1. Introduction

The polarization state of light can be described by one vector, known as the Stokes vector S. Through its four components (S ₀, S ₁, S ₂, S ₃), this vector provides valuable information about reflecting objects that traditional intensity-based cameras ignore. Concretely, geometrical, chemical, physical, physiological and metabolic properties of the target such as surface smoothness, shape, size, color, orientation, molecular structure can be extracted if the Stokes vector components are captured [1, 2]. Polarimetric imaging systems are typically not capable of full Stokes polarization imaging [3–6], relying instead on only a subset of the Stokes vector components: (S ₀, S ₁, S ₂) for linear polarization imaging [3, 4] or just S ₃ for circular polarization imaging [5, 6]. For instance, in [3, 4], Rowe et al. describe how the difference of orthogonal linearly polarized components (also known as polarization-difference imaging) can be used to improve the object’s visibility in scattering media. It is attributed to the fact that light reflected by the targeted object is linearly polarized and the effects of background scattering can be removed by examining the polarization difference [3]. In [5, 6], Gilbert et al. demonstrate a circular polarization imaging system to improve the contrast of the underwater image, which is based on the principle that the handedness of circularly polarized light changes with each reflection. Therefore, the light reflected from the targeted object can be easily distinguished from that reflected from the medium by simply examining the difference in handedness through a set of circular polarization analyzers.

Full Stokes polarization imaging systems have been proposed to enable the simultaneous capture of both linear and circular components of the Stokes vector [2,7–10]. These implementations consist typically of a combination of image sensors, electro/mechanically controlled linear polarizers, retarders and DSPs/CPUs [2]. To sense all possible polarization states of light, these systems would typically require the capture of multiple images of the same scene, each of which is acquired by means of looking through different polarization elements [2]. In [9, 10], electronically-controlled liquid crystal variable retarders (LCVRs) are used in combination with an image sensor, to capture different polarization images in successive frames. The obvious drawback of this approach is that both the scene and the camera must be stationary across multiple frames, to avoid introducing interframe motion. To eliminate these errors, some systems acquire multiple images at the same time, but then the problem becomes spatial registration since each camera will image the scene from a slightly different perspective [2, 7, 8]. Spatial registration of multiples images is complicated by the need to compensate for both mechanical misalignment and aberrations due to separate optical paths [2].

To alleviate the above obstacles, a promising avenue is to directly pattern micro-optical polarization elements on top of each pixel of the image sensor to form a micropolarimeter array [2, 11]. In this way, each pixel will image through a micropolarizer element of a given orientation with a single polarization component sensed by each pixel. The three other missing components of the Stokes vector are recovered by examining the intensity values of neighboring pixels. In essence, this process is similar to color filter array interpolation or demosaicing. The adopted approach tolerates a 1-pixel registration error to allow for all polarization measurements to be made simultaneously at each pixel [2]. Because it uses semiconductor industry standard complementary metal-oxide-semiconductor (CMOS) fabrication process, this approach offers other significant advantages in terms of manufacturing cost, system volume, weight, power dissipation and system integration on a single silicon chip. A number of micropolarimeter array implementations have been reported in the literature [12–18]. In [12–15], reactive-ion-etching (RIE) is used to pattern dichroic polymer films and form a micropolarimeter array capable of extracting (S ₀, S ₁, S ₂) for partial-linear polarization imaging. In [16], Momeni et al. demonstrate a micropolarimeter array made of refractive YVO ₄ crystal for linear polarization imaging. An aluminum film is evaporated on top of the YVO ₄ crystal then patterned by liftoff to form the birefringent micropolarizer array. In [17], Harnett et al. present a liquid-crystal micropolarizer array for linear polarization imaging with evaporated gold films used as orientation layers. Liftoff is subsequently used to pattern the gold film. More recently, we reported a superior high resolution liquid-crystal micropolarimeter array fabrication technology, removing the need for complex selective etching. A 2µm pitch was achieved using ultraviolet (UV) light to define the micropolarimeter elements [18]. However, the latter micropolarimeter array is only capable of linear polarization imaging.

