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The construction is described of a monolithic thick-crystal perfect silicon neutron interferometer using an ultra-high-precision grinding technique and a combination of annealing and chemical etching that differs from the construction of prior neutron interferometers. The interferometer is the second to have been annealed after machining and the first to be annealed prior to chemical etching. Monitoring the interference signal at each post-fabrication step provides a measurement of subsurface damage and its alleviation. In this case, the strain caused by subsurface damage manifests itself as a spatially varying angular misalignment between the two relevant volumes of the crystal and is reduced from ∼10−5 rad to ∼10−9 rad by way of annealing and chemical etching.