Development and validation of an inverse method for identification of thermal characteristics of a short laser pulse

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.