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This book explores the lenses analogous to conic mirrors, the only kind of mirrors free of spherical aberration. With new ideas and results appearing in the field of optics, this second edition presents an in-depth look at lenses free of spherical aberrations and uses illustrative examples. Based on ideas from the first edition, this text contains six new chapters, which are not limited to stigmatic lenses but also discuss aplanatic lenses, stigmatic mirror systems and aplanatic mirrors. A newly added fourth part studies stigmatism and aplanetism in systems made purely with mirrors. The characteristics of these lenses and the equations that describe them are also studied. Finally, several implications of these lenses are analysed, such as freeform lenses, optical systems, axicons, telescopes and more. Scenarios with on-axis objects and off-axis objects are considered. Cases where the object is real or virtual and the image is real or virtual are also presented.
Key Features
- Provides worked examples throughout
- Includes end-of-chapter problems
- Provides mathematical tools such as Mathematica
- Discusses physical concepts
- Has been revised and expanded to discuss stigmatic mirror systems
Part I A historical, mathematical and optical introduction for beginners
1 A brief history of stigmatic lens design
2 A mathematical toolkit for stigmatic imaging
3 An introduction to geometrical optics
Part II Stigmatic singlets
4 On-axis stigmatic aspheric lens
5 Geometry of on-axis stigmatic lenses
6 Topology of on-axis stigmatic lenses
7 The gaxicon
8 On-axis spherochromatic singlet
Part III Stigmatic and astigmatic freeform singlets
9 On-axis stigmatic freeform lens
10 On-axis astigmatic freeform lens
Part IV Stigmatic optical systems
11 On-axis sequential optical systems
12 On-axis sequential refractive–reflective telescope
Part V Aplanatic singlets and optical systems
13 Off-axis stigmatic lens
14 Aplanatic singlet lens: general setting part 1
15 Aplanatic singlet lens: general setting part 2
16 Abbe aplanatic singlet
17 Abbe aplanatic optical systems
Part VI Stigmatic mirror systems
18 The set of all possible pairs of stigmatic mirrors
19 Design of a pair of aplanatic mirrors
20 The stigmatic three-freeform-mirror system
21 The power set of mirror-based stigmatic optical systems
Algorithms