The resolution of optical microscopy is limited by the numerical aperture and the wavelength of light. Many strategies for improving resolution such as 4Pi and I⁵M have focused on an increase of the numerical aperture. Other approaches have based resolution improvement in fluorescence microscopy on the establishment of a nonlinear relationship between local excitation light intensity in the sample and in the emitted light. However, despite their innovative character, current techniques such as stimulated emission depletion (STED) and ground-state depletion (GSD) microscopy require complex optical configurations and instrumentation to narrow the point-spread function. We develop the theory of nonlinear patterned excitation microscopy for achieving a substantial improvement in resolution by deliberate saturation of the fluorophore excited state. The post acquisition manipulation of the acquired data is computationally more complex than in STED or GSD, but the experimental requirements are simple. Simulations comparing saturated patterned excitation microscopy with linear patterned excitation microscopy (also referred to in the literature as structured illumination or harmonic excitation light microscopy) and ordinary widefield microscopy are presented and discussed. The effects of photon noise are included in the simulations.