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Abstract
We demonstrate a single-shot and image-based polarization detection system for material recognition. The Stokes parameters are measured under a single-shot measurement using 4 electrically tunable liquid crystal wave plates, 4 polarizers, and 4 camera modules. The optical principle is introduced and the experiments are performed. We also use a metallic plate and a glass substrate to demonstrate the material recognition. The impact of this study is to provide a practical way in image-based polarization detection in Advanced Driver Assistance Systems for material recognition which could help in driving safety.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Three-dimensional (3D) sensing technology are widely spreading in many applications, such as Advanced Driver Assistance Systems (ADAS), industrial inspections, and face recognition for security applications [1]. The fundamental mechanism for 3D sensing is to measure topography-determined wavefronts after light is reflected by an object. However, conventional cameras can only capture two-dimensional (2D) irradiance-based-images. Several methods are developed to measure wavefronts in order to reconstruct 3D images, such as phase-contrast microscopic technology developed by Dr. Fritz Zernike (Nobel laureate in 1953) [2], the method of Shack-Hartmann sensor which utilizes microlens arrays to sample wavefronts during wavefront reconstruction [3,4], the method of interferometric technique or holography developed by Dr. Dennis Gabor (Nobel laureate in 1971) based on interference of beams to store and rebuild the wavefronts of recorded objects [5], and the technique of conoscopic holography which works for incoherent light and vibration insensitive [6]. In 2000, K. Buse and M. Luennemann demonstrated a method to utilize a birefringent crystal and a polarizer to realize wavefront sensing of 3D imaging which is rather insensitive against mechanical instability compared to interferometric and holographic techniques [7]. Later, the wavefront sensing techniques evolved into three 3D sensing methods for measuring the distance or surface topography: a method of stereo vision, a method of time-of-flight, and structured light method which obtain information of optical phases or depths of objects by means of measuring phases from disparity of images, time difference between incident light and reflected light to objects, and deformations of optical pattern, respectively [8–12]. Nevertheless, those 3D sensing methods have difficulty when the detecting objects are transparent, highly reflected, or have similar colors to the environments (or backgrounds). The famous example is that the car's driverless technology failed to distinguish the white side of a turning tractor-trailer from a brightly lit sky, and the car did not automatically brake in 2016 [13]. Nowadays, many vehicle companies still prefer images captured by cameras to perform the 3D sensing. Besides light intensity, polarization could provide extra information when light is reflected by the object, especially the materials of objects. In Nature, polarizations of light spread all over surroundings besides light irradiance and optical phase. For instance, distributive polarizations of light in the sky due to Rayleigh scattering [14], difference in TE and TM polarization at mirror reflection [15], and circularly polarized light after light is reflected by beetles [16]. Polarization imaging helps squids to prey and birds to identify the orientations on earth [15]. It motivates researchers to investigate 3D sensing with adding polarization imaging for material recognition.
For polarization of light, researchers measure Stokes parameters which fully describe polarization of light [17]. Four methods are usually used to determine polarizations. The first one is a method using two crossed polarizers [18,19]. The polarization is predicted by the measured irradiance ratio of TE and TM. This method is good for prediction of a linearly polarized light, but it does not obtain information of circularly polarized light, elliptically polarized light, and Stokes parameters. The second one is a method of so-called polarizer matrix [20]. The polarizer matrix method uses many polarizer-arrays to predict degree of polarization and angle of polarization for linearly polarized light. This method does not provide information of circularly polarized light as well as full Stokes parameters. The third one is the metasurface method [21]. The metasurface method is that the different polarized light is reflectively diffracted by the metasurfaces spreading toward different directions. The Stokes parameters of light could be obtained after analyzing diffracted light. The major challenges are the diffraction efficiency and wavelength dependency. The last one is a method using a combination of a wave retarder and a polarizer [22]. This method measures Stoke parameters by means of rotations of the wave retarder and the polarizer. The different combinations of wave retardations of the retarder and the angles of transmissive axis of the polarizer help to predict the polarizations of light. However, it takes time for the measurement due to the mechanical operations of the wave retarder and the polarizer. Alternatively, it could use polarizer-arrays and phase-retarder-arrays to measure at once, but it sacrifices the resolution of the photosensors. From those methods, the method using a wave retarder and a polarizer can measure full Stokes parameters, but it does not have the drawback of diffraction efficiency and zero diffraction order noise due to intrinsic diffractive feature of metasurfaces. It motivates us to develop a simple polarization detection system based on this method and apply it in material recognition. In this paper, we develop a single-shot and imaging-based polarization detection system adopting 4 tunable liquid crystal wave retarders and 4 polarizers for the measurement of Stoke parameters as well as material recognition [23–25]. The optical principles are introduced and we introduce how to use such a polarization detection system. The glass substrate and metallic plate are also used in the measurement for proof-of-concept. The impact of this study is to provide a practical way for material recognition based on image-based polarization detection. With the proposed image system, the transparent materials, such as glass, metallic materials, and different materials with the same color, now could be differentiated based on polarization properties of the reflected light. One of the advantages of the proposed image-based system is to offer the image with a single shot and to support the video rate recording in principle. Such a polarization detection could be useful in Advanced Driver Assistance Systems for providing information of material recognition which helps in driving safety.
