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Extended Planckian locus
Optics Express
|December 19, 2025
Summary
This study extends Planck and Wien formulas to negative temperatures, revealing continuity at infinite temperatures but a discontinuity at zero. This research strengthens theoretical foundations for lighting indices like correlated color temperature.
Area of Science:
- Color science
- Thermodynamics
- Radiometry
Background:
- The Planckian locus and Wien locus describe black body radiator colors at different temperatures.
- These loci are crucial for understanding everyday illuminations and color temperature.
- Existing models do not fully encompass negative temperature color properties.
Purpose of the Study:
- To extend the Planck and Wien formulas to include negative temperatures.
- To analyze the behavior of these extended loci, particularly at temperature limits.
- To provide a stronger theoretical basis for lighting indices.
Main Methods:
- Mathematical extension of Planck and Wien formulas to negative temperatures.
- Analysis of the resulting chromaticity diagram loci.
- Investigation of locus continuity and discontinuities at temperature limits (0 and ∞).
Main Results:
- The extended Wien locus intersects the spectral locus at 360 nm.
- Continuity is observed between positive and negative infinite color temperatures.
- A significant discontinuity exists at positive and negative zero color temperatures.
Conclusions:
- The extended Wien locus offers a more complete representation of color temperature, including negative values.
- The findings enhance the theoretical underpinnings of correlated color temperature and related lighting metrics.
- This work improves the practical applicability of color temperature calculations in illumination science.
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