Abstract

In this paper, we present a liquid-crystal-polymer (LCP)-based dual-layer micro-quarter-wave-retarder (MQWR) array for active polarization image sensors. The proposed MQWRs, for the first time, enable the extraction of the incident light’s circularly polarized components in the whole visible regime, which correspond to the fourth parameter of Stokes vector. Compared with the previous implementations, our proposed MQWRs feature high achromaticity, making their applications no longer limited to monochromatic illumination. In addition, the presented thin structure exhibits an overall thickness of 2.43μm, leading to greatly alleviated optical cross-talk between adjacent photo-sensing pixels. Moreover, the reported superior optical performance (e.g. minor transmittance, extinction ratio) validates our optical design and optimization of the proposed MQWRs. Furthermore, the demonstrated simple fabrication recipe offers a cost-effective solution for the monolithic integration between the proposed MQWR array and the commercial solid-state image sensors, which makes the multi-spectral full Stokes polarization imaging system on a single chip feasible.

© 2014 Optical Society of America

1. Introduction

The past few years have witnessed a rapid development of monolithic polarization image sensors, known as division of focal plane (DoFP) polarimeters [116]. With integrated micro-polarizing filters, the incident light’s different polarized components can be extracted and processed to reveal the imaged objects’ wide range of physical or chemical properties in real time [1, 2]. According to the exploited light sources, the polarization imaging can be divided into two categories: passive polarization imaging and active polarization imaging. In most passive polarization imaging scenarios, natural light source (e.g. sunlight) or typical man-made indoor/outdoor illumination light source is adopted and it is found that the circularly polarized components are rare [36, 810, 12, 13, 15]. This is an important factor that very few of the previously reported DoFP implementations can have circularly polarized components extracted [11, 14]. However, it was reported by Roberts et al. that circular polarization vision is an everyday behavior for a series of ocean creatures [17, 18]. In addition, in scenarios where the aforesaid natural or typical illumination light sources are very poor even not available, the active polarization imaging with specifically-designed light source can play a key role, where the circularly polarized components are non-neglectable [19]. Moreover, Stokes vector is known as the full description of all possible polarization states and its fourth parameter just represents the circularly polarized components [20]. As a result, the extraction of the circularly polarized components is not only a theoretical requirement for complete polarization imaging (so-called full Stokes imaging), but also inevitable in a wide range of active polarization imaging applications.

In [11], we reported the first micro-polarizing device for DoFP-based full Stokes imaging, where the demonstrated liquid crystal micro-polarimiter array is capable of exacting both right-handed and left-handed circularly polarized components. Due to the non-ideal achromaticity of the proposed nematic liquid crystal based phase retarder, the light source for the reported implementation is limited to very narrow spectrum. Recently, Myhre et al. proposed to fabricate the circular micropolarimeter with liquid crystal polymer (LCP) and a monolithic system was presented for full Stokes imaging [14]. Nevertheless, the proposed implementation still suffers from the same problem of large chromaticity, which means the device can only be operated at a specific visible wavelength, which is not tunable once the whole system is manufactured. This poses a great challenge for field application and makes the promising multi-spectral polarization imaging infeasible [19, 21]. In [22], only an optical design of wideband quarter-wave plate was proposed, there is neither real physical implementation demonstrated nor minimum achievable spatial resolution reported.

In this paper, we design, fabricate and characterize, to the best of our knowledge, the first patterned dual-layer micro-quarter-wave-retarder (MQWR) array with high achromaticity for the whole visible spectrum. Combined with unpatterned linear polarizer, the proposed implementation can extract both the right-handed and left-handed circularly polarized components in real time. Moreover, the demonstrated MQWRs, featuring high spatial resolution, are validated by the reported simulation and experimental results. With the proposed low-cost manufacturing process flow, they can be readily integrated on top of the commercial or customized solid-state image sensor wafer. The rest of this paper is organized as follows: the optical design and optimization of our dual-layer MQWRs are presented in Section 2; Section 3 describes the detailed fabrication process of our proposed implementations; the experimental results are reported and discussed in Section 4; this paper is finally concluded in Section 5.

2. Optical design of the dual-layer MQWRs

It is well-known that single-layer zero order phase retarder can provide the following phase retardation Γ to the incident light with a given wavelength λ:

Γ=2πΔn(λ)dλ
where Δn(λ) and d are the phase retarder’s birefringence and thickness, respectively. According to Eq. (1), in the visible spectrum, a single-layer based zero order quarter wave retarder (QWR) can exert a phase retardation of 0.5π for a specific λ0; meanwhile, for birefringent materials with low birefringence variation over the visible spectrum, the same QWR can provide a phase retardation largely different from 0.5π due to the non-ideal achromaticity, especially for the wavelengths far from λ. Take the liquid crystal E7 for example, the single-layer based zero order QWR for 520nm (Δn ≈ 0.25) can have retardations of 0.62π and 0.37π for 460nm (Δn ≈ 0.275) and 625nm (Δn ≈ 0.225) of visible spectrum [23], which correspond to deviations as large as 24% and 26%, respectively. In order to improve the poor achromaticity of single-layer zero-order retarder, we propose a dual-layer thin MQWR to provide quarter wave retardation for the whole visible spectrum. Although ultra-high achromaticity can be achieved with triple or even more retarder layers [20,24], we stick to dual layers to minimize the overall thickness as well as the DoFP polarimeter’s optical cross-talk induced by oblique incidence.

As illustrated in Fig. 1(a), the optical cross-talk is caused by the fact that the micro-polarizing elements’ top surface are typically located at some vertical distance from the photo-sensing pixel, where the vertical distance is equal to the overall thickness of the micro-polarizing elements and their underlying passivation layers. Consequently, light coming from non-orthogonal directions and passing through the target micro-polarizing element can be partially absorbed by its adjacent photo-sensing pixel. From Fig. 1(b), it is straightforward to find that the optical cross-talk can be effectively alleviated by reducing the micro-polarizing elements’ thickness, which is proportional to the aspect ratio between its thickness and pitch size. Figure 2 presents the proposed MQWR array consisting of MQWRs with 45° and 135° equivalent fast axes, which are denoted as 45° MQWR and 135° MQWR, respectively. Each MQWR includes two stacked micron-scale retardation layers, both of which are customized QWR and half wave retarder (HWR) for the wavelength of 550nm. For simplicity, the birefringence Δn is assumed constant over the visible spectrum and its color dispersion is not included in the following deductions. It is known that the Mueller matrix fully describes any optical device’s polarization property [20]. Given a retarder with retardation of φ and fast axis angle of θ, its Mueller matrix Mretarder can be expressed as follows [20]:

