Polarization Color Chart

You can see colors when you put a double reflex substance between crossed polarizers. This color is called polarization color. This color sometimes called interference color, probably because of the color order is similar between two. But this color does not come from the interference of light. Two light waves having the same wavelength and polarization can interfere each other. And interference color happens without polarizers. In the double reflex substance between crossed polarizers, polarized incident light propagate the substance as the two intrinsic rays. The polarization planes of intrinsic rays crossed at a right angle. Such rays cannot interfere each other. A phase difference between rays happens after passing through the substance. Ray becomes elliptically polarized light and the projection to the second polarizer pass through it.

Polarization color Chart

In polarization color, an important variable is a retardation, which is defined as the product of the thickness and birefringence of the sample. The polarization color starts from black when the retardation is zero. As the retardation increases, color changes from gray, yellow, red-purple, blue, cyan, yellow, and finally becomes gray. Polarization color tells us information about the retardation. Therefore, a color chart showing polarization color of each retardation is a useful tool for estimate the retardation of the sample.

A polarization color chart is a two-dimensional color chart. The vertical axis of the chart is birefringence. The horizontal axis is the thickness of a sample. Several oblique lines are drawn in the chart. They show the relationship between the retardation and thickness. Figure 1 shows a typical polarization color chart. The maximum value of the retardation is usually taken around 1500nm. Polarization color becomes dull beyond this value and estimation of retardation from the color becomes difficult.

Such charts were made by hand painting in the old days. Now the polarization color chart can be easily made using a computer. Most of polarization color charts have been made assuming the birefringence is independent of the wavelength of light. In other words, the dispersion of the birefringence is ignored. We call such charts as standard polarization color charts.

Fig. 1 Standard Polarization Color Chart

Every substance has a dispersion of refractive index. The birefringence of double reflex substance also has dispersion. The dispersion makes a deviation in color from that of the standard chart. Tsuboi proposed an indication number of the birefringence dispersion defined by the following equation.

This number is small for large dispersion substances and big for small dispersion substances. It diverges when the birefringence is independent of the wavelength. According to Tsuboi, the deviation from the standard color becomes serious when the number is smaller than 10. Calculated numbers for 5CB and MBBA are 7.2 and 4.5 at 20 degrees C. Hence, the polarization color charts of these materials should have a deviation from the standard one. It was difficult to make charts for these strongly disperse materials. Thanks to the development of personal computers and published dispersion data of these materials, it becomes possible to make the charts of these materials.

The vertical axis of the conventional polarization color chart is retardation. This implementation is possible when the birefringence is independent of wavelength. When the birefringence depends on the wavelength, we need to set the standard wavelength to define the retardation of the sample. It is one method to set the wavelength and take the retardation as the vertical axis. Figure 2 is an example of such color chart. The vertical axis is the birefringence at Fraunhofer D-line. The horizontal axis is the Tsuboi’s indication number. Dispersion is calculated using the first and the second terms of Cauchy’s approximation formula by setting B equals 0.

Fig. 2 Polarization Color Chart with consideration for dispersion

The measured B coefficients of 5CB and MBBA have finite values. Therefore, color deviation of them can be different from those in Fig. 2 at each indication value. Using reported Cauchy’s coefficients of 5CB and MBBA[1], it is possible to calculate their the polarization colors. Polarization color of a particular molecule like 5CB and MBBA directly relates to the cell thickness. It is more convenient to take cell thickness as the vertical axis of the chart. In that case, horizontal axis cannot be thickness.

We have space for setting other parameters on the horizontal axis. The birefringence of the nematic phase has strong temperature dependence. It is interesting to make a chart showing temperature-dependent polarization color change. At this moment, this trial is hard to work out since Cauchy’s coefficients of all nematic temperature range are not variable. Instead, we show you polarization color charts of 5CB(Fig. 3) and MBBA(Fig. 4) showing a color change in three temperatures using Cauchy’s coefficients.

Fig.3 Polarization Color Chart created using Cauchy’s coefficients of 5CB

Fig. 4 Polarization Color Chart created using Cauchy’s coefficients of MBBA