Interpreting Diffuse Reflectance and Transmittance: A Theoretical Introduction to Absorption Spectroscopy of Scattering Materials

A jar of sweets may not appear to be a serious introduction to the attempt to progress the understanding of the challenging nature of what is usually termed "diffuse reflection". However, this book by the father and son team of Don and Kevin Dahm is the first such attempt since the famous book by Wendlandt and Hecht some forty years ago. The sweets are not only useful models, they also indicate the desire of the authors to make this a readable and entertaining book as well as a very serious attempt to advance our theoretical understanding of this complex and confusing topic. The Dahms have been developing and advancing a new theory for the last few years.This book brings it together. It explains the nature of reflected radiation and then the problem of finding a mathematical description of it. In their quest, they have rediscovered and used mathematics that was invented by Sir George Stokes in the 1860s! Much of the current use of near infrared spectroscopy utilises diffuse reflection or transmission. According to Karl Norris "The development of NIR analysis is being restricted by our lack of a theoretical understanding of diffuse reflection" and he should know! The book also includes a reproduction of Chapter III from "Diffuse Reflectance" by Wesley Wm. Wendlandt and Harry G. Hecht with introductions by Don Dahm and Harry Hecht. The chapter, in the opinion of Don Dahm, "is the best compilation that will ever be printed of theoretical work done in the area of diffuse reflectance".

Table of Contents:
ForewordsAcknowledgementsPrefaceA. Approach Used in the --Representative Layer TheoryA-1. What Makes a Layer Representative?A-2. The Absorption/Remission Function for a SampleA-3. Some Principles and Mathematical Formulas Underlying the Representative Layer TheoryB. Background and Such (the Stuff Spectroscopists Are Supposed to Know)B-1. Background Information Related to Absorption SpectroscopyB-2. Absorption of Light Is Different from Absorption of WaterB-3. Considerations Related to ExperimentationB-4. Definitions and an Illustration of Diffuse ReflectionB-5. What's This About a Calibration?C. Redoing the Basics of the Spectroscopist's Theory of Absorption for Scattering SamplesC-1. What Is Absorbance?C-2. The Bouguer-Lambert Law and Absorbing PowerC-3. Is There Something Like a Bouguer-Lambert Law for Scattering Samples?C-4. The Stokes FormulasC-5. What Is an Absorption Coefficient of a Sample?C-6. Relationship Between Absorbing Power (k) and Apparent Coefficients (K and B) for a Stokes SampleC-7. The Dahm EquationC-8. And What About Beer's Law?C-9. Is There a "Beer's Law" for Scattering Samples?D. Application of Spectroscopic Theory to Scattering SamplesD-1. Absorption and Remission Coefficients for Scattering SamplesD-2. The Effect of Diffuse Radiation on Absorption CoefficientsD-3. Non-linear Absorbance DataD-4. Optimizing Linearity of Data from a Single SpectrumD-5. Three-Flux Planar ModelD-6. Numerical Determination of kd from Samples for which a Suitable Model ExistsE. Remission From and Transmission Through Layers of Modified SheetsE-1. The Case of a Directly Illuminated SheetE-2. Direct Illumination of Modified SheetsE-3. Summary of ResultsE-4. Using the Sheet Model for Chemical AnalysisE-5. Experimental ProcedureE-6. Using a Single Sheet to Model a SampleF. Relationships Proportional to the Absorbing PowerF-1. The Stray-Light CorrectionF-2. Truncated Absorbance, the "Zero Absorption" CorrectionF-3. A General Form for the Relationship Between the Apparent Absorption Coefficient K and the Absorbing Power kG. Remission From and Transmission Through a Representative Layer of ParticlesG-1. Formation of a Representative LayerG-2. Effect of VoidsG-3. Effect of Particle SizeG-4. Applying Representative Layer Theory to Mixtures of Particles Having Different PropertiesH. Additional Theoretical ConsiderationsH-1. Terms Used to Describe Scattering PhenomenaH-2. Reflection From and Refraction at a SurfaceH-3. Mie TheoryH-4. Simplified Spherical Particle ModelsH-5. Early Models of Diffuse ReflectanceI. The Continuum TheoriesI-1. Continuum Versus Discontinuum TheoriesI-2. Diffusion TheoryI-3. The Equation of Radiative TransferI-4. The Schuster-Kortum TheoryI-5. The Kubelka-Munk TheoryJ. Perspective on the Theory of Diffuse ReflectanceJ-1. Theoretical SummaryJ-2. Matching Theoretical Treatment with Experiment ArrangementJ-3. A Few Notes on the Various TheoriesJ-4. Illustration of Failure of Continuum Models of Diffuse ReflectanceAppendix I. Definition of Terms and Symbols1. Definition of Symbols2. Definitions of Terms3. Concepts Related to Absorption and ScatterAppendix II. ReferencesPreface to Appendix III by Donald J. DahmPreface to Appendix III by Harry G. HechtAppendix III. Theory of Diffuse ReflectanceA. IntroductionB. The Nature of Reflection from Diffusing MediaC. Differential Equation MethodD. Integral Equation MethodE. Statistical MethodF. Luminescent MaterialsReferencesIndex

