# Can angular information be known more precisely than the diffraction limit?

The diffraction limit deals with the ability to determine if two things are separate. I am interested in the ability to find the the centroid of a single object.

Imagine a star with no near neighbors would it be possible to determine the centroid of that star at a resolution higher than the diffraction limit?

The star is essentially a point source and I wonder if looking at the edges of the airy disk would allow a centroid to be determined if I had a magical camera with infinite pixels.

It seems to me that I should be able to see the disk and then calculate a centroid that is smaller than the airy disk.

Yes, Gaia makes extensive use of this technique.

The measurement accuracy of star positions for the brightest stars is 10 to 20 micro- arcseconds – up to 100 times better than that the precursor mission, Hipparcos; this angular resolution corresponds to the observed diameter of a Euro coin on the Moon, viewed from Earth.

The underlying principle is the standard deviation of the mean. It depends on the sample size, more precisely on the square root of the sample size. In this case the sample size is the number of the measured photons. Therefore it works better for bright stars.