Comparison of the η-PDFs produced from the column density images of Herschel/HOBYS covering W43-Main (25″ beam, without W43-MM1, gray-shaded histogram) and of ALMA-IMF toward W43-MM2&MM3 (0.51″ × 0.40″ beam, colored histograms). Panel a: Determination of the background column density of W43-MM2&MM3 that best reconciles the ALMA and Herschel η-PDFs: 0.7 × 10²³ cm⁻². The η-PDFs are built with this column density offset (blue histogram) and the lower and upper limits of the offset uncertainty (yellow and red histograms, respectively). The Herschel η-PDF has been multiplied by 15 to emphasize its relative agreement with the ALMA η-PDF. Panel b: η-PDF tails of Herschel/HOBYS and ALMA-IMF with consistent power-law indices: (dotted black segment) and (continuous red segment). The first η-PDF tail with power-law index s₁ (continuous black segment) is only traced by the Herschel image; the third tail with power-law index s₃ (dotted red segment) is only traced by ALMA.