LensClean - an algorithm for inverting extended, gravitationally lensed images with application to the radio ring lens PKS 1830-211

We develop a new algorithm, LensClean, based on the Clean algorithm of radio astronomy, for consistently inverting partially or poorly resolved gravitational lens systems. The method is superior to previous algorithms, particularly when there is inadequate resolution in the observed image, and is significantly more effective at discriminating between good and bad lens models. We have applied LensClean to the 1. 7 GHz Merlin and 8 GHz VLA maps of the radio ring lens PKS 1830 - 211. The quality of the inversions is largely limited by systematic errors in the radio maps, primarily the varying flux ratio of the two compact components. We estimate that the critical radius of the lens in PKS 1830-211 is b = 0. 51", the dimensionless ellipticity is γ = 0. 050, and the position angle of the major axis of the lens potential is -2ᵈeg^. The 99% confidence limits on the lens parameters, based on inversions of both the Merlin and VLA maps, are 0. 48" <b < 0. 52", 0. 04 < γ < 0. 08, and -11ᵈeg^ < P. A. < 11ᵈeg^.