2D histograms of the vertical magnetic field (at log τ = −0.9) and of the continuum intensity in two sunspots, the large spot AR 10923 observed on 14 November 2006 (left) and the small spot AR 11041 observed on 26 January 2010 (right). The histograms are plotted on a logarithmic scale. The dashed horizontal line at 150 G (i.e., the penumbral filaments) indicates the position of a horizontal cut across the histograms, which are shown in the left panel of Fig. 5. The vertical lines (at I_C = 0.30, 0.475, 0.60, and 0.80) mark the position of vertical cuts (shown in Fig. 6). The red circles show the position of the maximum of the part of the histogram that is affected by the filaments. See text for more details.