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Chapter 2:
Optical Basics and Zernike Polynomials
Published: 2002
DOI: 10.1117/3.460595.ch2
The goal of this chapter is to discuss common optical performance metrics and the basics of image formation such that the mechanical engineer may relate their designs, concepts, and response quantities to the performance of the optical system. The second half of this chapter addresses the use of orthogonal polynomials, such as the Zernike polynomials, to describe optical surface data. These polynomials are useful to describe optical surface deformations and wavefront error due to temperature and mechanical stress. 2.1 Electromagnetic Basics A characteristic of all imaging systems is their ability to modify and reshape the incident electromagnetic radiation into an image. Thus, understanding the propagation of light is fundamental to our goal. Ultimately, we are concerned with how the environment impacts this propagation, but that will be addressed in later chapters. Light may be defined as a transverse electromagnetic wave where the electric and magnetic fields vibrate or oscillate perpendicular to the direction of propagation. For our purposes, the easiest way to consider light propagation is in 1D, as illustrated in Fig. 2.1. The mathematical equation describing the electric field vector, E, is given by E(z,τ)=Aei(wτ−kz), where the electric field is a function of both position, z, and time, τ.
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