Liquid-crystal Micropolarimeter Array for Visible Linear and Circular ...
Liquid-crystal Micropolarimeter Array for Visible Linear and Circular Polarization Imaging 1
Xiaojin Zhao1,2, Amine Bermak1, Farid Boussaid2 and Vladimir G. Chigrinov1 Department of ECE, Hong Kong University of Science & Technology, Hong Kong SAR, China 2 School of EECE, University of Western Australia, Perth, WA 6009, Australia Email: [email protected]
Abstract—In this paper, we propose a liquid-crystal micropolarimeter (LCMP) array with high spatial resolution for real-time linear and circular polarization imaging in visible spectrum. LCMPs for extracting 0◦ , 90◦ linearly and righthanded circularly polarized components of incident light are implemented by micro-patterning a liquid crystal (LC) layer on top of a 45◦ oriented ultra-thin metal-wire-grid polarizer (MWGP). A compact LCMP pitch of 5µm×5µm is achieved with sulfonic-dye-1 (SD1) as the LC alignment material. In addition, these micron-scale LCMPs feature ∼ 5µm overall thickness and ∼1100 extinction ratio. Reported experimental results validate the concept of real-time linear and circular polarization image sensing and processing with targets illuminated by collimated artificial light.
I. I NTRODUCTION Polarization imaging ignored in conventional intensity/color based imaging has been proven to be a very important feature [1]. Demonstrated applications include remote satellite image sensing/segmentation [1], machine vision with scattering media [2], non-contact fingerprint detection [3] and classification/analysis of biological tissues [4]. Promising realtime polarization imaging/processing is enabled by sensing polarimetries of different polarization components of a targeted image scene. A commercially available complementary metaloxide-semiconductor (CMOS) camera can be applied for realtime polarization imaging/processing by covering its individual photo-sensitive pixels with micrometer-scale polarizing elements. A micropolarimeter array, which is composed of micropolarimeters for extracting different polarization components of incident light, is thus an indispensable optical device [5]. Previously reported micropolarimeter array implementations mainly concentrate on the extraction of linearly or partiallylinear polarized components [6]–[9]. These approaches are generally adequate for passive polarization imaging, where image scene is illuminated by sunlight or some other natural sources with rare circularly polarized component. Circular polarization imaging enabled by the circularly polarized component extraction can further reveal the information regarding the object surface features, shape, shading and roughness [10]. G. D. Gilbert et al paved the way of active circular polarization imaging by using collimated artificial light with intentionally added circularly polarized components as the active source [10]. Several related implementations were reported subsequently [11]–[13]. However, with unpatterned mechanically or
978-1-4244-5309-2/10/$26.00 ©2010 IEEE
electrically configured phase retardation device, none of them can simultaneously extract and analyze the polarized components in real-time. In addition, complex image registration algorithm cannot be avoided to address the issues induced by any movement in image scene. In this paper, a high-resolution liquid-crystal micropolarimeter (LCMP) array is proposed to realize real-time linear and circular polarization imaging. LCMPs for extracting 0◦ , 90◦ linearly and right-handed circularly polarized components of incident light are implemented by micro-patterning a liquid crystal (LC) layer on top of a 45◦ oriented ultra-thin metalwire-grid polarizer (MWGP). This paper is organized as follows. In Section II, the principle of liquid crystal based polarimeter is reviewed. In Section III, pattern design and fabrication process flow of the proposed LCMP array are described. Section IV presents the reported experimental results. Finally, this paper is concluded by Section V. II. P RINCIPLE OF L IQUID C RYSTAL BASED P OLARIMETER Liquid crystal based polarimeter (LCP) has been proven a powerful tool for extracting and analyzing all kinds of polarization components in the incident light [14][15]. By orienting the LC alignment layers to configure the LC molecules arrangement, the LC cell can behave optically as polarization rotator, polarization phase retarder, .etc. Fig. 1 presents three LCPs with different LC molecules arrangements. LC molecules are oriented by aligning the top alignment layer along one reference direction and the bottom alignment layer along another direction having a twist angle φ with respect to the above-mentioned reference direction. In Fig. 1 (A) and (B), 45◦ twisted (φ = 45◦ ) and -45◦ twisted (φ = −45◦ ) LC cells are optically equal to 45◦ and -45◦ polarization rotators if Mauguin condition is satisfied: Δn · d >> λ
(1)
where Δn is the LC birefringence, d is the thickness of the LC layer, λ is the wavelength of the incident light. In Fig. 1 (C), untwisted (φ = 0◦ ) LC cell is optically equal to quarter wavelength retarder for the wavelengths: λ=
4 · Δn · d , (m = 0, 1, 2...) 4m + 1
(2)
Combining the 45◦ linear polarizing film (Fig. 1), three different LCPs can be used for extracting 0◦ , 90◦ linearly
637
polarized and right-handed circularly polarized components of the incident light, respectively. This can be verified by the following analysis with Stokes vector and Mueller matrix.
