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We present measurements of the full Jones matrix of individual pixels in a liquid-crystal display (LCD) panel. Employing a polarization-sensitive digital holographic microscopy based on Mach-Zehnder interferometry, the complex amplitudes of the light passing through individual LCD pixels are precisely measured with respect to orthogonal bases of polarization states, from which the full Jones matrix components of individual pixels are obtained. We also measure the changes in the Jones matrix of individual LCD pixels with respect to an applied bias. In addition, the complex optical responses of a LCD panel with respect to arbitrary polarization states of incident light were characterized from the measured Jones matrix.
© 2014 Optical Society of America
1. Introduction
Liquid crystals are one of the most fascinating optical materials that exhibit both liquid and solid crystals phase [1, 2]. Liquid crystal molecules are arranged to their own orientations during solid crystal phase; however they undergo fluidization and rearrange molecular orientations above specific temperature. Liquid crystals have been extensively used in numerous optical devices due to their extraordinary optical properties; liquid crystal molecules exhibit birefringence, and their orientations can be controlled by externally applying electric field.
One of the most popular applications of liquid crystals is liquid-crystal display (LCD) technology which utilizes birefringence of rod-like liquid crystal molecules [2–4]. In LCDs, the polarization states of light are spatially modulated by rotating the orientations of liquid crystal molecules, thus allowing the control of the transmittance of light through the LCD panel. Since the first demonstration in 1968 by Heilmeier and colleagues [4, 5], various types of LCD panels have been developed and utilized. Conventionally, LCD techniques are classified by the types of arrangements of liquid crystal molecules: twisted nematic, vertically aligned, homogeneous aligned LCDs, fringe field switching and so on [3, 6–10]. Recently developed in-plane switching liquid-crystal displays (IPS-LCD) has been widely used in commercial LCD products, because it provides larger viewing angle and higher transmission efficiency compared to conventional LCD techniques [11].
The optical characterization of LCD panels is crucial for the developing and testing of LCDs. Conventional techniques for LCD characterizations were mostly based on intensity measurements since the transmittance of light after propagating through a polarizer and analyzer is the figure of merit for LCD performance characterization [12]. However, the optical responses of LCDs can only be fully described in the manner of polarization states, which is the working principle of LCDs. Polarization-sensitive LCD characterizations using the Stokes parameters have been reported in which the polarization ellipse of the observed electric field is measured to characterize LCDs [13, 14]. In these cases, the Poincaré sphere has been used to visualize the relationship between the Stokes parameters and orthogonal vectors in the lab-axis [15–17]. However, although the Stokes parameters can define the polarization ellipse of light, it does not directly describe the complex nature of electric field.
Jones matrix measurement can be used for the full characterization of the complex optical responses of materials to incident polarized light [18]. When polarized light propagates through optical elements, the progressive alterations in the polarization state can be found by multiplying the Jones matrix describing the optical elements to the Jones vector describing the initial polarization state. Components of the Jones matrix represent the complex optical transformation between the orthogonal axes. Although degree of polarization is not accounted in Jones matrix formalism, Jones matrix directly describes the complex optical responses of optical materials. To access this information, measurement of both amplitude and phase of the complex field in terms of orthogonal polarization states must be achieved. Digital holography has been utilized to determine the polarization states of various samples ranging from polarization-sensitive optical fibers, to liquid crystal droplets, and to biological cells and tissues [19–24]. Recently, there has also been attempts to measure polarization states of light in LCDs [21, 25]. Polarization eigenvectors [25] and Jones matrix [21, 26, 27] of LCDs have been measured using interferometry. However, spatially resolved full Jones matrix characterization of LCD display at the individual pixel scales has yet to be demonstrated.
Here, we employ polarization-sensitive digital holographic microscopy (DHM) for characterizing the full-Jones matrix of individual pixels in an IPS-LCD panel. Using Mach-Zehnder interferometry and off-axis holographic recording [28, 29], 2-D complex optical amplitude containing both the amplitude and phase of light are quantitatively measured. A set of a polarizer and an analyzer are controlled in order to selectively record electrical fields of light passing a LCD pixel in terms of the orthogonal polarization components. The optical responses of the LCD panel with respect to the incident light of arbitrary polarization are systematically measured as a function of the applied bias (grayscale value) to the LCD panel, allowing the complete optical characterization of individual pixels in a LCD panel.
