Conventional display systems based on integral imaging (InI) suffer from a major tradeoff between depth of field and spatial resolution. In this Letter, a new, to the best of our knowledge, a method for an InI-based light field display with an extended depth of field is proposed, where a digitally switchable multi-focal micro lens array can yield a depth of field spanning a depth range from zero to over three diopters without sacrificing either spatial resolution or form factor. A high optical performance display prototype was built and demonstrated with printed aperture arrays as a substitute for a custom-designed programmable shutter array that is still under construction.