Optical see-through augmented reality (AR) systems are a next-generation computing platform that offer unprecedented user experiences by seamlessly combining physical and digital content. Many of the traditional challenges of these displays have been significantly improved over the last few years, but AR experiences offered by today's systems are far from seamless and perceptually realistic. Mutually consistent occlusions between physical and digital objects are typically not supported. When mutual occlusion is supported, it is only supported for a fixed depth. We propose a new optical see-through AR display system that renders mutual occlusion in a depth-dependent, perceptually realistic manner. To this end, we introduce varifocal occlusion displays based on focus-tunable optics, which comprise a varifocal lens system and spatial light modulators that enable depth-corrected hard-edge occlusions for AR experiences. We derive formal optimization methods and closed-form solutions for driving this tunable lens system and demonstrate a monocular varifocal occlusion-capable optical see-through AR display capable of perceptually realistic occlusion across a large depth range.