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The two galaxies were discovered in the mid-nineties by Renee Kraan-Korteweg and collaborators when they used the Dwingeloo dish to do a survey called DOGS (Dwingeloo Obscured Galaxy Survey) with the aim to find galaxies hidden behind the Milky Way. The gas and dust in the Milky Way absorbs optical light, so objects that are behind the Milky Way are very hard to see with normal telescopes. However, the Milky Way is transparent for radio waves, so radio telescopes can see right through it and galaxies behind the Milky Way are easily spotted.
Actually, only Dwingeloo 1 was discovered with the Dwingeloo dish. The Dwingeloo dish has very low resolution, it can cannot distinguish objects that are close to each other. So when later Dwingeloo 1 was observed with the WSRT to study the galaxy in detail, it turned out that there was a second, smaller galaxy, right next to Dwingeloo 1. It was named Dwingeloo 2, but perhaps that should have been Westerbork 1...
The left image shows the atomic hydrogen of Dwingeloo 1 and 2 as seen by the 'old' WSRT, the right image as seen with Apertif.