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 Planck’s 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.
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 Planck’s equation and its other closely related functions. With over 700 references, it provides an excellent research resource.
"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 Planck’s 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
The blackbody problem. Thermal radiation and the blackbody problem. Towards a solution to the blackbody problem. Planck and the blackbody problem. The work of the experimentalists. Thermal laws from dimensional analysis. Transition and new beginnings. Theoretical and numerical matters. Theoretical developments. Spectral representations. Two important special functions. Polylogarithms. The Lambert W function. Two common spectral scales used to represent blackbody radiation. Other spectral scale representations. Ephemeral spectral peaks. Logarithmic spectral scales. The radiometric and actinometric cases. Normalized spectral exitance. The Stefan–Boltzmann law. The traditional approach. A polylogarithmic approach. Fractional functions of the first kind. Fractional functions of other kinds. Centroid and median wavelengths. The standard probability distribution and cumulative probability distribution functions for blackbody radiation. Infrared, visible, and ultraviolet components in the spectral distribution of blackbody radiation. Computational and numerical developments. Approximations to the spectral exitance. The laws of Wien and Rayleigh–Jeans.Extended Wien and Rayleigh–Jeans approximations. Polynomial interpolation and logarithmic correction factors. Laurent polynomials and non-rational approximations of Erminy. Computation of the fractional function of the first kind. Series expansion methods. Large arguments. Small arguments. Division point. Approximation of the integrand first. Gauss–Laguerre and generalized. Gauss–Laguerre quadrature. Asymptotic expansion. Other methods. Blackbody sources and basic radiometry. Blackbody sources. Goniometric characteristics of surfaces. Inverse square law. Extended source radiometry. Radiometry of images. Example problem. Computational aids. Nomograms and graphs used for thermal radiation calculations. Nomograms. Graphs. The legacy of graphical aids. Slide rules used for thermal radiation calculations. Three early slide rules from Germany, England, and the United States. The System Czerny rule. General Electric Radiation Calculators. The Admiralty rule. Two mysterious rules. The DENEM Nuclear Radiation Calculator. A circular slide rule. "Do-it-yourself" slide rules and charts. Radiation slide charts from the 1960s. The Block rule. The Infrared Slide Rule. The last of the real slide rules. Tables used for thermal radiation calculations. Notational conventions used for tables. From the earliest tables to 1939. Tables from 1940 to 1954. Tables from 1955 onwards. Tables then and now. Beyond the analogue aids of old. Appendix A Miscellaneous mathematical results. A.1 Series expansion for the Lambert W function. A.2 Bernoulli numbers and the Riemann zeta function. A.3 Number of real roots to an equation. Appendix B Computer program for the fractional function of the first kind. Appendix C Chronological table of events. References. Reference Author Index. Index