I am using an optical spectrometer to measure some surfaces in the visible, and since the signal is quite noisy I wondering what would be the best way to reduce the noise. In particular, are there some computational solutions to characterize the noise and then filter it, as it is used in signal processing (e.g. something like the optimum filtering)?
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The most common noise filter used in spectroscopy is the Savitzky-Golay algorithm. It requires equally spaced data on the x-axis. SG is basically a least squares polynomial fit to the data with the center point being replaced by the calculated result. The filter can be generated by partially solving the least matrix equation with the final computation being a convolution of the smoothing function with the data. See the original paper by SG. Be aware there are a couple of mistakes in it. To understand the fine details of SG smoothing see Willson and Polo, J. Opt. Soc. Am., V71 (1981), p599. SG filters can also generate derivative spectra.
