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We compare the absolute gain photometric calibration of the Planck/HFI andHerschel/SPIRE instruments on diffuse emission. The absolute calibration of HFIand SPIRE each relies on planet flux measurements and comparison withtheoretical far-infrared emission models of planetary atmospheres. We measurethe photometric cross calibration between the instruments at two overlappingbands, 545 GHz / 500 $\mu$m and 857 GHz / 350 $\mu$m. The SPIRE maps used havebeen processed in the Herschel Interactive Processing Environment (Version 12)and the HFI data are from the 2015 Public Data Release 2. For our study we used15 large fields observed with SPIRE, which cover a total of about 120 deg^2. Wehave selected these fields carefully to provide high signal-to-noise ratio,avoid residual systematics in the SPIRE maps, and span a wide range of surfacebrightness. The HFI maps are bandpass-corrected to match the emission observedby the SPIRE bandpasses. The SPIRE maps are convolved to match the HFI beam andput on a common pixel grid. We measure the cross-calibration relative gainbetween the instruments using two methods in each field, pixel-to-pixelcorrelation and angular power spectrum measurements. The SPIRE / HFI relativegains are 1.047 ($\pm$ 0.0069) and 1.003 ($\pm$ 0.0080) at 545 and 857 GHz,respectively, indicating very good agreement between the instruments. Theserelative gains deviate from unity by much less than the uncertainty of theabsolute extended emission calibration, which is about 6.4% and 9.5% for HFIand SPIRE, respectively, but the deviations are comparable to the values 1.4%and 5.5% for HFI and SPIRE if the uncertainty from models of the commoncalibrator can be discounted. Of the 5.5% uncertainty for SPIRE, 4% arises fromthe uncertainty of the effective beam solid angle, which impacts the adoptedSPIRE point source to extended source unit conversion factor (Abridged)

Comparison of absolute gain photometric calibration between Planck/HFI and Herschel/SPIRE at 545 and 857 GHz