In fact, none of the reported micropolarimeter implementations can extract the complete polarization information. In this paper, we report the first micropolarimeter array capable of full Stokes polarization imaging. The proposed micropolarimeter is fabricated by patterning a liquid-crystal (LC) layer on top of a visible-regime metal-wire-grid polarizer (MWGP) using UV sensitive sulfonic-dye-1 (SD1) as the LC photoalignment material. This arrangement enables the formation of either micrometer-scale LC polarization rotators, neutral density filters or quarter wavelength retarders. These elements are in turn exploited to acquire all components of the Stokes vector. This paper is organized as follows. The design and implementation of the proposed micropolarimeter array are described in Section 2. Details of its fabrication process are provided in Section 3. Its optical characterization is described in Section 4 together with a discussion of experimental results. Finally, a conclusion is drawn in Section 5.

2. System design and implementation

An integrated polarization image sensing system consists of three fundamental building blocks: optics, light polarizing elements and underlying photodetectors. By redirecting the light reflected from an illuminated scene through the optical lens to its focal plane, the different polarized components of light can be filtered by the polarizing elements covering individual photodetectors. For example, linearly polarized components with different polarization orientations can be examined by a combination of a polarization rotator and a linear polarizer [19]. On the other hand, circularly polarized components can be examined by a combination of a polarization retarder and a linear polarizer [19]. In this paper, we propose to combine a visible-regime MWGP, used as a linear polarizer, together with a patterned LC layer, used here as either polarization rotator, polarization retarder or neutral density filter depending on the LC orientation layers. Figure 1 illustrates how the proposed LCMP array can be integrated on top of a CMOS image sensor to extract the full Stokes components for every pixel of the captured image.

 

Fig. 1. CMOS polarization image sensor architecture with integrated LCMP array for full Stokes polarization imaging.

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Suppose the initial Stokes parameters for the incident light are (S ₀, S ₁, S ₂, S ₃), they become (S′₀, S′₁, S′₂, S′₃) after passing through the LC cell and (S″₀, S″₁, S″₂, S″₃) after passing through the MWGP. As a unitary intensity-lossless system, the Mueller matrix of the LC cell can be expressed as [20]:

When an electric field is applied and exceeds a given threshold value, the LC cell can be represented by a neutral density filter. When there is no electric field applied, the LC cell can be represented by the combination of a polarization phase retarder and a polarization rotator. Its Mueller matrix is given as follows [20]:

with

where ϕ is the LC twist angle, d is the LC layer thickness, Δn(λ) is the LC birefringence and λ is the wavelength of the incident light. The twist angle ϕ and the phase retardation 2δ are the two main design parameters in the design and fabrication of the LC cell. The Mueller matrix of the MWGP with its polarization axis oriented at an angle of θ is [19]:

The Stokes parameters of the emerging light, depicted in Fig. 1, can be thus expressed by multiplying the above-mentioned initial Stokes parameters (in vector form) by the Mueller matrices of the LC cell and the MWGP successively as follows:

The total intensity, S″₀, of the emerging light (Fig. 1) is given:

with

Mathematically, at least four intensity measurements taken through four different LCMPs, each with its unique set of parameters (J, L, N), are needed to determine the four Stokes parameters S ₀, S ₁, S ₂, S ₃. The four intensity measurements can be quantitatively expressed as:

To determine all four Stokes parameters simultaneously, we propose to adopt an approach similar to that used in a color filter array, with each pixel making only one of the four necessary intensity measurements (I ₁ – I ₄). The three other intensities are recovered by examining the intensity values of neighboring pixels. This approach trades-off spatial resolution to allow for the acquisition of all Stokes components in a single image capture. The basic element of the LCMP array, referred to as superpixel, consists of four micropolarimeters. Equation (11) suggests that one can choose from a number of different possible combinations of four micropolarimeters, with parameters (J_i, L_i, N_i) for i = [1,2,3,4]. However, a judicious choice of the design parameters (θ, ϕ and δ) and coefficients (J, L, N) of each micropolarimeter can significantly reduce the complexity of the silicon implementation of the Stokes parameters computation circuitry.

 

Fig. 2. Relationship between the LC Mueller matrix elements and the LC twist angle ϕ: (A) D versus ϕ; (B) E versus ϕ; (C) F versus ϕ.

