4.1 Introduction

First-order theory tells us the location, magnification, and orientation of an image. In this chapter, we introduce analysis tools to assess image quality within the framework of geometrical raytrace aberration theory. Geometrical aberration theory is used for designing and tolerancing opto-mechanical systems. Geometric waves are normal to rays and are a geometric construct to aid in visualizing the effects of aberrations. These are not diffraction waves, nor are they optical wavefronts but rather are surfaces normal to rays drawn from a point. The common center of the emerging wave is a point on the object.

Think of object space as comprising an ensemble of point sources, each having a different intensity that reveals the structure in the object. We then draw an expanding geometrical wave from each point. The system aperture truncates the expanding spherical geometric wave. Optical elements within the system change the geometrical wavefront from expanding to converging toward the image plane. If the system has no aberrations, this geometric wave converges to form a point image of the point in space. Note that geometric waves are not subject to diffraction. The effects of diffraction on image formation will be discussed in Chapter 9.

Ideally, an observer at any point on the image plane when looking back into the system will see the geometrical spherical wavefront converging to the point. This wavefront is called the reference wavefront. The wave aberration theory presented here examines perturbations on this geometric reference spherical wavefront. Geometric aberrations in white-light image-formation systems are divided into two types: (1) chromatic aberration and (2) monochromatic aberration. Chromatic aberrations arise because the optical power of the transmission elements is wavelength dependent. Monochromatic aberrations arise because the family of rays from the same point in the image encounters different physical paths in passing through the optical system to the image plane.