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Chapter 9:
Scalar Diffraction and Image Formation

9.1 Introduction

The principles of diffraction, interferometry, and image formation are based on the wave nature of light. The first experiments to offer a glimpse into the wave nature of light were done in the early 17th century by Francesco Grimaldi (1613-1663). He recorded his observation that when he illuminated a human hair, its shadow showed a periodicity. Today, we explain this phenomenon as a property of the wave nature of light and call it the diffraction of light waves around an object, in this case, a human hair. Thomas Young (1803) was the first scientist to perform an experiment that demonstrated the wave nature of light. Both diffraction and interferometry are based on the wave nature of light discovered by Young. [This is the same Thomas Young who developed the theory of elasticity (Young's modulus) and first deciphered the ancient Rosetta stone].

Diffraction theory provides the mathematical framework for describing the wavelike propagation of light. For our purposes here, we choose to apply scalar diffraction theory to two practical problems in astronomical telescopes and instruments: image formation and spectrometer design. Analysis of diffraction using scalar wave theory is adequate to describe the general properties of imageforming systems and grating spectrometers. Scalar theory is used for image quality assessment, design and performance evaluation of holograms, holographic optical elements, diffraction-grating spectrometers, diffractive-optics imaging systems, and propagation of wavefronts through atmospheric turbulence.

Vector theory, discussed in Chapter 8, provides an additional level of understanding of image formation, grating spectrometer and optical thin film design, and the interaction of light and matter. Solar astronomy requires an understanding of the vector theory of light to explain magnetic fields on the sun and narrowband imaging spectrometer instruments such as the Lyot filter.

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