Simulating the vibrant colors of polarizing microscopy images of liquid crystals

When viewed with crossed polarized optical microscope (POM), liquid crystals display vibrant colors and complex patterns that make them suitable for optical applications. The color patterns provide rich information for the intricate alignments and intrinsic optical properties of the liquid crystal molecules. While calculations of black and white images from single wavelengths using calculated director fields have been demonstrated, color images produced to date do not always make quantitative agreement with experiments. In this work, we extend the Jones matrix method to calculate the colored images from arbitrary director fields, and exemplify our method by simulating radial and bipolar droplets of 5CB. We compare simulation results to experiments of 5CB droplets of various sizes and alignments generated by microfluidic devices and vortex. The effect of elastic constants, refractive indices and particle geometry are discussed. Our results provide a powerful way of quantitatively comparing POM images from experiments and the director fields from simulations, thereby paving the way for the inverse design of materials with internal microstructure.