Transmit-arrays have been mostly used for beam collimation applications, either with fixed or scanning beam capability. But transmit-arrays can also be used to synthesize power radiation patterns complying with power pattern templates. A new analytical formulation is presented here to obtain a phase-only correction function corresponding to a given power template. The transmit-array transforms the known power radiation pattern of the primary source into a desired output power pattern. The proposed formulation, specialized for axial-symmetric structures, is based on Geometrical Optics and provides the solution directly from the evaluation of two closed-form first-order differential equations. As a proof of concept, a sec2 with a roll-off at 45º is defined as the target power pattern, at the 30 GHz Ka-band. A 10.8 dBi radiation pattern with circular polarization is used to illuminate a 180 mm × 180 mm transmit-array with 60 mm focal distance. Previously designed 3.35 mm thick phase-delay unit-cells are used as an example to implement the calculated phase distribution over the transmit-array aperture. The measured antenna radiation pattern matches quite well the template, with a steep fall of the radiation at the roll-off angle and low cross-polarization. This validates the concept, the formulation and the fabricated prototype.