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A new procedure for the identification and quantification of spectral signals based on the method of maximum likelihood is presented. It is particularly appropriate for the analysis of signal interference or cases of a small signal in a sizeable noisy background. The formulation yields precise signal intensity values and has advantages in its estimation of detection limits over established signal processing methods. The method developed is applicable to spectroscopic techniques where net counts are proportional to acquisition time, such as particle induced x-ray emission (PIXE) and other x-ray fluorescence spectroscopic methods, Mössbauer spectroscopy, some cases of a, b and g spectroscopy, etc. The proposed method was applied in two experimental instances to the quantification of traces of the XRF mercury signal in the presence of a large, strongly interfering gold signal: (i) In liquid solutions assayed by means of total reflection x-ray fluorescence (TXRF) spectrometry, where mercury amalgamated on a gold-plated thin film sputtered on pure quartz reflectors was irradiated with a molybdenum anode x-ray tube; detection limits achieved by the method were 100 ppb, significantly lower than obtained by standard net-area processing procedures; (ii) solid sample XRF spectra analyzed with the proposed method yielded consistent and reliable signal intensities and evidence of detection limits almost an order of magnitude smaller than achieved by standard net-area processing procedures.

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We studied the applicability and validity range of a mathematical procedure on the basis of the principia of maximum likelihood for the identification and quantification of arsenic and lead. This procedure has showed to be appropriate for analyzing two or more signals that interfere with each other or for the quantification of a small signal in a very noisy environment, but a complete study of determination of its confidence interval in samples in which one element in the overlap is present in a concentration lower than the other elements was not studied previously. The identification implemented provides very exact values of relative concentrations for cases that are difficult to process using other adjustment methods. The proposed procedure is applied to experimental cases, analyzing liquid solutions through total reflection X‐ray fluorescence to determine a range of concentrations for the detection of traces of arsenic signals in the presence of large lead interfering signals and vice versa. Copyright © 2013 John Wiley & Sons, Ltd.

We developed a general procedure that includes external standard calibration and a deconvolution of spectral signals, which determined with high accuracy the relative proportion and absolute quantification of elements that habitually overlap in total reflection X‐ray fluorescence spectroscopy. The deconvolution proposed takes advantage of the well‐known method of a cross‐correlation technique, offering improvements in identification of simultaneous signals and in the determination of the relative elemental proportions. The external standard calibration was studied determining its range of application for the elements of interest and implemented in certified standard samples producing excellent results for the quantification of the mentioned elements. In this paper, we show the quality of the results obtained for specific heavy metals of currently health and industrial interest in the range of linear response of 0.2–200 ng. Copyright © 2013 John Wiley & Sons, Ltd.