Design and calibration of a Mueller matrix microscope based on liquid crystal variable retarders

•A Mueller matrix microscope based on LCVRs is developed.•An extended eigenvalue calibration method for double-pass system is proposed.•The polarization difference between two kind Morpho butterflies is revealed. Polarization imaging techniques have achieved broad applications in areas such as material characterization, nano-scale measurement, and biomedical diagnosis. The Mueller matrix microscopy, as one of the polarization imaging techniques, can provide the most comprehensive polarization information of a sample, such as anisotropy and depolarization. However, the instrumentation of Mueller matrix microscopy is typically complex and the associated calibration process is usually difficult due to the presence of many polarization and imaging components. In this work, we present an easy-to-follow approach for the instrumentation of Mueller matrix microscopy, not from scratch, but by easily modifying a commercial microscope into a Mueller matrix microscope (MMM) based on liquid crystal variable retarders (LCVR). Optimal configurations have been generated by the genetic algorithm at wavelengths of 400-800 nm. An extended eigenvalue calibration method is proposed to accurately calibrate the polarization and imaging components of the modified instruments in a model-free approach. Experiments performed on standard samples at the wavelength of 532nm, such as a polarizer and a waveplate, have indicated the performances of the developed MMM with a measurement error of less than 0.01 and a mean standard deviation of around 0.0042.