Left: I_inh/I_⋆ as a function of the distance to the star a (in au) for different photo-centre displacements (Δα = [ 0.01,1,100 ] μas) in black solid lines. WISE (12 μm) detection limit in terms of I_inh/I_⋆ are shown in red for a dust cloud orbiting at a around a sun-like star and observed at different wavelengths representing different potential instruments, 0.55 (solid, Gaia or NEAT), 2.2 (dotted, GRAVITY) and 20 (dashed, TMT) microns. The position of an Earth-like planet is represented with a red square. Right: Same for a dust cloud orbiting a β-Pic like A6V star. In this case, the Earth-like planet having the same irradiation and mass as Earth, is located at 2.83 au (see text for details).