Methods of investigating a specimen using tomographic imaging include directing a beam of radiation through a specimen and onto a detector, thereby generating an image of the specimen. The directing is repeated for different specimen orientations relative to the beam, thereby generating a corresponding set of images. An iterative mathematical reconstruction technique is used to convert the images into a tomogram. The reconstruction is mathematically constrained to curtail a solution space using three-dimensional SEM imagery of at least a part of the specimen that overlaps the tomogram by requiring iterative results of the reconstruction to be consistent with pixel values derived from the SEM imagery.