Schematic illustration of a single T−T plot evaluated for an ideal low-frequency Planck simulation (30 and 44 GHz). Each dot represents the observed values at two frequencies for a single pixel. The slope of the distribution is given by the spectral index of the signal component in the field, as indicated by the dashed lines. A constant offset in either frequency map simply translates the entire T−T plot either horizontally or vertically. For maps without spurious offsets, the best-fit straight line should pass through the origin; the fundamental idea of the algorithm presented in this paper is to ensure that this is the case for any sufficiently small patch of the sky.