Introduction of adaptive optics technology into astronomy and ophthalmology has made great contributions in these fields, allowing one to recover images blurred by atmospheric turbulence or aberrations of the eye. Similar adaptive optics improvement in microscopic imaging is also of interest to researchers using various techniques. Current technology of adaptive optics typically contains three key elements: wavefront sensor, wavefront corrector and controller. These hardware elements tend to be bulky, expensive, and limited in resolution, involving, e.g., lenslet arrays for sensing or multi-acuator deformable mirrors for correcting. We have previously introduced an alternate approach to adaptive optics based on unique capabilities of digital holography, namely direct access to the phase profile of an optical field and the ability to numerically manipulate the phase profile. We have also demonstrated that direct access and compensation of the phase profile is possible not only with the conventional coherent type of digital holography, but also with a new type of digital holography using incoherent light: self-interference incoherent digital holography (SIDH). The SIDH generates complex – i.e. amplitude plus phase – hologram from one or several interferograms acquired with incoherent light, such as LEDs, lamps, sunlight, or fluorescence. The complex point spread function can be measured using a guide star illumination and it allows deterministic deconvolution of the full-field image. We present experimental demonstration of aberration compensation in holographic fluorescence microscopy using SIDH. The adaptive optics by SIDH provides new tools for improved cellular fluorescence microscopy through intact tissue layers or other types of aberrant media.