Michel-Levy Birefringence Chart
Quantitative analysis of the interference colors observed in birefringent samples is usually accomplished by consulting a Michel-Levy chart similar to the one illustrated in the tutorial window below. As is evident from this graph, the polarization colors visualized in the microscope and recorded onto film or captured digitally can be correlated with the actual retardation value, thickness, and birefringence of the specimen. The chart is relatively easy to use with birefringent samples if two of the three required variables are known. This interactive tutorial enables visitors to determine the interference color associated with all three values by clicking on selected regions of the interactive chart.
The tutorial initializes with a classical Michel-Levy graph appearing in the window, which contains interference colors from the first to the sixth order, and the associated diagonal birefringence lines traversing the entire chart from the lower left-hand corner to the upper and right-hand boundaries of the graph. A small white circle appears upon initialization at the coordinates (displayed in yellow boxes): Birefringence = 0.02; Thickness = 0.03 millimeters; and, Path Difference = 570 nanometers (first order). The specific interference color (magenta) associated with these values is displayed in the lower right-hand side of the window. In order to operate the tutorial, click the mouse cursor anywhere within the Michel-Levy graph to display the corresponding values and interference color for that region of the chart.
When the specimen is placed between crossed polarizers in the microscope and rotated to a position of maximum brightness with any one of a variety of retardation plates, the color visualized in the eyepieces can be traced on the retardation axis to find the wavelength difference between the ordinary and extraordinary waves passing through the specimen. Alternatively, by measuring the refractive indices of a specimen and calculating their difference (the birefringence), the interference color(s) can be determined from the birefringence values along the top of the chart. By extrapolating the angled lines back to the ordinate, the thickness of the specimen can also be estimated.
The lower section of the Michel-Levy chart (x-axis) marks the orders of retardation in multiples of approximately 550 nanometers. The area between zero and 550 nanometers is known as the first order of polarization colors, and the magenta color that occurs in the 550 nanometer region is often termed first-order red. Colors between 550 and 1100 nanometers are termed second-order colors and so on up the chart. The black color at the beginning of the chart is known as zero-order black. A majority of the Michel-Levy charts printed in textbooks plot higher-order colors up to the fifth or sixth order.
The most sensitive area of the chart is first-order red (550 nanometers), because even a slight change in retardation causes the color to shift dramatically either up in wavelength to cyan or down to yellow. Many microscope manufacturers take advantage of this sensitivity by providing a full-wave retardation plate or first-order red compensator with their polarizing microscopes to assist scientists in determining the properties of birefringent materials.