New insights into black bodies

TL;DR

This paper presents a new mathematical analysis of Planck's law, deriving formulas for black body temperature estimation from image data, enabling rapid temperature mapping and emission predictions.

Contribution

It introduces novel analytical formulas for black body temperature determination from dual-filter images and provides tools for efficient data analysis of black body radiation.

Findings

Derived exact locus in color-color diagrams.

Developed a formula for precise temperature estimation.

Enabled fast temperature mapping from images.

Abstract

Planck's law describes the radiation of black bodies. The study of its properties is of special interest, as black bodies are a good description for the behavior of many phenomena. In this work a new mathematical study of Planck's law is performed and new properties of this old acquaintance are obtained. As a result, the exact form for the locus in a color-color diagrams has been deduced, and an analytical formula to determine with precision the black body temperature of an object from any pair of measurements has been developed. Thus, using two images of the same field obtained with different filters, one can compute a fast estimation of black body temperatures for every pixel in the image, that is, a new image of the black body temperatures for all the objects in the field. Once these temperatures are obtained, the method allows, as a consequence, a quick estimation of their emission in other frequencies, assuming a black body behavior. These results provide new tools for data analysis.