Light microscopy of thick biological samples, such as tissues, is often limited by aberrations caused by refractive index variations within the sample itself. This problem is particularly severe for live imaging, a field of great current excitement due to the development of inherently fluorescent proteins. We describe a method of removing such aberrations computationally by mapping the refractive index of the sample using differential interference contrast microscopy, modeling the aberrations by ray tracing through this index map, and using space-variant deconvolution to remove aberrations. This approach will open possibilities to study weakly labeled molecules in difficult-to-image live specimens.