  We present and analyse SO and SO$_2$, recently observed with high angular
resolution and sensitivity in a spectral line survey with ALMA, for two
oxygen-rich AGB stars: the low mass-loss rate R Dor and high mass-loss rate IK
Tau. We analyse 8 lines of SO detected towards both stars, 78 lines of
SO$_2$detected towards R Dor and 52 lines of SO$_2$ detected towards IK Tau. We
detect several lines of $^{34}$SO, $^{33}$SO and $^{34}$SO$_2$ towards both
stars, and tentatively S$^{18}$O towards R Dor, and hence derive isotopic
ratios for these species. The spatially resolved observations show us that the
two sulphur oxides are co-located towards R Dor and trace out the same wind
structures in the circumstellar envelope (CSE). Much of the emission is well
reproduced with a Gaussian abundance distribution spatially centred on the
star. Emission from the higher energy levels of SO and SO$_2$ towards R Dor
provide evidence in support of a rotating inner region of gas identified in
earlier work. The new observations allow us to refine the abundance
distribution of SO in IK Tau derived from prior observations with single
antennas, and confirm the distribution is shell-like with the peak in the
fractional abundance not centred on the star. The confirmation of different
types of SO abundance distributions will help fine-tune chemical models and
allows for an additional method to discriminate between low and high mass-loss
rates for oxygen-rich AGB stars.
