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Chapter 1:
Optical Aberrations
Author(s): Virendra N. Mahajan
Published: 2011
DOI: 10.1117/3.903924.ch1

This chapter starts with the concepts of aperture stop and entrance and exit pupils of an optical imaging system. Certain special rays, such as the chief and the marginal, are defined. The wave aberration associated with a ray is defined and its relationship to the corresponding transverse ray aberration is given. Representations of wavefront defocus and tilt aberrations are given. We introduce different forms of the primary aberration function of a rotationally symmetric system. How this function changes as the aperture stop of the system is moved from one position to another is discussed. The primary aberration function for the simplest imaging system, namely, a single spherical refracting surface, is given for an arbitrary position of the aperture stop. Finally, we outline a procedure by which the aberration function of a multielement system may be calculated. This procedure is utilized in later chapters, for example, to calculate the aberration of a thin lens (Chapter 2) and a plane-parallel plate (Chapter 3). This chapter forms the basis of Part I on geometrical optics.


An optical imaging system consists of a series of refracting and/or reflecting surfaces. The surfaces refract or reflect light rays from an object to form its image. The image obtained according to geometrical optics in the Gaussian approximation, i.e., according to Snell's law in which the sines of the angles are replaced by the angles, is called the Gaussian image. The Gaussian approximation and the Gaussian image are often referred to as the paraxial approximation and the paraxial image, respectively. We assume that the surfaces are rotationally symmetric about a common axis called the optical axis (OA). Figure 1-1 illustrates the imaging of an on-axis point object P0 and an off-axis point object P, respectively, by an optical system consisting of two thin lenses. (For definition of a thin lens, see Section 2.2.) P′ and P0 are the corresponding Gaussian image points. An object and its image are called conjugates of each other, i.e., if one of the two conjugates is an object, the other is its image.

An aperture in the system that physically limits the solid angle of the rays from a point object the most is called the aperture stop (AS). For an extended (i.e., a nonpoint) object, it is customary to consider the aperture stop as the limiting aperture for the axial point object, and to determine vignetting, or blocking of some rays, by this stop for offaxis object points. The object is assumed to be placed to the left of the system so that initially light travels from left to right. The image of the stop by surfaces that precede it in the sense of light propagation, i.e., by surfaces that lie between it and the object, is called the entrance pupil (EnP). When observed from the object side, the entrance pupil appears to limit the rays entering the system to form the image of the object.

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Imaging systems

Geometrical optics

Optical aberrations

Optical imaging

Paraxial approximations


Spherical lenses

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