An Adaptive Dispersion Formula for Chromatic Aberration Correction and Polarization Aberration Analyses in Plane Symmetric Optical Systems

Abstract

This dissertation consists of two parts: an adaptive dispersion formula and polarization aberration functions for general plane symmetric optical systems. First, an adaptive glass dispersion formula is defined and discussed. The formula exhibits superior convergence with a minimum number of coefficients. Using this formula, the correction of chromatic aberration per spectrum order can be rationalized. Comparisons between the formula and the Sellmeier or Buchdahl formulas for glasses in the Schott catalogue are made. The six-coefficient adaptive formula is found to be the most accurate with an average maximum index of refraction error of 2.91×10-6 within the visible band. Second, a new set of polarization aberration functions for general plane symmetric optical systems is proposed. These new polarization aberration functions are derived based on the paraxial approximation and the second-order approximation. The polarization aberrations of an optical system are the sum of the contributions from each surface. In other words, this new set of polarization aberration functions provides insight of polarization aberration surface by surface. The polarization aberrations of optical systems with tilted or decentered elements, and refractive or reflective elements, are discussed and analyzed. Compared with CODE V real ray tracing simulation, the difference is less than 2.5% for an imaging system with three curved mirrors.