# A Camera Calibration Method for Temperature Measurements of Incandescent Objects Based on Quantum Efficiency Estimation

## TL;DR

The paper introduces a new camera calibration method to measure the temperature of glowing objects using standard cameras, which could improve industrial processes and environmental monitoring.

## Contribution

The novel contribution is a calibration method that estimates the quantum efficiency of the entire optical system to measure temperatures of incandescent objects.

## Key findings

- The method enables high-resolution temperature measurements of glowing materials between 700–2500 °C using standard cameras.
- The calibration procedure achieves temperature prediction accuracy and precision within tens of Celsius degrees.
- The technique generalizes well to a wider temperature range and is robust to noise.

## Abstract

What are the main findings?
We present a novel method for calibrating the temperature-to-color relation (Planckian locus), enabling the measurement of incandescent object temperatures using a standard Bayer-pattern CMOS camera.Our method estimates the quantum efficiency of the entire optical system—including the camera, lens, and filters—using images of a black body furnace.

We present a novel method for calibrating the temperature-to-color relation (Planckian locus), enabling the measurement of incandescent object temperatures using a standard Bayer-pattern CMOS camera.

Our method estimates the quantum efficiency of the entire optical system—including the camera, lens, and filters—using images of a black body furnace.

What is the implication of the main finding?
Our method enables high-resolution, high-frame-rate temperature measurement of glowing hot materials in the range of 700–2500 °C with standard cameras and lenses improving process control in metal, semiconductor, and ceramic industries, and accelerating the development of additive manufacturing.Our technique is designed for standard cameras and lenses, potentially enhancing environmental monitoring by estimating the temperature in wildfires and volcanic activity, improving predictive modeling and hazard assessment.

Our method enables high-resolution, high-frame-rate temperature measurement of glowing hot materials in the range of 700–2500 °C with standard cameras and lenses improving process control in metal, semiconductor, and ceramic industries, and accelerating the development of additive manufacturing.

Our technique is designed for standard cameras and lenses, potentially enhancing environmental monitoring by estimating the temperature in wildfires and volcanic activity, improving predictive modeling and hazard assessment.

High-temperature thermal images enable monitoring and controlling processes in metal, semiconductors, and ceramic manufacturing but also monitor activities of volcanoes or contrasting wildfires. Infrared thermal cameras require knowledge of the emissivity coefficient, while multispectral pyrometers provide fast and accurate temperature measurements with limited spatial resolution. Bayer-pattern cameras offer a compromise by capturing multiple spectral bands with high spatial resolution. However, temperature estimation from color remains challenging due to spectral overlaps among the color filters in the Bayer pattern, and a widely accepted calibration method is still missing. In this paper, the quantum efficiency of an imaging system including the camera sensor, lens, and filters is inferred from a sequence of images acquired by looking at a black body source between 700 °C and 1100 °C. The physical model of the camera, based on the Planck law and the optimized quantum efficiency, allows the calculation of the Planckian locus in the color space of the camera. A regression neural network, trained on a synthetic dataset representing the Planckian locus, predicts temperature pixel by pixel in the 700 °C to 3500 °C range from live images. Experiments done with a color camera, a multispectral camera, and a furnace for heat treatment of metals as ground truth show that our calibration procedure leads to temperature prediction with accuracy and precision of a few tens of Celsius degrees in the calibration temperature range. Tests on a temperature-calibrated halogen bulb prove good generalization capability to a wider temperature range while being robust to noise.