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Research Article | | Peer-Reviewed

Limitations of Pyrometer Technology in the Ultraviolet and Visible Spectral Bands According to Planck's Law on the Real Body

Ratianarivo Paul Ezekel*,  Rastefano Elisee
Published in Journal of Electrical and Electronic Engineering (Volume 14, Issue 3)
Received: 23 April 2026     Accepted: 6 May 2026     Published: 14 May 2026
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Abstract

This article investigates the limitations of pyrometric technology in the visible and ultraviolet spectral bands. These studies rely on a theoretical analysis of thermal radiation, Planck's fundamental laws, and multispectral processing methods based on nonlinear models. Accurate high-temperature measurement is a major challenge in many scientific and industrial fields, including thermal processes, metallurgy, energy, and fundamental research. Uncertainty in emissivity is the main source of error in conventional pyrometric measurements. To reduce the influence of emissivity and improve measurement reliability, several approaches have been developed, including monochromatic, bichromatic, and multispectral pyrometry based on Planck's law. The chromatic luminance characteristics in the visible and ultraviolet bands, obtained from a temperature range across both spectral domains, highlight the high potential of pyrometry for measuring high temperatures in complex environments. These characteristics will be applied with different wavelengths in each visible and ultraviolet spectral band. Comparative studies of the results will be able to highlight the limitations for each band. Compared to traditional approaches, this pyrometry technology offers a small advantage for detecting very high temperatures despite variations in emissivity and environmental uncertainties. The luminance for these two spectral bands exhibits a very low flux almost at temperatures below 1900K.

Published in Journal of Electrical and Electronic Engineering (Volume 14, Issue 3)
DOI 10.11648/j.jeee.20261403.12
Page(s) 135-142
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2026. Published by Science Publishing Group
Previous article
Keywords

Wavelength, Pyrometer, Visible Spectrum, Ultraviolet Spectrum, Temperature, Luminance, Emissivity

