# Systematic Approach for Alignment of Light Field Mirage
## 4 Calibration Technique for LFDs  
Because the light field Mirage consists of a small number of LFDs, this study developed a calibration strategy suitable for it. First, each LFD is calibrated mechanically. Then, the alignment of multiple LFDs is calibrated mechanically. Finally, electronic calibration is performed to finely adjust the 3D images generated by the multiple LFDs.  
In the first step, each LFD was calibrated individually so that the uniformity of all LFDs was ensured. The lateral and transverse positions of the lens array should be mechanically aligned against the LCD. The longitudinal position of the lens array was made equivalent for all LFDs using acrylic plates, which were sandwiched between the lens arrays and LCDs. Two kinds of acrylic plates with thicknesses of 15.00 and 0.65 mm were attached to precisely maintain the longitudinal position. The transverse position of the lens array was made equivalent for all LFDs using a camera located in front of the LFD. The camera was positioned so that its optical axis passed through the center of the lens array, and the  
Figure 3: Constructed light field Mirage consisted of eight LFDs.  
distance between the camera and lens array was set as the viewing distance. For all lenses in the lens array, one pixel in all elementary images that emitted rays passing through the camera position was calculated. Then, only the determined pixels were made to emit light. The lens array was slid on the acrylic spacers so that the camera observed light from all lenses.  
In the second step, the positions of the eight LFDs were adjusted. The LFDs were attached to the upper and lower aluminum plates using off-the-shelf 45-degree angle brackets. A sheet of tracing paper was placed at the top hole of the light field Mirage and each LFD displayed a grid pattern at the top hole position (the CDP position). The positions of the LFDs were moved along the aluminum plates so that all grid patterns were superimposed on one another. The grid pattern used a different color for each LFD to easily identify the shifted LFD. The resultant superimposed image is shown in Figure 4a. As shown in this figure, it was impossible to superimpose all grid patterns at the same position, because of the residual non-uniformity among the eight LFDs after the first step. Then, the tracing paper was moved upward over a distance of 14 mm, and all the LFDs displayed the grid patterns at the same position at this height. Figure 4b shows the superimposition of the grid patterns. The mismatch of the grid pattern positions became larger compared with that shown in Figure 4a. Therefore, adjustment to the ray directions among the LFDs was required.  
In the last step, the electronic calibration was conducted for the adjustment of the ray directions. The positions of the elementary images, as well as the pitches of the elementary images displayed on the LCDs, were manually adjusted so that all grid patterns were superimposed on one another. The adjustments were conducted using the tracing paper positioned at the top hole. The maximum shift of the elementary images among the eight displays was three pixels. From the resultant image shown in Figure 5a, the superposition of the grid patterns improved. Then, the tracing paper was moved, as explained in the second step, and the obtained image is shown in Figure 5b. The result shown in Figure 5b was colored because a part of the displays was hindered by the top hole, but the coincidence of the grid patterns was as good as that shown in Figure 5a. Therefore, the ray directions of all the LFDs were well-calibrated.  
Figure 4: Adjustments of positions of eight LFDs using grid patterns displayed by all LFDs on (**a**) CDP and (**b**) plane above CDP with a length of 14 mm.  
Figure 5: Electronic calibration of eight LFDs using grid patterns displayed by all LFDs on (**a**) CDP and (**b**) plane above CDP with a length of 14 mm.