Mueller matrix of an LC cell with twist angle φ is given as follows [17]: MLC = 1 0 0 0 ⎢ 0 1 − 2(c2 + d2 ) 2(bd − ac) −2(ad + bc) ⎢ ⎣ 0 2(ac + bd) 1 − 2(b2 + c2 ) 2(ab − cd) 0 2(ad − bc) −2(ab + cd) 1 − 2(b2 + d2 ) ⎡
incident light
incident light
incident light
LC alignment layers
45 degree linear polarizing film emerging light
emerging light
emerging light
(A) 45r twisted LC
(B) -45r twisted LC
(C) Untwisted LC
a
= cos(φ)cos(χ) +
b
=
c
=
d =
Fig. 1. Three LCPs with different LC molecules arrangements: (A) LCP for extracting 0◦ linearly polarized component with 45◦ twisted LC cell; (B) LCP for extracting 90◦ linearly polarized component with -45◦ twisted LC cell; (C) LCP for extracting right-handed circularly polarized component with untwisted LC cell.
χ
=
Γ
=
Provided with the film [16]:
Liquid crystal based polarimeter
Stokes vector
Stokes vector
Stokes vector
S
S’
S’’
incident light
Liquid-crystal layer with Mueller matrix MLC
⎥ ⎥ ⎦
with
LC molecules
LC molecules
⎤
M45
φ sin(φ)sin(χ) χ
(4)
Γ cos(φ)sin(χ) (5) 2χ φ sin(φ)cos(χ) − cos(φ)sin(χ) (6) χ Γ sin(φ)sin(χ) (7) 2χ 2 Γ 2 φ + (8) 2 2π · Δn · d (9) λ Mueller matrix of the 45◦ linear polarizing ⎡
0.5 ⎢ 0 =⎢ ⎣ 0.5 0
⎤ 0 0.5 0 0 0 0 ⎥ ⎥ 0 0.5 0 ⎦ 0 0 0
(10)
the Stokes vector of the emerging light (Fig. 2) can be expressed as: ⎡ ⎤ S0 → − − → → ⎢ − 0 ⎥ ⎢ S = M45 · S = M45 · MLC · S = ⎣ ⎥ (11) S0 ⎦ 0
emerging light
45 degree linear polarizing film with Mueller matrix M45
Fig. 2. Interaction between an LCP and any incident light with Stokes vector → − S.
Stokes vector (also known as Stokes parameters) fully describes all possible polarization states of incident light → − → − [16]. Stokes vector S of an incident light is changed to S (Stokes vector of the emerging light) after passing an arbitrary polarizing element. The Stokes vector of the emerging light → − S can then be expressed as a linear combination of the four Stokes parameters of the incident light: ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ S0 m00 m01 m02 m03 S0 ⎢ S1 ⎥ ⎢ m10 m11 m12 m13 ⎥ ⎢ S1 ⎥ ⎥ ⎢ ⎥ ⎢ ⎥=⎢ (3) ⎣ S2 ⎦ ⎣ m20 m21 m22 m23 ⎦ · ⎣ S2 ⎦ S3 m30 m31 m32 m33 S3 where the 4 × 4 matrix is known as the Mueller matrix and it can quantitatively characterize the interaction between the incident light and any polarizing element [16]. Fig. 2 illustrates the interaction between an LCP and the → − incident light with Stokes vector S according to Fig. 1. The
where S0 = 0.5S0 + (ac + bd)S1 + [0.5 − (b2 + c2 )]S2 +(ab − cd)S3 (12) Since the first Stokes parameter S0 represents the total intensity of the light, the total intensity of the emerging light in Fig. 2 is: I(φ) = 0.5S0 + (ac + bd)S1 + [0.5 − (b2 + c2 )]S2 +(ab − cd)S3 (13) Therefore, by measuring the intensities after passing the three LCPs in Fig. 1, we can have: I45 = I(φ = 45◦ ) ≈ 0.5S0 + 0.5S1 I−45 = I(φ = −45◦ ) ≈ 0.5S0 − 0.5S1 I0 = I(φ = 0◦ ) = 0.5S0 + 0.5S3
(14)
for the wavelengths in Equation (2), if Mauguin condition in Equation (1) is satisfied. Then the Stokes parameters S0 , S1
638
and S3 including linear and circular polarization information can be acquired: S0 =
I45 + I−45
S1 = S3 =
I45 − I−45 2I0 − I45 − I−45
LCMP (with 45r twisted LC cell) for extracting 0r linearly polarized component LCMP (with -45r twisted LC cell) for extracting 90r linearly polarized component
(15)
LCMP (with untwisted LC cell) for extracting right-handed circularly polarized component
III. L IQUID - CRYSTAL M ICROPOLARIMETER A RRAY I MPLEMENTATION
Superpixel