2. Optical mechanism
The optical mechanism we used to measure Stokes parameters is based on classical measurement method: a quarter wave-plate and a polarizer method [26]. Assume a plane wave propagates along z-direction with angular frequency ω and wave number k. The electric field vector of a polarization state of the plane wave is expressed as:
In Eq. (2), S0 stands for total irradiance of light, S1 is the irradiance difference between x-linearly polarized light and y-linearly polarized light, S2 is the irradiance difference between 45°-linearly polarized light and 135°-linearly polarized light, S3 is the irradiance difference between right-handed-circularly polarized light and left-handed–circularly polarized light. The degree of polarization (DoP) is defined as: $\textrm{DoP} = {{\sqrt {S_1^2 + S_2^2 + S_3^2} } / {{S_0}}}$. DoP = 1 for completely polarized light, 0< DoP <1 for partially polarized light, and DoP = 0 for unpolarized light. As long as we know ${E_{0x}}$, ${E_{0y}}$, and $\delta$, the polarization state of light is determined by 4 Stokes parameters S0, S1, S2, and S3.
A wave retarder, a polarizer, and a photo-detector could be adopted to measure Stokes parameters in Eq. (2) and the experimental setup is depicted in Fig. 1. The transmissive axis of the polarizer is θ with respect to x-axis. The fast axis of the wave retarder is parallel to x-axis and the phase retardation of the wave retarder is ϕ. The Muller matrices of a phase retarder (Mretarder) and a polarizer (Mpolarizer) are written in Eqs. (3) and (4), respectively [27].
Fig. 1. Measurement of Stokes parameters based on classical polarization measurement: a quarter wave-plate and a polarizer method. The system consists of a color filter, a phase retarder, a polarizer and a photo-detector.
The Stokes vector ${\vec{S}_{out}}$ after light propagates through a phase retarder and a polarizer is:
From Eqs. (2) to (5), the total irradiance of light ($I(\theta ,\phi )$) is ${S_0} = E_{0x}^2 + E_{0y}^2$ which could be expressed as Stokes’s famous intensity relation:
From Eqs. (2) to (6), the Stokes parameters are then found from the following conditions on θ and ϕ :
Basically, by using a quarter wave plate and a polarizer to measure I(0°, 0), I(90°, 0), I(45°, 0), and I(45°, π/2), the corresponding Stoke’s parameters ${\vec{S}_{out}} = (S{^{\prime}_0},S{^{\prime}_1},S{^{\prime}_2},S{^{\prime}_3})$ could be determined. To achieve a single-shot polarization measurement for Stoke’s parameters, here we use 4 electrically tunable phase retarders using nematic liquid crystals, 4 polarizers, and 4 camera modules as photo-detectors to measure Stoke’s parameters in Eqs. (7) to (10) which means we measure the polarization of light by means of taking 4 photos at the same time (Fig. 2). Because 4 camera modules are used, we could maintain the resolution of the proposed system. In addition, 4 camera modules provide information of depth information of image by a traditional stereo vision method.
