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Infrared Temperature Measurement by the Numbers
Planck's law, emissivity, wavelength, ratio pyrometers, reflections, spot size, thermography and calibration, worked through one forging billet heater
Measure hot parts and running plant without contact, with numbers: thermal radiation, emissivity errors, wavelength choice, ratio pyrometers, reflections, spot size, thermography and uncertainty.
Start readingAbout this book
Everything warmer than absolute zero gives off thermal radiation, and an infrared thermometer turns that radiation into a temperature. It can read a billet leaving an induction coil at 1,200 °C, a moving strip, a rotating shaft or a live busbar, none of which a thermocouple could touch. It can also read the wrong number with complete confidence. The radiation it collects depends on the surface as much as the temperature, it includes whatever the surface reflects, it passes through windows, steam and dust on the way, and it comes from a spot that may or may not be filled by the object. An instrument that reads to a tenth of a degree can be wrong by fifty.
This book works through infrared temperature measurement with numbers. It starts with Planck’s law, the physics of thermal radiation, and uses it to show why the wavelength an instrument works at decides how badly a wrong emissivity hurts. It then deals with emissivity itself, the choice of wavelength, ratio pyrometers, reflections and windows, spot size and alignment, thermal imaging for maintenance, and finally calibration and the uncertainty budget. Each chapter follows one running case, includes a plausible mistake and how it was found, and ends with an exercise and its worked answer.
It is for production, process, quality and maintenance engineers, instrument technicians and technical students who choose, install or rely on pyrometers and thermal cameras. It assumes school algebra and physics; the radiation physics is built up from there. Detector design, spectroscopy and the details of particular instruments are outside its scope.
The running case
Every chapter follows one fictional installation. This is an illustration. A forge heats carbon steel billets, 40 mm in diameter and 100 mm long, in an induction heater, IH-40, and feeds them to a forging press. A billet leaves the coil every 12 seconds, and its temperature must be 1,200 °C, within an accepted band of 1,170 to 1,230 °C; a diverter sends cold billets back for reheating and hot ones to a scrap bin, because overheated steel forges badly. The billet surface carries a thin oxide scale.
The exit temperature is read by a single-wavelength pyrometer working at 1.0 µm, mounted 0.6 m from the billets’ path, looking through a protective window, with its emissivity set to 0.85. The forge is considering a ratio pyrometer. Its maintenance team also uses an 8 to 14 µm thermal imaging camera to survey the heater’s power cabinet and the press’s motor.
The forge, its heater, its instruments and its problems are invented. None describes KEVOS® work or a real business.
How to use the book
Read Chapters 1 and 2 first: they set out the radiation physics and the emissivity problem that every later chapter builds on. Chapters 3 to 6 deal with choosing and installing a pyrometer, Chapter 7 with thermal imaging for maintenance, and Chapter 8 with calibration and the uncertainty budget. Every calculation was checked by running it with the CODATA constants, using the full Planck law rather than an approximation unless the text says otherwise.
Source limits and professional responsibility
The physics is standard. Emissivity values from makers’ tables are indicative only, and the right value for a real surface is the one measured on it under the conditions of use. The instrument settings, temperatures and tolerances in the running case are illustrations. Hot billets, induction heaters, live switchboards and running machinery are hazardous: thermography of energised electrical equipment is done by trained people under the applicable electrical safety rules and work health and safety law, and qualified review governs process settings for real work. This book teaches how infrared thermometry works and how to check it. It is not a procedure for any installation.
Who this book is for
Production, process, quality and maintenance engineers, instrument technicians and technical students who choose, install, set up or rely on pyrometers and thermal imaging cameras.
What you will learn
- Use Planck's law to explain what an infrared thermometer measures and why short wavelengths suit hot metal.
- Calculate the temperature error from a wrong emissivity setting at any wavelength, and choose a wavelength that limits it.
- Explain when a ratio pyrometer helps, when it does not, and what limits its accuracy.