A. Array Pattern Design It is indicated in Section II that linear and circular information can be revealed by constructing three LCPs to extract Stokes parameters S0 , S1 and S3 . In order to conduct these polarimetries simultaneously and realize real-time linear/circular polarization imaging, a CMOS polarimetric image sensor architecture is proposed with a micro-patterned LCMP array on top (Fig. 3 (A)). The CMOS polarimetric image sensor consists of an LC layer, two LC alignment layers, a metal-wire-grid polarizer (MWGP) and a commerciallyavailable CMOS imager substrate. Fig. 4 illustrates the LCMP array pattern for extracting Stokes parameters S0 , S1 and S3 . In Fig. 4, each “superpixel” contains four LCMPs: one with 45◦ twisted LC cell for 0◦ linearly polarized component, one with -45◦ twisted LC cell for 90◦ linearly polarized component and two with untwisted LC cells for right-handed circularly polarized component. With processing circuitry built adjacent to the four photodetectors covered by the four LCMPs in one “superpixel”, Stokes parameters (S0 , S1 and S3 ) can be generated in real time from I45 , I−45 and I0 according to Equation (15). monochromatic filter photo-patterned LC layer LC alignment layers spacer first substrate (glass)
Fig. 4. Proposed LCMP array pattern with each “superpixel” comprising of LCMPs for extracting 0◦ , 90◦ linearly polarized and right-handed circularly polarized components of incident light.
sulfonic-dye-1 (SD1) was synthesized as the LC alignment material. After sufficient exposure to linearly polarized UV light, SD1 molecules can be photo-aligned with their long molecular axes perpendicular to the polarizing axis of the UV light. Detailed fabrication steps are summarized as follows:
incident light first substrate (glass)
~5˩m CMOS imager substrate
second substrate (glass) as the “dummy” CMOS imager substrate
photodetector
emerging light
45r oriented metal-wire-grid polarizer
(A)
(B)
Fig. 3. (A) Proposed CMOS polarimetric image sensor architecture for linear and circular polarization imaging; (B) Fabricated LCMP array with second glass substrate as “dummy” CMOS imager substrate to enable the LCMP array’s optical characterization (CMOS imager substrate is opaque).
B. Fabrication Process Flow Fig. 3 (B) presents the LCMP array architecture implemented in this work. Opaque CMOS imager substrate with nano-scale patterned MWGP on top in Fig. 3 (A) is replaced by the transparent second glass substrate with nano-scale patterned MWGP on top (from MOXTEK) to enable the optical characterization of fabricated LCMP array. An inner surface and an outer surface are defined for the first glass substrate (Fig. 3 (B)). In addition, ultraviolet(UV)-sensitive
639
1) Clean the inner surface of the first substrate and the MWGP side of the second substrate with an ultravioletozone (UVO) cleaner for 20min to remove organic contaminants and improve the spin coat uniformity of the LC alignment material. 2) Spin coat a solution of SD1 in dimethylformamide (DMF) with a concentration of 1% by weight on the inner surface of the first substrate and the MWGP side of the second substrate at 800rpm for 10s then 3000rpm for 40s. 3) Bake the inner surface of the first substrate and the MWGP side of the second substrate at 110◦ C for 20min to remove the remaining solvent and strengthen the adhesion of SD1 to both substrates. 4) Expose the inner surface of the first substrate to 90◦ linearly polarized UV light for 15min without mask applied, resulting in a 0◦ photoalignment of the SD1 molecules. 5) Expose the MWGP side of the second substrate to -45◦ , 45◦ and 90◦ linearly polarized UV lights, successively with three masks exposing the microdomains of 45◦ twisted, -45◦ twisted and untwisted LC cells, resulting in 45◦ , -45◦ and 0◦ photoalignment of the SD1 molecules in the exposed microdomains, respectively. Each exposure time is 15min. 6) Spray spacers with diameters of 5μm on the inner surface of the first substrate. 7) Assemble the two substrates with the inner surface of the first substrate and the MWGP side of the second substrate facing each other (a 5μm cell gap is formed). 8) Fill the 5μm cell gap with LC E7 (from Merck, Δn=0.225). 9) Laminate a monochromatic filter (500nm according to Equation (2)) on the outer surface of the first substrate to provide monochromatic incident light and protect the whole device from life environmental UV exposure.
