1. Introduction

Optical sensing methods are increasingly used to image object embedded in turbid medium, such as fog, cloud, underwater, and biological tissue. It should be noted that when photons propagate through turbid medium, the process of absorption and scattering caused by medium can weaken the intensity and randomize the phase, propagating direction and polarization state of the transmitted light. As a result, optical scattering and absorption in turbid medium could seriously degrade the signal-to-noise ratio for target detection. Many useful optical methods, such as range-gated technology [1–3], frequency-domain method [4,5] and polarized detection technology [6–10], have been developed to overcome this problem. Range-gated technology is well known for its good reliability, large field of view (FOV) and low cost in target detection through scattering or turbid medium [1,2]. It could be able to realize glimmer imaging and suppress backscattering noise effectively. However, the latest research shows that the imaging quality improvement made by tail-gated technology is limited in higher turbidity [11,12]. In this case, target detection thus suffers from reduced signal-to-noise ratio due to superposition of photons reflected from the target and these diffusive ones backscattered from the turbid medium. Those two types of photons above are difficult to differentiate from each other using conventional range-gated technology. Polarization properties of diffusive photons emerging from the turbid medium are investigated to overcome this problem.

Polarization-based method is a powerful tool to image object through turbid or scattering medium [6–10] for their simple use to differentiate photons with different scattering behaviors. The main principle of polarization detection depends on the difference of polarization properties between the target and the turbid medium. However, turbid medium is usually seen as a whole [7,9,13] in conventional polarization detection method. When polarized light is incident on turbid medium, light scattered by the turbid medium can be classified into three categories: ballistic photons, snake photons and diffusive photons. They usually act as noise in the detected signal. In the previous study, light reflected from the man-made target has the same polarization direction with that of most part of light which is backscattered from the turbid medium [8,14,15]. Polarization degree image provides limited improvement by merely cutting diffuse photons. It should be noted that few scattering photons and multiply scattering photons have different polarization properties [16]. Since detailed research on polarization properties of photons with different scattering processes has not been reported, thus we introduce it as a complement to conventional radiation detection.

2. Theory

Polarization is an inherent property of light. Polarization properties of wave is usually presented by Stokes vector (I, Q, U, V) as shown in Eq. (1).

The symbol I is radiation intensity, Q represents difference of radiation intensity between horizontal and vertical polarization direction, U indicates difference of radiation intensity between 45°and 135°direction respect to horizontal axis, V is computed by difference of radiation intensity between left-handed and right-handed circularly polarized light.

Mueller matrix of $4\times 4$array is usually used to completely describe the polarization properties of object. When polarized light interacts with object, the polarized state of that could be changed by object. The process of modulation above can be expressed in a mathematical form, which is shown in Eq. (2).

$S^{\text{'}}$and$S$ indicate Stokes parameters of the scattered light and the incident light respectively. $M$is Mueller matrix of the object which modulates the incident polarization state.

In the water with high turbidity, the signal from target is mixed with the diffusive light when we use the range-gated technology. And under conventional radiation detection, they cannot be separated from each other. To solve this problem, polarization properties of diffusive photons emerging from the turbid medium are studied. We assume that photons undergoing different scattering processes are not coherent. Mueller matrix of turbid medium can be seen as superimposition of photons with different polarization properties. Therefore Mueller-Stokes formalism can be expressed as the sum of photons with different scattering behaviors, which is shown in Eq. (3).

$a_i$ is the proportion of incident light scattered by i times, and $M_i$ is Mueller matrix of the turbid medium associated with i times scattering.

In the case of polarization-based range-gated technology, Mueller matrix of the turbid medium is divided into the front part and the tail one in the simplified form of Eq. (4) to replace that shown in Eq. (3).

$a_f$and $a_t$ are the front part and tail part components and $M_f$ and $M_t$ are the corresponding Mueller matrix in the range-gated technology.

3. Experimental setup

The experimental setup is schematically shown in Fig. 1. The 632.8nm output obtained from a He-Ne laser is expanded to 20mm through the beam expander B firstly, and then it goes through the linear polarizer P1 to be incident on a glass tank. The tank contains deionized water mixed with 20% Intralipid solution (Sino-Swed Pharmaceutical Corp. Ltd., China). Anisotropy scattering g = 0.73 of the Intralipid solution in the case of 632.8nm is given referring to [17]. The refractive index of the Intralipid solution is 1.50 which is measured using method provided by [18]. Laser power meter is placed in a backscattering geometry (~170°with respect to the propagation direction of the incident light) to detect the intensity of the backscattered light emerging from the Intralipid solution. Another linear polarized analyzer P2 is set in front of the lens to select specific polarization state of light. The narrow band filter F is used to pick out light in the central wavelength of 632.8nm. In this experiment, the Intralipid solution is diluted, but still needs to keep a relatively high level of turbidity, considering the limited image quality made by the conventional range-gated technology. A Nikon CD with a cross size of 16mm$\times$18mm is used as a target and suspends in the middle of the tank. The smooth surface of the printed letters “Nik” on the CD is polarized, but the remaining part of the CD is depolarized. A 8 bit CCD (DMK 41BU02, Germany), which replacing the laser power meter, is applied to record images.

