Illustration of the various data analysis methods that have been proposed and used to estimate and subtract the stellar halo and speckles at the position of a faint companion. The star, halo, and speckles are represented in dark grey, respectively, with a five-pointed star, a wide radial gradient, and small grey circles; the companion is represented by a smaller red five-pointed star; the portion of starlight used to calibrate the halo/speckles at the position of the companion is represented by a hashed green area. The chromatic motion of the halo and speckle pattern is represented by dark grey arrows starting from the speckles and pointing outwards (i.e. motion for increasing wavelength). A short explanation of the methods is given beneath each illustration. In the Vigan et al. (2008) configuration, the slit is coupled with a Lyot coronagraph, represented by a circular focal-plane mask at the center of the slit.