A theoretical foundation is given for the ability of programmed-probe based aberration targets to measure individual Zernike terms. The optimum targets are inverse Fourier transforms of the Zernikes and this allows the main features of the family of targets to be predicted in advance. Simulation of discretized versions shows an impressive 27%-36% increase, per 0.01 lambda of rms aberration, in the intensity at the center of the target relative to the clear field intensity. The cross contamination by other targets is about 1/6 as large and it is thus possible to measure spherical aberration independent of focus.