Second derivative analysis and alternative data filters for multi-dimensional spectroscopies: a Fourier-space perspective.

The second derivative image (SDI) method is widely applied to sharpen dispersive data features in multi-dimensional spectroscopies such as angle resolved photoemission spectroscopy (ARPES). Here, the SDI function is represented in Fourier space, where it has the form of a multi-band pass filter. The interplay of the SDI procedure with undesirable noise and background features in ARPES data sets is reviewed, and it is shown that final image quality can be improved by eliminating higher Fourier harmonics of the SDI filter. We then discuss extensions of SDI-like band pass filters to higher dimensional data sets, and how one can create even more effective filters with some a priori knowledge of the spectral features.