5˩m
5˩m
0 degree linearly polarized input
90 degree linearly polarized input
5˩m
left-handed circularly polarized input
(A) (B) (C) Fig. 5. Microphotographs of the fabricated LCMP array: (A) illuminated by 0◦ linearly polarized light; (B) illuminated by 90◦ linearly polarized light; (C) illuminated by left-handed circularly polarized light.
IV. E XPERIMENTAL R ESULTS According to Equation (2), provided with Δn=0.225 and d=5μm, 500nm monochromatic light was used for the fabricated LCMP array’s optical characterization. Fig. 5 shows the microphotographs of the fabricated LCMP array with 0◦ , 90◦ linearly and left-handed circularly polarized lights as input (500nm), respectively. High spatial resolution is achieved with an LCMP pixel size as small as 5μm. Malus measurements were conducted to characterize the LCMPs for extracting 0◦ and 90◦ linearly polarized components. From Fig. 6 (A), it is indicated that Malus’ law is well satisfied for both LCMPs. Fig. 6 (B) presents the spectral measurement results of LCMP for extracting right-handed circularly polarized component. Extinction ratios defined by the quotients of maximum and minimum transmittances are calculated for the three LCMPs at the wavelength of 500nm (Table I). LCMP with untwisted LC cell
Malus measurement with linearly polarized input (500nm)
100
LCMP with 45q twisted LC cell LCMP with -45q twisted LC cell
80 Transmittance (%)
Transmittance (%)
80 60 40
Right-handed circularly polarized input Left-handed circularly polarized input
60 (500nm)
40 20
20 0 0
100
20
40
60
0 80 100 120 140 160 180 400
450
Polarization orientation of incident light (degree)
(A)
500 550 600 Wavelength (nm)
650
700
(B)
Fig. 6. (A) Malus measurement results of LCMPs for extracting 0◦ and 90◦ linearly polarized components; (B) spectral measurement results of LCMP for extracting right-handed circularly polarized component. TABLE I E XTINCTION RATIOS OF DIFFERENT LCMP S LCMP (45◦ twisted LC cell) LCMP (-45◦ twisted LC cell) LCMP (untwisted LC cell)
Wavelength (500nm) 1132 1125 1158
V. C ONCLUSION We have demonstrated a high-resolution LCMP array for visible linear and circular polarization imaging in real time. With LC layer aligned by photo-patterned SD1, an LCMP pixel size as small as 5μm is achieved. Proposed implementation is validated by the reported experimental results and
exhibits an extinction ratio as high as ∼1100 at the wavelength of 500nm. ACKNOWLEDGMENT The authors would like to thank the support from the Research Grant Council of Hong Kong SAR, China. (Project number: 610608) R EFERENCES [1] J. Scott Tyo, D. L. Goldstein, D. B. Chenault and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt., vol. 45, no. 22, pp. 5453-5469, 2006. [2] M. P. Rowe, E. N. Pugh, Jr., J. Scott Tyo and N. Engheta, “Polarizationdifference imaging: a biologically inspired technique for imaging in scattering media,” Opt. Lett., vol. 20, no. 6, pp. 608-610, 1995. [3] S. Lin, K. M. Yemelyanov, E. N. Pugh, Jr. and N. Engheta, “Polarizationbased and specular-reflection-based noncontact latent fingerprint imaging and lifting,” J. Opt. Soc. Am. A, vol. 23, no. 9, pp. 2137-2152, 2006. [4] G. C. Giakos, “Multifusion, multispectral, optical polarimetric imaging sensing principles,” IEEE Trans. Inst. Meas., vol. 55, no. 5, pp. 16281633, 2006. [5] A. G. Andreou and Z. K. Kalayjian, “Polarization Imaging: Principles and Integrated Polarimeters,” IEEE Sens. J., vol. 2, no. 6, pp. 566-576, 2002. [6] J. Guo and D. Brady, “Fabrication of thin-film micropolarizer arrays for visible imaging polarimetry,” Appl. Opt., vol. 39, no. 10, pp. 1486-1492, 2000. [7] M. Momeni and A. H. Titus, “An analog VLSI chip emulating polarization vision of octopus retina,” IEEE Trans. Neur. Netw., vol. 17, no. 1, pp. 222-232, 2006. [8] V. Gruev, Jan Van der Spiegel and N. Engheta, “Image sensor with focal plane polarization sensitivity,” Proc. ISCAS, pp. 1028-1031, 2008. [9] X. Zhao, F. Boussaid, A. Bermak and V. G. Chigrinov, “Thin Photopatterned Micropolarizer Array for CMOS Image Sensors,” IEEE Photon. Technol. Lett., vol. 21, no. 12, pp. 805-807, 2009. [10] G. D. Gilbert and