2. Method
2.1 Experimental setup
The polarization-sensitive DHM setup for measuring the full Jones matrix is shown in Fig. 1(a). Mach-Zehnder interferometry with off-axis holographic recording is employed in order to record the 2-D full-field complex amplitude of the beam passing through LCD panels. An unpolarized He-Ne laser (λ = 633 nm, 5.0 mW, Thorlabs, USA) is used for an illumination source. The beam from the laser is first spatially filtered, then the polarization state and intensity of the laser beam is modulated by placing a polarizer (LPVISE100-A, ∅1″ linear polarizer with N-BK7 protective windows, 400-700 nm) and rotating a half-wave plate (WPH10M-633, ∅1″ zero-order half-wave plate, 633 nm, Thorlabs, USA). The beam is then divided by a beam splitter (BS1) into two arms: a sample and a reference arm. One beam passes through an IPS-LCD (FLATRON 20EA34TQ, LG electronics, Korea) panel and serves as a sample arm. In order to characterize LCD pixels only, polarization sheets attached to the LCD panel were removed before measurements. The beam transmitted through the IPS-LCD is collected by an objective lens (LMPLFLN, × 20, NA = 0.4 Olympus, USA) and projected onto the image plane, where a CMOS camera (C11440-22C, 2048 × 2048 pixels with a 6.5-μm pixel size, Hamamatsu, Japan) is placed, via a 4-f telescopic imaging system. The total lateral magnification from the sample to the image plane is × 8.33. The reference arm is recombined with the sample arm by a beam splitter with a slightly tilted angle, and both the sample and reference arms interfere at the image plane. A neutral density filter is placed in the path of the reference arm to enhance the fringe contrast of the interferograms by equalizing the intensity of the sample and reference arms. The field of view of IPS-LCD panel is set to an area covering 800 μm × 800 μm. An analyzer (LPVISE100-A, ∅1″ linear polarizer with N-BK7 protective windows, 400-700 nm) was placed in front of the camera in order to selectively record a specific component of the polarization states of the electric field.
Fig. 1 (a) Polarization-sensitive DHM based on Mach-Zehnder interferometry. (b) A set of measured interferograms with different polarizer and analyzer compositions. Inset: Single pixels of the IPs-LCD is constituted by two subpixels. (c) Amplitude and (d) phase maps of corresponding interferograms. Scale bar, 300 μm.
In order to reconstruct one spatially resolved Jones matrix map from a sample, interferograms with two different polarization states should be measured for two incident beams with different polarization states; a total of four independent interferograms need to be measured. To achieve this, the polarization state of illumination was controlled by the rotation of the half wave plate before BS1 (BS004, 50:50 non-polarizing beamsplitter, 400-700 nm, 1/2″, Thorlabs, USA), the polarization state of interferograms was selected by the orientation of the analyzer placed after BS2 (BS013, 50:50 non-polarizing beamsplitter, 400-700 nm, 1″, Thorlabs, USA). The representative four different interferograms of LCD pixels obtained with different polarization states are shown in Fig. 1(b), in which 9 LCD pixels are shown while each pixel contains two sub pixels − the characteristic feature of IPS-LCD. The inset of Fig. 1(b) shows the magnified view of an interferogram which shows spatial fringe patterns due to off-axis modulation. From the measured interferograms, complex amplitude maps containing both the amplitude and phase information can be retrieved via appropriate field retrieval algorithm [30]. Figures 1(c) and 1(d) show corresponding amplitude and phase images obtained from the interferograms shown in Fig. 1(b). The details of DHM, quantitative phase imaging, and field retrieval can be found elsewhere [31, 32].
