The mid-IR (8.5−13 μm) spectral indices in f_ν are plotted in red against normalized half-light radii R_1/2/R_in at 13 μm. Also plotted in purple are spectral indices between 2.2 and 13 μm against thin-ring radii at 2.2 μm normalized by R_in. For the four objects without near-IR interferometry data, we indicated the near- to mid-IR spectral indices in dashed lines over the thin-ring radius range of 1−2 R_in, roughly expected based on other targets observed with the Keck interferometer (see Fig. 7). The dotted line shows the grid for a simple power-law model with radial surface density index α of (−2.0, −1.0, −0.0) and temperature index β of (−0.5, −0.4, −0.3) with the innermost tempeture T_in = 1400 K. The grid covers the observed range of R_1/2/R_in, but systematically bluer in spectral shape. The dashed lines show the same grid but with T_in = 700 K, which apparently matches the mid-IR observations over the sample when the density index ranges from  ~− 1 to 0 in different objects with a temperature index of  ~− 0.35 ± 0.05 (for details, see Sect. 4.4).