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The bright regions in the solar chromosphere and temperature minimum have agood spatial correspondence with regions of intense photospheric magneticfield. Their observation started more than a hundred years ago with theinvention of the spectroheliograph. While the historical spectroheliograms areessential for studying the long-term variability of the Sun, the modernsatellite-borne observations can help us reveal the nature of chromosphericbrightenings in previously unattainable detail. Our aim is to improve theunderstanding of the relation between magnetic fields and radiative structuresby studying modern seeing-free observations of far-ultraviolet (FUV) radiationaround 1600 \r{A} and photospheric magnetic fields. We used Helioseismic andMagnetic Imager (HMI) observations of photospheric magnetic fields andAtmospheric Imaging Assembly (AIA) observations of FUV contrast around 1600\r{A}. We developed a robust method to find contrast thresholds defining brightand dark AIA 1600 \r{A} pixels, and we combine them to bright and darkclusters. We investigate the relation of magnetic fields and AIA 1600 \r{A}radiation in bright and dark clusters. We find that the percentage of brightpixels entirely explains the observed variability of 1600 \r{A} emission. Wedeveloped a multilinear regression model based on the percentages of bright anddark pixels, which can reliably predict the magnitude of the disk-averagedunsigned magnetic field. We find that bright and dark clusters closelycorrespond respectively to the populations of moderate (B > 55 G) and strong (B> 1365 G) magnetic field HMI clusters. The largest bright clusters have aconstant mean unsigned magnetic field, as found previously for Ca II K plages.However, the magnetic field strength of bright clusters is 254.7$\pm$0.1 G,which is roughly 100 G larger than found earlier for Ca II K plages.

Reconstructing solar magnetic fields from historical observations VIII. AIA 1600 {\AA} contrast as a proxy of solar magnetic fields