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For example, if we orient the MWGP’s polarizing axis at θ = 45°, (J, L, N) are simplified to (D, E, F) and Eq. (11) becomes:

Let’s now constrain the phase retardation 2δ of each cell to quarter wavelength:

for m = 1,2,3…, where m is referred to as the phase retardation factor. According to Eq. (2)–(8), when there is no electric field, the coefficients (D, E, F) in Eq. (14) become functions of the LC twist angle ϕ and the phase retardation factor m, as shown in Fig. 2. The following observations can be exploited to simplify the expressions of the elements (D, E, F) of the LC Mueller matrix:

The above observations have motivated our choice of 45° twisted, −45° twisted and untwisted LC cells for three out of the four micropolarimeters covering a superpixel (Fig. 3). For the fourth LCMP, we chose to operate the LC cell in electrically controlled birefringence (ECB) mode. If the electric field exceeds a threshold value, this fourth LC cell is optically equivalent to a neutral density filter, which has no influence on the polarization state of incident light. It follows that the Mueller matrix elements (D, E, F) are equal to (0, 1, 0). Note that in conjunction with the 45° oriented visible-regime MWGP, the LCMP with the neutral density filter LC cell is optically equivalent to a 45° linear polarization analyzer.

Figure 3 shows cross-sections for the four micropolarimeters. Note the different LC molecules arrangements are achieved by using LC photoalignment layers. By selectively photo-patterning the inner surfaces of the LC cells, we can make an LC cell act as a retarder, neutral density filter or rotator (Fig. 3). The latter occurs wherever the orientation of the bottom inner layer is not identical to the top inner layer, in which case incoming light follows the rotation of the molecules. In E-field mode, the orientation of the LC molecules is that of the applied electric field.

3. Liquid-crystal micropolarimeter array fabrication

To demonstrate the proposed micropolarimeter array technology, we have fabricated LCMP arrays comprising 40000 superpixels (200 × 200). The size of each superpixel is 20µm × 20µm. Each LCMP was fabricated on a transparent glass substrate, referred to as “second substrate” in Fig. 4. The use of this dummy CMOS imager substrate enables the optical characterization of each fabricated LCMP, since a CMOS imager substrate is itself opaque. Future work will focus on the actual integration of the proposed LCMP on top of custom made CMOS imager. Figure 4 shows a cross-section of the fabricated LCMP array. The two transparent thin glass slides, used to encapsulate the LC layer, are referred to as “first substrate” and “second substrate”. Note that the visible-regime 150nm-thick MWGP (from Moxtek Inc.) is placed on the inner surface of the second substrate. Azo-dye SD1 was synthesized and used as photoalignment layer to orient the LC molecules [21]. This SD1 material is sensitive to UV light with its peak absorbance at a wavelength of 360nm. This material exhibits a molecular photo-reorientation mechanism characterized by SD1 long molecular axis perpendicular to the polarization direction of projected polarized UV light [21]. Depending on the orientation of the photo-patterned inner surfaces of the LC cell, the latter can act as a retarder, neutral density filter, or a rotator [18]. The fabrication of the proposed liquid-crystal micropolarimeter array can be summarized as follows:

 

Fig. 4. (A) Cross-section of proposed CMOS polarization image sensor with integrated LCMP array; (B) fabricated LCMP array with the second substrate as “dummy” CMOS imager substrate to enable LCMPs’ optical characterization (CMOS imager substrate is opaque).

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4. Experimental results

In order to characterize the optical performance of the fabricated micropolarimeters, a polarization state generator (PSG) composed of a commercial linear polarizer (from Moxtek Inc.) and a commercial broadband quarter wavelength retarder (from Nitto Denko Corp.) was used to generate six different polarized inputs: 0° linearly polarized, 90° linearly polarized, 45° linearly polarized, −45° linearly polarized, right-handed circularly polarized and left-handed circularly polarized. Their corresponding normalized Stokes parameters (S ₁/S ₀, S ₂/S ₀, S ₃/S ₀) are (1, 0, 0), (−1, 0, 0), (0, 1, 0), (0, −1, 0), (0, 0, 1) and (0, 0, −1), respectively [19]. The fabricated LCMP array was placed under a microscope with back illumination collimated by a 500nm monochromatic filter and the above-mentioned PSG. Figure 5 presents recorded microphotographs. Note that LCMP _45°twisted, LCMP _{−45°twisted} and LCMP _E−field should appear dark when the polarization state of the input light is 90°, 0° and −45° linearly polarized, respectively. LCMP_Untwisted should be insensitive to linearly polarized input and should theoretically attenuate half of the input light intensity [19]. This is why it appears grey in Fig. 5(A)–5(C). In addition, LCMP_Untwisted appears bright when the input is right-handed circularly polarized [Fig. 5(D)] and dark when the input is left-handed circularly polarized [Fig. 5(E)]. It follows that LCMP_Untwisted behaves as a right-handed circular polarization analyzer.

