The skew aberration is a form of polarization aberration causes a rotation of polarization states across the pupil. Skew aberration is intrinsic to the optical system depending on the ray path only and whose magnitude is independent of the coatings or other polarization effects. Skew aberration has a much greater effects in high numerical aperture optical systems. A critical angle corner cube system is analyzed as an example to review the skew aberration’s effects.
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.
A three-by-three polarization ray tracing matrix method for polarization ray tracing in optical systems is presented
for calculating the polarization transformations associated with ray paths through optical systems. The method is a
three dimensional generalization of a Jones matrix. Diattenuation of the optical system is calculated via singular
The retardance associated with a three-by-three polarization ray tracing matrix is analyzed. The retardance of the
polarization ray tracing matrix contains both a geometrical transformation and the polarization properties of
diattenuation and retardance associated with a ray path through the optical and polarization elements. A method
using parallel transport of transverse vectors is able to separate the geometrical transformation from the "physical"
retardance, allowing the retardance to be calculated. A non-polarizing ray tracing matrix provides proper local
coordinates to calculate the physical retardance without the geometrical transformation.
A three-by-three polarization ray tracing matrix P which is defined in global coordinates characterizes the
polarization transformations associated with single ray through optical system. The P matrix contains both a
geometrical transformation effect and the polarization characteristics of diattenuation and retardance from the
optical and polarization elements. In order to separate the geometrical transformation and calculate the "physical"
retardance, a non-polarizing ray tracing matrix Q is used. The diattenuation and the retardance of a dove prism are
analyzed as an example.
The properties of a 3 × 3 polarization ray tracing matrix formalism are presented and the role of this method in
optical design. Properties of diattenuator matrices are derived and methods for analyzing diattenuation of arbitrary
homogeneous and inhomogeneous matrices are presented. The 3 × 3 matrix formalism is used to analyze
polarization properties of an example corner cube.
Polarized Light and Optical Systems surveys polarization effects in optical systems and their simulation by polarization ray tracing. First polarized light is reviewed with Jones vector and Stokes parameter descriptions. Polarization elements and effects, including retardance and diattenuation, can be described by Jones matrices for coherent and ray tracing calculations, or with Mueller matrices for incoherent calculations. A framework for polarization ray tracing is presented for nearly spherical waves in optical systems to include the large set of polarization effects which occur: polarization elements, Fresnel equations, thin films, anisotropic materials, diffractive optical elements, stress birefringence, and thin films. These polarization aberrations adversely affect the point spread function/matrix and optical transfer function/matrix.