This paper investigates a new approach to minimize dependency of absorbance on the angle of incidence (thetas) and polarization angle (φ) for frequency selective surfaces (FSS) absorbers based on previous theoretical analysis of single rectangular and circular patch antennas. It is shown how when a single antenna is treated as a unit cell in a FSS absorber its performance preserves key features. The absorbance pattern of incident TE and TM polarized radiation on the FSS absorber is comparable to the power radiation pattern of a single antenna in the H-plane and the E-plane respectively. Based on this concept an FSS absorber of hollow hemispherical unit cells is proposed to maintain the absorbance of both incident TE and TM modes above 50% for all thetas  80°. The outcome of this work can aid in optimising angular stability and polarization insensitivity of FSS absorbers by adopting previous studies of beam-width enhancement in antenna arrays to FSS absorbers.