J. C. Pernicka, “Improvement of underwater visibility by reduction of backscatter with a circular polarization technique,” Appl. Opt., vol. 6, no. 4, pp. 741-746, 1967. [11] J. Cariou, B. L. Jeune, J. Lotrian and Y. Guern, “Polarization effects of seawater and underwater targets,” Appl. Opt., vol. 29, no. 11, pp. 16891695, 1990. [12] P. C. Y. Chang, J. G. Walker, K. I. Hopcraft, B. Ablitt and E. Jakeman, “Polarization discrimination for active imaging in scattering media,” Opt. Commun., vol. 159, no. 1, pp. 1-6, 1999. [13] K. Turpin, J. G. Walker, P. C. Y. Chang, K. I. Hopcraft, B. Ablitt and E. Jakeman, “The influence of particle size in active polarization imaging in scattering media,” Opt. Commun., vol. 168, no. 5, pp. 325-335, 1999. [14] L. B. Wolff, T. A. Mancini, P. Pouliquen and A. G. Andreou, “Liquid Crystal Polarization Camera,” IEEE Trans. Robot. Autom., vol. 13, no. 2, pp. 195-203, 1997. [15] F. Goudail, P. Terrier, Y. Takakura, L. Bigue, F. Galland and V. DeVlaminck, “Target detection with a liquid-crystal-based passive Stokes polarimeter,” Appl. Opt., vol. 43, no. 2, pp. 274-282, 2004. [16] D. Goldstein, Polarized Light, 2nd Edition, New York: Marcel Dekker, 2003. [17] S. T. Tang and H. S. Kwok, “Mueller calculus and perfect polarization conversion modes in liquid crystal displays,” J. Appl. Phys., vol. 89, no. 10, pp. 5288-5294, 2001.
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Xiaojin Zhao1,2, Amine Bermak1, Farid Boussaid2 and Vladimir G. Chigrinov1 Department of ECE, Hong Kong University of Science & Technology, Hong Kong SAR, China 2 School of EECE, University of Western Australia, Perth, WA 6009, Australia Email: [email protected]
Abstract—In this paper, we propose a liquid-crystal micropolarimeter (LCMP) array with high spatial resolution for real-time linear and circular polarization imaging in visible spectrum. LCMPs for extracting 0◦ , 90◦ linearly and righthanded circularly polarized components of incident light are implemented by micro-patterning a liquid crystal (LC) layer on top of a 45◦ oriented ultra-thin metal-wire-grid polarizer (MWGP). A compact LCMP pitch of 5µm×5µm is achieved with sulfonic-dye-1 (SD1) as the LC alignment material. In addition, these micron-scale LCMPs feature ∼ 5µm overall thickness and ∼1100 extinction ratio. Reported experimental results validate the concept of real-time linear and circular polarization image sensing and processing with targets illuminated by collimated artificial light.
I. I NTRODUCTION Polarization imaging ignored in conventional intensity/color based imaging has been proven to be a very important feature [1]. Demonstrated applications include remote satellite image sensing/segmentation [1], machine vision with scattering media [2], non-contact fingerprint detection [3] and classification/analysis of biological tissues [4]. Promising realtime polarization imaging/processing is enabled by sensing polarimetries of different polarization components of a targeted image scene. A commercially available complementary metaloxide-semiconductor (CMOS) camera can be applied for realtime polarization imaging/processing by covering its individual photo-sensitive pixels with micrometer-scale polarizing elements. A micropolarimeter array, which is composed of micropolarimeters for extracting different polarization components of incident light, is thus an indispensable optical device [5]. Previously reported micropolarimeter array implementations mainly concentrate on the extraction of linearly or partiallylinear polarized components [6]–[9]. These approaches are generally adequate for passive polarization imaging, where image scene is illuminated by sunlight or some other natural sources with rare circularly polarized component. Circular polarization imaging enabled by the circularly polarized component extraction can further reveal the information regarding the object surface features, shape, shading and roughness [10]. G. D. Gilbert et al paved the way of active circular polarization imaging by using collimated artificial light with intentionally added circularly polarized components as the active source [10]. Several related implementations were reported subsequently [11]–[13]. However, with unpatterned mechanically or
