Overview

Birefringence is the difference in a material’s refractive index for difference incident polarization states of light.  We define birefringence as Δn = n_max – n_min, where n_max and n_min are the maximum and minimum refractive indices for all possible launched polarization states.

As light passes through a birefringent material, the polarization state parallel to n_max will progressively lag further and further behind the polarization state aligned with n_min. This lag is called the 'retardance' or 'retardation'.  In units of length, this retardation is simply δ = Δn t where t is the material thickness.  In units of phase, where 360° is one wavelength, the retardance is δ = 360° Δn t / λ where λ is the wavelength of the light.

Most users wanting to map the birefringence of a sample are actually more interested in mapping the retardance.  And while AxoScan and AxoStep do not directly measure birefringence, they both excel at retardance measurements. Or if the actual birefringence is needed, it is a simple matter of mechanically measuring the sample thickness and calculating birefringence from the measured retardance in degrees as Δn = δ λ / 360° t. 

Our systems can measure retardance with levels as low as 0.01° or λ/36,000.  If only a single measurement wavelength is used, the maximum retardance that can be measured is 180° or λ/2. Retardance values higher than 5,000° or  approximately 14λ can be measured by testing multiple wavelengths and applying curve-fitting algorithms.

AxoScan completes a single-point retardance measurement in 0.03 seconds. Including time to move an XY stage, users can typically measure up to three locations per second allowing for high-resolution line scans and XY maps of samples.  Typically AxoScan is used for testing samples with features larger than 3 mm.

AxoStep is an imaging microscope system that provides retardance measurements of every location within a image in 14 seconds. This allows for very high resolution maps of small areas.  AxoStep is used for measuring features smaller than 3 mm.

Example Measurements

A 2 mm diameter injection-molded plastic lens measured with AxoStep reveals retardation near the filling gate. In addition to affecting polarization states, retardation will cause a phase error that distorts the optical wavefront produced by the lens resulting in lower-quality imaging.

The glass used to manufacture LCD panels requires very low internal stress so that it does not affect polarization states and so that the glass does not change dimensions when diced into smaller pieces.  The figure below shows the very small stress pattern (less than 0.5 nm of retardation) present in a Gen 5 (1,100 mm x 1,300 mm) LCD glass substrate as measured by AxoScan.

In a Vickers test, a pyramidal diamond indenter is pressed into a sample to determine the hardness of the sample.  An AxoStep system was used to map the resulting strain-induced birefringence when a glass plate was tested.