Mretarder(φ,θ)=[10000cos22θ+cosφsin22θ(1cosφ)sin2θcos2θsinφsin2θ0(1cosφ)sin2θcos2θsin22θ+cosφcos22θsinφcos2θ0sinφsin2θsinφcos2θcosφ]

As shown in Fig. 2(a), for 45° MQWR, its HWR with φ1 = π and QWR with φ2 = 0.5π are placed with their fast axes along θ1 and θ2, respectively. Consequently, its equivalent Mueller matrix M45°MQWR is derived as:

M45°MQWR=Mretarder(π2,θ2)Mretarder(π,θ1)

If we set θ1 = 45° and θ2 = 135°, for the wavelength of 550 nm, M45°MQWR is equal to the Mueller matrix M45°ideal–QWR of an ideal achromatic QWR with its fast axis along 45° [20]:

M45°idealQWR=[1000000100100100]
As a result, for our achromatic MQWR design, we minimize the number of the parameters-to-be-determined by assuming θ2 = 2θ1 + 45°. This can significantly reduce the total computation complexity and its effectiveness is validated by both the reported simulation and experimental results. Here we assume a circularly polarized incident light with its Stokes vector expressed as (1,0,0,±1). Provided with an ideal achromatic QWR (fast axis along 45°), the emerging light is linearly polarized with its polarization orientation along 90° or 0° [20]. Therefore, we can obtain the most optimized MQWR design by comparing its equivalent Mueller matrix M45°MQWR to that of the ideal achromatic QWR (i.e. M45°ideal–QWR). Specifically, we calculate the root-mean-square error (RMSE) of the Mueller matrix’s corresponding elements for different wavelengths ranging from 400nm to 700nm; meanwhile, the HWR’s fast axis angle θ1 is tuned to minimize the RMSE. As presented in Fig. 3, it is indicated that the RMSE achieves the minimum with the HWR’s fast axis angle θ1 set to be 15°. Therefore, according to Eq. (3), θ1 = 15° and θ2 = 75° are chosen as the fast axis orientations of the proposed dual-layer 45° MQWR’s HWR and QWR, respectively. The same strategy is applied for the design of 135° MQWR in Fig. 2(b), and its HWR’s fast axis angle θ3 is determined to be 165° and QWR’s fast axis angle θ4 is determined to be 105°. In addition, in order to illustrate the achromaticity improvement of our proposed dual-layer MQWRs, we plot the calculated retardation figures of both our proposed MQWR and the traditional single-layer zero order retarder in Fig. 4. The second vertical axis is added to describe the detailed dispersion of our proposed MQWRs. It is observed that the proposed thin dual-layer MQWR exhibits significantly improved achromaticity compared with its single-layer counterpart.

 figure: Fig. 1

Fig. 1 Optical cross-talk caused by the oblique incidence: (a) thick patterned retarder layer; (b) thin patterned retarder layer.

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 figure: Fig. 2

Fig. 2 Optical design of the proposed MQWRs: (a) 45°MQWR; (b) 135°MQWR.

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 figure: Fig. 3

Fig. 3 The relationship between the RMSE and the fast axis angle θ1 of the HWR.

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 figure: Fig. 4

Fig. 4 The achromaticity comparison between the single-layer zero order QWR for 550 nm light and the proposed dual-layer achromatic MQWR.

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3. Fabrication of the proposed dual-layer MQWR array

According to the optimized design parameters, we fabricated the proposed MQWRs by patterning a layer of QWR (550nm) and a layer of HWR (550nm) on two transparent glass substrates separately. Then the two substrates were well-aligned and assembled with ultraviolet (UV) curable glue under high-resolution microscope. The 550nm QWR and HWR with predetermined thickness were formed by spin-coating LCP (from DIC corp.) on the two substrates. Suppose the LCP’s birefringence is equal to Δn, the effective retardation in Eq. (1) can be varied by changing the layer’s thickness, which is closely correlated to the adopted spin coat speed. The spin-speed dependence of the LCP layer thickness is characterized and plotted in Fig. 5. In addition, the aforesaid patterned QWR/HWR layers are formed by photo-aligning a layer of sulfonic-dye-1 (SD1) from DIC corp., which features ultra-high spatial resolution and functions as the alignment layer of the adopted LCP [25]. As illustrated in Fig. 6, the whole fabrication process flow is detailed as follows:

  1. An ultraviolet-ozone cleaning machine is used to remove the organic contaminants from the surfaces of two transparent glass substrates.
  2. A solution of SD1 in dimethylformamide with a concentration of 1% by weight is prepared in advance and filtered in order to eliminate the particle impurities.
  3. The aforesaid SD1 solution is spin-coated onto the two glass substrates (first at 800rpm for 10s then 3000rmp for 40s).
  4. The two glass substrates are then soft-baked at 110°C for 20min, which can eliminate the remaining solvent and strengthen the adhesion between the SD1 and the glass substrates.
  5. The spin-coated SD1 layers on the two glass substrates are subsequently photo-aligned using four successive masked exposures. 105°, 165°, 75° and 15° linearly polarized UV light (365nm) are adopted to form the QWR/HWR microdomains with their fast axis angles θ1, θ2, θ3, θ4 equal to 15°, 75°, 165°, 105°, respectively. For each exposure, the duration is around 25min with the UV light intensity equal to 3.36mW/cm2.
  6. After patterning the photoalignment layer SD1, the LCP solution is spin-coated on top of the first substrate at a speed of 800rpm for 30s to form the HWR and the second substrate at a speed of 3000rpm for 30s to form the QWR.
  7. Successively, the two substrates are baked at 50°C for 3min to eliminate the solvents. Then UV light (254nm) with an intensity of 2mW/cm2 is applied for 5min to polymerize the LCP material.
  8. Finally, the two substrates are assembled with the UV curable glue under high-resolution microscope: 15° HWR microdomain of the first substrate and the 75° QWR microdomain of the second substrate are aligned to each other; while the 165° HWR microdomain of the first substrate and the 105° QWR microdomain of the second substrate are aligned to each other.

 figure: Fig. 5

Fig. 5 Measured LCP film thickness with different spin coat speeds.

