Interpreting Diffuse Reflectance and Transmittance

A Theoretical Introduction to Absorption Spectroscopy of Scattering Materials

by Donald J. Dahm and Kevin D. Dahm

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”.

Interpreting Diffuse Reflectance and Transmittance is now available, priced at £62.50.

Bibliographic details

xx + 286 pp.
Publication: June 2007
ISBN: 978-1-901019-05-6
Price: £62.50
Order from our bookshop or IM Publications LLP, 6 Charlton Mill, Charlton, Chichester, West Sussex PO18 0HY, UK,

Contents

Forewords
Acknowledgements
Preface
A. Approach Used in the ­Representative Layer Theory
A-1. What Makes a Layer Representative?
A-2. The Absorption/Remission Function for a Sample
A-3. Some Principles and Mathematical Formulas Underlying the Representative Layer Theory
B. Background and Such (the Stuff Spectroscopists Are Supposed to Know)
B-1. Background Information Related to Absorption Spectroscopy
B-2. Absorption of Light Is Different from Absorption of Water
B-3. Considerations Related to Experimentation
B-4. Definitions and an Illustration of Diffuse Reflection
B-5. What’s This About a Calibration?
C. Redoing the Basics of the Spectroscopist’s Theory of Absorption for Scattering Samples
C-1. What Is Absorbance?
C-2. The Bouguer–Lambert Law and Absorbing Power
C-3. Is There Something Like a Bouguer–Lambert Law for Scattering Samples?
C-4. The Stokes Formulas
C-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 Sample
C-7. The Dahm Equation
C-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 Samples
D-1. Absorption and Remission Coefficients for Scattering Samples
D-2. The Effect of Diffuse Radiation on Absorption Coefficients
D-3. Non-linear Absorbance Data
D-4. Optimizing Linearity of Data from a Single Spectrum
D-5. Three-Flux Planar Model
D-6. Numerical Determination of kd from Samples for which a Suitable Model Exists
E. Remission From and Transmission Through Layers of Modified Sheets
E-1. The Case of a Directly Illuminated Sheet
E-2. Direct Illumination of Modified Sheets
E-3. Summary of Results
E-4. Using the Sheet Model for Chemical Analysis
E-5. Experimental Procedure
E-6. Using a Single Sheet to Model a Sample
F. Relationships Proportional to the Absorbing Power
F-1. The Stray-Light Correction
F-2. Truncated Absorbance, the “Zero Absorption” Correction
F-3. A General Form for the Relationship Between the Apparent Absorption Coefficient K and the Absorbing Power k
G. Remission From and Transmission Through a Representative Layer of Particles
G-1. Formation of a Representative Layer
G-2. Effect of Voids
G-3. Effect of Particle Size
G-4. Applying Representative Layer Theory to Mixtures of Particles Having Different Properties
H. Additional Theoretical Considerations
H-1. Terms Used to Describe Scattering Phenomena
H-2. Reflection From and Refraction at a Surface
H-3. Mie Theory
H-4. Simplified Spherical Particle Models
H-5. Early Models of Diffuse Reflectance
I. The Continuum Theories
I-1. Continuum Versus Discontinuum Theories
I-2. Diffusion Theory
I-3. The Equation of Radiative Transfer
I-4. The Schuster–Kortüm Theory
I-5. The Kubelka–Munk Theory
J. Perspective on the Theory of Diffuse Reflectance
J-1. Theoretical Summary
J-2. Matching Theoretical Treatment with Experiment Arrangement
J-3. A Few Notes on the Various Theories
J-4. Illustration of Failure of Continuum Models of Diffuse Reflectance
Appendix I. Definition of Terms and Symbols
1. Definition of Symbols
2. Definitions of Terms
3. Concepts Related to Absorption and Scatter
Appendix II. References
Preface to Appendix III by Donald J. Dahm
Preface to Appendix III by Harry G. Hecht
Appendix III. Theory of Diffuse Reflectance
A. Introduction
B. The Nature of Reflection from Diffusing Media
C. Differential Equation Method
D. Integral Equation Method
E. Statistical Method
F. Luminescent Materials
References
Index