Analysis and optimization approaches for wide-viewing-angle λ/4 plate in polarimetry for immersion lithography

A waveplate is usually used to measure the polarization effects in optical systems. For a hyper numerical aperture imaging system with a large angle of incidence, the incident plane of light concerned may be neither parallel nor perpendicular to the optical axis of the waveplate, which makes a conventional waveplate produce undesired nonuniform retardation in any incident plane determined by the incident light and the wave normal of the crystal surface. To compensate effectively for this nonuniform retardation, the authors propose approaches to analyze and optimize the wide-viewing-angle (WVA) λ/4 plate. First, the retardation between the p and s components of a light wave propagating through the WVA waveplate is analyzed based on light propagation theory. Then, the authors develop an optimization method for the thickness parameters of the waveplates that compose the WVA λ/4 plate, which is used extensively in polarimetry for immersion lithography. It is found that the proposed approach is effective for WVA λ/4 plate design. The best WVA λ/4 plate has a small variation in retardation of less than ± 0.5 ° for angles of incidence between ± 20 °.