Nonimaging Optics

Solar and Illumination System Methods, Design, and Performance

Roland Winston, Lun Jiang, Vladimir Oliker

• Publisher: CRC Press
• Year: 2020
• eBook ISBN: 9780429528279
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Civil Engineering
• Index: Technology & Engineering

This book provides a comprehensive look at the science, methods, designs, and limitations of nonimaging optics. It begins with an in-depth discussion on thermodynamically efficient optical designs and how they improve the performance and cost effectiveness of solar concentrating and illumination systems. It then moves into limits to concentration, imaging devices and their limitations, and the theory of furnaces and its applications to optical design. Numerous design methods are discussed in detail followed by chapters of estimating the performance of a nonimaging design and pushing their limits of concentration. Exercises and worked examples are included throughout.

1 Nonimaging Optical Systems and Their Uses

1.1 Nonimaging Collectors

Nonimaging concentrators and illuminators have several current and some potential applications. It is best to explain the general concept of a nonimaging concentrator by highlighting one of its applications: the utilization of solar energy. The radiation power density received from the sun at the earth’s surface, often denoted by S, peaks at approximately 1 kW/m², depending on many factors. If we collect this power by absorbing it on a perfect blackbody, the equilibrium temperature T of the blackbody will be given by^*

* Ignoring various factors such as convection and conduction losses and radiation at lower effective emissivities.

σ T 4 = S

(1.1)

where σ is the Stefan Boltzmann constant, 5.67 × 10⁻⁸ Wm⁻² K⁻⁴. In this example, the equilibrium temperature would be 364°K, or just below the boiling point of water. For many practical applications of solar energy this is sufficient, and many systems for domestic hot water heating based on this principle are available commercially for installation in private dwellings. However, for larger scale purposes or for generating electric power, a source of heat at 364°K has a low thermodynamic efficiency, since it is not practicable to get a very large temperature difference in whatever working fluid is being used in the heat engine. If we wanted, say, ≥300°C—a useful temperature for the generation of motive power—we would need to increase the power density S on the absorbing blackbody by a factor C of about 6 to 10 in Equation (1.1). This, briefly, is one use of a concentrator—to increase the power density of solar radiation. When it is stated plainly like that, the problem sounds trivial. The principles of the solution have been known since the days of Archimedes and his burning glass:^† we simply have to focus the image of the sun with an image-forming system—a lens—and the result will be an increased power density. The problems to be solved are technical and practical, but they also lead to some interesting pure geometrical optics. The first question is that of the maximum concentration: how large a value of C is theoretically possible? The answer to this question is simple in all cases of interest. The next question—can the theoretical maximum concentration be achieved in practice?—is not as easy to answer. We shall see that there are limitations involving materials and manufacturing, as one would expect. But there are also limitations involving the kinds of optical systems that can actually be designed, as opposed to those that are theoretically possible. This is analogous to the situation in classical lens design. The designers sometimes find that a certain specification cannot be fulfilled because it would require an impractically large number of refracting or reflecting surfaces. And sometimes they do not know whether it is in principle possible to achieve aberration corrections of a certain kind.

† For an amusing argument concerning the authenticity of the story of Archimedes, see Stavroudis (1973).

The natural approach of the classical optical physicist is to regard the problem as one of designing an image-forming optical system of a very large numerical aperture—that is, a small aperture ratio or f-number. One of the most interesting results to have emerged in this field is a class of very efficient concentrators that would have very large aberrations if they were used as image-forming systems. Nevertheless, as concentrators, they are substantially more efficient than image-forming systems and can be designed to meet or approach the theoretical limit. We shall call them nonimaging concentrating collectors, or nonimaging concentrators for short. Nonimaging is sometimes substituted by the word anidolic (from the Greek, meaning “without image”) in languages such as Spanish and French because it’s more specific. These systems are unlike any previously used optical systems. They have some of the properties of light pipes and some of the properties of image-forming optical systems but with very large aberrations. The development of the designs of these concentrators and the study of their properties have led to a range of new ideas and theorems in geometrical optics. In order to facilitate the development of these ideas, it is necessary to recapitulate some basic principles of geometrical optics, which is done in Chapter 2. In Chapter 3, we look at what can be done with conventional image-forming systems such as concentrators, and we show how they necessarily fall short of ideal performance. In Chapter 4, we describe one of the basic nonimaging concentrators, the compound parabolic concentrator, and we obtain its optical properties. Chapter 5 is devoted to several developments of the basic compound parabolic concentrator: with plane absorber, mainly aimed at decreasing the overall length; with nonplane absorber; and with generalized edge-ray wave fronts, which is the origin of the tailored designs. In Chapter 6, we examine in detail the flowline approach to nonimaging. Chapter 7 will be about the exposition of the emerging field of freeform optics. Chapter 8 is about the wave description of the optical measurements.

1.2 Failure of Imaging Optics

An example of the failure of imaging optics to confront real-world situations is shown in Figure 1.1. The point object A is at the center of a spherical reflecting cavity and is also one focus of an elliptical reflecting cavity. The point object B is at the other focus. If we start A and B at the same temperature, the probability of radiation from B reaching A is clearly higher than A reaching B. So we conclude that A warms up while B cools off, in violation of the second law of thermodynamics. The paradox is resolved by making A and B extended objects, no matter how small. In fact, a physical object with te...

Table of contents

• Cover
• Half-Title
• Series
• Title
• Copyright
• Contents
• Preface
• Authors
• Chapter 1 Nonimaging Optical Systems and Their Uses
• Chapter 2 Some Basic Ideas in Geometrical Optics
• Chapter 3 Some Designs of Image-Forming Concentrators
• Chapter 4 Nonimaging Optical Systems
• Chapter 5 Developments and Modifications of the Compound Parabolic Concentrator
• Chapter 6 The Flowline Method for Nonimaging Optical Designs
• Chapter 7 Freeform Optics and Supporting Quadric Method Introduction
• Chapter 8 Supporting Quadric Method (SQM)
• Chapter 9 Variational Approach
• Chapter 10 A Paradigm for a Wave Description of Optical Measurements
• Appendix A: Derivation and Explanation of the Étendue Invariant, Including the Dynamical Analogy; Derivation of the Skew Invariant
• Appendix B: The Luneburg Lens
• Appendix C: The Geometry of the Basic Compound Parabolic Concentrator
• Appendix D: The θi/θo Concentrator
• Appendix E: The Truncated Compound Parabolic Concentrator
• Appendix F: Skew Rays in a Hyperboloidal Concentrator
• Appendix G: Sine Relation for Hyperboloidal/Lens Concentrator
• Index