Skew aberration analysis

Skew aberration is an intrinsic rotation of polarization states due to the geometric transformation of local coordinates via parallel transport of vectors. Skew aberration is a component of polarization aberration but is independent of the incident polarization state or the coatings applied to the optical interface. Skew aberration occurs even for rays propagating through ideal, aberration-free, and non-polarizing optical systems. Skew aberration is typically a small effect in optical systems but it should be of concern in microlithography optics and other polarization sensitive systems with high numerical aperture and large field of view. The variation of skew aberration across the exit pupil causes undesired polarization components in the exit pupil. Typically cross polarized satellites form around the point spread function (PSF). The PSF and optical transfer function (OTF) are different from ideal PSF or OTF and thus the image quality can be degraded. In the presence of polarization aberration, the scalar PSF and OTF can be generalized to a two-by-two point spread matrix (PSM) or optical transfer matrix (OTM) in Jones matrix notation. We demonstrate analysis of skew aberration effects separate from other polarization aberrations by using a two-by-two PSM and OTM of the U.S. patent 2,896,506. We demonstrate a relationship between skew aberration, Lagrange invariant and the sum of the individual surface powers of the system, using paraxial optics.