Electron tomography in conical tilt geometry. The accuracy of a direct Fourier method (DFM) and the suppression of non-tomographic noise

SPARK is a direct Fourier method (DFM) to reconstruct 3D structures from projections observed in the electron microscope. It is suitable for both single axis tilting and random conical tilting. The present article reports accuracy tests performed in reconstructing phantom structures from analytical projections in conical tilt geometry, both noise-free and corrupted with noise. Statistical reliability indices, similar to those used in X-ray crystallography, are proposed and reported for all tests. Phase agreement tests are discussed in connection with the possibility of determining the internal consistency of data without dividing projections into two sets and are presented for the reconstructions of phantoms and of a haematic pigment. The mathematical formulation of the 3D Fourier transform of an ordered stack of projections is illustrated. With conical tilt geometry, the transform is almost zero within an elliptic cone. This property is exploited to suppress “non-tomographic noise” (NTN) and to recover missing projections in a POCS-like implementation. The suppression of non-tomographic noise, which is possible even if reconstructions are done by back-projection methods, allows one to push low-pass filtering to a higher frequency and to achieve improved resolution.