Spectral reconstruction of dental X-ray tubes using laplace inverse transform of the attenuation curve A. Malezan a,n , A. Tomal b , M. Antoniassi a,c , P.C.A. Watanabe d , L.D. Albino a , M.E. Poletti a a Departamento de Física, FFCLRP, Universidade de São Paulo,14040-901 Ribeirão Preto, SP, Brazil b Instituto de Física Gleb Wataghin, Universidade de Campinas, 13083-859 Campinas, SP, Brazil c Departamento Acadêmico de Física, Universidade Tecnológica Federal do Paraná, 80230-901 Curitiba, PR, Brazil d Faculdade de Odontologia de Ribeirão Preto, Universidade de São Paulo,14040-901 Ribeirão Preto, SP, Brazil HIGHLIGHTS  Inverse Laplace transform.  A spectral reconstruction method, based on the inverse Laplace transform of the attenuation curve, was implemented to dental X-ray units.  The validity of the method is verified and dental X-ray spectra are studied. article info Article history: Received 1 October 2014 Accepted 2 May 2015 Keywords: Dental X-ray Attenuation curves Spectra measurements Laplace transform abstract In this work, a spectral reconstruction methodology for diagnostic X-ray, using Laplace inverse transform of the attenuation, was successfully applied to dental X-ray equipments. The attenuation curves of 8 commercially available dental X-ray equipment, from 3 different manufactures (Siemens, Gnatus and Dabi Atlante), were obtained by using an ionization chamber and high purity aluminium filters, while the kV p was obtained with a specific meter. A computational routine was implemented in order to adjust a model function, whose inverse Laplace transform is analytically known, to the attenuation curve. This methodology was validated by comparing the reconstructed and the measured (using semiconductor detector of cadmium telluride) spectra of a given dental X-ray unit. The spectral reconstruction showed the Dabi Atlante equipments generating similar shape spectra. This is a desirable feature from clinic standpoint because it produces similar levels of image quality and dose. We observed that equipments from Siemens and Gnatus generate significantly different spectra, suggesting that, for a given operating protocol, these units will present different levels of image quality and dose. This fact claims for the necessity of individualized operating protocols that maximize image quality and dose. The proposed methodology is suitable to perform a spectral reconstruction of dental X-ray equip- ments from the simple measurements of attenuation curve and kV p . The simplified experimental ap- paratus and the low level of technical difficulty make this methodology accessible to a broad range of users. The knowledge of the spectral distribution can help in the development of operating protocols that maximize image quality and dose. & 2015 Elsevier Ltd. All rights reserved. 1. Introduction The knowledge of the energy spectrum is an essential part of the complete characterization of an X-ray equipment and also a mathematical tool that allows, from theoretical approaches, the optimization of image quality parameters such as contrast and signal to noise ratio as well as reducing the dose delivered to patient (Duckworth et al., 1981). The characterization of an X-ray system can be performed by employing semi-analytical models (Birch and Marshall, 1979; Tucker et al., 1991), Monte Carlo simulation (Cunha et al., 2012; Ng et al., 2000) or experimental methods (Archer and Wagner, 1982, 1988; Miyajima, 2003; Rubio and Mainardi, 1984; Terini et al., 1999)). The difficulty in replicating the internal operating Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/radphyschem Radiation Physics and Chemistry http://dx.doi.org/10.1016/j.radphyschem.2015.05.008 0969-806X/& 2015 Elsevier Ltd. All rights reserved. n Corresponding author. E-mail addresses: malezan@usp.br (A. Malezan), marceloantoniassi@usp.br (M. Antoniassi). Please cite this article as: Malezan, A., et al., Spectral reconstruction of dental X-ray tubes using laplace inverse transform of the attenuation curve. Radiat. Phys. Chem. (2015), http://dx.doi.org/10.1016/j.radphyschem.2015.05.008i Radiation Physics and Chemistry ∎ (∎∎∎∎) ∎∎∎–∎∎∎