2.2 Extracting Jones matrix components
The polarization state of light can be described by a Jones vector. Conventionally, two components of the Jones vector describe x- and y-components of the complex electric field traveling along the z-direction optical axis. The linear optical response of a system to polarized light can be described by a Jones matrix:
where Jij (i, j = 1, 2) connects the jth axis component of the output electric field to the ith axis component of an input beam. Here, the 1st and 2nd axis corresponds to the x- and y-axis, respectively. A spatially resolved Jones matrix of an LCD panel can be extracted from four interferograms measured with different combinations of polarizer and analyzer orientations. Yij (i, j = 1, 2) indicates the complex electric field response with respect to the ith axis of the polarizer orientation and the jth axis of the analyzer orientation. To decide the normalized amplitude of Jones matrix components, the amplitudes of the electric fields of the reference and the sample arms without the LCD were calibrated before measuring LCD panels.By rotating the half-wave plate by the angle of + 22.5° and −22.5°, the polarization state of the incident beam can be rotated by the angle of + 45° and −45° with respect to the y-axis, then the Jones vector components of the incident wave can be expressed as below, respectively:
where c1, c2 are constants with real values which can be determined from measurements without a sample. In Eq. (2), the first row indicates the x-axis and the second row indicates the y-axis components of Jones vector. The linear relationship between Jones matrix components and the measured complex electric field response can then be described as:where Yij (i,j = 1,2) represents the complex-valued optical field of a sample with the ith polarization state of the incident beam and the jth polarization state of the analyzer orientation. For example, Y11 represents the sample field information that was measured with a linearly polarized incident beam where the polarization direction is tilted by an angle of + 45 degree, and the horizontally aligned analyzer. In order to determine the real-value constants c1 and c2, the optical fields of the sample are divided by optical fields measured without the sample. Then spatially resolved Jones matrix maps with complex values can be retrieved from the measurement of a set of four holograms with independent polarization states Yij (i,j = 1,2) using Eq. (3).2.3 Visualization of polarization states
For an intuitive representation, polarization states of light are usually described by polarization ellipses. The x- and y-axis in the observing plane are commonly chosen for describing the polarization ellipses [33]. The polarization ellipse can be reconstructed from the complex field information of both axes of the orthogonal polarization states, as follow:
where the Ai and ϕi (i = 1, 2) indicates the amplitude and phase delay of the polarization state along the 1st and 2nd axis which corresponds to the x- and y-axis, respectively. The polarization ellipse can then be described by a parametric equation of a curve as:where t varies between 0 and 2π. When the ellipticity of the polarization ellipse is zero or infinity, it represents a linearly polarized state. The ellipticity of one corresponds to a circularly polarized state. An oscillating orientation of the polarization state can be effectively described by the dynamic modulation of the azimuthal angle of the polarization ellipse.3. Results and discussions
In order to systematically characterize the optical response of individual pixels in a LCD panel, we quantitatively measured the Jones matrix components of individual pixels as a function of an applied bias β. The bias was controlled by using the IPS-LCD via a RGB output cable and displaying gray-scale images to all three color channels within a range from β = 0 (min) to β = 255 (max). As we have used the illumination laser with a wavelength of 633 nm, only the red channel in the LCD display among the three color channels were used to measure the Jones matrix components. Figure 2 shows the amplitude and phase maps of each Jones matrix components (J11, J12, J21 and J22) for 9 LCD pixels, in which the applied bias was half of the full dynamic range, i.e. β = 128. As can be seen in Fig. 2, a single pixel unit in an IPS-LCD panel is composed of two subpixels and each subpixel displays a different optical response, which is a characteristic feature of an IPS-LCD. The 3 × 3 rectangular patterns in Fig. 2(a) correspond to the controlled pixels in the red channels where dim rectangular patterns adjacent to the controlled pixels are green and blue channels [indicated by the block dotted box in Fig. 2(b)]. Due to the embedded color filters in the LCD panel, light can only passes through the red channels although the optical field itself can also be modulated in the other channels. The phase modulation characteristics of the green and blue channels as indicated as the dotted square in Fig. 2(b) were also be resolved even under low transmittance, demonstrating the sensitivity of the present polarization-sensitive DHM in recovering the phase information even from a hologram with low light intensity.
Fig. 2 Measurements of the full Jones matrix of individual pixels in a IPS-LCD. (a) Amplitude and (b) phase of spatially resolved Jones matrix components of the individual pixels. Half of the maximum bias was applied to the pixel in the center. Scale bar, 300 μm.
