Reconstruction of laser-induced plasma spectral emissivity in non-axisymmetric conditions B G. Cristoforetti * , S. Legnaioli, V. Palleschi, A. Salvetti, E. Tognoni, P. Tomassini IPCF-CNR, Area della Ricerca di Pisa, Via G. Moruzzi 1, 56124 Pisa, Italy Received 2 November 2004; accepted 26 April 2005 Available online 20 June 2005 Abstract The problem of determining the spectral emissivity in each spatial position of a laser induced plasma is extremely important in order to calculate the spatial distributions of physical and thermodynamical parameters characterizing the plume. Supposing that the plume is optically thin and axisymmetric, the problem is theoretically solved by the Abel inversion of the integral spectral emission. The work presented here is a generalization of the Aguilera et al. method of solving the Abel inversion, based on the modelization of the plume by discrete shells of constant emissivity, in the case of slightly non-axisymmetric plasmas. Some tests and examples of the application of the new algorithm are given. D 2005 Elsevier B.V. All rights reserved. Keywords: Abel inversion; LIBS; Plasma modelling; Plasma inhomogeneity 1. Introduction In many applications of laser-induced plasma spectro- scopy the plasma parameters (temperature, electron density, etc.) are determined by measuring the volume-integrated, spectrally resolved emissivity of the plasma [1–4]. On the other hand, several studies have been devoted to the reconstruction of the spatial distribution of the plasma emissivity, in order to understand more deeply the complex phenomena involved in the laser-target interaction and the dynamics of the laser-induced plasma [5–10]. In this kind of measurements, the intensity of the plasma emission is measured at different points along a grid encompassing the plasma plume and at different wave- lengths (see Figs. 1 and 2 for the definition of the variables used). The experimental result is then the quantity I (k , y, z ), which depends on the unknown plasma emissivity e (k, x , y, z ) integrated along the line of sight I k; y; z ð Þ¼ 2F Z kþDk=2 kDk=2 Z yþDy=2 yDy=2 Z zþDz=2 zDz=2  Z x max 0 e k V ; x V ; y V ; z V ð Þdk V dx V dy V dz V ð1Þ In deriving Eq. (1) the plume is assumed optically thin and the plasma emissivity mirror-symmetric with respect to the ( y, z ) plane. The Dz , Dy and Dk parameters account for the spatial and spectral resolution of the experimental apparatus, respectively, while the F constant is related to the efficiency of the detection system. When the resolution of the measurement is high (Dz / z , Dy / y and Dk / k N 1) the plasma emissivity can be safely considered constant in the integration interval and the corresponding integrals in dkV,dy V and dz V are trivially performed. Including all the relevant factors in the FV constant, we have: I k; y; z ð Þ¼ F V Z x max 0 e k; x V ; y; z ð Þdx V F V ¼ 2F DkDyDz ð2Þ 0584-8547/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.sab.2005.05.003 i This paper was presented at the 3rd International Conference on Laser Induced Plasma Spectroscopy and Applications (LIBS 2004), held in Torremolinos (Ma ´laga, Spain), 28 September – 1 October 2004, and is published in the special issue of Spectrochimica Acta Part B, dedicated to that conference. * Corresponding author. Tel.: +39 50 315 2222; fax: +39 50 315 2230. E-mail address: gabriele@ipcf.cnr.it (G. Cristoforetti). URL: http://als.ipcf.cnr.it (G. Cristoforetti). Spectrochimica Acta Part B 60 (2005) 888 – 896 www.elsevier.com/locate/sab