1. Introduction
Pyrometry is based on the fundamental principle that any body with a temperature above absolute zero emits electromagnetic radiation whose intensity and spectral distribution depend on its temperature. However, the relationship between the measured radiation and the actual temperature is strongly influenced by the radiative properties of materials, particularly emissivity
[1-3]
. Applying the spectral length allows for the characterization of chromatic radiance according to Planck's law
[4, 5]
.
2. Methodology and Law of Radiation
2.1. Physical Model
Multispectral pyrometry modeling is based on the fundamental laws of thermal radiation. Planck's law describes the spectral radiance of a black body at temperature T
[6-8]
.
L0(λ,T)=2hc2λ-5ehckλT-1(1)
where h =6,6255 x 10-34Js: constant of Planck,
k =1,38 x 10-23 JK-1: constant of Boltzmann,
c =2,996 x 108 ms-1: Speed of electromagnetic waves in a vacuum.
For a real material, the measured luminance is weighted by the spectral emissivity ελ,T.
Lλ,T=ελ,T.L0λ,T(2)
Kirchhoff's fundamental relationship linking emissivity and absorptivity is written, for an opaque body
[9]
.
ελ=1-ρλ(3)
where ρ(λ) is the spectral reflectivity.
In multispectral pyrometry, the temperature is estimated from the measured fluxes
[10, 11]
.
For materials with non-linear emissivity, such as steels, that is to say, emissivity does not depend on wavelength. In that case, the emissivity can be modelled as a second-degree polynomial.
ελ=aλ2+bλ+c(4)
The parameters a, b, and c are to be estimated during the measurement
[12-14]
.
2.2. Different Regions of the Ultraviolet and Visible Spectrum
The ultraviolet range covers wavelengths from 0.2μm to 0.4μm and that of visible is between 0.4μm and 0.8μm.
2.3. Theoretical Foundations of Thermal Radiation
The methodology is based primarily on the study of the physical principles of thermal radiation. The electromagnetic radiation emitted by a heated body extends from the ultraviolet to the infrared, with a spectral distribution governed by Planck's law. The black body serves as the reference model, representing an ideal emitter that absorbs and emits perfectly across the entire spectrum
[15, 16]
.
For a real material, the spectral radiance is weighted by an emissivity coefficient, ranging from 0 to 1. This emissivity can be defined in different forms: monochromatic or total, directional or hemispherical
[17]
. In pyrometry, directional monochromatic emissivity plays a central role, as it directly relates the measured radiance to the actual surface temperature
[18]
.
3. Variation of Chromatic Luminance According to Temperature and Wavelength
The characteristic results of chromatic luminance are illustrated by representative curves as a function of temperature at a given wavelength. Equation (2) describes how the measured luminance is weighted by the spectral emissivity ε(λ,T) in polynomial form.
3.1. Chromatic Luminance in the Ultraviolet Spectrum
The ultraviolet spectrum lies between the 0.2 μm and 0.4 μm bands. Characteristic luminance curves, according to Planck's law for real bodies with polynomial emissivity, are plotted from temperatures of 1000 K to 3000 K.
By experimenting with several wavelengths at 0.2 μm, 0.2 μm, 0.275 μm, 0.325 μm, 0.375 μm, and 0.4 μm within the ultraviolet spectral range, we obtain curves characterizing luminance as a function of temperature variation with these wavelengths.
Figure 1. Radiation in ultraviolet spectrum range at a wavelength of 0.2µm.
Figure 2. Radiation in ultraviolet spectrum range at a wavelength of 0.225µm.
Figure 3. Radiation in ultraviolet spectrum range at a wavelength of 0.275µm.
Figure 4. Radiation in ultraviolet spectrum range at a wavelength of 0.325µm.
Figure 5. Radiation in ultraviolet spectrum range at a wavelength of 0.375µm.
Figure 6. Radiation in ultraviolet spectrum range at a wavelength of 0.4µm.
3.2. Chromatic Luminance in the Visible Spectrum
The visible spectrum corresponds to an intermediate region of the electromagnetic spectrum, in which the variation of luminance with temperature remains significant, but less abrupt than in the ultraviolet. The visible spectrum lies between the 0.4 μm and 0.8 μm bands. Characteristic curves of luminance according to Planck's law for real bodies are plotted from temperatures of 500 K to 3000 K.
By experimenting with several wavelengths at 0.4 μm, 0.45 μm, 0.55 μm, 0.65 μm, 0.75 μm, and 0.8 μm within the visible spectral range, we obtain curves characterizing luminance according to the respective temperature variations with these wavelengths.
Figure 7. Radiation in visible spectrum range at a wavelength of 0.4 µm.
Figure 8. Radiation in visible spectrum range at a wavelength of 0.45µm.
Figure 9. Radiation in visible spectrum range at a wavelength of 0.55µm.
