Although, today, perpendicular magnetic recording receives substantial attention in the data storage industry, still conventional longitudinal readers (LR) are commonly used in perpendicular recording. Such a system cannot offer the optimal resolution because the LR is designed so that it is dominantly sensitive to the longitudinally written magnetization transitions. In this paper, the conformal mapping (CM) technique is used to develop a theory, which defines the guidelines on how to design an optimal perpendicular reader (PR), which is best suited for perpendicular recording. Schwartz-Christoffel transformation was used to find the requirements for optimal PR designs for providing the playback waveforms identical to the waveforms. provided by an equivalent LR in longitudinal recording. To support the theoretical conclusions, 3D boundary element modeling was developed to calculate the sensitivity field profiles for the yoke type PR and the conventional LR.