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E-grāmata: Blackbody Radiation: A History of Thermal Radiation Computational Aids and Numerical Methods

(Alabama A&M University, Huntsville, USA), (Nazarbayev University, Astana, Kazakhstan)
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Blackbody Radiation: A History of Thermal Radiation Computational Aids and Numerical MethodsPalielināt
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Shelving Guide: Electrical Engineering

In 1900 the great German theoretical physicist Max Planck formulated a correct mathematical description of blackbody radiation. Today, understanding the behavior of a blackbody is of importance to many fields including thermal and infrared systems engineering, pyrometry, astronomy, meteorology, and illumination. This book gives an account of the development of Plancks equation together with many of the other functions closely related to it. Particular attention is paid to the computational aspects employed in the evaluation of these functions together with the various aids developed to facilitate such calculations.

The book is divided into three sections.











Section I Thermal radiation and the blackbody problem are introduced and discussed. Early developments made by experimentalists and theoreticians are examined as they strove to understand the problem of the blackbody.











Section II The development of Plancks equation is explained as are the all-important fractional functions of the first and second kinds which result when Plancks equation is integrated between finite limits. A number of theoretical developments are discussed that stem directly from Plancks law, as are the various computational matters that arise when numerical evaluation is required. Basic elements of radiometry that tie together and use many of the theoretical and computational ideas developed is also presented.











Section III A comprehensive account of the various computational aids such as tables, nomograms, graphs, and radiation slide rules devised and used by generations of scientists and engineers when working with blackbody radiation are presented as are more recent aids utilizing computers and digital devices for real-time computations.

Scientists and engineers working in fields utilizing blackbody sources will find this book to be a valuable guide in understanding many of the computational aspects and nuances associated with Plancks equation and its other closely related functions. With over 700 references, it provides an excellent research resource.

Recenzijas

"This is an excellent history of the mathematical development behind radiation calculators and other computational aids told in terms of detailed mathematical analysis and historical narrative. It is well-written, comprehensive, and includes the most extensive treatment of the radiation slide rule I have seen anywhere." Barbara G. Grant, Author of Field Guide to Radiometry, Getting Started with UAV Imaging Systems: A Radiometric Guide and co-author of The Art of Radiometry, Cupertino, California, USA

"The historical and mathematical details presented cannot be found in other books. It is a historic document, an impressive milestone. This book is not only very valuable for someone who wishes to understand the behavior of a blackbody, I recommend it also to those who are familiar with the subject, but want to know it all." Max J. Riedl, Author and Lecturer, Germany

"Blackbody radiation is covered in a wide and comprehensive sense, covering historical context, mathematical details, computational means and applications. This is easily the most comprehensive and well-researched compilation on blackbody radiation ever written. The book broadly follows a historical timeline, showing how the best available technology available at the time was used to compute results from Plancks law. The book captures the ingenious beauty of mathematics, the nomogram and the slide rule to compute one of the most important physics laws in engineering." CJ (Nelis) Willers, Airbus Optronics South Africa

