The techniques of patterned excitation microscopy (PEM, also referred to in the literature as structured illumination, harmonic excitation light microscopy, or laterally modulated excitation microscopy), has recently been extended to the non-linear regime, permitting a further increase in resolution breaking the Abbe diffraction limit (saturated PEM, saturated patterned excitation microscopy (SPEM)). Fluorescence saturation was suggested as the non-linear effect employed to achieve this aim. Here a two-dimensional extension of the linear and the non-linear patterned excitation technique is introduced and simulations of the expected resolution improvement are presented. The simulations account for photon statistics, a sub-optimal degree of modulation and a high amount of background fluorescence in the sample. The resulting point-spread-functions achieve a full width at half maximum of 215 nm (widefield), 118 nm (linear PEM), and 57 nm (saturated PEM, 9×9 orders). For higher resolution, an increased number of detected photons and of raw data images are required. A potential method for substantially decreasing the required number of raw images in PEM and SPEM is discussed.