Transparent anisotropic films measurement with a polarized angle-resolved spectroscopy

Polarized angle-resolved spectroscopy is introduced to measure transparent anisotropic films with back focal plane imaging by virtue of its rich information provided at various incident and azimuthal angles. The polarized angle-resolved spectroscopy provides a conoscopic interferogram and angle-resolved spectrum to deal with the complex characterization parameters of an anisotropic film, including the thickness, principal refractive index, and optical axis. Firstly, the optics model of a transparent anisotropic film is built by superpositioning the incoherent waves from the front and rear surfaces with coherency matrices formalism when the optical length is larger than the coherent length, and the incoherent issue arises. Then the optical axis of the anisotropic sample can be determined by the conoscopic interference image with the melatope, which marks zero phase difference between the ordinary and extraordinary waves. The measured angle-resolved reflectance spectrum and anisotropic interference phase are fitted to the optics model of the film with coherency matrix formalism, utilizing the Levenberg-Marquardt algorithm to calculate the thickness and dispersion principal refractive index within a single shot. The thickness and anisotropic refractive index are determined for sapphire and polyethylene terephthalate (PET) samples with our homemade polarized angle-resolved spectrometer. The thickness measurement results show that the relative error of the proposed method is less than 1.45%.