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 figure: Fig. 6

Fig. 6 The fabrication process flow of our proposed MQWR array.

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4. Experimental results

In this section, we characterize our fabricated dual-layer MQWRs by measuring its minor transmittance and extinction ratio with collimated circularly polarized incident light. The test setup for our fabricated MQWR array is presented in Fig. 7. Specifically, a broadband circular polarizer was inserted between a mini deuterium halogen light source (from Ocean Optics Inc.) and the fabricated sample. The customized broad-band circular polarizer is composed of a high quality wire-grid-based linear polarizer from Moxtek Inc. and a commercial broad-band QWR from Nitto Denko Corp., which can provide a right-handed or left-handed circularly polarized input with the wavelength varied from 400nm to 700nm. After passing our fabricated MQWR array, a linear polarizer from Moxtek Inc. is oriented at 45° as the analyzer to differentiate the 45° MQWRs and 135° MQWRs.

 figure: Fig. 7

Fig. 7 Test setup of our fabricated MQWR array.

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Figure 8 presents the measured minor transmittance of our proposed dual-layer 45° MQWR, which is compared with that of the single-layer QWR. It is observed that our proposed implementation features much higher achromaticity, showing excellent agreement with our reported simulation results (Fig. 4). In addition, we also measured the extinction ratio between the right-handed and left-handed circularly polarized inputs and plot the results in Fig. 9. For 45° MQWRs, we define the extinction ratio as the ratio of the transmittance of left-handed circularly polarized input to the transmittance of right-handed circularly polarized input. Moreover, our fabricated sample was examined by a microscope with collimated right-handed and left-handed circularly polarized white light source, respectively. With the readily available photolithography masks featuring varied spatial resolutions from 8μm to 50μm, the MQWRs’ effectiveness have been proven by both fabricated 1D and 2D MQWR arrays shown in Fig. 10. The most compact MQWR pitch size is demonstrated to be 8μm. For Fig. 10(a) and (b), right-handed circularly polarized input is provided. After passing our fabricated MQWR array, the micro-domains of 45° MQWRs convert the right-handed circularly polarized input into 45° linearly polarized light, which is transmitted by the analyzer (i.e. linear polarizer along 45°); while the micro-domains of 135° MQWRs convert the right-handed circularly polarized input into 135° linearly polarized light, which is blocked by the same analyzer. Therefore, the micro-domains of 45° MQWRs appear bright and the micro-domains of 135° MQWRs appear dark. For Fig. 10(c) and (d), left-handed circularly polarized input is provided. After passing our fabricated MQWR array, the micro-domains of 45° MQWRs convert the left-handed circularly polarized input into 135° linearly polarized light, which is blocked by the aforesaid same analyzer; while the micro-domains of 135° MQWRs convert the left-handed circularly polarized input into 45° linearly polarized light, which is transmitted by the aforesaid same analyzer. Therefore, the micro-domains of 45° MQWRs appear dark and the micro-domains of 135° MQWRs appear bright.

 figure: Fig. 8

Fig. 8 Measured spectral minor transmittance for single-layer zero order QWR (550 nm) and the proposed dual-layer 45° MQWR (8μm spatial resolution) with left-handed circularly polarized incident light.

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 figure: Fig. 9

Fig. 9 Measured spectral extinction ratio for our proposed dual-layer 45° MQWR (8μm spatial resolution) with circularly polarized incident light.

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 figure: Fig. 10

Fig. 10 Microphotographs of the fabricated MQWR array with (a) (b) right-handed circularly polarized input polarized input polarized input; (c) (d) left-handed circularly polarized input.

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Furthermore, a 2.43μm overall thickness of the dual-layer MQWR was measured with a surface profiler from KLA-Tencor Corp. This corresponds to an aspect ratio of 0.304 (i.e. 2.43μm/8μm) and leads to an ultra-low optical cross-talk when the device is applied to large angle oblique incidence. Compared with the previous micro-polarizing devices, to the best of our knowledge, this is the first patterned MQWR array with high achromaticity ever reported. What is more, the proposed fabrication technology, featuring simplicity, low cost and low optical cross-talk, is fully compatible with the fabrication process of the solid-state image sensors. This paves the way of monolithic integration between our proposed MQWR array and the commercial or customized charge-coupled-device (CCD) or complementary-metal-oxide-semiconductor (CMOS) imagers. Concretely, our proposed fabrication recipe does not require any selective etching to expose the I/O pads for wire bonding. After spin-coating the LCP on top of the image sensor substrate, a photolithography mask is applied to shield the I/O pads region. As a result, the LCP in the exposed region is selectively polymerized while the unpolymerized LCP on top of the I/O pads can be completely washed away by rinsing the whole image sensor substrate with the corresponding solvent.

5. Conclusion

We demonstrate a high-resolution achromatic MQWR array for the DoFP-based polarization image sensors. The proposed MQWRs are capable of extracting the circularly polarized components at different wavelengths ranging from 400nm to 700nm. By patterning the MQWRs along perpendicular fast axis orientations, the emerging light passing through the two MQWRs can be sensed by the solid-state imager’s photo-sensing pixels and real-time processed with the on-chip analog/digital circuitry to generate the fourth parameter of Stokes vector. Combined with the previous widely-presented micro-polarizing devices for extracting the first three Stokes parameters, multi-spectral full Stokes polarization imaging in the whole visible spectrum is enabled. Additionally, the reported cost-effective fabrication process flow, featuring a high spatial resolution of 8μm, is fully compatible with the advanced semiconductor process for manufacturing solid-state image sensors. This motivates us to utilize the well-known mature liquid-crystal on silicon (LCoS) process to integrate our LCP based broad-band MQWR array and realize the mass production of the promising achromatic full Stokes polarization image sensors.

Acknowledgments

This work was supported by the National Natural Science Foundation of China ( 61204063, 61275167), the Natural Science Foundation of Guangdong Province ( S2012040008076), the Kongque Technology Innovation Foundation of Shenzhen ( KQCX20120807153227588), the Fundamental Research Foundation of Shenzhen ( JCYJ20120614084838357) and the HK Innovation and Technology Fund ITF ( GHP/018/11SZ).

