Geometrical Optics
This chapter shall discuss the basics and the applications of geometrical optical methods in modern optics. Geometrical optics has a long tradition and some ideas are many centuries old. Nevertheless, the invention of modern personal computers which can p
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Geometrical O 2. Geometrical Optics
2.1
The Basics and Limitations of Geometrical Optics ............................ 2.1.1 The Eikonal Equation .................... 2.1.2 The Orthogonality Condition of Geometrical Optics....................
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2.2
2.1.3 The Ray Equation ......................... 2.1.4 Limitations of the Eikonal Equation 2.1.5 Energy Conservation in Geometrical Optics.................... 2.1.6 Law of Refraction ......................... 2.1.7 Law of Reflection .........................
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Paraxial Geometrical Optics ................... 2.2.1 Paraxial Rays in Homogeneous Materials ............ 2.2.2 Refraction in the Paraxial Case....... 2.2.3 The Cardinal Points of an Optical System ..................... 2.2.4 The Imaging Equations of Geometrical Optics.................... 2.2.5 The Thin Lens............................... 2.2.6 The Thick Lens ............................. 2.2.7 Reflecting Optical Surfaces............. 2.2.8 Extension of the Paraxial Matrix Theory to 3 × 3 Matrices .................
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2.3
Stops and Pupils................................... 2.3.1 The Aperture Stop......................... 2.3.2 The Field Stop ..............................
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2.4
Ray Tracing .......................................... 2.4.1 Principle ..................................... 2.4.2 Mathematical Description of a Ray ...................................... 2.4.3 Determination of the Point of Intersection with a Surface ........ 2.4.4 Calculation of the Optical Path Length ............. 2.4.5 Determination of the Surface Normal ................... 2.4.6 Law of Refraction ......................... 2.4.7 Law of Reflection ......................... 2.4.8 Non-Sequential Ray Tracing and Other Types of Ray Tracing ......
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Aberrations .......................................... 2.5.1 Calculation of the Wave Aberrations................ 2.5.2 Ray Aberrations and the Spot Diagram ................... 2.5.3 The Seidel Terms and the Zernike Polynomials ......... 2.5.4 Chromatic Aberrations ..................
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2.5
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Part A 2
This chapter shall discuss the basics and the applications of geometrical optical methods in modern optics. Geometrical optics has a long tradition and some ideas are many centuries old. Nevertheless, the invention of modern personal computers which can perform several million floating-point operations in a second also revolutionized the methods of geometrical optics and so several analytical methods lost importance whereas numerical methods such as ray tracing became very important. Therefore, the emphasis in this chapter is also on modern numerical methods such as ray tracing and some other systematic methods such as the paraxial matrix theory. We will start with a section showing the transition from wave optics to geometrical optics and the resulting limitations of the validity of geometrical optics. Then, the paraxial matrix theory will be used to introduce the traditional parameters such as
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