# Systematic Approach for Alignment of Light Field Mirage
## 1 Introduction  
Observing 360-degree three-dimensional (3D) display systems can be used for digital change, medical demonstrations, and Internet shopping. We previously proposed techniques to eliminate repeated 3D images produced by the light field Mirage, which produces 360-degree 3D images to simulate the conventional Mirage [1]. However, we only constructed a part of the system to verify the elimination techniques. Thus, the previous system could not achieve 360-degree visibility. In this study, we develop a technology that connects multiple light field displays (LFDs) to complete the 360-degree visibility, which includes calibration for LFDs, stitching of images in overlapped LFDs, and matching of LFDs' brightness.  
Various techniques of 360-degree 3D displays have been proposed. Early displays used 3D glasses [2], in which a hole was used to distribute different 3D images to different viewers. Subsequent glasses-free 360-degree 3D displays used time-multiplexing systems, which adopted a combination of 1D LED arrays and a rotating mechanism [3; 4] or a high-speed projector and circular scanning system [5; 6; 7; 8; 9]. Multi-projection systems [10; 11; 12; 13; 14; 15; 16] and flat-panel systems [17; 18] have since been developed for glasses-free 360-degree 3D displays. The former systems project on to a screen from a large number of videos projectors. The latter systems consist of a high-resolution flat-panel display and specially designed lenses.  
For multi-projection systems, alignment techniques are essential as they consist of a large number of projectors, i.e., between 64 and 288 [10; 11; 12; 13; 14; 15; 16]. Mechanical adjustments require laborious work and are impractical for aligning them; therefore, multi-projection systems greatly rely on electronic calibration, which ultimately causes image quality degradation. The correction and distortion of images reduce its effective resolution. Mechanical adjustment among multiple display devices is preferable because the image quality is not reduced. Although an alignment technique is also required for the light field Mirage [19], its number of display devices is much smaller than for multi-projection systems.  
Flat-panel systems require a specially designed lens array, which consists of triplet lenses or aspheric conical lenses used to reduce the aberration, to distribute rays in 360-degree directions from the lens array [17; 18]. The aspheric conical lens array is designed to distribute the light rays emitting from the elemental images with a ring-type distribution instead of a uniform distribution [18]. A large number, such as 1196 pieces of aspheric conical lens are required to be molded and assembled, which is expensive and requires complex assembly. To prevent using specially designed lens arrays, the light field Mirage used multiple slanted LFDs aligned in a circular manner to emit rays in 360-degree directions. This enables commercially available lens arrays to be used. The adjustment of a lens array and flat-panel display for each LFD is required.  
In this study, we aim to develop an effective alignment technique to combine multiple LFDs. Because the system utilizes a limited number of LFDs with normal lens arrays, we prioritize mechanical adjustment over electronic adjustment, i.e., the image calibration, to minimize image degradation. Thus, we developed a systematic approach for the alignment of the light field Mirage as three steps, i.e., (1) calibration for LFDs, (2) stitching of images, and (3) matching of image brightness.