References and links

1. A. G. Andreou and Z. K. Kalayjian, “Polarization imaging: principles and integrated polarimeters,” IEEE Sens. J. 2, 566–576 (2002). [CrossRef]  

2. J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006). [CrossRef]   [PubMed]  

3. J. Guo and D. Brady, “Fabrication of thin-film micropolarizer arrays for visible imaging polarimetry,” Appl. Opt. 39, 1486–1492 (2000). [CrossRef]  

4. C. K. Harnett and H. G. Craighead, “Liquid-crystal micropolarizer array for polarization-difference imaging,” Appl. Opt. 41, 1291–1296 (2002). [CrossRef]   [PubMed]  

5. M. Momeni and A. H. Titus, “An analog VLSI chip emulating polarization vision of octopus retina,” IEEE Trans. Neur. Netw. 7, 222–232 (2006). [CrossRef]  

6. V. Gruev, A. Ortu, N. Lazarus, Jan Van der Spiegel, and N. Engheta, “Fabrication of a dual-tier thin film micropolarization array,” Opt. Express 15, 4994–5007 (2007). [CrossRef]   [PubMed]  

7. R. Harding, I. Gardiner, H. J. Yoon, T. Perrett, O. Parri, and K. Skjonnemand, “Reactive liquid crystal materials for optically anisotropic patterned retarders,” Proc. SPIE 7140, 71402J (2008). [CrossRef]  

8. X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “Thin photo-patterned micropolarizer array for CMOS image sensors,” IEEE Photon. Technol. Lett. 21, 805–807 (2009). [CrossRef]  

9. V. Gruev, R. Perkins, and T. York, “CCD polarization imaging sensor with aluminum nanowire optical filters,” Opt. Express 18, 19087–19094 (2010). [CrossRef]   [PubMed]  

10. V. Gruev, Jan Van der Spiegel, and N. Engheta, “Dual-tier thin film polymer polarization imaging sensor,” Opt. Express 18, 19292–19303 (2010). [CrossRef]   [PubMed]  

11. X. Zhao, A. Bermak, F. Boussaid, and V. G. Chigrinov, “Liquid-crystal micropolarimeter array for full Stokes polarization imaging in visible spectrum,” Opt. Express 18, 17776–17787 (2010). [CrossRef]   [PubMed]  

12. V. Gruev, “Fabrication of a dual-layer aluminum nanowires polarization filter array,” Opt. Express 19, 24361–24369 (2011). [CrossRef]   [PubMed]  

13. X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “High-resolution thin ’guest-host’ micropolarizer arrays for visible imaging polarimetry,” Opt. Express 19, 5565–5573 (2011). [CrossRef]   [PubMed]  

14. G. Myhre, W. Hsu, A. Peinado, C. LaCasse, N. Brock, R. A. Chipman, and S. Pau, “Liquid crystal polymer full-stokes division of focal plane polarimeter,” Opt. Express 20, 27393–27409 (2012). [CrossRef]   [PubMed]  

15. K. Sasagawa, S. Shishido, K. Ando, H. Matsuoka, T. Noda, T. Tokuda, K. Kakiuchi, and J. Ohta, “Image sensor pixel with on-chip high extinction ratio polarizer based on 65-nm standard CMOS technology,” Opt. Express 21, 11132–11140 (2013). [CrossRef]   [PubMed]  

16. W. Hsu, J. Ma, G. Myhre, K. Balakrishnan, and S. Pau, “Patterned cholesteric liquid crystal polymer film,” J. Opt. Soc. Am. A 30, 252–258 (2013). [CrossRef]  

17. T. H. Chiou, S. Kleinlogel, T. Cronin, R. Caldwell, B. Loeffler, A. Siddiqi, A. Goldizen, and J. Marshall, “Circular polarization vision in a stomatopod crustacean,” Curr. Biol. 18, 429–434 (2008). [CrossRef]   [PubMed]  

18. N. W. Roberts, T. H. Chiou, N. J. Marshall, and T. W. Cronin, “A biological quarter-wave retarder with excellent achromaticity in the visible wavelength region,” Nat. Photonics 3, 641–644 (2009). [CrossRef]  

19. G. C. Giakos, “Multifusion, Multispectral, Optical Polarimetric Imaging Sensing Principles,” IEEE Trans. Instrum. Meas. 55, 1628–1633 (2006). [CrossRef]  

20. D. Goldstein, Polarized Light (Marcel Dekker, 2003). [CrossRef]  

21. M. Kulkarni and V. Gruev, “Integrated spectral-polarization imaging sensor with aluminum nanowire polarization filters,” Opt. Express 20, 22997–23012 (2012). [CrossRef]   [PubMed]  

22. W. S. Kang, B. J. Mun, G. D. Lee, J. H. Lee, B. K. Kim, H. C. Choi, Y. J. Lim, and S. H. Lee, “Optimal design of quarter-wave plate with wideband and wide viewing angle for three-dimensional liquid crystal display,” J. Appl. Phys. 111, 103119 (2012). [CrossRef]  

23. S. T. Wu, “Birefringence dispersions of liquid crystals,” Phys. Rev. A 33, 1270–1274 (1986). [CrossRef]   [PubMed]  

24. P. Hariharan and P. E. Ciddor, “Broad-band superachromatic retarders and circular polarizers for the UV, visible and near infrared,” J. Mod. Opt. 51, 2315–2322 (2004). [CrossRef]  

25. X. Zhao, A. Bermak, F. Boussaid, T. Du, and V. G. Chigrinov, “High-resolution photo-aligned liquid-crystal micropolarizer array for polarization imaging in visible spectrum,” Opt. Lett. 34, 3619–3621 (2009). [CrossRef]   [PubMed]  