Preface xiii
List of Figures
xxiii
List of Tables
xxvii
Authors xxix
SECTION I The blackbody problem
Chapter 1 Thermal radiation and the blackbody problem
3(30)
1.1 Towards a solution to the blackbody problem
4(5)
1.2 Planck and the blackbody problem
9(3)
1.3 The work of the experimentalists
12(4)
1.4 Thermal laws from dimensional analysis
16(10)
1.5 Transition and new beginnings
26(7)
SECTION II Theoretical and numerical matters
Chapter 2 Theoretical developments
33(64)
2.1 Spectral representations
33(3)
2.2 Two important special functions
36(5)
2.2.1 Polylogarithms
36(3)
2.2.2 The Lambert W function
39(2)
2.3 Two common spectral scales used to represent blackbody radiation
41(5)
2.4 Other spectral scale representations
46(6)
2.5 Ephemeral spectral peaks
52(5)
2.6 Logarithmic spectral scales
57(1)
2.7 The radiometric and actinometric cases
58(3)
2.8 Normalized spectral exitance
61(1)
2.9 The Stefan-Boltzmann law
62(6)
2.9.1 The traditional approach
63(3)
2.9.2 A polylogarithmic approach
66(2)
2.10 Fractional functions of the first kind
68(5)
2.11 Fractional functions of other kinds
73(4)
2.12 Centroid and median wavelengths
77(6)
2.13 The standard probability distribution and cumulative probability distribution functions for blackbody radiation
83(3)
2.14 Infrared, visible, and ultraviolet components in the spectral distribution of blackbody radiation
86(11)
Chapter 3 Computational and numerical developments
97(34)
3.1 Approximations to the spectral exitance
97(10)
3.1.1 The laws of Wien and Rayleigh-Jeans
97(3)
3.1.2 Extended Wien and Rayleigh-Jeans approximations
100(1)
3.1.3 Polynomial interpolation and logarithmic correction factors
101(2)
3.1.4 Laurent polynomials and non-rational approximations of Erminy
103(4)
3.2 Computation of the fractional function of the first kind
107(24)
3.2.1 Series expansion methods
108(1)
3.2.1.1 Large arguments
108(6)
3.2.1.2 Small arguments
114(2)
3.2.1.3 Division point
116(2)
3.2.2 Approximation of the integrand first
118(1)
3.2.3 Gauss--Laguerre and generalised Gauss--Laguerre quadrature
119(4)
3.2.4 Asymptotic expansion
123(3)
3.2.5 Other methods
126(5)
Chapter 4 Blackbody sources and basic radiometry
131(26)
4.1 Blackbody sources
131(2)
4.2 Goniometric characteristics of surfaces
133(4)
4.3 Inverse square law
137(2)
4.4 Extended source radiometry
139(4)
4.5 Radiometry of images
143(9)
4.6 Example problem
152(5)
SECTION III Computational aids
Chapter 5 Nomograms and graphs used for thermal radiation calculations
157(26)
5.1 Nomograms
157(13)
5.2 Graphs
170(10)
5.3 The legacy of graphical aids
180(3)
Chapter 6 Slide rules used for thermal radiation calculations
183(60)
6.1 Three early slide rules from Germany, England, and the United States
184(26)
6.1.1 The System Czerny rule
184(7)
6.1.2 General Electric Radiation Calculators
191(11)
6.1.3 The Admiralty rule
202(8)
6.2 Two mysterious rules
210(2)
6.3 The DENEM Nuclear Radiation Calculator
212(3)
6.4 A circular slide rule
215(5)
6.5 "Do-it-yourself" slide rules and charts
220(2)
6.6 Radiation slide charts from the 1960s
222(7)
6.6.1 The Block rule
222(4)
6.6.2 The Infrared Slide Rule
226(3)
6.7 The last of the real slide rules
229(14)
Chapter 7 Tables used for thermal radiation calculations
243(58)
7.1 Notational conventions used for tables
246(1)
7.2 Prom the earliest tables to 1939
247(13)
7.3 Tables from 1940 to 1954
260(10)
7.4 Tables from 1955 onwards
270(26)
7.5 Tables then and now
296(5)
Chapter 8 Beyond the analogue aids of old
301(6)
Appendix A Miscellaneous mathematical results
307(10)
A.1 Series expansion for the Lambert W function
307(1)
A.2 Bernoulli numbers and the Riemann zeta function
308(4)
A.3 Number of real roots to an equation
312(5)
Appendix B Computer program for the fractional function of the first kind
317(4)
Appendix C Chronological table of events
321(8)
References 329(38)
Reference Author Index 367(8)
Index 375
Seįn M. Stewart recently joined Nazarbayev University in Astana where he is an associate professor of engineering mathematics. Before moving to Kazakhstan, he spent eleven years working at The Petroleum Institute in Abu Dhabi, United Arab Emirates, where he was an associate professor in the Department of Mathematics. His main research interests lie in the fields of applied mathematics and in the history of computation.

R. Barry Johnson has been involved for over 40 years in infrared technology, lens design, optical systems design, and electro-optical systems engineering, and has used many of the devices and techniques described in this book, and knew many of the individuals mentioned therein. He developed the method of integrating Plancks equation using the method of GaussLaguerre quadrature. Dr Johnson is a Senior Research Professor at Alabama A&M University and has been a faculty member at two other academic institutions engaged in optics education and research, employed by a number of companies, and has provided consulting services within the field. Dr. Johnson is an SPIE Fellow and Life Member, OSA Fellow, and is an SPIE past president (1987). He has been awarded many patents and has published numerous scientific and technical articles. Dr. Johnson was awarded the 2012 OSA/SPIE Joseph W. Goodman Book Writing Award for Lens Design Fundamentals, Second Edition. He is a perennial co-chair of the annual SPIE Conference Current Developments in Lens Design and Optical Engineering.
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