And you shall know them by their color-color diagrams

Imagine this situation:

You're trying to find an astronomical object. It looks, at first glance, like an ordinary star; It's a bright point source. But to make sure you don't have it easy, this object (or perhaps many of this object) is hidden amongst a field of tens to hundreds of thousands of genuine stars. How do you pick them out?

This is the problem that astronomers have when trying to pick out Active Galactic Nuclei behind clusters or other galaxies. Active Galactic Nuclei (AGNs) are, as the name describes, the cores of unusually energetic galaxies.

While they're useful in their own right to constrain models of galactic evolution and cosmology, they can also be important as background sources to study foreground ones. Since AGNs are broadly similar, we can characterize their spectrum. If that light then passes through a foreground galaxy or cluster, the foreground object will modify the light in ways that can allow us to analyze the makeup of that object. Additionally, since they're so far away, they have no apparent motion and as such, can be used as static markers to map out the minute motions of other (nearby) objects.

So finding AGNs that are behind objects we'd like to study is a very useful tool. But since they're often so far away, they look just like stars until you start breaking down the spectrum. But doing a full spectrographic study of every object when you're looking for AGNs is not practical since spectroscopy takes a relatively long time.

But that's why astronomers developed photometry. It's a quick and dirty way of getting a lot of the same information.

This recent study built on previous work suggesting that by comparing the differences in various filters in the right way, it would be possible to weed out most of the stars, leaving only the AGNs.

Applying this technique, the group singled out nearly 5,000 probably AGNs behind the Large Magellanic Cloud. Of course, the method does can be fooled. Stars enshrouded in dust like late Asymptotic Giant Branch stars or ones encased in Planetary Nebulae can end up in the same color region.

But still, this method filters out a significant number of the stars leaving only a few to be sorted out.

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Kozłowski, S., & Kochanek, C. (2009). DISCOVERY OF 5000 ACTIVE GALACTIC NUCLEI BEHIND THE MAGELLANIC CLOUDS The Astrophysical Journal, 701 (1), 508-513 DOI: 10.1088/0004-637X/701/1/508