References

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  1. A. G. Andreou and Z. K. Kalayjian, “Polarization imaging: principles and integrated polarimeters,” IEEE Sens. J. 2, 566–576 (2002).
    [Crossref]
  2. J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006).
    [Crossref] [PubMed]
  3. J. Guo and D. Brady, “Fabrication of thin-film micropolarizer arrays for visible imaging polarimetry,” Appl. Opt. 39, 1486–1492 (2000).
    [Crossref]
  4. C. K. Harnett and H. G. Craighead, “Liquid-crystal micropolarizer array for polarization-difference imaging,” Appl. Opt. 41, 1291–1296 (2002).
    [Crossref] [PubMed]
  5. M. Momeni and A. H. Titus, “An analog VLSI chip emulating polarization vision of octopus retina,” IEEE Trans. Neur. Netw. 7, 222–232 (2006).
    [Crossref]
  6. V. Gruev, A. Ortu, N. Lazarus, Jan Van der Spiegel, and N. Engheta, “Fabrication of a dual-tier thin film micropolarization array,” Opt. Express 15, 4994–5007 (2007).
    [Crossref] [PubMed]
  7. R. Harding, I. Gardiner, H. J. Yoon, T. Perrett, O. Parri, and K. Skjonnemand, “Reactive liquid crystal materials for optically anisotropic patterned retarders,” Proc. SPIE 7140, 71402J (2008).
    [Crossref]
  8. X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “Thin photo-patterned micropolarizer array for CMOS image sensors,” IEEE Photon. Technol. Lett. 21, 805–807 (2009).
    [Crossref]
  9. V. Gruev, R. Perkins, and T. York, “CCD polarization imaging sensor with aluminum nanowire optical filters,” Opt. Express 18, 19087–19094 (2010).
    [Crossref] [PubMed]
  10. V. Gruev, Jan Van der Spiegel, and N. Engheta, “Dual-tier thin film polymer polarization imaging sensor,” Opt. Express 18, 19292–19303 (2010).
    [Crossref] [PubMed]
  11. X. Zhao, A. Bermak, F. Boussaid, and V. G. Chigrinov, “Liquid-crystal micropolarimeter array for full Stokes polarization imaging in visible spectrum,” Opt. Express 18, 17776–17787 (2010).
    [Crossref] [PubMed]
  12. V. Gruev, “Fabrication of a dual-layer aluminum nanowires polarization filter array,” Opt. Express 19, 24361–24369 (2011).
    [Crossref] [PubMed]
  13. X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “High-resolution thin ’guest-host’ micropolarizer arrays for visible imaging polarimetry,” Opt. Express 19, 5565–5573 (2011).
    [Crossref] [PubMed]
  14. G. Myhre, W. Hsu, A. Peinado, C. LaCasse, N. Brock, R. A. Chipman, and S. Pau, “Liquid crystal polymer full-stokes division of focal plane polarimeter,” Opt. Express 20, 27393–27409 (2012).
    [Crossref] [PubMed]
  15. K. Sasagawa, S. Shishido, K. Ando, H. Matsuoka, T. Noda, T. Tokuda, K. Kakiuchi, and J. Ohta, “Image sensor pixel with on-chip high extinction ratio polarizer based on 65-nm standard CMOS technology,” Opt. Express 21, 11132–11140 (2013).
    [Crossref] [PubMed]
  16. W. Hsu, J. Ma, G. Myhre, K. Balakrishnan, and S. Pau, “Patterned cholesteric liquid crystal polymer film,” J. Opt. Soc. Am. A 30, 252–258 (2013).
    [Crossref]
  17. T. H. Chiou, S. Kleinlogel, T. Cronin, R. Caldwell, B. Loeffler, A. Siddiqi, A. Goldizen, and J. Marshall, “Circular polarization vision in a stomatopod crustacean,” Curr. Biol. 18, 429–434 (2008).
    [Crossref] [PubMed]
  18. N. W. Roberts, T. H. Chiou, N. J. Marshall, and T. W. Cronin, “A biological quarter-wave retarder with excellent achromaticity in the visible wavelength region,” Nat. Photonics 3, 641–644 (2009).
    [Crossref]
  19. G. C. Giakos, “Multifusion, Multispectral, Optical Polarimetric Imaging Sensing Principles,” IEEE Trans. Instrum. Meas. 55, 1628–1633 (2006).
    [Crossref]
  20. D. Goldstein, Polarized Light (Marcel Dekker, 2003).
    [Crossref]
  21. M. Kulkarni and V. Gruev, “Integrated spectral-polarization imaging sensor with aluminum nanowire polarization filters,” Opt. Express 20, 22997–23012 (2012).
    [Crossref] [PubMed]
  22. W. S. Kang, B. J. Mun, G. D. Lee, J. H. Lee, B. K. Kim, H. C. Choi, Y. J. Lim, and S. H. Lee, “Optimal design of quarter-wave plate with wideband and wide viewing angle for three-dimensional liquid crystal display,” J. Appl. Phys. 111, 103119 (2012).
    [Crossref]
  23. S. T. Wu, “Birefringence dispersions of liquid crystals,” Phys. Rev. A 33, 1270–1274 (1986).
    [Crossref] [PubMed]
  24. P. Hariharan and P. E. Ciddor, “Broad-band superachromatic retarders and circular polarizers for the UV, visible and near infrared,” J. Mod. Opt. 51, 2315–2322 (2004).
    [Crossref]
  25. X. Zhao, A. Bermak, F. Boussaid, T. Du, and V. G. Chigrinov, “High-resolution photo-aligned liquid-crystal micropolarizer array for polarization imaging in visible spectrum,” Opt. Lett. 34, 3619–3621 (2009).
    [Crossref] [PubMed]

2013 (2)

2012 (3)

2011 (2)

2010 (3)

2009 (3)

N. W. Roberts, T. H. Chiou, N. J. Marshall, and T. W. Cronin, “A biological quarter-wave retarder with excellent achromaticity in the visible wavelength region,” Nat. Photonics 3, 641–644 (2009).
[Crossref]

X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “Thin photo-patterned micropolarizer array for CMOS image sensors,” IEEE Photon. Technol. Lett. 21, 805–807 (2009).
[Crossref]

X. Zhao, A. Bermak, F. Boussaid, T. Du, and V. G. Chigrinov, “High-resolution photo-aligned liquid-crystal micropolarizer array for polarization imaging in visible spectrum,” Opt. Lett. 34, 3619–3621 (2009).
[Crossref] [PubMed]

2008 (2)

R. Harding, I. Gardiner, H. J. Yoon, T. Perrett, O. Parri, and K. Skjonnemand, “Reactive liquid crystal materials for optically anisotropic patterned retarders,” Proc. SPIE 7140, 71402J (2008).
[Crossref]

T. H. Chiou, S. Kleinlogel, T. Cronin, R. Caldwell, B. Loeffler, A. Siddiqi, A. Goldizen, and J. Marshall, “Circular polarization vision in a stomatopod crustacean,” Curr. Biol. 18, 429–434 (2008).
[Crossref] [PubMed]

2007 (1)

2006 (3)

M. Momeni and A. H. Titus, “An analog VLSI chip emulating polarization vision of octopus retina,” IEEE Trans. Neur. Netw. 7, 222–232 (2006).
[Crossref]

