Karlton Crabtree

Three-dimensional polarization ray-tracing calculus I: definition and diattenuation

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 the Jones calculus. Reflection and refraction algorithms are provided. Diattenuation of the optical system is calculated via singular value decomposition. Two numerical examples, a three fold-mirror system and a hollow corner cube, demonstrate the method.

Formulation of rigorous coupled-wave theory for gratings in bianisotropic media

A formulation of rigorous coupled-wave theory for diffraction gratings in bianisotropic media that exhibit linear birefringence and/or optical activity is presented. The symmetric constitutive relations for bianisotropic materials are adopted. All of the incident, exiting, and grating materials can be isotropic, uniaxial, or biaxial, with or without optical activity. The principal values of the electric permittivity tensor, the magnetic permeability tensor, and the gyrotropic tensor of the media can take arbitrary values, and the principal axes may be arbitrarily and independently oriented. Procedures for Fourier expansion of Maxwells equations are described. Distinctive polarization coupling effects due to optical activity are observed in sample calculations.

Skew aberration: a form of polarization aberration.

We define a new class of aberration, skew aberration, which is a component of polarization aberration. Skew aberration is an intrinsic rotation of polarization states due to the geometric transformation of local coordinates, independent of coatings and interface polarization. Skew aberration in a radially symmetric system has the form of a circular retardance tilt plus coma aberration. Skew aberration causes undesired polarization distribution in the exit pupil. We demonstrate statistics on skew aberration of 2383 optical systems described in Code Vs U.S. patent library [Code V Version 10.3 (Synopsys, 2011), pp. 22-24]; the mean skew aberration is 0.89° and the standard deviation is 1.37°. The maximum skew aberration found is 17.45° and the minimum is -11.33°. U.S. patent 2,896,506, which has ±7.01° of skew aberration, is analyzed in detail. Skew aberration should be of concern in microlithography optics and other high NA and large field of view optical systems.

Polarization conversion cube-corner retroreflector

Polarization conversion cube-corner retroreflectors rotate the major axis of the incident electric field by 90°. We show that polarization conversion cube-corner retroreflectors cannot be created with isotropic reflecting surfaces, but can be created by incorporating nonisotropic reflecting surfaces. Two types are considered-cube corners with surfaces having elliptical eigenstates and cube corners having subwavelength gratings. Implementations that use subwavelength surface relief phase gratings are investigated, and three examples are shown.

Properties of the polarization ray tracing matrix

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.

Airborne multiangle spectropolarimetric imager (AirMSPI) observations over California during NASA's polarimeter definition experiment (PODEX)

The Airborne Multiangle SpectroPolarimetric Imager (AirMSPI) is an ultraviolet/visible/near-infrared pushbroom camera mounted on a single-axis gimbal to acquire multiangle imagery over a ±67° along-track range. The instrument flies aboard NASA’s high-altitude ER-2 aircraft, and acquires Earth imagery with ~10 m spatial resolution across an 11- km wide swath. Radiance data are obtained in eight spectral bands (355, 380, 445, 470, 555, 660, 865, 935 nm). Dual photoelastic modulators (PEMs), achromatic quarter-wave plates, and wire-grid polarizers also enable imagery of the linear polarization Stokes components Q and U at 470, 660, and 865 nm. During January-February 2013, AirMSPI data were acquired over California as part of NASA’s Polarimeter Definition Experiment (PODEX), a field campaign designed to refine requirements for the future Aerosol-Cloud-Ecosystem (ACE) satellite mission. Observations of aerosols, low- and mid-level cloud fields, cirrus, aircraft contrails, and clear skies were obtained over the San Joaquin Valley and the Pacific Ocean during PODEX. Example radiance and polarization images are presented to illustrate some of the instrument’s capabilities.

Subwavelength-grating-induced wavefront aberrations: a case study

The on-axis wavefront aberrations of a one-dimensional subwavelength-grating antireflection coating on an f/1.7 lens surface are shown to be small with noticeable contributions of defocus, astigmatism, and piston. The astigmatism is 0.02 wave, and the magnitude of the piston approaches one wave peak-to-valley. The difference in aberrations between orthogonally polarized wavefronts, or the retardance aberration, shows 0.01 wave of astigmatismlike variation and more than 0.01 wave of retardance-induced defocuslike variation. A small coupling between polarization states occurs in the form of the familiar Maltese cross, yielding a maximum of 3% coupling in the four diagonal edges of the pupil.

Illumination system design in a project-based course

This past spring a new for-credit course on illumination engineering was offered at the College of Optical Sciences at The University of Arizona. This course was project based such that the students could take a concept to conclusion. The main goal of the course was to learn how to use optical design and analysis software while applying principles of optics to the design of their optical systems. Projects included source modeling, displays, daylighting, light pollution, faceted reflectors, and stray light analysis. In conjunction with the course was a weekly lecture that provided information about various aspects of the field of illumination, including units, étendue, optimization, solid-state lighting, tolerancing, litappearance modeling, and fabrication of optics. These lectures harped on the important points of conservation of étendue, source modeling and tolerancing, and that no optic can be made perfectly. Based on student reviews, future versions of this course will include more hands-on demos of illumination components and assignments.

Diffraction analysis of large segmented mirror concepts for exoplanet exploration

Diffraction effects of large segmented mirror gaps and secondary mirror support struts produce diffraction peaks or flares that are a detriment to exoplanet detection. In this paper we present detailed parametric diffraction analyses of an innovative “Pinwheel Pupil” segmented mirror concept utilizing curved segment gaps and secondary support struts that can potentially eliminate these diffraction flares that can obscure a faint exoplanet image. The resulting numerical diffraction performance predictions are quantitatively compared to that of both ideal monolithic circular pupils and classical annular pupils with straight secondary mirror struts. We utilize performance – based merit functions consisting of both radial and azimuthal profiles of the resulting telescope point spread function.

Three-dimensional polarization ray tracing and diattenuation calculation

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 value decomposition.