# Accurate Image Locating by Hologram Multiplexing in Off-Axis Digital Holography Display
## 1 Introduction  
Benefits from the invention of laser, the technique of off-axis holography [1] can make the original image separated from other diffraction terms during hologram recovery so that the image quality is improved greatly. After the off-axis optical holography became popular in many application areas, digital holography (DH) [2; 3; 4; 5] also began to show the prosperous potential in applications and attract the interests of researchers because of its merits including the convenient processing procedure, robust signal processing capability in computer, and precise image locating in display.  
The weakness of DH is the low resolution of the current recording device used for recording (the pixel size is about several microns), which is much lower than that of wet photographic material by one or two orders of magnitude. For off-axis DH, there exists the contradiction of the need for a largeTARW to separate the original image and the requirement of a small one to satisfy the low resolution of the recording device sensors, which limits the angle to several degrees. Although such on-axis DH method as phase-shifting holography [6; 7; 8; 9; 10; 11; 12] can solve the problem to a certain extent, these methods need more holograms recorded to eliminate the zero-order and the twin image by interferogram calculation, which makes it difficult for dynamic recording and three-dimensional (3D) video display.  
Recently, a spatial spectrum operation technique makes it possible to reconstruct the original image by choosing the correspondent spectra of the object term in Fourier domain [13; 14; 15], where the off-axis angle is crucial for image recovery and the locating of the original image. Unfortunately, the TARW angle is always difficult to control because the usable scope is only several degrees, and it is also inconvenient to record another parameter for the TARW. We have designed the recording geometry to control and monitor the TARW [16]. Two charge coupled devices (CCDs) are needed to record both the anglemonitoring interference frame and the hologram separately, which increases the inconvenience by more operation steps, and computer storing, and processing burden. Hologram multiplexing can increase the information capacity in one single hologram [17; 18; 19; 20], and it is always rescued to reduce such inconvenience discussed in application practice. The development of integrated phase-change materials (PCMs) can also enable the phase modulation and control on the object waves in DH [21]. Such new modern metamaterial is also expected to replace the spatial light modulators in holography display. Here we design a multiplexing recording setup to record both the TARW and object wave information in only one single interference frame. The TARW can be extracted easily by detecting the corresponding spectrum on Fourier domain and can then be used in the recovery and accurate locating of the object image in hologram display. We derive the theory of the proposed method first and then carry out numerical simulations and optical experiments to verify our idea before the conclusion.