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Introduction to Nonimaging Optics, Second Edition
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Table of Contents

NONIMAGING OPTICS
Why Use Nonimaging Optics
Area and Angle
Collimators: Illumination of a Large Receiver
Concentrators: Illumination of a Small Receiver
Collimators and Concentrators Summary
Collimators Tolerances
Concentrators Tolerances
Nonuniform Sources
Solar Concentrators
Light Flux
Wavefronts and the SMS
References

Fundamental Concepts
Introduction
Imaging and Nonimaging Optics
The Compound Parabolic Concentrator
Maximum Concentration
Examples
References

Design of Two-Dimensional Concentrators
Introduction
Concentrators for Sources at a Finite Distance
Concentrators for Tubular Receivers
Angle Transformers
The String Method
Optics with Dielectrics
Asymmetrical Optics
Examples
References

Etendue and the Winston-Welford Design Method
Introduction
Conservation of Etendue
Nonideal Optical Systems
Etendue as a Geometrical Quantity
Two-Dimensional Systems
Etendue as an Integral of the Optical Momentum
Etendue as a Volume in Phase Space
Etendue as a Difference in Optical Path Length
Flow-Lines
The Winston-Welford Design Method
Caustics as Flow-Lines
Maximum Concentration
Etendue and the Shape Factor
Examples
References

Vector Flux
Introduction
Definition of Vector Flux
Vector Flux as a Bisector of the Edge Rays
Vector Flux and Etendue
Vector Flux for Disk-Shaped Lambertian Sources
Design of Concentrators Using the Vector Flux
Examples
References

Combination of Primaries with Flow-Line Secondaries
Introduction
Reshaping the Receiver
Compound Elliptical Concentrator Secondary
Truncated Trumpet Secondary
Trumpet Secondary for a Large Receiver
Secondaries with Multiple Entry Apertures
Tailored Edge Ray Concentrators Designed for Maximum Concentration
Tailored Edge Ray Concentrators Designed for Lower Concentration
Fresnel Primaries
Tailored Edge Ray Concentrators for Fresnel Primaries
Examples
References

Stepped Flow-Line Nonimaging Optics
Introduction
Compact Concentrators
Concentrators with Gaps
Examples
References

Luminaires
Introduction
Luminaires for Large Source and Flat Mirrors
The General Approach for Flat Sources
Far-Edge Diverging Luminaires for Flat Sources
Far-Edge Converging Luminaires for Flat Sources
Near-Edge Diverging Luminaires for Flat Sources
Near-Edge Converging Luminaires for Flat Sources
Luminaires for Circular Sources
Examples
Appendix A: Mirror Differential Equation for Linear Sources
Appendix B: Mirror Differential Equation for Circular Sources
References

Minano-Benitez Design Method (Simultaneous Multiple Surface)
Introduction
The RR Optic
SMS with a Thin Edge
The XR, RX, and XX Optics
The Minano-Benitez Design Method with Generalized Wavefronts
The RXI Optic: Iterative Calculation
The RXI Optic: Direct Calculation
SMS Optical Path Length Adjustment
SMS 3-D
Asymmetric SMS 3-D
SMS 3-D with a Thin Edge
Other Types of Simultaneous Multiple Surface Optics
Examples
References

Wavefronts for Prescribed Output
Introduction
Wavefronts for Prescribed Intensity
Wavefronts for Prescribed Irradiance
Bundle Coupling and Prescribed Irradiance
References

Infinitesimal Etendue Optics
Introduction
Infinitesimal Etendue Optics
Continuous Optical Surfaces
Fresnel Optics
Finite Distance Source
Examples
References

Koehler Optics and Color-Mixing
Introduction
Koehler Optics
Solar Energy Concentration Based on Koehler Optics
Prescribed Irradiance Koehler Optics
Color-Mixing Based on Koehler Optics
SMS-Based Koehler Optics
Color-Mixing with Grooved Reflectors
Examples
References

The Minano Design Method Using Poisson Brackets
Introduction
Design of Two-Dimensional Concentrators for Inhomogeneous Media
Edge Rays as a Tubular Surface in Phase Space
Poisson Brackets
Curvilinear Coordinate System
Design of Two-Dimensional Concentrators
An Example of an Ideal Two-Dimensional Concentrator
Design of Three-Dimensional Concentrators
An Example of an Ideal Three-Dimensional Concentrator
References

