We estimate the typical spectrum of spatial fluctuations of intensity due to the penumbral filaments. High angular resolution continuum images are used (cut-off frequencies equivalent to 0.28" wavelength of about 5257 Å). The amplitude of the observed spectra follows the modulation transfer function of our optical system. In other words, the spectrum of real penumbral fluctuations seems to be flat up to the higher observable spatial frequency. We expect it to continue far beyond the artificial instrumental cutoff, which implies that the structure of the penumbra remains unresolved to the present solar observations.