Context : For many years , there seemed to be significant differences between the continuum intensity distributions derived from observations and simulations of the solar photosphere .

Aims : In order to settle the discussion on these apparent discrepancies , we present a detailed comparison between simulations and seeing-free observations that takes into account the crucial influence of instrumental image degradation .

Methods : We use a set of images of quiet Sun granulation taken in the blue , green and red continuum bands of the Broadband Filter Imager of the Solar Optical Telescope ( SOT ) onboard Hinode .
The images are deconvolved with Point Spread Functions ( PSF ) that account for non-ideal contributions due to instrumental stray-light and imperfections .
In addition , synthetic intensity images are degraded with the corresponding PSFs .
The results are compared with respect to spatial power spectra , intensity histograms , and the centre-to-limb variation of the intensity contrast .

Results : The intensity distribution of SOT granulation images is broadest for the blue continuum at disc-centre and narrows towards the limb and for longer wavelengths .
The distributions are relatively symmetric close to the limb but exhibit a growing asymmetry towards disc-centre .
The intensity contrast , which is connected to the width of the distribution , is found to be ( 12.8 \pm 0.5 ) % , ( 8.3 \pm 0.4 ) % , and ( 6.2 \pm 0.2 ) % at disc-centre for blue , green , and red continuum , respectively .
Removing the influence of the PSF unveils much broader intensity distributions with a secondary component that is otherwise only visible as an asymmetry between the darker and brighter than average part of the distribution .
The contrast values increase to ( 26.7 \pm 1.3 ) % , ( 19.4 \pm 1.4 ) % , and ( 16.6 \pm 0.7 ) % for blue , green , and red continuum , respectively .
The power spectral density of the images exhibits a pronounced peak at spatial scales characteristic for the granulation pattern and a steep decrease towards smaller scales .
The observational findings like the absolute values and centre-to-limb variation of the intensity contrast , intensity histograms , and power spectral density are well matched with corresponding synthetic observables from three-dimensional radiation ( magneto- ) hydrodynamic simulations .

Conclusions : We conclude that the intensity contrast of the solar continuum intensity is higher than usually derived from ground-based observations and is well reproduced by modern radiation ( magneto- ) hydrodynamic models .
Properly accounting for image degradation effects is of crucial importance for comparisons between observations and numerical models .