The cosmic microwave background (CMB) has provided a precise template for features in the linear power spectrum: the matter-radiation turnover, sound horizon drop, and acoustic oscillations. In a two dimensional power spectrum in redshift and angular space, the features appear as distorted rings, and yield simultaneous, purely geometric, measures of the Hubble parameter H(z) and angular diameter distance D_A(z) via an absolute version of the Alcock-Paczynski test. Employing a simple Fisher matrix tool, we explore how future surveys can exploit these rings of power for dark energy studies. High-z CMB determinations of H and D_A are best complemented at moderate to low redshift (z < 0.5) with a population of objects that are at least as abundant as clusters of galaxies. We find that a sample similar to that of the ongoing SDSS Luminous Red Galaxy (LRG) survey can achieve statistical errors at the ~5% level for D_A(z) and H(z) in several redshift bins. This, in turn, implies errors of sigma(w)=0.03-0.05 for a constant dark energy equation of state in a flat universe. Deep galaxy cluster surveys such as the planned South Pole Telescope (SPT) survey, can extend this test out to z~1 or as far as redshift followup is available. We find that the expected constraints are at the sigma(w)=0.04-0.08 level, comparable to galaxies and complementary in redshift coverage.

8 pages, 5 figures submitted to PRD