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Chapter 2:
Optical Wavefronts and Their Aberrations
Abstract
The position and the size of the Gaussian image of an object formed by an optical imaging system is determined by using its Gaussian imaging equations. We have stated in Chapter 1 that the quality of the diffraction image depends on the aberrations of the system. A spherical wave originating at a point object is incident on the system. The image formed by the system is aberration free and perfect if the wave exiting from the system is also spherical. In this case, the rays originating at the point object and traced through the system all pass through the Gaussian image point. If the optical wavefront exiting from the exit pupil is not spherical, its optical deviations from a spherical form represent its wave aberrations. These wave aberrations play a fundamental role in determining the quality of the aberrated image. The rays traced from the object point through the system, instead of passing through the Gaussian image point, intersect the image plane in its vicinity. The distance of the point of intersection of a ray in the image plane from the Gaussian image point is called the transverse ray aberration, and the distribution of the rays is referred to as the spot diagram. In this chapter, we define the wave and ray aberrations and give a relationship between them. We relate the longitudinal defocus of an image to the defocus wave aberration, and its wavefront tilt to the wavefront tilt aberration. Next, the possible aberrations of an imaging system that is rotationally symmetric about its optical axis are described. The aberration function of the system is expanded in a power series of the object and pupil coordinates, and primary (or Seidel), secondary (or Schwarzschild), and tertiary aberrations are introduced. We also discusss briefly how the aberrations may be observed using a Twyman–Green interferometer and what the fringe pattern of a primary or Seidel aberration looks like. A short summary of the chapter is given at the end.