Contents lists available at ScienceDirect International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts Inverse analysis for the identification of temporal and spatial characteristics of a short super-Gaussian laser pulse interacting with a solid plate Karol Pietrak a,* , Piotr Łapka a , Małgorzata Kujawińska b a Institute of Heat Engineering, Warsaw University of Technology, 21/25 Nowowiejska St, 00-665, Warsaw, Poland b Institute of Micromechanics and Photonics, Warsaw University of Technology, 8 Sw. A. Boboli St, 02-525, Warsaw, Poland ARTICLE INFO Keywords: Inverse method Transient thermal problem Numerical method Laser beam Laser-solid matter interactions ABSTRACT In this paper, the results of numerical experiments verifying a novel setup for laser beam profiling are presented. The experimental setup is based on infrared thermography and includes laser beam illuminating a thin metal plate. The method allows to determine four parameters of the short high-power laser pulse, namely the Super- Gaussian profile coefficient, laser power, pulse start time and duration. The unknown parameters are retrieved based on temporal and spatial temperature distributions at the rear side of the illuminated plate. The applied inverse method is based on Levenberg-Marquardt technique and is implemented in the GNU Octave environ- ment. Solutions of the forward problem are obtained numerically, with the aid of three-dimensional transient heat transfer model implemented in the commercial software ANSYS Fluent. The paper presents the results of the sensitivity analysis as well as calibration and verification of the developed inverse algorithm through application of numerically-generated simulated (artificial) experimental data instead of the physical one. Strengths and weaknesses of the applied approach are widely discussed. 1. Introduction Laser beams of high-energy are encountered in material processing [1] and characterization [2], electro-optical systems [3] and weapon technology [4] among other engineering applications. Many aspects of such laser beam interactions with matter are well-described in the work of von Allmen [5]. The presented study focuses on the identification of transient and spatial characteristics of a high-power super-Gaussian laser pulse interacting with a solid specimen. In the case of a high-power beam formed in an optical system, the component elements of this system undergo heating during laser op- eration and their optical surfaces may deform changing the beam pro- file from the desired Gaussian one to super-Gaussian or even more complex form. It means that it is required to check the profile of a working laser beam. In the industry today, typical laser beam profilers include scanning aperture profilers using slits, knife-edges, or pinholes that utilize single large area detectors, or camera-based profilers using CCD's or photodiode arrays. The high sensitivity of camera profilers require the laser light to be reduced in intensity by many orders of magnitude using beam sampling or optical attenuation [6]. Recently a new profiling technique that uses Rayleigh scatter from the beam overcomes the power obstacle and allows measurement and monitoring of the beam caustic and determination of M 2 parameters of laser beams with power from 1kW to 100kW [7]. In many applications where the Gaussian profile is desired, M 2 describes the relative characteristics of the beam and is determined by making multiple measurements of the beam width. However, this instrumentation is very expensive and re- quires great care in its usage during signalizing possible changes of a beam parameters. Recently the new approach to this problem was proposed by Kujawińska et al. [8] which is very simple and therefore may be easily applied in the industrial or field conditions with a relatively low cost compared to the other methods. This method assumes that the char- acteristics of the laser pulse may be found based on temperature dis- tributions recorded with high-speed infrared camera at the rear surface of the heated aluminum plate. The rear surface was selected for col- lecting the data in order to mitigate the risk of damaging the camera sensors by high-power laser beam which might be reflected from the front surface of the sample. Additional refining of estimated parameter values based on maps of displacements acquired with the aid of Digital Image Correlation (DIC) method [9] is also planned. The DIC method allows to track sample deformation resulting from thermal stresses in- duced by significant sample heating by the laser pulse [8]. Never- theless, the current paper is focused only on the details of the thermal part of the introduced problem. It means that the measurement of displacements is not included in the considered inverse method at this https://doi.org/10.1016/j.ijthermalsci.2018.08.040 Received 3 April 2018; Received in revised form 29 June 2018; Accepted 23 August 2018 * Corresponding author. E-mail address: karol.pietrak@itc.pw.edu.pl (K. Pietrak). International Journal of Thermal Sciences 134 (2018) 585–593 Available online 31 August 2018 1290-0729/ © 2018 Elsevier Masson SAS. All rights reserved. T