Surface Laplacian (Current Source Density)
The surface Laplacian is a reference-free spatial filter that estimates the second spatial derivative of the scalp potential across the head surface. Because a spatial second derivative acts as a high-pass spatial filter, it sharply attenuates the broad, low-spatial-frequency smearing produced by volume conduction and by distant sources, emphasizing shallow, focal generators roughly beneath each electrode. It also has a physical interpretation as the radial current density entering and leaving the scalp, hence the synonym current source density.
In practice it is computed by the local nearest-neighbour Hjorth approximation on regular montages, or, more accurately, by fitting a spherical spline to the potential and differentiating it analytically. A key practical benefit is that it removes dependence on the choice of reference electrode entirely, which makes topographies and some connectivity estimates more interpretable.
A sensorimotor mu-rhythm ERD that looks like a diffuse blob over one hemisphere in the raw referenced data collapses to a tight focus over the hand-knob of motor cortex once the surface Laplacian is applied.
The Laplacian trades depth sensitivity for spatial resolution.
Because it is a high-pass spatial filter it discards genuinely widespread or deep activity, so it is a poor choice when the source of interest is broad or subcortical.