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Chapter 7:
Image Formation
Abstract

In the derivation of optical imaging concepts, the object space is assumed to be a collection of an infinite number of points, with each point being an irradiance source of diverging spherical wavefronts. An optical wavefront is a collection of rays. A ray is defined as a line marking the direction of flow of optical energy. An optical wavefront is characterized by the locus of points of constant phase. The shape of a wavefront depends on its source (Sec. 7.5.1). A lens transforms the shapes of these emerging wavefronts. The refracted wavefronts from an ideal lens are perfectly spherical and converge at the focal point on the optical axis of the lens [Fig. 7.1(a)]. Variations in the incident lens surface shape from a chosen reference sphere are manifested in the deviation of the refracted wavefronts from the ideal spherical surface. The resulting error, referred to as the wavefront aberration or wavefront error, introduces a phase difference between the converging wavefronts that moves the focusing point of the refracted rays away from the ideal location. The root mean square of all point-by-point deviations is generally quoted as the wavefront error of the lens, with the common notation W (lens coordinates ξ,η). It is expressed as multiples or fractions of the wavelength λ of the incident wavefront. An error of λ/4 (quarter wavelength) is a near-perfect lens for general optical work.

The concept of the reference sphere stems from the geometric property that rays are perpendicular to the wavefront, so any ray that hits a perfectly spherical lens surface will converge at the center of the sphere. From geometric definitions, if a lens gives a perfect image, all rays from the object space intersect at the Gaussian image point. In this ideal case, the focal point coincides with the center of the spherical surface, and the converging rays arrive exactly in phase. For practical purposes, the reference sphere is taken as a sphere of radius R with its center at the ideal focal point of the lens. For a simple lens, R is the distance between the exit pupil (or the lens axis) and a point on the image plane [Fig. 7.1(b)]. As a spherical wavefront continues to diverge from its source, its radius of curvature expands to become a collection of parallel traveling waves (planar wavefront). For general optical imaging, the incident wavefront on the lens is assumed to be planar [Fig. 7.1(c)].