978-1-4244-5309-2/10/$26.00 ©2010 IEEE
electrically configured phase retardation device, none of them can simultaneously extract and analyze the polarized components in real-time. In addition, complex image registration algorithm cannot be avoided to address the issues induced by any movement in image scene. In this paper, a high-resolution liquid-crystal micropolarimeter (LCMP) array is proposed to realize real-time linear and circular polarization imaging. LCMPs for extracting 0◦ , 90◦ linearly and right-handed circularly polarized components of incident light are implemented by micro-patterning a liquid crystal (LC) layer on top of a 45◦ oriented ultra-thin metalwire-grid polarizer (MWGP). This paper is organized as follows. In Section II, the principle of liquid crystal based polarimeter is reviewed. In Section III, pattern design and fabrication process flow of the proposed LCMP array are described. Section IV presents the reported experimental results. Finally, this paper is concluded by Section V. II. P RINCIPLE OF L IQUID C RYSTAL BASED P OLARIMETER Liquid crystal based polarimeter (LCP) has been proven a powerful tool for extracting and analyzing all kinds of polarization components in the incident light [14][15]. By orienting the LC alignment layers to configure the LC molecules arrangement, the LC cell can behave optically as polarization rotator, polarization phase retarder, .etc. Fig. 1 presents three LCPs with different LC molecules arrangements. LC molecules are oriented by aligning the top alignment layer along one reference direction and the bottom alignment layer along another direction having a twist angle φ with respect to the above-mentioned reference direction. In Fig. 1 (A) and (B), 45◦ twisted (φ = 45◦ ) and -45◦ twisted (φ = −45◦ ) LC cells are optically equal to 45◦ and -45◦ polarization rotators if Mauguin condition is satisfied: Δn · d >> λ
(1)
where Δn is the LC birefringence, d is the thickness of the LC layer, λ is the wavelength of the incident light. In Fig. 1 (C), untwisted (φ = 0◦ ) LC cell is optically equal to quarter wavelength retarder for the wavelengths: λ=
4 · Δn · d , (m = 0, 1, 2...) 4m + 1
(2)
Combining the 45◦ linear polarizing film (Fig. 1), three different LCPs can be used for extracting 0◦ , 90◦ linearly
637
polarized and right-handed circularly polarized components of the incident light, respectively. This can be verified by the following analysis with Stokes vector and Mueller matrix.
Mueller matrix of an LC cell with twist angle φ is given as follows [17]: MLC = 1 0 0 0 ⎢ 0 1 − 2(c2 + d2 ) 2(bd − ac) −2(ad + bc) ⎢ ⎣ 0 2(ac + bd) 1 − 2(b2 + c2 ) 2(ab − cd) 0 2(ad − bc) −2(ab + cd) 1 − 2(b2 + d2 ) ⎡
incident light
incident light
incident light
LC alignment layers
45 degree linear polarizing film emerging light
emerging light
emerging light
(A) 45r twisted LC
(B) -45r twisted LC
(C) Untwisted LC
a
= cos(φ)cos(χ) +
b
=
c
=
d =
Fig. 1. Three LCPs with different LC molecules arrangements: (A) LCP for extracting 0◦ linearly polarized component with 45◦ twisted LC cell; (B) LCP for extracting 90◦ linearly polarized component with -45◦ twisted LC cell; (C) LCP for extracting right-handed circularly polarized component with untwisted LC cell.
χ
=
Γ
=
Provided with the film [16]:
Liquid crystal based polarimeter
Stokes vector
Stokes vector
Stokes vector
S
S’
S’’
incident light
Liquid-crystal layer with Mueller matrix MLC
⎥ ⎥ ⎦
with
LC molecules
LC molecules
⎤
M45
φ sin(φ)sin(χ) χ
(4)
Γ cos(φ)sin(χ) (5) 2χ φ sin(φ)cos(χ) − cos(φ)sin(χ) (6) χ Γ sin(φ)sin(χ) (7) 2χ 2 Γ 2 φ + (8) 2 2π · Δn · d (9) λ Mueller matrix of the 45◦ linear polarizing ⎡
0.5 ⎢ 0 =⎢ ⎣ 0.5 0
⎤ 0 0.5 0 0 0 0 ⎥ ⎥ 0 0.5 0 ⎦ 0 0 0
(10)
the Stokes vector of the emerging light (Fig. 2) can be expressed as: ⎡ ⎤ S0 → − − → → ⎢ − 0 ⎥ ⎢ S = M45 · S = M45 · MLC · S = ⎣ ⎥ (11) S0 ⎦ 0
emerging light
45 degree linear polarizing film with Mueller matrix M45
Fig. 2. Interaction between an LCP and any incident light with Stokes vector → − S.
