The course begins with an overview of basic aberrations and tolerance analysis in optical imaging systems. Zernike circle polynomials and their use in wavefront data analysis are presented as are analytical methods for cases involving non-circular pupils such as annular, square, hexagonal and elliptical pupils. The calculation of orthonormal aberration coefficients from the wavefront error data obtained by phase-shifting interferometery or wavefront slope error data obtained with a Shack-Hartmann sensor is explained, and numerical analyses of both types of data are demonstrated.

Gaussian optics yields the location and size of the image formed by an imaging system. However, the quality of the image depends on the aberrations of the system. We start with an aberration-free image, and explain how aberrations affect it. The concept of Strehl ratio is introduced, and how fabrication tolerances can be obtained from it is illustrated. We explain what Zernike polynomials are, and why they are used in optical design and testing. We briefly discuss how aberrations affect the line of sight of an optical system. We also discuss the optical transfer function of a system, and illustrate how aberrations introduce contrast reversal at certain bands of spatial frequencies.