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

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 <i>T</i> increases, the chromaticity of a Wien spectrum at <i>T</i> diverges from that of a Planck spectrum of the same <i>T</i>. That is in spectral space. However, in (<i>u</i>', <i>v</i>') chromaticity space, the Planck and Wien loci are closely parallel, so it is plausible that, for any target Planck spectrum at <i>T</i>^<i>P</i>, there is a Wien temperature <i>T</i>^<i>W</i> that produces nearly the same chromaticity (hence nearly the same spectrum). In this paper, we derive a temperature adjustment function <i>f</i>() such that the Wien spectrum calculated with the temperature <i>T</i>^<i>W</i> is close to the Planck spectrum calculated at any given <i>T</i>^<i>P</i>: <i>T</i>^<i>W</i> = <i>f</i>(<i>T</i>^<i>P</i>). 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.