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With this chapter, we begin to cover the third bracket of our simplified radiometric performance equation [Eq. (1.7)]. where τ0 is the net transmittance after absorption and Fresnel losses of all optical elements, which includes not only lenses and mirrors but windows and filters as well. As mentioned earlier, even though d′ is the linear size of the detector element, it is included in the “optics bracket” because it is the dimension for the field stop. Included in this chapter are some numerical examples of S∕N calculations for the reader who is not concerned about optical aberrations and is satisfied with a very preliminary performance prediction for a conceptual system configuration. But, at some point, more detailed analysis of the optics is required to do the job. For that purpose, a fundamental understanding of optics is essential. We begin with the foundation of geometric optics, which is Snell's law, named after Willibrord Snel van Royen (1581–1626), a Dutch astronomer and mathematician who worked at the University of Leiden in Holland. It states that the sine-index product is equal across an interface when light passes from one transparent medium into another. The index of refraction is simply the ratio of the velocity of light in a vacuum to the light velocity in a medium. With reference to Fig. 2.1 we can write
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