Stokes vector (also known as Stokes parameters) fully describes all possible polarization states of incident light → − → − [16]. Stokes vector S of an incident light is changed to S (Stokes vector of the emerging light) after passing an arbitrary polarizing element. The Stokes vector of the emerging light → − S can then be expressed as a linear combination of the four Stokes parameters of the incident light: ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ S0 m00 m01 m02 m03 S0 ⎢ S1 ⎥ ⎢ m10 m11 m12 m13 ⎥ ⎢ S1 ⎥ ⎥ ⎢ ⎥ ⎢ ⎥=⎢ (3) ⎣ S2 ⎦ ⎣ m20 m21 m22 m23 ⎦ · ⎣ S2 ⎦ S3 m30 m31 m32 m33 S3 where the 4 × 4 matrix is known as the Mueller matrix and it can quantitatively characterize the interaction between the incident light and any polarizing element [16]. Fig. 2 illustrates the interaction between an LCP and the → − incident light with Stokes vector S according to Fig. 1. The
where S0 = 0.5S0 + (ac + bd)S1 + [0.5 − (b2 + c2 )]S2 +(ab − cd)S3 (12) Since the first Stokes parameter S0 represents the total intensity of the light, the total intensity of the emerging light in Fig. 2 is: I(φ) = 0.5S0 + (ac + bd)S1 + [0.5 − (b2 + c2 )]S2 +(ab − cd)S3 (13) Therefore, by measuring the intensities after passing the three LCPs in Fig. 1, we can have: I45 = I(φ = 45◦ ) ≈ 0.5S0 + 0.5S1 I−45 = I(φ = −45◦ ) ≈ 0.5S0 − 0.5S1 I0 = I(φ = 0◦ ) = 0.5S0 + 0.5S3
(14)
for the wavelengths in Equation (2), if Mauguin condition in Equation (1) is satisfied. Then the Stokes parameters S0 , S1
638
and S3 including linear and circular polarization information can be acquired: S0 =
I45 + I−45
S1 = S3 =
I45 − I−45 2I0 − I45 − I−45
LCMP (with 45r twisted LC cell) for extracting 0r linearly polarized component LCMP (with -45r twisted LC cell) for extracting 90r linearly polarized component
(15)
LCMP (with untwisted LC cell) for extracting right-handed circularly polarized component
III. L IQUID - CRYSTAL M ICROPOLARIMETER A RRAY I MPLEMENTATION
Superpixel
A. Array Pattern Design It is indicated in Section II that linear and circular information can be revealed by constructing three LCPs to extract Stokes parameters S0 , S1 and S3 . In order to conduct these polarimetries simultaneously and realize real-time linear/circular polarization imaging, a CMOS polarimetric image sensor architecture is proposed with a micro-patterned LCMP array on top (Fig. 3 (A)). The CMOS polarimetric image sensor consists of an LC layer, two LC alignment layers, a metal-wire-grid polarizer (MWGP) and a commerciallyavailable CMOS imager substrate. Fig. 4 illustrates the LCMP array pattern for extracting Stokes parameters S0 , S1 and S3 . In Fig. 4, each “superpixel” contains four LCMPs: one with 45◦ twisted LC cell for 0◦ linearly polarized component, one with -45◦ twisted LC cell for 90◦ linearly polarized component and two with untwisted LC cells for right-handed circularly polarized component. With processing circuitry built adjacent to the four photodetectors covered by the four LCMPs in one “superpixel”, Stokes parameters (S0 , S1 and S3 ) can be generated in real time from I45 , I−45 and I0 according to Equation (15). monochromatic filter photo-patterned LC layer LC alignment layers spacer first substrate (glass)
Fig. 4. Proposed LCMP array pattern with each “superpixel” comprising of LCMPs for extracting 0◦ , 90◦ linearly polarized and right-handed circularly polarized components of incident light.
sulfonic-dye-1 (SD1) was synthesized as the LC alignment material. After sufficient exposure to linearly polarized UV light, SD1 molecules can be photo-aligned with their long molecular axes perpendicular to the polarizing axis of the UV light. Detailed fabrication steps are summarized as follows:
incident light first substrate (glass)
~5˩m CMOS imager substrate
second substrate (glass) as the “dummy” CMOS imager substrate
photodetector
emerging light
45r oriented metal-wire-grid polarizer
(A)
(B)
Fig. 3. (A) Proposed CMOS polarimetric image sensor architecture for linear and circular polarization imaging; (B) Fabricated LCMP array with second glass substrate as “dummy” CMOS imager substrate to enable the LCMP array’s optical characterization (CMOS imager substrate is opaque).
