Orientation-independent measurement of birefringence with polarizing microscopy

   It was recently published a new method of measuring birefringence [Shribak M. J Opt Soc Am A Opt Image Sci Vis, 2011 March 1; 28(3): 410–419; http://dx.doi.org/10.1364/JOSAA.28.000410] which is independent of sample orientation and much faster than the traditional technique with compensators (e.g. Berek, de Senarmont). The technique is similar to that to the Polscope (Cambridge Research Instruments, MA, USA), but the system is < 20% of the price of a Polscope making it much easier to implement. It is likely to be become as popular as the traditional methods with compensators.
   Traditional methods have the following limitations:

- each point of interest in a sample has to be oriented at a particular position of maximum birefringence (diagonal position), making measurements of difference points at the same time impossible (this is particularly important for dental enamel where prisms orientation might vary considerably at short distances);
- placing the point of interest at the diagonal position might take up 5 minutes (for an experienced operator), resulting in a poor temporal resolution for studying kinetics of variation in birefringence;
- at each point of interest, a mean of 5-10 measurements has to be obtained, further contributing to decrease temporal resolution.
   Thus, traditional methods are very time-consuming. 
    
   The new method, called single polscope (uses a single variable crystal retarder to control the state of polarization of light), has the following advantages:
- measurements are performed concomitantly at all sample points captured in a photomicrograph;
- orientation-independent, which means that points of interest do not have to be at the diagonal position;
- a single birefringence measurement can be performed in 10-20 seconds (or even less) and the same is valid for the interval between measurements, increasing temporal resolution.
  Single polscope allows a huge improvement in temporal resolution. For comparison, birefringence at ten points at intervals of 0.1 mm in a ground section of dental enamel take ~ 1.5 hour to be measured, and the single polscope is able to measure all points of the sample in an image (it can be 1000 points of interest) in less than 1 minute. All measurements are archived in images that can be saved, so that one can check back data whenever he needs.

   The following components and arrangements (in sequence from the base to the head of the microscope) are used in a single polscope:

- light source  + green filter (546 nm) + rotating polarizer at 0° (aligned east-west; X axis) + liquid crystal (LC) variable retarder with its slow axis at 0° (aligned east-west; X axis) + first lambda/4 filter at -45° (northwest-southeast) + sample + first lambda/4 filter at -45° (northwest-southeast) + second polarizer   at 0° (aligned east-west; X axis). Both polarizers and the slow axis of LC are parallel; both lambda/4 retarders are parallel too, but at -45° to the slow axis of the LC. 
   Such arrangement yield a dark background. Frequently, small alterations in the orientation of the second polarizer and second lambda/4 retarder are needed to get a dark background. Then, the first polarizer is rotated relative to the liquid crystal (LC) slow axis depending on the amount of birefringence to be measured (retardance/2). A maximum retardance of lambda/2 (546 nm/2) can be measured. For dental enamel, fist polarizer can be positioned at 80° relative to the slow axis of the LC. Fours images (using different polarizations states, created by different input voltages from a function generator, of the incoming light) are taken and light intensities are measured with an image analysis software (it can be ImageJ from NIH) in order to get phase retardance (using formulas published in Shribak, 2011). The ration of phase retardance by sample thickness is the birefringence.