Relaxation of the Crowther criterion in multislice tomography

For objects larger than the depth of focus of an imaging system, one must account for wavefield propagation effects within the object as is done in diffraction tomography, diffraction microscopy, and multislice ptychographic tomography. We show here that if the imaging method used reconstructs N _a planes along each viewing direction, one can reduce the number of illumination directions required to fill Fourier space by a factor of 1∕N _a, relaxing the usual Crowther criterion for tomography. This provides a conceptual basis to explain two recent experiments where multiple axial planes were imaged per viewing direction, and tomographic images were obtained with good 3D spatial resolution, even though fewer illumination directions were used than one would have expected from the Crowther criterion.