A common goal of many watermarking techniques is to produce a mark that remains detectable after the geometric transformations of Rotation, Scale and Translation; also known as RST invariance. We present a simple approach to achieving RST invariance using pixel-by-pixel addition of oscillating homogeneous patterns known as Logarithmic Radial Harmonic Functions [LRHFs]. LRHFs are the basis functions of the Fourier-Mellin transform and have perfect correlation, orthogonality, and spread-spectrum properties. Once the patterns have been embedded in an image they can be detected directly regardless of RST and with great sensitivity by correlation with the corresponding complex LRHFs. In contrast to conventional methods our approach is distinguished by the utilization of signal phase information and the absence of interpolation artifacts. Data encoding is based on the information in the relative centre positions of multiple spatially overlapping patterns.