GEOMETRICAL OPTICS
Lagrangian and Hamiltonian Geometrical Optics
Fermat's Principle
Lagrangian and Hamiltonian Formulations
Optical Lagrangian and Hamiltonian
Another Form for the Hamiltonian Formulation
Change of Coordinate System in the Hamilton Equations
Integral Invariants
Movements of the System as Canonical Transformations
References

Rays and Wavefronts
Optical Momentum
The Eikonal Equation
The Ray Equation
Optical Path Length between Two Wavefronts
References

Reflection and Refraction
Reflected and Refracted Rays
The Laws of Reflection and Refraction
References

Symmetry
Conservation of Momentum and Apparent Refractive Index
Linear Symmetry
Circular Symmetry and Skew Invariant
References

Etendue in Phase Space
Etendue and the Point Characteristic Function
Etendue in Hamiltonian Optics
Integral Invariants and Etendue
Refraction, Reflection, and Etendue 2-D
Etendue 2-D Examples
References

Classical Mechanics and Geometrical Optics
Fermat's Principle and Maupertuis' Principle
Skew Invariant and Conservation of Angular Momentum
Potential in Mechanics and Refractive Index in Optics
References

Radiometry, Photometry, and Radiation Heat Transfer
Definitions
Conservation of Radiance in Homogeneous Media
Conservation of Basic Radiance in (Specular) Reflections and Refractions
Etendue and the Shape Factor
Two-Dimensional Systems
Illumination of a Plane
References

Plane Curves
General Considerations
Parabola
Ellipse
Hyperbola
Conics
Involute
Winding Macrofocal Parabola
Unwinding Macrofocal Parabola
Winding Macrofocal Ellipse
Unwinding Macrofocal Ellipse
Cartesian Oval for Parallel Rays
Cartesian Oval for Converging or Diverging Rays
Cartesian Ovals Calculated Point by Point
Equiangular Spiral
Functions Definitions
References

About the Author

Julio Chaves completed his undergraduate studies in physics engineering at the Higher Technical Institute, Technical University of Lisbon, Portugal in 1995. He received his Ph.D in physics from the same institute. Dr. Chaves did postgraduate work at the Solar Energy Institute, Technical University of Madrid, Spain in 2002, and in 2003, he joined Light Prescriptions Innovators (LPI), LLC, Altadena, California, USA. In 2006, he moved back to Madrid, Spain, and has been working with LPI since. Dr. Chaves developed the new concepts of stepped flow-line optics and ideal light confinement by caustics (caustics as flow lines). He is the co-inventor of several patents and the coauthor of many papers in the field of nonimaging optics. He also participated in the early development of the simultaneous multiple surface design method in three-dimensional geometry.

Reviews

"... an essential book for those wanting to improve their knowledge of nonimaging optical design theory and techniques. It is extremely comprehensive, well organized, well written, and well edited, with numerous excellent figures and detailed examples."
-John C. Bortz, JCB Research, LLC, Spokane, Washington, USA

"Outstanding book with many thoroughly worked-out examples that make learning nonimaging optics easy."
-Dr. William Cassarly, SPIE Fellow

"... provides a comprehensive coverage of the field of nonimaging optics, describing both basic and advanced concepts and design methods. Explanations are intuitive; it is profusely illustrated and contains many useful examples. ... appropriate for those starting in the field, as well as for those already working in nonimaging optics."
-Juan Carlos Minano, Universidad Politecnica de Madrid, Spain

"The second edition of this book reflects the significant and recent developments in the field of nonimaging optical devices. More than 45 percent of the material in this edition is new, including four new chapters. The amount of material covered by Chaves is enormous, ranging from the Winston-Welford design method to Kohler optics and to luminaries. This book is aimed at optical engineers and designers of all levels; however, it is not meant to serve as an introduction to geometrical optics. Some of the results are given as exercises which will be useful for undergraduate engineering and science students."
-Optics & Photonics News, February 2016

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