Figure 10. Radiation in visible spectrum range at a wavelength of 0.65µm.
Figure 11. Radiation in visible spectrum range at a wavelength of 0.75µm.
Figure 12. Radiation in visible spectrum range at a wavelength of 0.8µm.
4. Interpretation of Results and Discussion
The results obtained highlight the high potential of pyrometry for measuring high temperatures in complex environments. Compared to traditional approaches, this technology offers greater robustness to variations in emissivity and environmental uncertainties.
4.1. Luminance in the Ultraviolet and Visible Spectral Band
The increased sensitivity in the ultraviolet and visible ranges must be weighed against the practical difficulties related to atmospheric attenuation and stray light sources.
In the ultraviolet range, corresponding to short wavelengths, spectral luminance exhibits a strongly non-linear dependence on temperature, in accordance with Planck's law. The dominant exponential term in this region induces a rapid variation in luminance for small temperature changes. Luminance is only usable above approximately 2300 K, regardless of the wavelengths within the band. Measurement at low temperatures is strongly discouraged due to very low and almost zero luminance levels. From 2800 K onwards, the curves become almost linear, meaning there is a direct affine relationship between luminance and temperature, regardless of the wavelength.
However, measurements in the visible spectrum can be affected by stray light sources (ambient lighting, reflections), necessitating controlled experimental conditions. Measurement is only possible at temperatures above approximately 1900 K. Luminance is very low at temperatures below this value, regardless of wavelength within this spectral band. From 2500 K onwards, the curves become almost linear, meaning there is a direct affine relationship between luminance and temperature, regardless of wavelength.
4.2. Selection of Optimal Wavelengths
According to spectral emission curves of real materials in the ultraviolet and visible ranges, for the ultraviolet range, short wavelengths offer high temperature sensitivity, but they are also more susceptible to environmental disturbances and emissivity variations depending on the sequential selection method. In the visible range, a trade-off is observed between thermal sensitivity and robustness against interference.
In both spectral bands, the use of longer wavelengths offers a slightly wider temperature range. Conversely, shorter wavelengths can only be used for measuring a narrower temperature range.
4.3. Error and Uncertainty Analysis
Error analysis highlights several sources of uncertainty: spectral variations in emissivity, detector noise, influence of the radiative environment, and approximation of mathematical models. The results show that the gray-body assumption, often used in bichromatic pyrometry, is not always valid for real materials at high temperatures.
5. Conclusions
In conclusion, in the visible spectral range, spectral luminance exhibits a wide region of nonlinearity at temperatures below 1900 K. This nonlinearity indicates the difficulty in detecting fluxes. Similarly, in the ultraviolet range, luminance obtained at temperatures below 2600 K also exhibits strong nonlinearity.
In these nonlinear regions of the ultraviolet and visible spectra, the design of such a pyrometer becomes very complex and requires a compensation system due to ambient radiation. Furthermore, measurement at low temperatures is completely impossible due to the very high and uncorrectable error rate.
Acknowledgments
I express sincere gratitude to the electronic engineering de-partment teams at the Polytechnical High School of Antsirabe at the University of Vakinankaratra, Madagascar and the team of Polytechnical High School of Antananarivo, and Doctoral School of Science ond Technology of Engineering and Innovation, University of Antananarivo.
I give thanks especially to my family indeed my new born daughter for the happiness that they offer to. I never forget my colleagues for their support and advices during the realization of this article.
Author Contributions
Ratianarivo Paul Ezekel: Conceptualization, Investigation, Methodology, Resources, Writing – original draft, Writing – review & editing
Rastefano Elisee: Project administration, Supervision, Validation
Data Availability Statement
The data is available from the corresponding author upon reasonable request.
Conflicts of Interest
The authors declare no conflicts of interest.
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    Ezekel, R. P., Elisee, R. (2026). Limitations of Pyrometer Technology in the Ultraviolet and Visible Spectral Bands According to Planck's Law on the Real Body. Journal of Electrical and Electronic Engineering, 14(3), 135-142. https://doi.org/10.11648/j.jeee.20261403.12