J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45, 5453–5469 (2006).
[Crossref] [PubMed]

G. C. Giakos, “Multifusion, Multispectral, Optical Polarimetric Imaging Sensing Principles,” IEEE Trans. Instrum. Meas. 55, 1628–1633 (2006).
[Crossref]

2004 (1)

P. Hariharan and P. E. Ciddor, “Broad-band superachromatic retarders and circular polarizers for the UV, visible and near infrared,” J. Mod. Opt. 51, 2315–2322 (2004).
[Crossref]

2002 (2)

A. G. Andreou and Z. K. Kalayjian, “Polarization imaging: principles and integrated polarimeters,” IEEE Sens. J. 2, 566–576 (2002).
[Crossref]

C. K. Harnett and H. G. Craighead, “Liquid-crystal micropolarizer array for polarization-difference imaging,” Appl. Opt. 41, 1291–1296 (2002).
[Crossref] [PubMed]

2000 (1)

1986 (1)

S. T. Wu, “Birefringence dispersions of liquid crystals,” Phys. Rev. A 33, 1270–1274 (1986).
[Crossref] [PubMed]

Ando, K.

Andreou, A. G.

A. G. Andreou and Z. K. Kalayjian, “Polarization imaging: principles and integrated polarimeters,” IEEE Sens. J. 2, 566–576 (2002).
[Crossref]

Balakrishnan, K.

Bermak, A.

Boussaid, F.

Brady, D.

Brock, N.

Caldwell, R.

T. H. Chiou, S. Kleinlogel, T. Cronin, R. Caldwell, B. Loeffler, A. Siddiqi, A. Goldizen, and J. Marshall, “Circular polarization vision in a stomatopod crustacean,” Curr. Biol. 18, 429–434 (2008).
[Crossref] [PubMed]

Chenault, D. B.

Chigrinov, V. G.

Chiou, T. H.

N. W. Roberts, T. H. Chiou, N. J. Marshall, and T. W. Cronin, “A biological quarter-wave retarder with excellent achromaticity in the visible wavelength region,” Nat. Photonics 3, 641–644 (2009).
[Crossref]

T. H. Chiou, S. Kleinlogel, T. Cronin, R. Caldwell, B. Loeffler, A. Siddiqi, A. Goldizen, and J. Marshall, “Circular polarization vision in a stomatopod crustacean,” Curr. Biol. 18, 429–434 (2008).
[Crossref] [PubMed]

Chipman, R. A.

Choi, H. C.

W. S. Kang, B. J. Mun, G. D. Lee, J. H. Lee, B. K. Kim, H. C. Choi, Y. J. Lim, and S. H. Lee, “Optimal design of quarter-wave plate with wideband and wide viewing angle for three-dimensional liquid crystal display,” J. Appl. Phys. 111, 103119 (2012).
[Crossref]

Ciddor, P. E.

P. Hariharan and P. E. Ciddor, “Broad-band superachromatic retarders and circular polarizers for the UV, visible and near infrared,” J. Mod. Opt. 51, 2315–2322 (2004).
[Crossref]

Craighead, H. G.

Cronin, T.

T. H. Chiou, S. Kleinlogel, T. Cronin, R. Caldwell, B. Loeffler, A. Siddiqi, A. Goldizen, and J. Marshall, “Circular polarization vision in a stomatopod crustacean,” Curr. Biol. 18, 429–434 (2008).
[Crossref] [PubMed]

Cronin, T. W.

N. W. Roberts, T. H. Chiou, N. J. Marshall, and T. W. Cronin, “A biological quarter-wave retarder with excellent achromaticity in the visible wavelength region,” Nat. Photonics 3, 641–644 (2009).
[Crossref]

Du, T.

Engheta, N.

Gardiner, I.

R. Harding, I. Gardiner, H. J. Yoon, T. Perrett, O. Parri, and K. Skjonnemand, “Reactive liquid crystal materials for optically anisotropic patterned retarders,” Proc. SPIE 7140, 71402J (2008).
[Crossref]

Giakos, G. C.

G. C. Giakos, “Multifusion, Multispectral, Optical Polarimetric Imaging Sensing Principles,” IEEE Trans. Instrum. Meas. 55, 1628–1633 (2006).
[Crossref]

Goldizen, A.

T. H. Chiou, S. Kleinlogel, T. Cronin, R. Caldwell, B. Loeffler, A. Siddiqi, A. Goldizen, and J. Marshall, “Circular polarization vision in a stomatopod crustacean,” Curr. Biol. 18, 429–434 (2008).
[Crossref] [PubMed]

Goldstein, D.

D. Goldstein, Polarized Light (Marcel Dekker, 2003).
[Crossref]

Goldstein, D. L.

Gruev, V.

Guo, J.

Harding, R.

R. Harding, I. Gardiner, H. J. Yoon, T. Perrett, O. Parri, and K. Skjonnemand, “Reactive liquid crystal materials for optically anisotropic patterned retarders,” Proc. SPIE 7140, 71402J (2008).
[Crossref]

Hariharan, P.

P. Hariharan and P. E. Ciddor, “Broad-band superachromatic retarders and circular polarizers for the UV, visible and near infrared,” J. Mod. Opt. 51, 2315–2322 (2004).
[Crossref]

Harnett, C. K.

Hsu, W.

Kakiuchi, K.

Kalayjian, Z. K.

A. G. Andreou and Z. K. Kalayjian, “Polarization imaging: principles and integrated polarimeters,” IEEE Sens. J. 2, 566–576 (2002).
[Crossref]

Kang, W. S.

W. S. Kang, B. J. Mun, G. D. Lee, J. H. Lee, B. K. Kim, H. C. Choi, Y. J. Lim, and S. H. Lee, “Optimal design of quarter-wave plate with wideband and wide viewing angle for three-dimensional liquid crystal display,” J. Appl. Phys. 111, 103119 (2012).
[Crossref]

Kim, B. K.

W. S. Kang, B. J. Mun, G. D. Lee, J. H. Lee, B. K. Kim, H. C. Choi, Y. J. Lim, and S. H. Lee, “Optimal design of quarter-wave plate with wideband and wide viewing angle for three-dimensional liquid crystal display,” J. Appl. Phys. 111, 103119 (2012).
[Crossref]

Kleinlogel, S.