For further material recognition, the complex refractive indices, reflectance and transmittance of materials should be considered in Stoke-Muller matrix. Assume the incident angle of light is ${\theta _i}$ propagates from one material with a refractive index ni to another material with a refractive index nt. We replace TE and TM polarizations to x- and y- linear polarizations. The corresponding Stoke-Muller matrix of reflective light Mmaterial satisfies relation in Eqs. (11) and (12) [27]:
Fig. 2. Schematic setup of the proposed single-shot polarization measurement for Stokes parameters and material recognition.
From Eqs. (11) and (12), Mmaterial is:
In practice, we build up a look-up table of Stokes parameters for different materials first. Given an incident polarization state of light (${\vec{S}_{in}}$), we can predict the output polarization state (${\vec{S}_{out}}$) by means of the Stoke-Muller matrix of materials. The prediction of polarization of light is then compared with the measure output polarization for material recognition.
3. Experiments and discussions
In experiments, we first fabricated four electrically tunable wave retarders using nematic liquid crystals. For each LC wave retarder, we sandwiched nematic liquid crystals E7 (Merck, Δn = 0.2255, λ=589.3 nm) between two ITO glass substrates coated with mechanically buffed alignment layers (polyimide). The rubbing directions of two alignments were anti-parallel. The thickness of a LC layer was around 8 microns. We placed each LC wave retarder between crossed polarizers and the rubbing direction of the LC wave retarder was 45 degrees with respect to one of the transmissive axis of a polarizer. We then measured the transmittance and plotted transmittance as a function of voltage. After that, we converted the transmittance(T) into phase retardation as a function of applied voltage(V) according to the relation [27]:
where Γ is phase retardation and $\Gamma (V) = 2\pi {{ \cdot ({n_{eff}}(V) - {n_o}) \cdot d} / \lambda }$ which depends on wavelength of incident light (λ), ordinary refractive index of LC (n0), molecular-orientation dependent refractive index (neff), and thickness of the LC layer (d). The measured phase retardation as a function of applied voltage for one of the LC wave retarder is shown in Fig. 3. In our design, a LC wave retarder is operated as either a zero-wave plate or quarter-wave plate (i.e., the phase retardation is either 0 or π/2 radians or $({\pi / 2}) + 2m\pi$, where m is integral). From Fig. 3, we applied 50 Vrms to make sure LC molecules almost perpendicular to the glass substrate for the purpose of zero phase retardation and 4.3 Vrms in order to satisfy the condition of a quarter-wave plate (phase retardation=$({\pi / 2}) + 2m\pi$).The camera modules we used were SONY IMX 179 CMOS Image Sensors (size: 38mmx38mm; resolution: 3264 × 2448; field-of-view: 80°; Focal length: 3.6 mm). We first calibrated the camera modules by means of a conversion table for light intensity vs. grey level for red light. Thereafter, the camera modules could be used to measure the light intensity for red light. We set up a polarization detection system with a single camera module in Fig. 1, first consisting of a color filter, one LC wave retarder, one camera module and a linear polarizer whose rotational angle was controlled by a motorized controller, as depicted in Fig. 1. To test the accuracy of the polarization detection system in Fig. 1, we used a polarizer attached on a small white light table (we set the transmissive axis of the polarizer is 0° with respect to x-axis) as a target and the target was 50 cm away from the polarization detection system. After we adjusted the transmissive axis of the polarizer θ and phase retardation ϕ of the wave retarder, we took photos and recorded four light intensities I (θ, ϕ) : $I({45^ \circ },\frac{\pi }{2})$,$I({45^ \circ },0)$,$I({90^ \circ },0)$, and $I({0^ \circ },0)$. We attached a pupil with 14.5 cm in diameter to the target (the polarizer). Figures 4(a) to 4(d) show recorded four photos for testing a polarizer at (θ, ϕ) = (45°, π/2), (45°, 0), (90°, 0) and (0°, 0). In Figs. 4(a) to 4(d), the intensities in the circle area are different. By image process of photos in Figs. 4(a) to 4(d) according to Eqs. (7) to (10), we further obtained 4 images in Figs. 4(e), 4(f), 4(g), and 4(h) which represents 4 Stokes parameters S0, S1, S2, and S3.