Review :
Applied Spectroscopy (2008) by Peter Wilhem (Graz University of Technology) When working in the field of infrared spectroscopy, forced to deal with all sorts of so-called "read Samples," one prefers transmittance experiments, but, sooner or later, one also comes across diffuse reflection methods (at least when no other sampling method will work because of sample structure and surface) While applying these techniques, one wonders why they sometimes work pretty well, but often give really strange results. Sooner or later, one wishes to understand what is happening with this phenomenon, but - as a simple experimentalist not very happy with theories and equations - probably despairs in view of all this clever literature that is so hard to read and understand. I must admit that I had a similar feeling when I opened the book by Donald and Kevin Dahm, but after reading the first chapter I was really surprised. This book is no only an interesting teaching of theoretical optical considerations, made fruitful for practical work, but also of a successful father - son relation (the authors are father and son). The first impression when glancing over the pages is that of a well-thought-out page layout (though a little lavish with space), which promotes easy reading. A reasonable font sized main body (with varying typefaces related to the importance of the respective section) is complemented by small notes, and equations and figures at the margins, with references to their original places in the text. As hinted above, the book is mainly written for readers with a poor background in theory, avoiding advanced mathematics, and making some simple assumptions, about scattering and sample geometry (two parallel surfaces perpendicular to the incident beam). Moreover, the text is spiced with a pinch of humor and is, therefore, really fun reading. In spectroscopy a sample can be regarded as a series of layers. Consequently, the book starts with a chapter introducing the so-called "representative layer theory," because each of the layers is representative of the sample as a whole. To make mathematical description simpler, the sample is assumed to be homogeneous, though a truly homogeneous sample would not scatter light at all. Some key terms are defined and described, e.g. absorption, transmission, or remission (reflected and scattered light, travelling in the opposite direction to the incident beam), first in a descriptive manner, and later on more theoretically and mathematically. In the next chapter the reader is provided with the basics of absorption spectroscopy. Though a spectroscopist is supposed to know this stuff, the chapter is anything but boring. But in the third chapter the authors start to confront the reader with their own approach to the theory of absorption spectroscopy of both homogeneous and scattering samples, which might seem somewhat strange to those having learned NIR or DRIFTS the conventional way. After an overview of their theory, particulate samples (scattering samples, layers of modified sheets) are discussed in detail, together with consideration about the relationship between observable parameters and the absorbing power More theoretical considerations about scattering phenomena deal with reflection from and refraction at a surface., The Mie theory, which treats scatter from a single spherical particle, is complemented by a simplified model of absorption, remission, and transmission, to overcome the lack of a definite theory for particles of other shapes than spherical or plane parallel ones. Diffuse reflection has been approached by two theoretical treatments, the "continuum theory" (which treats the sample as a continuum with no boundaries within the sample) and the "discontinuum theory" (the sample has an internal structure). The historical development of techniques to model diffuse reflectance is summarized and the continuum theories are criticized for their fatal flaw (real samples scattering light are not continuous) in a very passionate way (the authors themselves calling their argumentation "irreverent" and "vitriolic"). A short discussion of the diffusion theory (random walk of photons), the equation of radiative transfer (extinction of a light flux), and the Schuster - Kortuem theory (a particle theory) finally leads to the Kubelka - Munk theory. A concluding chapter ("Perspective on the Theory of Diffuse Reflectance") summarizes the pros and cons of the theories considered previously and tries to match theoretical treatment of the scattering and reflection phenomena with experimental arrangement. In a very comprehensive appendix, the reader can find definitions of terms and symbos, as well as references. Appendix III is a reprinting of a chapter from Reflectance Spectroscopy, by Wendlandt and Hecht ( a book published in 1966 by Interscience Publishers, which has been referenced repeatedly by other authors, but which has been out of print for a long time). I can warmly recommend this excellent compilation of theoretical considerations to all those spectroscopist trying to understand what is really going on in their diffuse reflectance and transmittance experiments.