T. H. Chiou, S. Kleinlogel, T. Cronin, R. Caldwell, B. Loeffler, A. Siddiqi, A. Goldizen, and J. Marshall, “Circular polarization vision in a stomatopod crustacean,” Curr. Biol. 18, 429–434 (2008).
[Crossref] [PubMed]

Kulkarni, M.

LaCasse, C.

Lazarus, N.

Lee, G. D.

W. S. Kang, B. J. Mun, G. D. Lee, J. H. Lee, B. K. Kim, H. C. Choi, Y. J. Lim, and S. H. Lee, “Optimal design of quarter-wave plate with wideband and wide viewing angle for three-dimensional liquid crystal display,” J. Appl. Phys. 111, 103119 (2012).
[Crossref]

Lee, J. H.

W. S. Kang, B. J. Mun, G. D. Lee, J. H. Lee, B. K. Kim, H. C. Choi, Y. J. Lim, and S. H. Lee, “Optimal design of quarter-wave plate with wideband and wide viewing angle for three-dimensional liquid crystal display,” J. Appl. Phys. 111, 103119 (2012).
[Crossref]

Lee, S. H.

W. S. Kang, B. J. Mun, G. D. Lee, J. H. Lee, B. K. Kim, H. C. Choi, Y. J. Lim, and S. H. Lee, “Optimal design of quarter-wave plate with wideband and wide viewing angle for three-dimensional liquid crystal display,” J. Appl. Phys. 111, 103119 (2012).
[Crossref]

Lim, Y. J.

W. S. Kang, B. J. Mun, G. D. Lee, J. H. Lee, B. K. Kim, H. C. Choi, Y. J. Lim, and S. H. Lee, “Optimal design of quarter-wave plate with wideband and wide viewing angle for three-dimensional liquid crystal display,” J. Appl. Phys. 111, 103119 (2012).
[Crossref]

Loeffler, B.

T. H. Chiou, S. Kleinlogel, T. Cronin, R. Caldwell, B. Loeffler, A. Siddiqi, A. Goldizen, and J. Marshall, “Circular polarization vision in a stomatopod crustacean,” Curr. Biol. 18, 429–434 (2008).
[Crossref] [PubMed]

Ma, J.

Marshall, J.

T. H. Chiou, S. Kleinlogel, T. Cronin, R. Caldwell, B. Loeffler, A. Siddiqi, A. Goldizen, and J. Marshall, “Circular polarization vision in a stomatopod crustacean,” Curr. Biol. 18, 429–434 (2008).
[Crossref] [PubMed]

Marshall, N. J.

N. W. Roberts, T. H. Chiou, N. J. Marshall, and T. W. Cronin, “A biological quarter-wave retarder with excellent achromaticity in the visible wavelength region,” Nat. Photonics 3, 641–644 (2009).
[Crossref]

Matsuoka, H.

Momeni, M.

M. Momeni and A. H. Titus, “An analog VLSI chip emulating polarization vision of octopus retina,” IEEE Trans. Neur. Netw. 7, 222–232 (2006).
[Crossref]

Mun, B. J.

W. S. Kang, B. J. Mun, G. D. Lee, J. H. Lee, B. K. Kim, H. C. Choi, Y. J. Lim, and S. H. Lee, “Optimal design of quarter-wave plate with wideband and wide viewing angle for three-dimensional liquid crystal display,” J. Appl. Phys. 111, 103119 (2012).
[Crossref]

Myhre, G.

Noda, T.

Ohta, J.

Ortu, A.

Parri, O.

R. Harding, I. Gardiner, H. J. Yoon, T. Perrett, O. Parri, and K. Skjonnemand, “Reactive liquid crystal materials for optically anisotropic patterned retarders,” Proc. SPIE 7140, 71402J (2008).
[Crossref]

Pau, S.

Peinado, A.

Perkins, R.

Perrett, T.

R. Harding, I. Gardiner, H. J. Yoon, T. Perrett, O. Parri, and K. Skjonnemand, “Reactive liquid crystal materials for optically anisotropic patterned retarders,” Proc. SPIE 7140, 71402J (2008).
[Crossref]

Roberts, N. W.

N. W. Roberts, T. H. Chiou, N. J. Marshall, and T. W. Cronin, “A biological quarter-wave retarder with excellent achromaticity in the visible wavelength region,” Nat. Photonics 3, 641–644 (2009).
[Crossref]

Sasagawa, K.

Shaw, J. A.

Shishido, S.

Siddiqi, A.

T. H. Chiou, S. Kleinlogel, T. Cronin, R. Caldwell, B. Loeffler, A. Siddiqi, A. Goldizen, and J. Marshall, “Circular polarization vision in a stomatopod crustacean,” Curr. Biol. 18, 429–434 (2008).
[Crossref] [PubMed]

Skjonnemand, K.

R. Harding, I. Gardiner, H. J. Yoon, T. Perrett, O. Parri, and K. Skjonnemand, “Reactive liquid crystal materials for optically anisotropic patterned retarders,” Proc. SPIE 7140, 71402J (2008).
[Crossref]

Titus, A. H.

M. Momeni and A. H. Titus, “An analog VLSI chip emulating polarization vision of octopus retina,” IEEE Trans. Neur. Netw. 7, 222–232 (2006).
[Crossref]

Tokuda, T.

Tyo, J. S.

Van der Spiegel, Jan

Wu, S. T.

S. T. Wu, “Birefringence dispersions of liquid crystals,” Phys. Rev. A 33, 1270–1274 (1986).
[Crossref] [PubMed]

Yoon, H. J.

R. Harding, I. Gardiner, H. J. Yoon, T. Perrett, O. Parri, and K. Skjonnemand, “Reactive liquid crystal materials for optically anisotropic patterned retarders,” Proc. SPIE 7140, 71402J (2008).
[Crossref]

York, T.

Zhao, X.

