  We used a new realistic 3D radiative-hydrodynamical model atmosphere of
Procyon generated with the Stagger Code and synthetic spectra computed with the
radiative transfer code Optim3D to re-analyze interferometric and spectroscopic
data from the optical to the infrared of Procyon. We compute intensity maps in
two optical filters centered at 500 and 800 nm (MARK III) and one infrared
filter centered at 2200 nm (VINCI). We constructed stellar disk images
accounting for the center-to-limb variations and used them to derive visibility
amplitudes and closure phases. We provide 3D limb-darkening coefficients in the
optical as well as in the infrared. We show that visibility curves and closure
phases show clear deviations from circular symmetry from the 3rd lobe on. These
deviations are detectable with current interferometers using closure phases. We
derive new angular diameters at different wavelengths with two independent
methods based on 3D simulations. We find a diameter_Vinci = 5.390 \pm 0.03 mas
that this is confirmed by an independent asteroseismic estimation. The
resulting Teff is 6591 K, which is consistent with the infrared flux method
determinations. We find also a value of the surface gravity log g = 4.01 \pm
0.03 that is larger by 0.05 dex from literature values. Spectrophotometric
comparisons with observations provide very good agreement with the spectral
energy distribution and photometric colors, allowing us to conclude that the
thermal gradient of the simulation matches fairly well Procyon. Finally, we
show that the granulation pattern of a planet hosting Procyon-like star has a
non-negligible impact on the detection of hot Jupiters in the infrared using
interferometry closure phases. It is then crucial to have a comprehensive
knowledge of the host star to directly detect and characterize hot Jupiters. In
this respect, RHD simulations are very important to reach this aim.
