Fourier transform approach quantifies the performance of spectral linear noise-reduction filters

Across the various disciplines that use spectroscopy, the optimum noise-reducing filter remains elusive. To date, performance has generally been judged by inspection, which can make extracting information from very small samples difficult, particularly if needed quickly.

Aspnes et al. have now developed a method for quantifying the performance of linear noise-reduction filters in specific situations. It is based on Fourier transforms, a calculation that converts a spectrum into a set of waves that, when added, reproduce the spectrum.

“In a spectrum, information appears as point-to-point correlations and noise as point-to-point fluctuations. Hence, information is restricted to long waves whereas short waves are determined by noise,” said author David Aspnes. “This separation provides the opportunity to assess the action of a filter on these components independently.”

Based on this observation, the group derived a cost function that quantifies the residual error of the filtered spectrum in two terms, the first as degradation of information and the second as leakage of noise.

“The two terms compete, so a perfect filter is impossible. The error also depends on the data being analyzed, so a general filter is impossible,” Aspnes said. “However, tradeoffs and optimization are both possible.”

Using the cost function in various contexts, the group found that the recently introduced Gauss-Hermite filter is best. They then demonstrated its usefulness by analyzing data obtained by various techniques, including X-ray photoemission spectroscopy and spectroscopic ellipsometry.

The group is next turning its attention to nonlinear filters, with hopes to later identify a fundamental limit of our capability to eliminate noise from spectra.

Source: “Engineering the optimal filter: Quantitative assessment of linear noise-reducing filters in spectroscopy,” by David E. Aspnes, Long V. Le, and Young Dong Kim, Journal of Applied Physics (2026). The article can be accessed at https://doi.org/10.1063/5.0308052 .

This paper is part of the Advances in Spectroscopic Ellipsometry Methods and Materials Characterization Collection, learn more here .