Malus measurements were conducted for LCMP _45°twisted, LCMP _{−45°twisted} and LCMP_E−field to extract the two important figures of merit that are major principal transmittance and extinction ratio [19]. They are defined as the maximum transmittance and the ratio between the maximum transmittance and the minimum transmittance in the Malus measurement, respectively [19]. Single LCMP samples with a size of 2.5cm × 2.0cm were fabricated together with the LCMP array to cover the laser beam and enable the LCMP optical characterization. The above-mentioned PSG was inserted between a tunable mini deuterium halogen light source (Model DT-Mini-2-GS from Mikropack GmbH) and the LCMP samples to provide linearly polarized input light with wavelength varied from 400nm to 700nm. A high resolution spectrometer (Model HR2000 from Ocean Optics Inc.) and a computer control were used to calculate and record the light transmitted through the samples. Figure 6(A)–6(C) present the Malus measurement results for three different wavelengths: 450nm (blue light), 550nm (green light) and 650nm (red light). Note that Malus’ law is well satisfied for LCMP _45°twisted, LCMP _{−45°twisted} and LCMP_E−field for different wavelengths. Right-handed and left-handed circularly polarized inputs were also provided to illuminate the corresponding LCMP sample and measure its spectral responses. Figure 6(D) shows the spectral measurement results, with the transmittance maximum for a wavelength of 500nm. This means that the LC cell of LCMP_Untwisted behaves as a quarter wavelength retarder for a wavelength of 500nm. Table 1 reports the measured extinction ratios for the four LCMPs at a wavelength of 500nm. Note that the values are around 1100, indicating that the MWGP’s original extinction ratio is well retained [22].

 

Fig. 5. Microphotographs of a fabricated LCMP array illuminated by linearly or circularly polarized input: (A) 0° linearly polarized; (B) 90° linearly polarized; (C) −45° linearly polarized; (D) right-handed circularly polarized; (E) left-handed circularly polarized.

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Table 1. Extinction ratios of different LCMPs

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Fig. 6. (A) Malus measurement results of LCMP _45°twisted; (B) Malus measurement results of LCMP _{−45°twisted}; (C) Malus measurement results of LCMP_E−field; (D) spectral measurement results of LCMP_Untwisted.

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The PSG-collimated monochromatic light source (500nm) was used to evaluate the performance of the proposed LCMP optical model [Eq. (14)]. The recorded transmittances were compensated by taking into account the transmission loss due to non-polarizing effects, such as surface reflection of glass substrate, non-polarizing absorption/scattering of both LC and MWGP layers. A collimated unpolarized light beam was projected onto the samples to measure this transmission loss. The compensated transmittances through the single LCMP samples were fed into the proposed LCMP model [Eq. (14)], with the model parameters evaluated using Eq. (2)–(8):

Table 2. Comparison between experimentally extracted Stokes parameters and ideal values for different polarized inputs

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The extracted Stokes parameters, normalized to light intensity (i.e. S ₀), are reported in Table 2. The fabricated LCMPs are found to behave as expected within 2.3%. Errors can be attributed to measurement noise, round off errors in calculations but also to slight deviations of:

Future work will focus on integrating the proposed LCMP array on top of a custom made CMOS imager to evaluate the polarimetric imaging capabilities of a single-chip polarization CMOS imager.

5. Conclusion

In this paper, we have demonstrated a liquid-crystal based micropolarimeter array for full Stokes polarization imaging in visible spectrum. In contrast to previously reported micropolarizer arrays, the proposed implementation enables, for the first time, the extraction of circularly polarized components of light for real-time full Stokes polarimetry. To accommodate applications with large oblique incidence angle, a 150nm ultra-thin visible-regime MWGP is used to reduce the overall thickness of the micropolarimeter array layer to 5µm. This provides a relatively good aspect ratio for pixel size larger than 10µm. Experimental results indicate that the LC-MWGP structure retains MWGP’s superior optical characteristics with a major principal transmittance of 75% and extinction ratios of around 1100.