Large-spot laser energy measurement based on flat-plate calorimetry

The measurement of total energy on a target is a critical step in evaluating the performances of high-power laser systems. However, the laser spot on the target exhibits characteristics such as high power density, non-uniform spatial distribution and temporal distribution, and large spot size, which present a significant challenge to the accurate measurement of total energy. To meet the requirement for high-precision measurement of the total energy of a large spot, this work focuses on plate-based energy measurement technology. First, we investigate the physical processes of laser-heated plates and obtain analytical solutions, demonstrating that uniformly arranged temperature sensor arrays can shorten the relaxation period. Second, to overcome the limitations of traditional energy inversion algorithms, such as the need to preheat the absorber and potential non-uniform temperature effects, we propose correction methods. The non-preheated calorimetry method eliminates the requirement that the absorber temperature must be higher than the ambient temperature during the initial rating period. It iteratively optimizes the ambient temperature and heat loss coefficients based on corrected temperature invariance. Additionally, a non-uniform temperature correction algorithm is employed to minimize the errors caused by limited sensor sampling rates through reconstructing the temperature curve during the injection and adjustment periods. Finally, we develop a plate measurement device and conduct laser calibration tests, achieving a system repeatability of 2.7%, linearity of 0.3%, and a combined standard uncertainty of 4%. This study lays a theoretical foundation for flat-plate laser energy measurement technology, offering important insights into optimizing the apparatus design, improving usability, and achieving high-precision energy inversion.