Abstract The paper presents development and validation of an inverse method for the identification of thermal characteristics of a short super-Gaussian laser pulse interacting with a metal sample. The method was applied to find unknown power of the laser pulse, dimensionless shape parameter of the super-Gaussian function describing the spatial energy distribution of the beam as well as beginning and end times of its interaction with the heated body. The proposed inverse method is based on the Levenberg-Marquardt technique and utilizes temporal and spatial distributions of temperature on the rear surface of the sample, i.e., the opposite to the irradiated one. The temperature profiles were registered by a high-speed IR camera. During the experiments some of the laser beam parameters, i.e., the power, the laser beam spatial profile, beginning and end times of the exposition as well as thermophysical and optical parameters of the aluminum sample were known. Therefore, the measured data were used for both validation of the numerical model which described thermal interaction of a laser pulse with the sample as well as the assessment of correctness and accuracy of the inverse method. At the first step, numerical model of the forward problem, i.e., heat transfer in the aluminum sample irritated by the laser pulse, was developed and validated based on experimentally-determined temperature distributions. The validation was performed for both single and multiple laser pulses. The numerical model of the forward problem was implemented in the commercial software ANSYS Fluent. Then an inverse algorithm was developed and implemented with the aid of the GNU Octave environment. Subsequently, series of numerical tests were carried out. During these numerical simulations, sensitivity analysis as well as initial calibration and verification of the developed algorithm were performed. Parallel to the modeling tasks, the experimental stand was built and series of experiments were performed which allowed to assess the performance of the method using physical temperature data. Performed investigations showed that the problem is ill-conditioned. Nevertheless, relatively good accuracy of the retrieval has been obtained. It was revealed that the sensitivity of the objective function to the end time of the laser pulse is relatively low and that two of the parameters affect measured temperatures in a similar way. These two properties contributed to ill-conditioning of the inverse problem. Dependence of inverse problem solutions on the initial guess has been observed and methods allowing to minimize its influence have been identified. The accuracy of the method was affected by relatively low temporal resolution of the IR camera (500 Hz, with the exposure time approximately from 0.2 to 1 ms). Despite aforementioned problems, the method was abled to retrieve unknown laser pulse parameters with 20–25% accuracy.

中文翻译：

---

一种识别短激光脉冲热特性的逆方法的开发和验证

摘要 本文介绍了一种用于识别与金属样品相互作用的短超高斯激光脉冲的热特性的逆方法的开发和验证。该方法用于寻找激光脉冲的未知功率、描述光束空间能量分布的超高斯函数的无量纲形状参数以及光束与加热体相互作用的开始和结束时间。所提出的逆方法基于 Levenberg-Marquardt 技术，并利用样品后表面温度的时间和空间分布，即与照射的相反。温度曲线由高速红外相机记录。在实验过程中，一些激光束参数，即功率、激光束空间分布、暴露的开始和结束时间以及铝样品的热物理和光学参数都是已知的。因此，测量数据既用于验证描述激光脉冲与样品的热相互作用的数值模型，也用于评估逆方法的正确性和准确性。第一步，基于实验确定的温度分布，开发并验证了前向问题的数值模型，即受激光脉冲刺激的铝样品中的热传递。对单个和多个激光脉冲进行了验证。正向问题的数值模型在商业软件ANSYS Fluent中实现。然后在 GNU Octave 环境的帮助下开发并实现了逆算法。随后，进行了一系列数值试验。在这些数值模拟过程中，进行了灵敏度分析以及所开发算法的初始校准和验证。与建模任务并行，搭建了实验台并进行了一系列实验，允许使用物理温度数据评估该方法的性能。进行的调查表明问题是病态的。尽管如此，已经获得了相对较好的检索准确度。结果表明，目标函数对激光脉冲结束时间的敏感性相对较低，并且其中两个参数以类似的方式影响测量温度。这两个属性导致了逆问题的病态。已经观察到逆问题解对初始猜测的依赖性，并且已经确定了允许最小化其影响的方法。该方法的准确性受到红外相机相对较低的时间分辨率（500 Hz，曝光时间大约为 0.2 到 1 ms）的影响。尽管存在上述问题，该方法仍能够以 20-25% 的准确度检索未知的激光脉冲参数。