Fig. 1.

A. During imaging of the sample (green slab) at 0 degree tilt, objects at the positions marked by the blue and green circles have a defocus of d - Δ, while one at the position of the red circle has a defocus of d + Δ. When imaged at 60 degree tilt, the blue position has a defocus d - 2Δ, the green position has defocus of d - Δ, and the red position d + 2Δ. These objects are projected into an image. B. In this example, a defocus step of Δ is used, so each tilt image is CTF corrected seven times in steps of Δ, to give images #1 (d − 3Δ) to #7 (d + 3Δ). C. During back projection to generate the reconstruction volume (green cuboid), the blue voxel, corresponding to the position of the blue circle in A, will be reconstructed using image #3 at 0 degrees, and image #2 at 60 degrees; the green voxel, corresponding to the position of the green circle in A, will be reconstructed using image #3 at 0 degrees, and image #3 at 60 degrees; while the red voxel will be reconstructed using image #5 at 0 degrees, and image #6 at 60 degrees. Note that the reconstruction volume should be positioned such that its center has defocus d. This will be approximately the case if the center of mass corresponds to the center of the tomogram. If this is not the case, an additional defocus shift can be applied. D. Cartoon illustrating the defocus array. The defocus array is three-dimensional, with axes corresponding to x, z and tilt angle, and stores indices of images that should be used to reconstruct each voxel.