New infinite product identities are given, based on summed visible (from the origin) point vectors. Each result is found from summing on vpv lattices dividing space into radial regions from the origin. Recently, Baake et al. and Mosseri considered the 2-D visible lattice points as part of an optical experiment in which so-called Optical Fourier Transform was applied. Many of the techniques exposed by Glasser and Zucker, and Ninham et al. involving Mellin and Möbius inversions are also applicable to the current paper.