Category Archives: Libby


Since there is SO much literature on LCD technology and since this really is not that new of a field, I had a lot of trouble searching for something to investigate that had not already been modeled before. Instead, I ended up using preexisting equations to explore the things that I found interesting like the transmission peaks of twisted nematic field effect and how this led to LCD screens actually being a significant competitor in display technology.

My original plan was to compare LCD, PDP, and CRT screens, but the unfamiliar terminology of LCD technology made it difficult for me to dissect all of the literature in a timely enough manner to be able to explore PDP and CRT screens. My complete ineptitude in navigating Mathematica also delayed furthering my research. I am particularly disappointed that I did not get to further investigate EMI shields used in PDP screens, as there was not an extensive amount of texts focused on EMI shields, so it would have been interesting to piece together some of my own calculations or observations.

Since the twisted nematic field effect was first employed in LCD technology, research has been moving the field towards more cost effective, efficient, and quality display screens. If I were to further research this topic, I would look at comparing the TN-LCD screens with the LCD mode being used in the LCD touch screen of the iPhone. Since we are in constant contact with LCD technology in today’s world, I feel like we are prone to take for granted how LCD screens came into being, how they function, and the math that describes their existence and purpose.


Applications: MORI

A method used in behavior research, manipulation of overlapping rivalrous images by polarizing filters, or MORI, employs LCD projectors and polarizing glasses to test perception and memory. In a MORI experiment, two LCD projectors are used to project two different videos on a half-transparent screen. The test subjects view the movies together, wearing glasses that polarize the light from the screen differently, allowing them to see only one movie or the other.

Figure 2 from pg. 601 in "Surreptitiously projecting different movies to two subsets of viewers"

The light from projector A is polarized differently than projector B and the A and B groups of viewers have glasses that correspond to one projector’s polarization or the other. This method is useful particularly for studies on reliability of witness reports on crime. A typical set-up is one in which a mock-crime is filmed and small details like the color of a car, the size of an actor, or the time of day is changed slightly in order to create conflict between the two groups of viewers. This is especially useful when testing children since the previous method was to have confederates (people who are not actually test subjects, but are actors who know the goals of the study) insight conflict among the test subjects, but it is incredibly difficult to find reliable confederate children. The only difficulty with MORI is that if a participant tilts their head too much, the polarizer glasses will reveal the other movie being played. Usually, though, the subjects are unsuspecting of what the aims of the experiment are and the movies are short enough that the participants can remain alert and still for the necessary amount of time.

I found this use of LCD technology to be particularly interesting because it so effortlessly links the principles of polarization to a social science experiment. This research method very clearly expresses how physics (and, more specifically, the things we learned in Electromagnetism II) can be applied to vastly different areas of study.


Mori, Kazuo. “Surreptitiously projecting different movies to two subsets of viewers.” Behavior Research Methods Vol. 35.4 (2003): 599-604. 10 April 2012. <>.


Jones, Gooch and Tarry, and Transmission

I am going to start out my calculations by writing out the general form of a Jones matrix for TN-LCD as expressed in “Jones-matrix models for twisted-nematic liquid crystal devices” by Makoto Yamauchi:

(1)   \begin{equation*} J = \exp[-i(\phi_0 +\beta_T)]R(-\psi_D)R(-\alpha_T)MR(\psi_D) \end{equation*}


(2)   \begin{equation*} \phi_0 = \dfrac{\pi*d}{\lambda}(n_e + n_0) \end{equation*}

and represents the constant absolute phase.


(3)   \begin{equation*} \beta_T = \beta\dfrac{d}{2} \end{equation*}

representing the total birefrigence.

The R in equation (1) is the rotation matrix and is represented by

    \begin{equation} \[ R(\xi) = \begin{bmatrix} \cos{\xi} & \sin{\xi} \\-\sin{\xi} & \cos{\xi} \end{bmatrix} \] \end{equation}

And M is the MLC Jones matrix.

We can use this equation in conjunction with the Gooch and Tarry formula in order to help us model the transmission of TN-LCD.

