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Theory of reflectance and emittance spectroscopy, 2nd ed., edited by Bruce Hapke. Cambridge University Press, 2012, 513 p. $90, hardcover (ISBN #978-0-521-88349-8).

Bruce Hapke’s work on radiative transfer in particulate media has long been a cornerstone of planetary spectroscopy. From photometric corrections through modeling of intimate mixtures, the name Hapke is synonymous with radiative transfer theory to students of planetary spectroscopy, often being called “Hapke modeling” or “Hapke theory.” The release of the second edition of the Theory of Reflectance and Emittance Spectroscopy is extremely timely, arriving at a time when the previous decade successfully collected a large number of spatially resolved hyperspectral datasets for solid bodies throughout the solar system and is likely to continue to dramatically increase during the next 10 years. This edition maintains the rigor and depth of the first edition, while including more hands-on topics, such as where to find spectral libraries and computer programs for radiative transfer applications and brief discussions of specific science applications and other methodologies.

This book is aimed at students of the physical sciences who are interested in quantitative analysis of the composition or physical properties of airless body surfaces in the solar system. Although rich with physics and mathematical derivations, Hapke ties his logic together with clear prose and illustrative diagrams. While it is not a quick read, this book provides much of the critical background necessary for understanding the physics of light interacting with planetary surfaces at several scales, and will remain a key reference for those with careers in planetary science. Those familiar with the first edition of this book will probably also find it an interesting and useful read, as it has been reorganized and expanded, with more thorough discussions of the opposition effect, planetary photometry, and simultaneous transport of energy by radiation and thermal conduction.

The book begins in Chapters 2–4 with a discussion of the propagation of electromagnetic waves and descriptions of absorption, dispersion, polarization, and specular reflectance. These chapters provide a strong classical foundation that is then built upon by the subsequent discussions of the more complicated real-life cases in which scattering, illumination geometry, and intimate mixtures of different materials are considered. Although the book focuses on understanding how light propagates through generic particles, section 3.4 provides a good overview of the internal absorption processes for various materials, and includes key mineral and solid-state physics references, as well as information on where to find spectral libraries of reflectance and emission data.

In the second section of the book, Hapke focuses on scattering of light through single particles—first in the case of perfect spheres and then for irregular particles. In Chapter 5, he presents key concepts such as single-scattering albedo, Mie theory, and different scattering regimes. In Chapter 6, he describes the more realistic case of irregular particles, presenting both theoretical and empirical models for dealing with scattering through large and small nonspherical particles. This section is substantially revised and reorganized relative to the first edition, and includes a short discussion of scattering behavior for coated particles.

With the background in place, Hapke progresses into the main portion of the book: description of the transport of light through particulate medium from a small scale through the planetary scale. Chapter 7 introduces the equation of radiative transfer in a clear and comprehensible fashion, and includes descriptions of solution approaches, as well as online addresses for finding several computer programs to solve basic radiative transfer problems. Chapter 8 follows with a thorough description of bidirectional reflectance of an optically thick particulate target and presentation of methods to approximate reflectance for anisotropic scatterers. This chapter includes substantially more discussion than the first edition of the book, leading the reader more effectively through the equations and reasoning.

Chapter 9 is devoted to the opposition effect. The chapter begins with a brief and interesting historical introduction to the opposition surge, and continues with the concepts of the shadow hiding opposition effect and the coherent backscatter opposition effect. This more detailed discussion of the opposition effect is a welcome addition to the book, particularly now that more planetary spectral data sets are available that have measured the opposition surge. Chapter 10 provides a brief but useful accumulation of important equations, a description of reflectance and transmission through layered materials, and mixing formulas for intimate mixtures.

Moving from the laboratory to larger scale problems such as interpretation of planetary data collected at differing viewing geometries with spatial pixels on the order of 10s to 100s of meters in size, photometric effects become critical. In Chapter 12, planetary photometry is discussed, including derivation of a photometric model to account for roughness variability on a surface. Alternative planetary photometric models are also briefly presented. Through most of the text, polarization is assumed to be negligible. However, quantitative measurement of polarization can be used to extract information about the surface materials, as is described in Chapter 13.

In Chapter 14, Hapke addresses the practical methodology for extracting quantitative compositional and physical information from reflectance spectra. The chapter is straightforward and will stand alone (or with Chapter 15 on thermal emission) as a great introduction to reflectance spectroscopy for students new to planetary science. Important concepts such as how to relate reflectance to absorption coefficient, absorption band properties, and their relationship with scattering, intimate mixtures, and space weathering are discussed. Other methodologies are also briefly covered.

In the final two chapters, Hapke turns to the thermal infrared, discussing thermal emission, emissivity, Kirchoff’s law, and simultaneous transport of energy by radiation and thermal conduction. The inclusion of these chapters allows the reader to finish the book with the tools necessary to understand the wealth of spectroscopic data available for Mars, the Moon, and beyond. Overall, the second edition of the Theory of Reflectance and Emittance Spectroscopy is packed with information, and I found it a stimulating and enjoyable read. I encourage any students who read this early in their careers to work through the equations even if they look intimidating, as Hapke does a great job of articulating his logic. For those already familiar with the first edition of this text, it is still a worthwhile read. It centralizes Hapke’s pioneering early work with the developments in the almost 20 years since the first edition was published, and the reorganization of chapters and sections results in a more natural, accessible flow.