Approximate Voigt function formula for laser-induced breakdown spectroscopy fitting

Accurate and rapid spectrum fitting is very important for quantitatively analyzing laser-induced breakdown spectroscopy (LIBS). The Voigt function is often used to fit LIBS spectral lines. We propose a new approximate Voigt function formula. Based on the classic Lorentz–Gauss linear combination formula, a summation term was added that contained a specific convolution operation to improve the Voigt function’s calculation and fitting accuracy. This formula can be used for the approximate calculation of the Voigt function with an overall accuracy of 0.31% and a full width at half-maximum internal accuracy of 0.25% when the ratio of Lorentzian linewidth to Gaussian linewidth is 1:1. The formula was then applied to LIBS data processing to fit four element spectral lines of calcium (Ca-393.37, 396.85, and 422.67 nm) and potassium (K-766.49 nm). The fitting results showed that this new approximate formula could fit at least seven data points, and compared with the complex plane partition method and the classic linear combination formula, the new formula had better fitting speed and accuracy.