We introduce a rapid data acquisition and reconstruction method to image the crystalline structure of materials and associated strain and orientations at micrometer resolution using Laue diffraction. Our method relies on scanning a coded-aperture across the diffracted x-ray beams from a broadband illumination, and a reconstruction algorithm to resolve Laue microdiffraction patterns as a function of depth along the incident illumination path. This method provides a rapid access to full diffraction information at sub-micrometer volume elements in bulk materials. Here we present the theory as well as the experimental validation of this imaging approach.