Analysis of accuracy and ambiguities in spatial measurements of birefringence in uniaxial anisotropic media

Accuracy and ambiguities in retardance and optical axis orientation spatial measurements are analyzed in detail in the context of the birefringence imaging method introduced by Shribak and Oldenbourg [Appl. Opt. 42, 3009 (2003)]. An alternative formula was derived in order to determine the optical axis orientation more accurately, and without indetermination in the case of a quarter-wave plate sample. Following Shribak and Oldenbourg’s experimental configuration using two variable retarders, a linear polarizer, and five polarization probes, we examined the effect of the swing angle χ, which selected the ellipticity of each polarization state, on the accuracy of retardance (1) and axis orientation (φ) measurements. Using a quarter-wave plate, excellent agreement between measured and expected values was obtained for both the retardance and the axis orientation, as demonstrated by the statistical analysis of 1 and φ spatial distributions. The intrinsic ambiguity in the determination of 1 and φ for superimposed layers of transparent anisotropic cello-tape is discussed in detail, and solutions are provided to remove this ambiguity. An example of application of the method on geological samples is also presented. We believe our analysis will guide researchers willing to exploit this long-standing method in their laboratories.