Fig. 4. The recorded four photos for testing a polarizer at (a) (θ, ϕ) = (0°, 0), (b) (θ, ϕ) = (45°, π/2), (c) (θ, ϕ) = (90°, 0), and (d) (θ, ϕ) = (45°, 0) using polarization detection system with single camera module. (e),(f),(g), and (h) are corresponding Stokes parameters S0, S1, S2, and S3 after we have image processes from (a) to (d). The color bars stand for the Stokes parameters.
According to Figs. 4(e) to 4(h), $({S_0},{S_1},{S_2},{S_3}) = ({0.97,\textrm{ }0.99,\textrm{ } - 0.03,\textrm{ } - 0.08} )$ which is close to theoretical Stokes parameters of a x-linearly-polarized light: $({S_0},{S_1},{S_2},{S_3}) = (1,1,0,0)$. The Root-Mean-Square error, defined as $\sqrt {{{\sum\limits_{i = 1}^3 {{{(\Delta {S_i})}^2}} } / 3}}$, is around 0.0496 in our measurement. Figure 5 shows the measured Stokes parameters (color dots) as we rotated the transmissive axis of the polarizer (target). The solid lines in Fig. 5 is the theoretical Stokes parameters. In Fig. 5, the measurements quite agree with theoretical ones. The Root-Mean-Square errors for S1, S2, S3 are 0.021, 0.032, and 0.064 which are pretty small. We also calculate the angle of polarization (AoP), defined as $\textrm{AoP} = {\tan ^{ - 1}}({{{S_2}} / {{S_1}}})$. The Root-Mean-Square error of AoP equals to 0.89 degree which is less than 1 degree. As a result, the polarization detection system with single camera module exhibits good accuracy in measurement.
Fig. 5. Stokes parameters S0, S1, S2, S3 as a function of angle of the transmissive axis of the linear polarizer (target). The dots and solid lines are experimental and theoretical results, respectively.
Next, we set up the single-shot polarization measurement for Stokes parameters: the polarization detection system with four camera modules (Fig. 2). The setup consisted of 4 color filters, 4 polarizers, 4 LC wave retarders and 4 camera modules (SONY IMX 179 CMOS Image Sensors). The photo of the experimental setup is shown in Fig. 6(a). We adjusted transmissive axes of polarizers and the phase retardations of LC wave retarders in order to have a single shot for all camera modules. After taking a single-shot photo for each camera, we could obtain the photos exhibiting information of $I({45^ \circ },\frac{\pi }{2})$, $I({45^ \circ },0)$, $I({90^ \circ },0)$, and $I({0^ \circ },0)$. Figure 6(b) shows the measured Stokes parameters (color dots) as a function of the rotation of the transmissive axis of the polarizer (target). The solid lines in Fig. 6(b) are the theoretical Stokes parameters. In Fig. 6(b), the measurements quite agree with theoretical ones. The Root-Mean-Square errors for S1, S2, S3 are 0.036, 0.060, and 0.055, respectively. Then the Root-Mean-Square error of AoP equals to 1.51 degree which is larger than the previous one with single camera module. The polarization detection system with 4 camera modules still exhibits good accuracy of measurement. Moreover, we could obtain the Stokes parameters by means of taking photos using 4 camera modules at once.
Fig. 6. (a) The single-shot polarization measurement for Stokes parameters: polarization detection system with four camera modules. (b) Stokes parameters S0, S1, S2, S3 as a function of angle of the transmissive axis of linear polarizer (target). The distance between two adjacent cameras was 8 cm. The dots and solid lines are experimental and theoretical results, respectively.
