The slope/plateau transitions in Fig. 27(b) are nearly independent of the intensity. For the five reference targets, one obtains rising slope lengths of 4.3, 4.3, 4.2, 4.2, and 5.5 m; plateau lengths of 10.7, 10.6, 9.8, 9.8, and 9.2 m and falling slope lengths of 8.4, 8.5, 9.3, 9.2, and 9.6 m, respectively. On average, the rising slope has a length of 4.5 m, the plateau has a length of 10 m, and the falling slope has a length of 9 m. In order to cover a larger distance range, it is more convenient to process falling slope and plateau instead of rising slope and plateau. So, 3-D reconstruction of a distance range of 9 m can be achieved. By capturing slope and plateau GV images with a gate position difference of 9 m, the relative position within the slope can be calculated for each pixel by Display Formula
(3)where and are the pixel gray values in the slope and plateau image, respectively, and is the dark pixel gray value, i.e., the noise level without laser illumination. Equation (3) is obtained by application of the formulas of Cardano to invert the polynomial falling slope function of degree 3. In Fig. 28, 3-D reconstruction of the scene with the reference targets is performed by this slope method.