I. Introduction to the Aberrations of Optical Systems
Perfect image formation in an optical system occurs when all of the rays originating from a single object point cross at a single image point, or equivalently, when the geometrical wavefront in image space has a spherical shape centered on the image point. Lord Rayleigh provided a mathematical proof that in order for an optical system to produce a perfect image of an object, all of the optical path lengths (OPL’s) for each possible ray connecting an object point to its corresponding image point (conjugate points) must be equal. The only surfaces to rigorously satisfy this condition are the Cartesian oval and the conic sections at one pair of conjugates. This situation is never satisfied for a real optical system with spherical
1). Monochromatic aberrations are aberrations that arise due to geometrical deviations from paraxial (Gaussian) theory. First-order theory corresponds to the approximation sinθ ≈ θ. If we extend the approximation to the next term, we can predict deviations from paraxial theory when sinθ ≈ θ - θ3/6. This third-order theory describes the five primary or Seidel aberrations: spherical aberration, coma, astigmatism, field curvature, and distortion.
2). Chromatic aberrations result from the dependence of index of refraction on wavelength (n → n(λ)). This causes the properties of an optical system, such as magnification, focal length, and location of all the principal points, to be different for each color of light passing through the system.
3). Diffractive aberrations are caused by deviations from geometrical optics due to the wave nature of light. Diffraction effects place the ultimate limit on a system’s best possible imaging performance.
4). Aberrations may also result from the physical limitations of an optical system (surface quality, surface accuracy, limited aperture size, etc.).
II. Third-Order Aberration Theory
1). The first step in analyzing deviations from paraxial theory is to model the behavior of an optical system as a function that is an infinite series of terms of which the first term reproduces paraxial theory and the remaining terms correspond to successively smaller corrections. These expansions may be obtained many different ways: optical Hamiltonian, wavefront distortion, optical surfaces, sinθ, … Generally, the five Seidel terms are the only aberration terms that maintain the same functional form regardless of method of derivation.