B. Fabrication Process Flow Fig. 3 (B) presents the LCMP array architecture implemented in this work. Opaque CMOS imager substrate with nano-scale patterned MWGP on top in Fig. 3 (A) is replaced by the transparent second glass substrate with nano-scale patterned MWGP on top (from MOXTEK) to enable the optical characterization of fabricated LCMP array. An inner surface and an outer surface are defined for the first glass substrate (Fig. 3 (B)). In addition, ultraviolet(UV)-sensitive
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1) Clean the inner surface of the first substrate and the MWGP side of the second substrate with an ultravioletozone (UVO) cleaner for 20min to remove organic contaminants and improve the spin coat uniformity of the LC alignment material. 2) Spin coat a solution of SD1 in dimethylformamide (DMF) with a concentration of 1% by weight on the inner surface of the first substrate and the MWGP side of the second substrate at 800rpm for 10s then 3000rpm for 40s. 3) Bake the inner surface of the first substrate and the MWGP side of the second substrate at 110◦ C for 20min to remove the remaining solvent and strengthen the adhesion of SD1 to both substrates. 4) Expose the inner surface of the first substrate to 90◦ linearly polarized UV light for 15min without mask applied, resulting in a 0◦ photoalignment of the SD1 molecules. 5) Expose the MWGP side of the second substrate to -45◦ , 45◦ and 90◦ linearly polarized UV lights, successively with three masks exposing the microdomains of 45◦ twisted, -45◦ twisted and untwisted LC cells, resulting in 45◦ , -45◦ and 0◦ photoalignment of the SD1 molecules in the exposed microdomains, respectively. Each exposure time is 15min. 6) Spray spacers with diameters of 5μm on the inner surface of the first substrate. 7) Assemble the two substrates with the inner surface of the first substrate and the MWGP side of the second substrate facing each other (a 5μm cell gap is formed). 8) Fill the 5μm cell gap with LC E7 (from Merck, Δn=0.225). 9) Laminate a monochromatic filter (500nm according to Equation (2)) on the outer surface of the first substrate to provide monochromatic incident light and protect the whole device from life environmental UV exposure.
5˩m
5˩m
0 degree linearly polarized input
90 degree linearly polarized input
5˩m
left-handed circularly polarized input
(A) (B) (C) Fig. 5. Microphotographs of the fabricated LCMP array: (A) illuminated by 0◦ linearly polarized light; (B) illuminated by 90◦ linearly polarized light; (C) illuminated by left-handed circularly polarized light.
IV. E XPERIMENTAL R ESULTS According to Equation (2), provided with Δn=0.225 and d=5μm, 500nm monochromatic light was used for the fabricated LCMP array’s optical characterization. Fig. 5 shows the microphotographs of the fabricated LCMP array with 0◦ , 90◦ linearly and left-handed circularly polarized lights as input (500nm), respectively. High spatial resolution is achieved with an LCMP pixel size as small as 5μm. Malus measurements were conducted to characterize the LCMPs for extracting 0◦ and 90◦ linearly polarized components. From Fig. 6 (A), it is indicated that Malus’ law is well satisfied for both LCMPs. Fig. 6 (B) presents the spectral measurement results of LCMP for extracting right-handed circularly polarized component. Extinction ratios defined by the quotients of maximum and minimum transmittances are calculated for the three LCMPs at the wavelength of 500nm (Table I). LCMP with untwisted LC cell
Malus measurement with linearly polarized input (500nm)
100
LCMP with 45q twisted LC cell LCMP with -45q twisted LC cell
80 Transmittance (%)
Transmittance (%)
80 60 40
Right-handed circularly polarized input Left-handed circularly polarized input
60 (500nm)
40 20
20 0 0
100
20
40
60
0 80 100 120 140 160 180 400
450
Polarization orientation of incident light (degree)
(A)
500 550 600 Wavelength (nm)
650
700
(B)
Fig. 6. (A) Malus measurement results of LCMPs for extracting 0◦ and 90◦ linearly polarized components; (B) spectral measurement results of LCMP for extracting right-handed circularly polarized component. TABLE I E XTINCTION RATIOS OF DIFFERENT LCMP S LCMP (45◦ twisted LC cell) LCMP (-45◦ twisted LC cell) LCMP (untwisted LC cell)
Wavelength (500nm) 1132 1125 1158
V. C ONCLUSION We have demonstrated a high-resolution LCMP array for visible linear and circular polarization imaging in real time. With LC layer aligned by photo-patterned SD1, an LCMP pixel size as small as 5μm is achieved. Proposed implementation is validated by the reported experimental results and
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