Penumbral structure at 0".1 resolution -: I.: General appearance and power spectra

We analyse sunspot filtergrams of unprecedented quality obtained by Scharmer et al. (2002) with the Swedish 1-m Solar Telescope on La Palma. The observations comprise images in three different wavelength bands: 488, 436, and 430 nm (G-band). We find that there are still unresolved penumbral filaments which must have widths smaller than 80 km. The fine structuring along the filaments is limited. Penumbral grains have internal structure and look like they are split or crossed by narrow dark structures. We calculate intensity power spectra of the penumbra from images that are corrected for seeing using the Phase Diversity technique. The effects of high order aberrations that are not corrected for are estimated to be too low to be consistent with a flat power spectrum. The penumbral power spectra do not show any signs of bumps or peaks that could correspond to a preferred scale at 0."35 for the width of penumbral filaments. We argue that the power spectrum is not a very reliable source of information concerning preferred scales.