Aims. We present ground-based observations of the disk around the A-type star β Pictoris to obtain scattered light images at the highest angular resolution (60 mas, equivalent to about 1 AU at the distance of the star) and the highest contrast in the very close environment of the star. The purpose of this program is to perform a close inspection of the inner disk morphology. Methods. Images were collected with NACO, the AO-assisted near-IR instrument on the VLT (ESO) which includes two types of coronagraphs: classical Lyot masks and phase masks. In this program we took advantage of both types of coronagraphs in two spectral bands, H-band for the Lyot mask and Ks-band for the phase mask. The Lyot mask blocks a large central region around the star (radius < 0.35”) but allows deep integrations and hence good signal-to-noise ratio at large distances, while the phase mask allows imaging at very close separation (down to ∼ 0.15” in theory) but conversely is more sensitive to residual aberrations. In addition, we simulated an extended object to understand the limitations in deconvolution of coronagraphic images. Results. The reduced coronagraphic images allow us to carefully measure the structures of the debris disk and reveal a number of asymmetries of which some were not reported before (position, elevation and thickness of the warp). Our analysis also demonstrates the advantage of the phase mask coronagraph to explore the very close environment of stars. In this program, the circumstellar material is visible as close as 0.7” (13.5 AU) owing to the phase mask while the Lyot mask generates artifacts which hamper the detection of the dust at separations closer than 1.2” (23.2 AU). The point source detection limit is compared to recently published observations of a planet candidate. Finally, the simulations show that deconvolution of coronagraphic data may indeed produce artificial patterns within the image of a disk.