Ultra-fast detection of the center frequency of a spectral line from amplitude-weighted average

Spectroscopy methods often require calculating the central frequency of a resonance line, that is usually implemented by finding a best fit to the spectrum by a line-shape function. Such an iterative procedure is slow and requires an initial guess. We report an analytical method for calculating the central frequency of a spectral line by using the mean value of its frequencies, which are weighted by corresponding normalized intensities. We use this method to calculate two-dimensional arrays of central frequencies from parallely measured magnetic resonance spectra, which are optically detected by a camera sensor in a thin layer of NV centers with superparamagnetic hemozoin crystals on top of it. We demonstrate that our analytical method is more than 800 times faster than the fitting procedure without significant loss of accuracy. For a 400x400 pixels sensing array, this method is almost instantaneous, while fitting with the Lorentz function requires several minutes of post-processing on a 4-core MacBook Pro. When a resonance is beyond the spectral range, the amplitude-weighted-mean method does not fail, but it alternates its center frequency proportionally to the mismatch distance. Our method will be useful for spectroscopic applications that require high performance of data processing, allowing their fast optimization, inline processing and real-time output of results. It can also be used for automatic analysis of single spectra, when accuracy of the frequency detection could be slightly (<10%) reduced for sake of stability and simplicity of the data processing.