Impact of Birefringence on Large LCDs Top » Consulting » Tech Notes » Tech Note 1 
Jennifer M. Cohen
4Physics, Harrisburg, PA
Raymond G. Greene and Douglas H. Strope
Rainbow Displays, Inc., Endicott, NY
Andy Kaplan
Hinds Instruments, Inc., Hillsboro, OR
Abstract
Minimizing the spatial variation of polarization is critical to tiled AMLCD image quality. With the advent of large tiled AMLCD, low spatial frequency artifacts may become visible. Component birefringence variation of a few nanometers can produce viewer detectable luminance variations. Jones matrix formulation is used to model this effect and compare to experimental measurements.
Introduction
Large tiled AMLCDs^{1} present an exciting advance in display technology. AMCLD image quality depends critically upon control of any spatial variation in light polarization. The larger component size used in some subassemblies of tiled AMLCD systems enhances the influence of longer wavelength spatial variations in polarization as compared with smaller displays. Spatial modulation of polarization can arise from the birefringence due to stress and strain fields^{2} in component manufacture.
Light and dark wavy streaks such as those in Figure 1 have been observed in the display field of a 3×1 tiled AMLCD. The light and dark streaking contrast depends on the glass thickness used in the display's assembly with a reduction in the contrast seen for thinner glass. The source of these streaks is found in Corning Glass 1737 standard 1.1 mm LCD glass plates situated between the plane polarizers.
Fig. 1. 3×1 tiled AMLCD with birefringent streaking. 
The Model
Our objective is to understand the influence of birefringence on display quality. Therefore, we need only compare humanly observable effects of the stress induced birefringence to an ideal nonbirefringent glass sample.
Consider a piece of the stressed glass between two plane polarizers as shown in Fig. 2. Unpolarized light passes through a polarizer whose polarization axis is at 45° with respect to the xaxis. Transmitted light then encounters the glass sample with a retardation $d$ and fast axis direction $r$. The light passes through a second polarizer whose axis is set at $q$ before reaching the detector.
Fig. 2. Light path for a polarizersamplepolarizer system. 
We will treat the glass as a matrix of linear retarders between two ideal plane polarizers and initially ignore sample reflections. Using the Cartesian Jones matrix formalism, the electric field vector reaching the detector is given by
\[ \mathbf{E} = \sqrt{\frac{I_o T}{2}} \left( \begin{matrix} \cos^2 \theta & \sin \theta \cos \theta \\ \sin \theta \cos \theta & \sin^2 \theta \end{matrix} \right) \times \left( \begin{matrix} \cos \left( \frac{\delta}{2} \right) + i \cos \left( 2 \rho \right) \sin \left( \frac{\delta}{2} \right) & i \sin \left( 2 \rho \right) \sin \left( \frac{\delta}{2} \right) \\ i \sin \left( 2 \rho \right) \sin \left( \frac{\delta}{2} \right) & \cos \left( \frac{\delta}{2} \right)  i \cos \left( 2 \rho \right) \sin \left( \frac{\delta}{2} \right) \end{matrix} \right) \left( \begin{array}{c} 1 \\ 1 \end{array} \right) \] 
(1) 
where $I_o T$ is the transmission when the polarizers are parallel and no sample is present. (Equation hard to read or not there? Here's for an alternate version of Birefringence and Large LCDs).
Examining the Eq. (1) matrices from right to left, the twodimensional vector represents the directionality of the electric field vector after the light passes through the plane polarizer with a 45° axis with respect to the xaxis. The middle matrix allows for the polarization to be rotated by the glass sample acting as a linear retarder. Our second polarizer with an axis at some angle θ with respect to the xaxis is modeled through the final matrix.
Substituting in for the electric field from above and reducing we have
\[ \large{
I = I_{No\;Sample} + \left[ \sin 4\rho \cos 2\theta
 \left(2 \cos^2 2\rho \right) \sin 2\theta\right]
\left( \frac{I_o T}{2} \right) \sin^2 \left( \frac{\delta}{2} \right)
}\]
where $\;\large{I_{No\;Sample} = \left(\frac{I_o T}{2}\right) \left( 1+ \sin 2\theta\right)}$. 
(2) 
The light intensity at the detector is $ \, \mathbf{E^\dagger} \cdot \mathbf{E}$. The identification in Eq. (2) for the intensity without a sample present can be found by eliminating the sample in Eq. (1).
The intensity equation simplifies significantly for the case of crossed polarizers where $I_{No Sample}$ goes to zero. Setting the angle of the second polarizer to 45° yields
\[ \large{ I = I_o T \cos^2 \left( 2 \rho \right) \sin^2 \left( \frac{\delta}{2}\right) }\]  (3) 
where $\rho$ is the fast axis direction and $\delta$ is the retardation of the retarder.