 

Fig. 1 The schematic of experimental design for combination of range-gated technology and polarization method.

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In our experiment, the intensity of the backscattered light from turbid medium are selected in four polarization channels: I₀, I₄₅, I₉₀, I₁₃₅, which are subsequently measured in the 0°,45°, 90°,135°directions referring to the horizontal axis. This paper only studies the linear polarization properties because they are easily handled and calibrated. Then polar decomposition of $3\times 3$ Mueller matrix [19] is introduced to describe the linear polarization properties, including depolarization, retardance and diattenuation. The number of the scattering mfp’s is calculated by$N=L{\mu }_s$, where L is the distance from the front surface to the target, ${\mu }_s$is the scattering coefficient. Utilizing the method provided in [20] scattering, we can measure the coefficient${\mu }_s$and the absorption coefficient${\mu }_a$. The method described in [21] can be used to simulate the range-gated technology. Black ink is used as absorber at different concentrations when it added to the Intralipid solution. The absorber eliminates the multiply scattered photons that constitute the major part of long-path photons. Therefore, radiation intensity detected with different concentrations of ink can be obtained from subtracting the detected radiation intensity without the ink, and the tail component is consequently acquired in the range-gated technology. In a word, the higher the absorption coefficient is, the more photons are absorbed, i.e., absorption coefficient is in an inverse ratio to delaying time described in the gate-range technology. In this case, in our simulation of the range-gated technology, we use the absorption coefficient to describe the property of delaying time.

4. Experimental results and discussion

The measured polarization properties of the multiply scattered photons are shown in Fig. 2 in the form of polar decomposition of Mueller matrix.

 

Fig. 2 Polarization properties for the Intralipid solution with scattering coefficient 5.1cm⁻¹ at different absorption coefficient. (a) Depolarization curve for the Intralipid solution with scattering coefficient 5.1cm⁻¹ at different absorption coefficient. (b) Diattenuation curve for the Intralipid solution with scattering coefficient 5.1cm⁻¹ at different absorption coefficient. (c) Linear retardance curve for the Intralipid solution with scattering coefficient 5.1cm⁻¹ at different absorption coefficient.

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In Fig. 2(a), the tendency of the curve demonstrates that the depolarization increases as the absorption coefficient decreases. And the related reason comes from the high contributions in multiply-scattered events. It can be explained that when photons are multiply scattered, the plane of polarization of the scattered light is randomized. This result is in agreement with that acquired from [16]. The previous study neglects the influence of diattenuation and retardance on the depolarization property of photons. However, as shown in Figs. 2(b) and 2(c), our experimental results indicate that diattenuation and retardance sharply monotonically decrease when absorption coefficient decreases. The variation of diattenuation and retardance has their origins in the multiply scattering events. Diattenuation and retardation caused by single scattering and few scattering is obvious [21]. However, diattenuation and retardance is distorted when consequent more collision occurs between high multiply scattered light and turbid medium. When the absorption coefficient is below 4.5mm⁻¹, both diattenuation and retardance become zero, which is of great importance in imaging target in turbid medium. It can be observed that tendencies respectively in Figs. 2(a)-2(c) are completely different with the changes of the absorption coefficient. The influence of multiply scattering events on depolarization is smaller than that on diattenuation and retardance. Diattenuation and retardance become zero when the absorption coefficient is below 4.5mm⁻¹, but the photons are not completely depolarized. The clear changes in the polarization state of those high multiply scattered photons are caused by depolarization, and have nothing to do with retardance and diattenuation in the case of smaller absorption coefficient. It is meaningful to combine the range-gated technology with a simple polarization detection method.

