Introducing a temperature adjustment to make Wien’s law a more accurate approximation of Planckian blackbody radiation in the visible range

Daneshvar, Elaheh, Finlayson, Graham D., Brill, Michael H. and Deeb, Rada (2025) Introducing a temperature adjustment to make Wien’s law a more accurate approximation of Planckian blackbody radiation in the visible range. Optics Express, 33 (5). pp. 11956-11971. ISSN 1094-4087

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Abstract

Wien’s law is well known to approximate the Planckian blackbody radiator equation, in the visible range, for temperatures less than 4000 Kelvin. As temperature increases, however, the approximation degrades and ultimately for high temperatures the spectra generated by Wien’s law have significantly different spectral shapes compared to the actual Planckian lights. Accordingly, as temperature T increases, the chromaticity of a Wien spectrum at T diverges from that of a Planck spectrum of the same T. That is in spectral space. However, in (u′, v′) chromaticity space, the Planck and Wien loci are closely parallel, so it is plausible that, for any target Planck spectrum at TP, there is a Wien temperature TW that produces nearly the same chromaticity (hence nearly the same spectrum). In this paper, we derive a temperature adjustment function f() such that the Wien spectrum calculated with the temperature TW is close to the Planck spectrum calculated at any given TP: TW = f(TP). We investigate the utility of this result in the context of locus filter theory. A locus filter has the property that when it is applied to any Wien illuminant the resulting filtered light also is well described by Wien’s Law. Our temperature adjustment formula, in effect, extends locus filter theory so that it also applies to Planckian lights.

Item Type:	Article
Additional Information:	Data availability: No data were generated or analyzed in the presented research. Funding: Engineering and Physical Sciences Research Council (EP/S028730/1)
Faculty \ School:	Faculty of Science > School of Computing Sciences
UEA Research Groups:	Faculty of Science > Research Groups > Colour and Imaging Lab
Depositing User:	LivePure Connector
Date Deposited:	27 Jun 2025 12:30
Last Modified:	27 Jun 2025 19:30
URI:	https://ueaeprints.uea.ac.uk/id/eprint/99751
DOI:	10.1364/OE.544854

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