To this point reflections have been ignored. However, to examine the birefringence phenomenon under conditions approximating a large tiled LCD, light at angles other than strictly normal to the sample must be included. That, combined with uncoated glass surfaces leads us to add reflection effects to the model.
Light is lost due to reflection as the light enters and exits the glass sample as depicted in Figure 3. The bulk of this loss is found in the first and second reflections, which are labeled "Reflected light". The model takes these two deductions into account.
Fig. 3. Reflection and transmission through sample. 
Birefringence gives an optical path difference between the fast and slow axis directions corresponding to a relative phase shift of
\[\large{\delta = \frac{2\pi d}{\lambda_{\:\!o}} \left n_{slow}  n_{fast} \right} \]  (4) 
where $d$ is the sample thickness, $\lambda_{\:\!o}$ is the wavelength of the light, and the $n_i$ are the refractive indices.
Light and dark streaking are observed on a standard rectangular light box with an intensity versus angle profile that varies smoothly beneath the polarizersamplepolarizer system. With the polarization direction of the incoming light known, we used the Fresnel formulas^{4} to determine the amount of light lost to reflection. Thus, our model has a transmission intensity given by Eq. (3) with a period of 90° as the sample is rotated. This is modulated by the reflection losses, which have a period of 180°.
Experimental measures
A 6"×6" piece of the 1.1 mm Corning Glass 1737 standard LCD glass was used for a check of this model's applicability to the tiled AMLCD streaking. Effective retardation and fast axis direction were taken simultaneously with an Exicor 150AT birefringence measurement system by Hinds Instruments, Inc.
The Exicor system uses a photoelastic modulation (PEM) technique^{5}, which allows for detection of polarization change to below 1 ppm^{6}. Its dual detector system provides accurate measurement of both the magnitude of birefringence and the fast axis direction without the need to reorient the sample^{7}.
Figure 4 displays the data output for the glass sample. Colored pixels note the single points measured at a usercontrolled resolution or step size. The pixel color indicates the magnitude of linear birefringence within the range described in the legend. The line in each of the measurement points describes the direction of the fast axis of retardation. Points that are gray in color are nonmeasurement points or points for which the beam is blocked.
Fig. 4. Graphical output of retardation and fast axis direction. 
Results and conclusions
Inputting the retardation data into the model yields the light intensities across the glass sample rotated by an angle in the xyplane (see Figure 2). Expressing these intensities in various shades of gray produces the bottom row of Figure 5.
Black and white photographs were taken of the 6"×6" sample situated between crossed polarizers atop a light box. The background determined from photos of this setup without the sample was subtracted from the sample photos. These pictures with the sample at five different rotations appear in the top row of Figure 5.
Light and dark predominantly horizontal bands appear in both rows of Figure 5. These are most easily seen at the zero and ninety degree rotations. Close inspection across the rotational range finds a favorable comparison between the modeled and humanly observed birefringent streaking.
Fig. 5. Actual and expected birefringent observations. Black and white photographs after background subtraction appear in the top In the bottom row are the results of the model using the Hinds' data. The rotation of the glass sample with respect to the crossed polarizers (see Figure 2) is noted between the rows. Contrast is enhanced throughout to facilitate comparison. 
Having located the source of the light and dark streaking observed in the large tiled LCDs and shown in Figure 1, we are free to seek a solution to the problem. Several ideas have surfaced and are being actively examined.
Acknowledgments
The authors wish to gratefully acknowledge Dr. J. C. Lapp and his colleagues at Corning Glass for supplying the glass samples and for their support of this effort.
References
1. Greene, R., Krusius, P., Seraphim, D., Skinner, D., and Yost, B.
Information Display Mag. 17, 1, pp. 1620 (2001).
2. Born, M. and Wolf, E. Principles of Optics, 6th ed., Cambridge University
Press, pp. 703706, (1980).
3. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, Elsevier
Science Publishers (1989).
4. Jackson, J. D., Classical Electrodynamics, 2nd ed., pp. 278f, John Wiley
& Sons (New York, 1975).
5. Kemp, J. C., J. Opt. Soc. Am. 59, p. 950f (1969).
6. Kemp, J. C., Henson, G. D., Steiner, C. T. and Powell, E. R., Nature 326,
pp. 270f (London, 1987).
7. B. Wang and T. C. Oakberg, Rev. of Sci. Instrum. 70, No. 10, pp. 38473854
(1999).