Polarization properties of diffusive photons presented in Fig. 2 are useful for detecting target in turbid or scattering medium. In conventional tail-gated technology, signal-to-noise ratio suffers from superposition of photons scattered in the turbid medium and those reflected from the target in high level turbid medium. The polarization-based range-gated technology is proposed to filter out multiply scattered and few scattering photons in maximum. Result shown in Fig. 2(a) demonstrates that multiply backscattered photons from the turbid medium are almost completely depolarized while man-made object has better polarization maintaining property [22]. Conventional polarization component $\overline{)Q^2+U^2}$ [23] is considered to increase signal-to-noise ratio of the light reflected from the target and the light which is multiply scattered from the turbid medium. However, as can be seen from Figs. 2(b) and 2(c), when the scattering coefficient is below 4.5mm⁻¹, diattenuation and retardance of the multiply scattered photons become zero. It means that, in our experiment, when vertical polarized light is incident on the turbid medium, the plane of polarization of multiply scattered photons does not rotate. This phenomenon results in the same radiation intensity detected respectively at 45°and 135°direction with respect to horizontal axis, i.e., U equals zero. Therefore, we use polarization-difference method based on the phenomenon that diattenuation and retardance of the multiply scattered photons become zero when the scattering coefficient is below 4.5mm⁻¹. It should be noted that Mueller matrix of most man-made objects are diagonal, i.e., they are purely depolarizing [22,24,25]. Polarization-difference image, which we refer in Eq. (5) represents the subtraction of two orthogonal polarization components. With this polarization method, only co-polarization (parallel to the incident light polarization) and cross-polarization (perpendicular to the incident light polarization) need to be measured, which could effectively reduce the times of measurement.

$I_{difference}$ is the obtained intensity by polarization-difference method, and $I_{co}$ and $I_{cross}$ indicate polarization components that are parallel and vertical to the incident polarization respectively.

Images acquired using different detection methods in the diluted Intralipid solution with N = 5.1 are shown in Fig. 3.

 

Fig. 3 Images acquired using different detection methods in the diluted Intralipid solution with N = 5.1. (a) Intensity image (left) and curve along the line with a triangular symbol (right) without added ink. The contrast in the red circle area is 0.125. (b) Range-gated image (left) and curve along the line with a triangular symbol (right) with absorption coefficient 4.5mm⁻¹. The contrast in the red circle area is 0.217. (c) Combination of polarization-difference method and range-gated technology image (left) and curve along the line with a triangular symbol (right) with absorption coefficient 4.5mm⁻¹. The contrast in the red circle area is 0.446.

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Figures 3(a) and 3(b) in the left show the images of the target which is inside of the Intralipid solution with N = 5.3 and absorption coefficient ${\mu }_a$ = 4.5⁻¹mm, under the condition of using conventional intensity detection method and the range-gated technology respectively. Figure 3(c) in the left is the image of target achieved by combining the range-gated technology with the polarization-difference method. The intensity profiles of images along the vertical line where the triangular symbol shown in Fig. 3(a) belongs are presented correspondingly in the right parts of Figs. 3(a)-3(c). The contrast C is computed by Eq. (6), where I_max and I_min are consecutive local maximum and minimum intensity of the profiles in which the red circle is signed. To facilitate the comparison process, the same position is needed to be selected among Figs. 3(a)-3(c). In this condition, the range-gated technology has an advantage over the intensity detection. This is because single scattering photons and few-scattering ones in the turbid medium have been filtered out by range-gated technology. However, the image quality is limited due to the diffusive light. A significant improvement of the image contrast with 0.446 is presented when the range-gated technology and the polarization method are combined, the highest image contrast shown in Fig. 3(c). In our experiment, comparing with the conventional range-gated technology, we have observed that the contrast had been doubled in this technology. In this case, not only few scattering photons are filtered out by tail-gated technology, but also multiply scattered photons are eliminated mostly by polarization-difference method based on the depolarization properties of turbid medium, as demonstrated in Fig. 2(a). It should be noted that the intensity is measured at only two polarization channels: co-polarization and cross-polarization, due to the disappearance of retardance and diattenuation when the absorption coefficient is low, which is shown in Figs. 2(b) and 2(c). It is more convenient to operate if the times of measurements are effectively reduced. The imaging technology proposed here can be used to better detect the target submerged in turbid or scattering medium.

In practical application, man-made object detection through turbid medium is widely used. The imaging technology described here, with range-gated technology and polarization method, is of great importance to image object in a relatively high level of turbid medium. It is time-saving that only co-polarization and cross-polarization components are measured with this technology. It is exciting that, to promote this technology forward, wollaston prism can be introduced to separate the orthogonal components without rotation of the optical element [10]. It makes the real-time detection possible.

5. Conclusions

In conclusion, we have studied the linear polarization properties of diffusive photons, including depolarization, retardance and diattenuation in turbid medium of Intralipid solution at 632.8nm. Diffusive photons are high depolarized in the process of multiple scattering in turbid medium, while retardance and diattenuation become zero. On the basis of the study above, the combination of range-gated technology and polarization detection method is considered as a useful tool to generate better image quality than the conventional range-gated technology when we image a high reflective target inside high level turbidity. In our experiment, comparing with the conventional range-gated technology, we have observed that the contrast is doubled in this technology. Further work is considered to study the properties of circular polarized light in the application of range-gated technology.