The Spectral and Photometric Imaging Receiver on-board Herschel has been carrying out deep extragalactic surveys, one of the aims of which is to establish spectral energy distributions of individual galaxies spanning the infrared/submillimetre (IR/SMM) wavelength region. We report observations of the IR/SMM emission from the Lockman North field and Great Observatories Origins Deep Survey Field-North. Because galaxy images in the wavelength range covered by Herschel generally represent a blend with contributions from neighbouring galaxies, we present sets of galaxies in each field, especially free of blending at 250, 350 and 500 μm. We identify the cumulative emission of these galaxies and the fraction of the FIR cosmic background radiation they contribute. Our surveys reveal a number of highly luminous galaxies at redshift z≲ 3 and a novel relationship between IR and visible emission that shows a dependence on luminosity and redshift.