Broad-band images have been obtained at the extremes of the continuum absorption coefficient of the solar atmosphere, at lambda 0.8 mu m and lambda 1.55 mu m. Quiet regions have been observed for different heliocentric angles. The centre-to-limb variation of granulation contrast has been computed in both wavelength ranges and a steeper decrease in the contrast is obtained for lambda 0.8 mu m than for lambda 1.55 mu m. For positions near the solar limb the granulation contrast shows a tendency to increase at both wavelengths. Mean granular sizes vary from 1.25 arcsec2 at the disc centre to 2 arcsec2 at mu =0.6 in the lambda 0.8 mu m images and from 1.24 arcsec2 to 1.85 arcsec2 at lambda 1.55 mu m. Observations close to the limb detect granular structures of 0.arcsec 96 or even smaller at a distance from the limb of d= 0.arcsec 32, equal to the diffraction limit of the telescope at lambda 8000 Å. Using an Eddington-Barbier approximation this implies a penetration of the temperature fluctuations associated with granulation up to approximately z ~ 220 km, although the calculation of response functions defines a broader interval.