Figure 4.

Examinations with the general model shown in Fig. 5a using the basic reconstruction procedure and the improved procedure with a single base tilt angle (Θ). (a–c) Results for the nearly ideal conditions (tilt-angle range ± 90° with 5° steps) using the basic procedure. (a) Initial error map. (b) Reconstructed result of an artificial granular image created with many QU dots. (c) Final error map showing a granular distribution due to a discrete fine QU dots arrangement. Even with the full tilt-angle range, the basic procedure fails in reconstruction of the general model. (d–f) Results for the missing wedge case (tilt-angle range ± 70° with 5° steps) using the basic procedure. (d) Initial error map. (e) Similar reconstruction of an artificial wave-like granular image. (f) Final error map of the remaining errors, especially outside the model structure with a granular distribution inside the structure due to discrete fine QU dots (see centre inset of the amplified partial map). For a limited tilt-angle range, the result (e) is drastically degraded compared to (b). (g–i) Results for the same missing wedge case using the improved procedures with a single base tilt angle (Θ = 0°) is used. (g) Reconstruction in the image definition of $32\times 32$ pixels (QU piece size is 16 pixels). (h) Final reconstruction is clearly improved compared to (e), although some mosaic-like patterns are shown. (i) Final error map contains errors (see arrows) due to the incomplete mosaic-like patterns. Improved procedures to change the size of QU piece, large (32 pixels square as a standard case) to fine (1 pixel), in an iterative reconstruction manner and refinement of the current arrangement of QU pieces moving inside a specific $x_j^{\prime }$ column are effective (See text for details).