Stokes-Mueller calculus and θ-scan technology for investigating optical effects in liquid crystals doped with nanoparticles

•We combine Stokes-Mueller calculus and θ-scan technology to investigate the optical effects of nanoparticles in liquid crystals (LCs).•The optical axis of LCs doped with nanoparticles can be determined using the proposed measurement approach.•The doping of LCs with nanoparticles can enhance their optical properties, such as birefringence.