As stated in my Preliminary Data, the Gooch and Tarry formula is written as 

(4)   \begin{equation*} T=\dfrac{1}{1+u^2}\left\{u^2+cos^2\beta{d}\right\} \end{equation*}

Since we will be focusing on TN-LCDs, the twist angle will be 90and the transmission can then be modeled as

(5)   \begin{equation*} T= 1- \dfrac{\Phi^2}{(\beta^2)d^2}\sin^2{\beta*d} \end{equation*}


(6)   \begin{equation*} \beta*d= \sqrt{\left(\dfrac{\pi}{2}\right)^2 + \left(\dfrac{\pi*d\Delta{n}}{\lambda}\right)^2} \end{equation*}

I then used this variation on the Gooch and Tarry formula in order to graph transmission vs.  d∆n/λ

This graph shows us the first few transmission peaks (Mathematica Code). Transmission operates at 100% when

(7)   \begin{equation*} \beta*d= N\pi \end{equation*}

For N= 1, 2, 3…

Where N stands for the number of wave plates (an LC-cell being thought of as N wave plates).

With respect to our graph, then, the transmission peaks are occurring when

(8)   \begin{equation*} \dfrac{d\Delta{n}}{\lambda}= \dfrac{1}{2}\sqrt{(4N^2)-1} \end{equation*}

This helps us to visualize how the twisted nematic effect operates.


Gooch, C.H. and H.A. Tarry. “The optical properties of twisted nematic liquid crystal structures with twist angles less than or equal to 90 degrees.” Applied Physics Vol. 8(1975): 1575-1584.

Yamauchi, Makoto. “Jones-matrix models for twisted-nematic liquid crystal devices.” Applied Optics Vol. 44.21(2005): 4484-4493.



Twisted Nematic Effect

A big breakthrough in LCD technology came about in late 1970 when Martin Schadt and Wolfgang Helfrich constructed an LCD based on the twisted nematic effect (Buntz 2). This method employs liquid crystal in the nematic phase that exhibits an angle of 900 in its molecular alignment. The LC-configuration is twisted in a continuous rotation. When the light passes through the LC-cell it is rotated by 900, this allows the light to pass through a second polarizer that is crossed with the first. When a voltage is applied to the LC cell from the electrodes, the liquid crystal molecules align themselves with the field, causing transparency to decrease as the light is blocked when the liquid crystal does not reorient its polarization (Yeh 4). The electrodes applied to the LC-cell are generally made from transparent materials with good electrical conductivity, ITO (indium tin oxide) has been used often in conjunction with LCD screens (Yeh 4).

Super Twisted Nematic Displays came along in the 1980s and differ from TN-LCDs in twist angle and polarizer angle. Instead, STN-LCDs rotate from 1800-2700, while the polarizer angle—instead of 00 as with TN-LCDs—is 450.  The STN-LCDs allowed for more complex pictures. Color Super Twisted Nematic (CSTN) displays use red, green, and blue color filters to create a colored display. Double STN displays stack two STN films with opposite twist in order to achieve a better black/white display. When the color filters are added, the DSTN-LCD has a much wider range of colors than the STN-LCD.

I will be focusing on TN-LCDs as I am particularly interested in the “origin story” of LCD technology and the discovery of twisted nematic effect certainly provided a path for modern LCD improvements.


Buntz, Gerard H. (Patent Attorney, European Patent Attorney, Physicist, Basel). “Twisted Nematic Liquid Crystal Displays (TN-LCDs), an invention from Basel with global effects,” Information No. 118 (October 2005): issued by Internationale Treuhand AG, Basel, Genf, Zurich.

Yeh, Pochi and Claire Gu. Optics of Liquid Crystal Displays. Canada: John Wiley & Sons, Inc., 1999.


Brief Description of Liquid Crystal

Liquid Crystal is a state of matter between liquid and crystalline solid in which LC molecules align in an ordered array (Yeh 5). LC molecules are anisotropic to light, meaning that they exhibit properties with different effects when oriented in varied directions (Yeh 5).

These are very rough artistic interpretations of the nematic phase alignment that I made in Mathematica as inspired by Fig. 1.9 on pg. 12 of Liquid Crystal Display Drivers: Techniques and Circuits.

We will focus on the nematic phase (see Figure) of liquid crystal, as when aligned, the optical properties of the nematic phase are helpful in liquid crystal displays. Nematic phases are made up of rod-shaped molecules that are ordered with their long axes (the ones used with LCD are uniaxial) approximately parallel (Cristaldi 12).


