We have accurately determined the absorptance of three pyrheliometer cavities at 532 nm by measuring the residual reflectance using an angle-resolved bidirectional reflectometer. Measurements were performed at a normal incidence as a function of the viewing angle and position on the cavity cone. By numerically integrating the measured angle-resolved scatter over both the direction and position and accounting for an obstructed view of the cavity, we determined that the effective cavity reflectance was between 8×10-4 and 9×10-4. Thus, the absorptance of the three cavities ranged from 0.99909±0.00014 to 0.99922±0.00012 (k=2 combined expanded uncertainties). These measurements, when extended over the spectral range of operation of the pyrheliometer, are required to establish SI traceability for absolute solar irradiance measurements.