Two formalization on retardation of the waveplate with oblique incidence

As one common polarization components, the waveplate (λ/4 plate, λ/2 plate and 0λ plate) is widely used in polarimetry of high-NA imaging systems (microscope and immersion scanner). With increasing NA of the system, the accurate analysis and calculation of the retardation with respect to oblique incidence become significant. At present, there are two methods to analyze this quantity, one is based on the theory of wave propagation and the other is based on the ray-tracing method. Due to the retardation solved by some authors based on above two methods is not only so complicated without final expression, but also the final results exist much difference. First, the expressions on the two refractive indices of e-ray wave-normal and actual e-ray are reduced. Then, the retardation between e-ray and o-ray is formulated in which oblique incidence passing through the waveplate, using the theory of wave propagation and ray-tracing method respectively. As a result, the final expressions of retardation deduced by above two methods are consistent. The retardation property of the waveplate is described accurately, the rigorous theory basis is supplied for the design and error analysis of the waveplate, and it has important theoretical significance and application value.