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    ACS Style

    Ezekel, R. P.; Elisee, R. Limitations of Pyrometer Technology in the Ultraviolet and Visible Spectral Bands According to Planck's Law on the Real Body. J. Electr. Electron. Eng. 2026, 14(3), 135-142. doi: 10.11648/j.jeee.20261403.12

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    AMA Style

    Ezekel RP, Elisee R. Limitations of Pyrometer Technology in the Ultraviolet and Visible Spectral Bands According to Planck's Law on the Real Body. J Electr Electron Eng. 2026;14(3):135-142. doi: 10.11648/j.jeee.20261403.12

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  • @article{10.11648/j.jeee.20261403.12,
  author = {Ratianarivo Paul Ezekel and Rastefano Elisee},
  title = {Limitations of Pyrometer Technology in the Ultraviolet and Visible Spectral Bands According to Planck's Law on the Real Body},
  journal = {Journal of Electrical and Electronic Engineering},
  volume = {14},
  number = {3},
  pages = {135-142},
  doi = {10.11648/j.jeee.20261403.12},
  url = {https://doi.org/10.11648/j.jeee.20261403.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.jeee.20261403.12},
  abstract = {This article investigates the limitations of pyrometric technology in the visible and ultraviolet spectral bands. These studies rely on a theoretical analysis of thermal radiation, Planck's fundamental laws, and multispectral processing methods based on nonlinear models. Accurate high-temperature measurement is a major challenge in many scientific and industrial fields, including thermal processes, metallurgy, energy, and fundamental research. Uncertainty in emissivity is the main source of error in conventional pyrometric measurements. To reduce the influence of emissivity and improve measurement reliability, several approaches have been developed, including monochromatic, bichromatic, and multispectral pyrometry based on Planck's law. The chromatic luminance characteristics in the visible and ultraviolet bands, obtained from a temperature range across both spectral domains, highlight the high potential of pyrometry for measuring high temperatures in complex environments. These characteristics will be applied with different wavelengths in each visible and ultraviolet spectral band. Comparative studies of the results will be able to highlight the limitations for each band. Compared to traditional approaches, this pyrometry technology offers a small advantage for detecting very high temperatures despite variations in emissivity and environmental uncertainties. The luminance for these two spectral bands exhibits a very low flux almost at temperatures below 1900K.},
 year = {2026}
}

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AB  - This article investigates the limitations of pyrometric technology in the visible and ultraviolet spectral bands. These studies rely on a theoretical analysis of thermal radiation, Planck's fundamental laws, and multispectral processing methods based on nonlinear models. Accurate high-temperature measurement is a major challenge in many scientific and industrial fields, including thermal processes, metallurgy, energy, and fundamental research. Uncertainty in emissivity is the main source of error in conventional pyrometric measurements. To reduce the influence of emissivity and improve measurement reliability, several approaches have been developed, including monochromatic, bichromatic, and multispectral pyrometry based on Planck's law. The chromatic luminance characteristics in the visible and ultraviolet bands, obtained from a temperature range across both spectral domains, highlight the high potential of pyrometry for measuring high temperatures in complex environments. These characteristics will be applied with different wavelengths in each visible and ultraviolet spectral band. Comparative studies of the results will be able to highlight the limitations for each band. Compared to traditional approaches, this pyrometry technology offers a small advantage for detecting very high temperatures despite variations in emissivity and environmental uncertainties. The luminance for these two spectral bands exhibits a very low flux almost at temperatures below 1900K.
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Author Information

  • Ratianarivo Paul Ezekel

    Electronic Department, Polytechnical High School of Antsirabe, Antsirabe, Madagascar

    Biography: Ratianarivo Paul Ezekel is a professer at Polytechnical High School of Antsirabe, Vakinankaratra University, Electronic Engineering Department. He completed his PhD in Electronic Divices et Systems Engineering from Antananarivo University in 2018, and his Master of Engineering in Automatic Electronic Systems from Polytechnical High School of Antananarivo in 2010. Recognized for his exceptional contributions, Dr. Ratianarivo Paul Ezekel has been known as the chef department of electronic engineering at Polytechnical High School of Antsirabe.

    Research Fields: Electronic system, Instrumentation, Embedded systems, programmable system, spintronic

    Contact Email

    http://orcid.org/0009-0003-4003-1469

  • Rastefano Elisee

    Electronic Department, Polytechnical High School of Antananarivo, Antananarivo, Madagascar

    Biography: Rastefano Elisee is a professer at Polytechnical High School of Antananarivo, and Doctoral School of Science and Technology of Engineering and Innovation, University of Antananarivo, Electronic Engineering Department. As a teacher, he is the founder of electronic engineering formation in Madagascar. Recognized for his exceptional contributions, Rastefano Elisee has been known as the chef department of electronic engineering at Polytechnical High School of Antananarivo during long time and head of the doctoral reception team of embedded systems, instrumentation, electronic system modeling.

    Research Fields: Semiconductor, electronic system, signal processing, spintronic

    Contact Email

    http://orcid.org/0009-0002-6786-800X

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