1. Department of Physics & Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104, USA
2. School of Physics & Astronomy, Cardiff University, 5 The Parade, Cardiff CF24 3AA, UK
3. Instituto Nacional de Astrofísica Óptica y Electrónica, Aptdo. Postal 51 y 72000 Puebla, Mexico
4. Jet Propulsion Laboratory, Pasadena, California 91109-8099, USA
5. Department of Physics & Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, British Columbia V6T 1Z1, Canada
6. Department of Physics, University of Miami, 1320 Campo Sano Drive, Coral Gables, Florida 33146, USA
7. Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St George Street, Toronto, Ontario M5S 3H8, Canada
8. Department of Astronomy & Astrophysics, University of Toronto, 50 St George Street, Toronto, Ontario M5S 3H4, Canada
9. Department of Physics, University of Toronto, 60 St George Street, Toronto, Ontario M5S 1A7, Canada
10. University of Puerto Rico, Rio Piedras Campus, Physics Department, Box 23343, UPR Station 00931, Puerto Rico
11. INAF – Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, I-50125 Firenze, Italy
12. Université Paris Diderot, Laboratoire APC, 10 rue Alice Domon et Léonie Duquet, 75205 Paris, France
13. Department of Physics, Brown University, 182 Hope Street, Providence, Rhode Island 02912, USA

Correspondence to: Mark J. Devlin¹ Correspondence and requests for materials should be addressed to M.J.D. (Email: devlin@physics.upenn.edu).

Submillimetre surveys during the past decade have discovered a population of luminous, high-redshift, dusty starburst galaxies^{1, 2, 3, 4, 5, 6, 7, 8}. In the redshift range 1  z  4, these massive submillimetre galaxies go through a phase characterized by optically obscured star formation at rates several hundred times that in the local Universe. Half of the starlight from this highly energetic process is absorbed and thermally re-radiated by clouds of dust at temperatures near 30 K with spectral energy distributions peaking at 100 m in the rest frame⁹. At 1  z  4, the peak is redshifted to wavelengths between 200 and 500 m. The cumulative effect of these galaxies is to yield extragalactic optical and far-infrared backgrounds with approximately equal energy densities. Since the initial detection of the far-infrared background (FIRB)¹⁰, higher-resolution experiments have sought to decompose this integrated radiation into the contributions from individual galaxies. Here we report the results of an extragalactic survey at 250, 350 and 500 m. Combining our results at 500 m with those at 24 m, we determine that all of the FIRB comes from individual galaxies, with galaxies at z  1.2 accounting for 70% of it. As expected, at the longest wavelengths the signal is dominated by ultraluminous galaxies at z > 1.

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