To prove the concept of material recognition using the single-shot polarization measurement (Fig. 6(a)), we prepared two kinds of targets, metallic aluminium plate and a glass substrate, and placed them 100 cm in front of the single-shot polarization measurement system. We first measured Stokes parameters of two targets as light was reflected by two targets and then we analyzed the measured Stokes parameters to recognize whether the target is the metal or the dielectric material. The photo of two targets is shown in Fig. 7(a). The white light was adjusted and the incident light was 45 degrees with respect to the normal directions of two targets. The single-shot polarization measurement was placed at -45 degrees with respect to the normal directions of two targets. The experimental results of Stokes parameters S0, S1, S2, S3 and DoP are shown in Figs. 7(b)–7(f). The S0, total irradiance of light, is around 1 at the most of area for the metallic aluminium plate and 0.8 for the glass substrate in Fig. 7(b). This indicates the reflection of the metallic aluminium plate is stronger than the glass substrate. The measured S1 of the metallic aluminium plate and the glass substrate are ∼0 and -0.49, respectively. The measured S2 of the metallic aluminium plate and the glass substrate are similar∼0. The measured S3 of the metallic aluminium plate and the glass substrate are also similar∼0. The calculated DoP of the metallic aluminium plate and the glass substrate are 0 and 0.52, respectively. The refractive index of the metallic aluminium plate and the glass substrate are $\widetilde n = 1.269 + i \cdot 7284$ for wavelength of 633nm and $\widetilde n = 1.515$, respectively, the corresponding Stoke-Muller matrices of the reflected light for the metallic aluminium plate and for the glass substrate are calculated and listed in Eqs. (17) and (18):
Fig. 7. (a) The image of two kinds of targets, metallic aluminium plate and a glass substrate, were placed 100 cm in front of the polarization detection system. (b),(c), (d), and (e) are Stokes parameters S0, S1, S2, and S3 of (a). (f) is DoP of (a). The color bars stand for the Stokes parameters.
From Eqs. (17) and (18), the theoretical values of S1 for the metallic aluminium plate and the glass substrate are -0.014 and -0.827. In experiments, S1∼0 for the metallic aluminium plate and -0.49 for the glass substrate. Theoretical DoPs are 0.032 and 0.827 for the metallic aluminium plate and the glass substrate. In experiments, DoP∼0 for the metallic aluminium plate and DoP∼0.52 for the glass substrate. From experimental results, the Stokes parameters S1 and DoP indeed display difference between two materials. However, the difference between theoretical and experimental results might come from the estimated refractive index. For example, the metallic aluminium we used may not pure material and may have other metallic materials inside to affect the refractive index. In addition, the ambient unpolarized light could result in a decrease of degree of polarization and S1, especially the surface of the metal is not smooth. In addition, the detector receives light from all angles, not just 45 degree. The measurement presents the averaged results for the reflective angles in a range from 30 to 60 degrees. In spite of those factors, the measurement indeed shows differences in S1 and DoP between the metallic aluminium plate and the dielectric glass substrate, while S2 and S3 remain similar. Practically, we build up a look-up table for difference materials according to measured refractive index of materials as well as consideration of surface properties, such as flatness and coatings. Then we use this single-shot polarization measurement system to recognize the materials. Moreover, the bandwidth of the color filter could affect the accuracy of the Stoke parameter measurement. The narrower bandwidth of the color filter, the more accuracy of Stoke parameter measurement.
4. Conclusion
We develop a single-shot and imaging-based polarization detection system adopting 4 tunable liquid crystal wave retarders and 4 polarizers for the measurement of Stoke parameters as well as material recognition. To prove-of-concept, the glass substrate and metallic plate are used in the measurement. Between the glass substrate and the metallic plate, the measured DoP and Stokes parameter S1 are significantly different for distinguishing one from the another. The capability of polarization detection and material recognition of the single-shot system is demonstrated experimentally. Compared to light detection and ranging systems (LiDAR) which are not able to provide functions of material recognition, this study proposed a practical and simple way for material recognition based on image-based polarization detection. Such a image-based polarization detection could be useful in vehicles, such as Advanced Driver Assistance Systems for providing information of material recognition which helps in driving safety.
Funding
Ministry of Science and Technology, Taiwan (110-2112-M-A49-035); General Interface Solution Holding (GIS) Ltd.
Acknowledgments
The authors are indebted to Ms. Ting-Wei Huang for technical assistance.
Disclosures
YHL: GIS Ltd. (F), HHH: GIS Ltd. (F), YJW: GIS Ltd. (F), HAH: GIS Ltd. (F), PLC: GIS Ltd. (E).
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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