Cristaldi, David, Pennisi, Salvatorre and Francesco Pulvirenti. Liquid Crystal Display Drivers: Techniques and Circuits. Springer Science+Business Media B.V, 2009.



Preliminary Data

A very simplified way to look at LCD screens is to break them down into their most critical components. These would be the backlight, polarizer layer, liquid crystal layer, color filter (if it’s a color LCD screen), and second polarizer layer (there can be more than two polarizer layers, but we will visualize how the LCD screen works using this simple model).

What happens within these screens is that a voltage is applied to the liquid crystal layer, causing the liquid crystal to twist. Between the polarizer layers and the twisting liquid crystal, the intensity of the backlight is decreased in each cell depending on the voltage applied and, thus, how the liquid crystal twists, causing polarization effects. Color emerges as a result of red, blue and green color filters. In each pixel of the screen, different intensities of red, blue, and green will create the colors we perceive.

Liquid crystal cells (LC cells) act as wave plates (also known as retardation plates). Wave plates change the polarization of the incident beam.

If we have N equal the number of wave plates, then an LC cell will have a Jone’s matrix that looks like…

MLC = MN ….M3 M2 M1

An example of a corresponding Jone’s vector model of a wave plate would be this:

(1)   \begin{equation*} M_\delta = \dfrac{1}{\sqrt{2}}\left[ \begin {array}{ccc} e^{j\delta}&0\\ \noalign{\medskip} 0&e^{-j\delta} \end {array} \right] \end{equation*}


Where delta stands for the phase delay.

I am having trouble figuring out how to work Mathematica, but what I want to do is to create a graph that will show how each polarization has a different minimum, total twist angle, and retardation, and to particularly show this for viable commercial numbers.

The different twisting of the liquid crystal, as I said before, greatly affects what we see on the screen. When the twisting angle is much smaller than the double refraction (birefringence), the light is linearly polarized. While if the twist angle is large in comparison to the double refraction, the light in the cell will be circularly polarized.

The transmission of the LCD can be modeled using variations of the Gooch and Tarry formula:



I am going to continue to play with this equation in order to look at how transmission is altered and when and why it peaks as well as what typically produces the best results for commercial usage.

Since PDP and CRT screens do not rely on polarization in order to adjust the intensity of light, I intend to investigate EMI shields and how they contribute to PDP screens to be of a better picture quality than CRT screens.


Angelov, T.,  et. al. “High Temperature Formation of Polymer-Dispersed Hydrogen Bonded Liquid Crystals.” Journal of Optoelectronics and Advanced Materials Vol 7.1 (2005): 281-284.

Collett, Edward. Field Guide to Polarization. Washington: SPIE Press, 2005.



Project Plan

For this project I will be calculating, modeling, and discussing the differences in polarization effects, structure, and applications of liquid crystal display (LCD), plasma display panel (PDP), and cathode-ray tube display (CRT) screens and how such differences affect what we perceive and what we are meant to perceive with the human eye.

Calculations: I will be using the 2×2 Jones matrix (which represents a polarization state of light) as acting on a Jones vector in order to formulate a model for LCD screens. A sampling of equations I may need to employ can be found here in an excerpt from Field Guide to Polarization. I would also like to look at what effects the electromagnetic interference (EMI) shielding filter has in the PDP screens and how both of these models differ from the seemingly simpler CRT screens.

Visualization: I hope to make original models of polarization effects using Mathematica, while also illustrating how these effects come into play with regards to how LCD, PDP, and CRT screens function. I will also focus on how color is or is not affected or produced by different polarization.

Application: I will then relate my investigation with recent work being done to improve upon the optics employed in display screens, possibly in correcting perceived visual flaws or mechanics. I will also discuss how the effects of polarization with regards to display screens are currently being used in psychological studies in behavior based on group conflict and interaction with respect to perception.






Using Scratch Programming and Mathematica, I hope to model, investigate and illustrate the manipulation of electromagnetic waves and how this differs with respect to liquid crystal display (LCD), plasma display panel (PDP), and cathode-ray tube display (CRT) screens. I shall focus on polarization and the control of polarization effects for each screen and how these differences manifest with regards to our perception of light. Although one potential hurdle could be difficulty in selecting a proper method of investigation, I aim to develop this analysis based on my own calculations and personal observation.