Adaptive optics (AO) methods are widely used in microscopes to improve image quality through correction of phase aberrations. A range of wavefront-sensorless AO schemes exist, such as modal, pupil segmentation zonal, and pixelated piston-based methods. Each of these has a different physical implementation that makes direct comparisons difficult. Here, we propose a framework that fits in all sensorless AO methods and facilitates systematic comparisons among them. We introduce a general model for the aberration representation that encompasses many existing methods. Through modeling and experimental verification in a two-photon microscope, we compared sensorless AO schemes with a range of aberration representations to correct both simulated and sample induced aberrations. The results show that different representations can provide a better basis for correction in different experimental scenarios, which can inform the choice of sensorless AO schemes for a particular application.