Back to articles
Regular Article
Volume: 30 | Article ID: 34
Image
Approximating Planckian Black-body Lights using Wien's Approximation
  DOI :  10.2352/CIC.2022.30.1.34  Published OnlineNovember 2022
Abstract
Abstract

Planck’s law and Wien’s approximation of this law are both widely used to calculate the spectral radiation of a black-body based on its color temperature. The Wien approximation is a slightly simpler equation and has the advantage that the logarithm of a Wien light can be written as a linear sum of two basis vectors plus an offset (a fact that is exploited in some computer vision algorithms). In this paper, we show that the Wien formulation can, in general, be used to approximate Planckian lights assuming there is a mapping function taking Planckian to corrected Wien temperature. Significantly, we show that a correction function <i>f</i>() exists and for the range of color temperatures of interest the Wien spectrum calculated for <i>f</i>(T) has a very similar shape to the actual spectrum of a Planckian light with temperature T. We find that defining <i>f</i>() as a polynomial-type function models to a good extent the relationship between the color temperatures of Planckians and their closest Wien-Planckians lights both in terms of the angular error between their two respective spectral functions and their projections to u’v’ coordinates.

Subject Areas :
Views 13
Downloads 6
 articleview.views 13
 articleview.downloads 6
  Cite this article 

Rada Deeb, Graham Finlayson, Michael Brill, "Approximating Planckian Black-body Lights using Wien's Approximationin Color and Imaging Conference,  2022,  pp 194 - 199,  https://doi.org/10.2352/CIC.2022.30.1.34

 Copy citation
  Copyright statement 
Copyright ©2022 Society for Imaging Science and Technology 2022
cic
Color and Imaging Conference
color imaging conf
2166-9635
2166-9635
Society for Imaging Science and Technology
IS&T 7003 Kilworth Lane, Springfield, VA 22151 USA