- Correct for reflected radiation, windows and partly filled spots, and set up a pyrometer installation that stays accurate.
- Run a thermographic survey that finds real faults, and build an uncertainty budget traceable to a calibration.
Inside this book
Chapters
- 01Everything glows: Planck's law and the black bodyThermal radiation, Planck's law, Wien's peak and Stefan–Boltzmann for IH-40's 1,200 °C billets, why 1 µm signals swing 10% per 1% of temperature, and a pyrometer moved down the line.
- 02Emissivity: why real surfaces read lowWhat emissivity is, how a wrong setting moves the reading at 1 µm and 10 µm, IH-40's scaled billets, measuring emissivity on site, and bright bar that sent the heater 55 K too hot.
- 03Choosing the wavelengthThe shortest-wavelength rule, emissivity errors from 0.65 to 12 µm, the lower range limit, the air in the path, materials that are see-through, and a handheld gun that said IH-40 read 150 K high.
- 04Ratio pyrometers: two colours instead of oneHow a two-colour pyrometer cancels emissivity, windows and partial fill, why it amplifies non-greyness and noise, IH-40's trial on bright bar, and good billets rejected against a hot background.
- 05Reflections, windows and the pathThe measurement equation, reflection from hot surroundings, targets inside furnaces, window losses and correction, steam and dust, and a window that fogged over three weeks and sent IH-40 hot.
- 06Spot size, distance and alignmentDistance-to-spot ratio, filling the spot, the error from a part-filled spot at 1 µm and 10 µm, round targets, moving parts and response time, and smaller billets that wandered out of the spot.
- 07Thermography for maintenanceLong-wave cameras, emissivity and reflected temperature near room temperature, comparisons and trends, IH-40's cabinet and press motor, and a hot busbar joint that showed as the coolest of three.
- 08Calibration, traceability and the uncertainty budgetBlack-body sources, traceability, field checks with drilled-hole billets, IH-40's uncertainty budget of ±8 K, guard bands, and an emissivity set against a thermocouple read too soon.
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References and source notes
The manuscript and worked examples are original KEVOS® writing. References inform particular concepts; their authors do not endorse this book. Web references were consulted on 27 October 2026.
- H. Gould and J. Tobochnik. Thermal and Statistical Physics (draft edition) (2006). Supplied source, in copyright (later published by Princeton University Press). Read as a subject map for temperature and its measurement, the photon gas and black body radiation, the Planck distribution and the Stefan–Boltzmann law. No text, derivations as set out, figures, tables or problems are reproduced; the treatment, case, numbers and exercises in this book are its own.
- National Institute of Standards and Technology. CODATA values: second radiation constant and Stefan–Boltzmann constant (2019). The second radiation constant, 1.438776877 × 10⁻² m·K, and the Stefan–Boltzmann constant, 5.670374419 × 10⁻⁸ W/(m²·K⁴), used in every radiation calculation. The Planck-law values in the book were computed from these constants and checked by running the calculations.
- AMETEK Land. What is Emissivity? (2025). Source of the definition of emissivity used, the relation between emissivity and reflectivity for opaque bodies, and the indicative emissivities at 1 µm of oxidised steel (0.85) and unoxidised steel (0.35). Indicative values only.
- Optris. Emissivity Table (2026). Source of the indicative emissivities of polished and oxidised copper, painted surfaces and anodised aluminium used in Chapter 7, and of the maker's advice that tabulated values are recommendations to be verified under the actual measurement conditions.
- International Organization for Standardization. ISO 18434-1 Condition monitoring and diagnostics of machines: Thermography, Part 1: General procedures (edition as called up). Named by number and scope as the international standard for thermographic condition monitoring of machines. No values or criteria are quoted from it.
- Standards Australia and Standards New Zealand. AS/NZS 4836 Safe working on or near low-voltage and extra-low voltage electrical installations and equipment (edition as called up). Named in Chapter 7 by number and scope as one reference for safe work near live electrical equipment during thermal surveys. No values are quoted from it.