Ratio between the power spectrum of the derivative images (averaged over the four directions) computed by CuTEx and the power spectra of the intensity image for SPIRE 250 μm as a function of spatial scale expressed in arcseconds and in pixels (upper x axis). Each colour corresponds to a different map;black to the l037, red to the l039, blue to the l041, green to the l046, and yellow to the l048 field. All the functions overlap for scales larger than the PSF, indicated as a dark grey dashed line, and decrease following a power law with an exponent ~–3.9. The black dot-dashed line indicates the scale at which the transfer function is equal to unity. Scales smaller than this result in an overall amplification in the second derivative maps. The light grey dot-dashed line traces the scale above which the extended sources become confused with the background in the derivative image. This value corresponds approximately to ~3 times the PSF. Similar plots are found for other wavelengths, and the functions completely overlap when the spatial scales are expressed in pixels.
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