To address the optical modulation capability of LCD pixels, we measured the Jones matrix components of individual pixels as a function of applied bias. The amplitude and phase maps of each Jones matrix components (J11, J12, J21 and J22) for a specific pixel positioned in the center were measured as a function of bias. For other adjacent pixels, a fixed bias was applied, keeping the amplitude and phase values remain constant. These adjacent pixels were used as a set of reference pixels for determining the relative change in phases of Jones matrix components. Figures 3(a) and (b) show the amplitude and phase modulation characteristics of the Jones matrix components of individual pixels as a function of applied bias, respectively. The J21 component of the Jones matrix corresponds to the polarizer and analyzer orientations utilized in the IPS-LCD. When the applied bias is smaller than approximately an eighth of the maximum value (β = 32), the amplitude of the J21 component remain same with small offset from zero. The amplitude of the J21 component linearly increases as a function of the applied bias after this threshold value. The phase modulation on the other hand steeply increases as the bias become higher during the first quarter and then saturates after the bias reaches the half-maximum.
Fig. 3 (a) Amplitude and (b) phase modulation characteristics of the Jones matrix components of individual pixels in an IPS-LCD panel as a function of applied bias. Five measurements were performed for different pixels in the IPS-LCD. Blue lines, averaged value. Shade areas, standard error.
To address the capability of the measurements of the Jones matrix components of LCD pixels, we demonstrate the retrieval of polarization ellipses of the pixels from the measured Jones matrix. The measured Jones matrix information of individual pixels can be used to construct the polarization response of the IPS-LCD panel using Eqs. (4)-(5). Figure 4 shows the polarization ellipses of light transmitted through individual pixels with respect to the incident polarization states. The solid- and dotted lines denote for the response of the lower- and the upper subpixel of individual pixels. These polarization ellipses were calculated as a function of applied bias.
Fig. 4 Polarization ellipses of light transmitting individual pixels in IPS-LCD with respect to the (a) x-polarized and (b) y-polarized incident light.
Initially, when the applied bias is zero, the polarization state of the transmitted wave is unchanged and identical to that of the incident wave. When a non-zero bias is applied, the polarization direction of light passing each subpixel rotates in an opposite direction with respect to the each other; the direction of polarization rotates clockwise and counter-clockwise for lower- and upper subpixels, respectively. The polarization ellipses rotate up to a maximum azimuthal angle of 45° when the maximum bias was applied. The orientation of a polarizer for incident waves in the used IPS-LCD was set to x-direction. When the incident wave is y-polarized [Fig. 4(b)], an ellipticity of the polarization ellipse exhibits a higher degree in comparison with the case when the incident wave is x-polarized [Fig. 4(a)]. This result shows the asymmetry in the system response for the different orthogonal polarization states which is crucial for functional characterization.
4. Conclusion
We present a method to characterize the individual pixels in a LCD panel by measuring the spatially resolved Jones matrix components of the light passing through the pixels. Employing polarization-sensitive DHM based on off-axis Mach-Zehnder interferometry, the four spatially modulated holograms of the light field passing through LCD panel were sequentially measured as a set of orthogonal combinations of incident and transmitted polarizations; from which, the full-field amplitude and phase images of Jones matrix components were quantitative and precisely obtained. The responses of each Jones matrix components were systematically measured as a function of applied bias to the LCD panel. In addition, we demonstrated that the measured Jones matrix components can also be used for constructing the polarization ellipses. To date, this is the first reported experimental measurement of spatially resolved full Jones matrix components of individual LCD pixels.
Even though we focused on the measurements of an IPS-LCD for this work, the present approach can be directly employed to characterize and test individual pixels in other types of LCDs. The Jones matrix of full RGB channels of LCD pixels can also be characterized by employing the illumination with multiple lasers or spectroscopic modality in DHM [34–36]. Furthermore, fast dynamic responses of LCD pixels upon applied bias change can also be measured using an instrument which alternate the polarization states of probing laser beam in high speed [19]. Although this work characterized the polarization-sensitive response of individual pixels in an IPS-LCD using the Jones matrix formalism, the approach presented in this study is general so that it can be applied to various applications including formation of complex liquid crystal structures [37–39] and biophysical aspects of birefringent materials [40–42].
Acknowledgments
This work was supported by KAIST, the Korean Ministry of Education, Science and Technology (MEST), the National Research Foundation (2012R1A1A1009082, 2013M3C1A3063046, 2012-M3C1A1-048860, 2013K1A3A1A09076135, 2014M3C1A3052537), APCTP.
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