Appl. Opt. (3)

Curr. Biol. (1)

T. H. Chiou, S. Kleinlogel, T. Cronin, R. Caldwell, B. Loeffler, A. Siddiqi, A. Goldizen, and J. Marshall, “Circular polarization vision in a stomatopod crustacean,” Curr. Biol. 18, 429–434 (2008).
[Crossref] [PubMed]

IEEE Photon. Technol. Lett. (1)

X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “Thin photo-patterned micropolarizer array for CMOS image sensors,” IEEE Photon. Technol. Lett. 21, 805–807 (2009).
[Crossref]

IEEE Sens. J. (1)

A. G. Andreou and Z. K. Kalayjian, “Polarization imaging: principles and integrated polarimeters,” IEEE Sens. J. 2, 566–576 (2002).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

G. C. Giakos, “Multifusion, Multispectral, Optical Polarimetric Imaging Sensing Principles,” IEEE Trans. Instrum. Meas. 55, 1628–1633 (2006).
[Crossref]

IEEE Trans. Neur. Netw. (1)

M. Momeni and A. H. Titus, “An analog VLSI chip emulating polarization vision of octopus retina,” IEEE Trans. Neur. Netw. 7, 222–232 (2006).
[Crossref]

J. Appl. Phys. (1)

W. S. Kang, B. J. Mun, G. D. Lee, J. H. Lee, B. K. Kim, H. C. Choi, Y. J. Lim, and S. H. Lee, “Optimal design of quarter-wave plate with wideband and wide viewing angle for three-dimensional liquid crystal display,” J. Appl. Phys. 111, 103119 (2012).
[Crossref]

J. Mod. Opt. (1)

P. Hariharan and P. E. Ciddor, “Broad-band superachromatic retarders and circular polarizers for the UV, visible and near infrared,” J. Mod. Opt. 51, 2315–2322 (2004).
[Crossref]

J. Opt. Soc. Am. A (1)

Nat. Photonics (1)

N. W. Roberts, T. H. Chiou, N. J. Marshall, and T. W. Cronin, “A biological quarter-wave retarder with excellent achromaticity in the visible wavelength region,” Nat. Photonics 3, 641–644 (2009).
[Crossref]

Opt. Express (9)

V. Gruev, A. Ortu, N. Lazarus, Jan Van der Spiegel, and N. Engheta, “Fabrication of a dual-tier thin film micropolarization array,” Opt. Express 15, 4994–5007 (2007).
[Crossref] [PubMed]

V. Gruev, R. Perkins, and T. York, “CCD polarization imaging sensor with aluminum nanowire optical filters,” Opt. Express 18, 19087–19094 (2010).
[Crossref] [PubMed]

V. Gruev, Jan Van der Spiegel, and N. Engheta, “Dual-tier thin film polymer polarization imaging sensor,” Opt. Express 18, 19292–19303 (2010).
[Crossref] [PubMed]

X. Zhao, A. Bermak, F. Boussaid, and V. G. Chigrinov, “Liquid-crystal micropolarimeter array for full Stokes polarization imaging in visible spectrum,” Opt. Express 18, 17776–17787 (2010).
[Crossref] [PubMed]

V. Gruev, “Fabrication of a dual-layer aluminum nanowires polarization filter array,” Opt. Express 19, 24361–24369 (2011).
[Crossref] [PubMed]

X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “High-resolution thin ’guest-host’ micropolarizer arrays for visible imaging polarimetry,” Opt. Express 19, 5565–5573 (2011).
[Crossref] [PubMed]

G. Myhre, W. Hsu, A. Peinado, C. LaCasse, N. Brock, R. A. Chipman, and S. Pau, “Liquid crystal polymer full-stokes division of focal plane polarimeter,” Opt. Express 20, 27393–27409 (2012).
[Crossref] [PubMed]

K. Sasagawa, S. Shishido, K. Ando, H. Matsuoka, T. Noda, T. Tokuda, K. Kakiuchi, and J. Ohta, “Image sensor pixel with on-chip high extinction ratio polarizer based on 65-nm standard CMOS technology,” Opt. Express 21, 11132–11140 (2013).
[Crossref] [PubMed]

M. Kulkarni and V. Gruev, “Integrated spectral-polarization imaging sensor with aluminum nanowire polarization filters,” Opt. Express 20, 22997–23012 (2012).
[Crossref] [PubMed]

Opt. Lett. (1)

Phys. Rev. A (1)

S. T. Wu, “Birefringence dispersions of liquid crystals,” Phys. Rev. A 33, 1270–1274 (1986).
[Crossref] [PubMed]

Proc. SPIE (1)

R. Harding, I. Gardiner, H. J. Yoon, T. Perrett, O. Parri, and K. Skjonnemand, “Reactive liquid crystal materials for optically anisotropic patterned retarders,” Proc. SPIE 7140, 71402J (2008).
[Crossref]

Other (1)

D. Goldstein, Polarized Light (Marcel Dekker, 2003).
[Crossref]

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Figures (10)

Fig. 1
Fig. 1 Optical cross-talk caused by the oblique incidence: (a) thick patterned retarder layer; (b) thin patterned retarder layer.
Fig. 2
Fig. 2 Optical design of the proposed MQWRs: (a) 45°MQWR; (b) 135°MQWR.
Fig. 3
Fig. 3 The relationship between the RMSE and the fast axis angle θ1 of the HWR.
Fig. 4
Fig. 4 The achromaticity comparison between the single-layer zero order QWR for 550 nm light and the proposed dual-layer achromatic MQWR.
Fig. 5
Fig. 5 Measured LCP film thickness with different spin coat speeds.
Fig. 6
Fig. 6 The fabrication process flow of our proposed MQWR array.
Fig. 7
Fig. 7 Test setup of our fabricated MQWR array.
Fig. 8
Fig. 8 Measured spectral minor transmittance for single-layer zero order QWR (550 nm) and the proposed dual-layer 45° MQWR (8μm spatial resolution) with left-handed circularly polarized incident light.
Fig. 9
Fig. 9 Measured spectral extinction ratio for our proposed dual-layer 45° MQWR (8μm spatial resolution) with circularly polarized incident light.
Fig. 10
Fig. 10 Microphotographs of the fabricated MQWR array with (a) (b) right-handed circularly polarized input polarized input polarized input; (c) (d) left-handed circularly polarized input.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

Γ = 2 π Δ n ( λ ) d λ
M retarder ( φ , θ ) = [ 1 0 0 0 0 cos 2 2 θ + cos φ sin 2 2 θ ( 1 cos φ ) sin 2 θ cos 2 θ sin φ sin 2 θ 0 ( 1 cos φ ) sin 2 θ cos 2 θ sin 2 2 θ + cos φ cos 2 2 θ sin φ cos 2 θ 0 sin φ sin 2 θ sin φ cos 2 θ cos φ ]
M 45 ° MQWR = M retarder ( π 2 , θ 2 ) M retarder ( π , θ 1 )
M 45 ° ideal QWR = [ 1 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 ]

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