## 1 Introduction
However, since the narrow viewing-zone of the ordinary lens array-based integral imaging system was shared by two viewing-zones, sufficient viewing-areas for the DV 3-D display could not be offered. Thus, they tried to employ a polarization parallax barrier to improve the viewing angle [21], but it suffered from the degraded resolution and brightness of the displayed 3-D images due to the polarization barriers blocking light coming from the elemental image array (EIA). In fact, for the practical application of the 3-D DV display, two viewing-zones must be completely separated and have relatively large viewing-angles to experience the perspective changes of 3-D images. For this, [PERSON] et al. proposed a projection-type DV 3-D display based on integral imaging [23]. They used a series of optical elements, such as a collimator, a lenticular lens with a vertical diffuser, and convex lens array for generation of a collimated beam, separation of DV images with enhanced viewing-angles, and integration of 3-D images to be displayed in their viewing zones, respectively. These additional optical elements, however, may degrade the quality of the reconstructed 3-D images. Moreover, there exists an overlapped viewing-zone between the left and right 3-D images with some distortion due to the crossing of the left and right rays. The scale of this system may also depend on the practical sizes of the lenticular lens and collimator. Furthermore, this convex-lens-array-based projection integral imaging (CLA-PII) system shows a narrower viewing angle than the of the convex-mirror-array-based system [23]. To alleviate those problems, in this paper, we propose a practical type of a scalable DV 3-D display system based on convex-mirror-array-based direct projection integral imaging (CMA-DPII). The proposed system is simply composed of a projector and a CMA, where two kinds of EIAs for each of the two different input 3-D scenes are generated with the on-axis pickup integral imaging system and synthesized into a single EIA, which is called DV-EIA, based on the selective sub-image mapping (SSIM) method. Here, the DV-EIA contains all information of the intensities, perspectives, viewingzones of those two different input 3-D scenes. The divergent beam of the projector containing the information of the DV-EIA is directly projected onto the surface of the CMA without any additional optical elements. On every convex mirror, each of the left and right-scene components of the DV-EIs are instantaneously separated and reflected back into their viewing directions. Two different 3-D scene images are then integrated and displayed in their viewing zones with their viewing angles. In fact, the viewing angle of the proposed CMA-DPII system would be much more enhanced than that of the conventional CLA-PII system since each convex mirror can be made to have a much smaller \(f\)-number than the corresponding convex lens [24]. Moreover, contrary to the conventional system, each of the two viewing-zones and angles of the proposed system can be made changeable with the SSIM process, as well as a scalable DV 3-D display without flip-image and Moire disturbance problems can be implemented [25]. To confirm the feasibility of the proposed system, ray-optical analysis with the parallel-ray-approximation (PRA) method, as well as optical experiments with test 3-D objects on the implemented 22\({}^{\prime\prime}\) DV 3-D display prototype is performed, and the results are compared with those of the conventional system.