatterers, the forward-scattered light plays a dominant role in degrading the imaging quality.^[26] Furthermore, the difference of DoP of the target light between the two cases is 0.1 in the target area, which is lower than that of the forward-scattered light whose minimum value is 0.15. In other words, although linear polarization has the advantage in reserving the target information as well as circular polarization has the advantage in rejecting the forward-scattered light, the latter entails a greater advantage for the enhancement of image quality. Because of this, the forward-scattered light leads to better image quality for circularly polarized light, as compared to the case with linearly polarized light. These results presented here could explain the significantly pronounced image contrast with C-PR.

In summary, we have studied the image quality obtained by PR in the birefringent turbid mediums composed of smaller-sized and larger-sized scatterers with the aid of Monte Carlo simulation. We have shown that the image quality is significantly influenced by the scatterer size and the polarization state of incident light. For the scattering medium prepared using smaller-sized scatterers, the contrast is related to the optical thickness. C-PR yields better image quality under the condition of lower optical thickness while L-PR could do more efficiently under condition of higher optical thickness. In the medium prepared using larger-sized scatterers, circularly polarized light leads to a more noticeable enhancement of contrast as compared with linearly polarized light for all values of optical thickness. The contributions of backscattered light and target light on the image quality are analyzed by measuring their polarization characteristics expressed in terms of DoP and DP. These give a plausible explanation for the simulated results that could provide guidance for the practical application of PR, such as the selection of the appropriate polarization state of incident light according to the size of scatterer. Our further work will include a systematic investigation regarding the influence of the variation of birefringence and the type of target on PR. The simulated results should also be verified through an experimental study.