# Computer-Generated Hologram Based on Reference Light Multiplexing for Holographic Display
## 1 Introduction  
Holographic display is regarded as the ideal three-dimensional (3D) display technology because it offers all the visual information human eyes require [1, 2]. Computer-generated hologram (CGH) is a key method to realize holographic display by recording holograms digitally and has attracted attention in recent years [3, 4, 5, 6]. However, limited information capacity and the quality of reconstructed images are two main problems that restrict the development of holographic display. Multiplexing technology is widely applied to increase information capacity. In previous decades, various multiplexing methods for multiple-image encryption were proposed, such as angular multiplexing [7], wavelength multiplexing [8], and position multiplexing [9]. In recent years, metasurface holograms have attracted great interest because metasurface can overcome the challenges faced by traditional holography, such as wide viewing angles, and the elimination of unwanted diffraction orders. So far, different physical parameters, such as polarization [10], helicity [11], wavelength [12], incidence angle [13], and orbital angular momentum [14], have been utilized to increase information capacity in metasurface. In CGH, the time-multiplexing method [15, 16, 17] and spatial-multiplexing method [18, 19, 20] are widely applied to realize color holographic display or increase the field of view. Additionally, various multiplexing coding methods are also proposed to realize color holographic display, where three color sub-holograms are encoded into one hologram, such as depth-division multiplexing [21], space-division multiplexing [22, 23], frequency-division multiplexing [24, 25, 26], and so on. Currently, position multiplexing has also been used in CGH, where different images can be reconstructed at different positions by a multiplexed CGH (MCGH) [27, 28]. Furthermore, curvature multiplexing [29, 30] has been utilized to increase information capacity, where different images can be reconstructed at the same or different positions by changing the curvature of a MCGH. However, this method exhibits strong crosstalk noise in reconstructed images. Therefore, multiplexingmethods that can increase information capacity further and reconstruct multiple images are strongly required in the development of holographic display. In CGH, phase-only SLM, where the complex amplitude distribution is encoded into phase-only information by considering the amplitude distribution as constant, is widely utilized because of its high diffraction efficiency. Furthermore, the addition of an initial random phase is also widely used to diffuse object information in a calculation, which causes speckle noise and decays the reconstructed image quality [31; 32]. There are two methods to solve this problem; one is complex amplitude modulation methods, and the other is iteration algorithms. The complex amplitude modulation method encodes target complex amplitude distribution into amplitude-only or phase-only holograms by encoding specific algorithms or through optical devices. Scholars have presented many complex amplitude modulation methods, such as double-phase method [33; 34; 35; 36], superpixel method [37; 38], iteration method [39], and so on [40; 41]. However, it is known that the amount of information for complex amplitude holograms is double that for amplitude-only or phase-only holograms. Hence, complex amplitude modulation has been realized with the reduction of space bandwidth product. The iteration algorithm optimizes phase distribution in the hologram plane after an iterations calculation by controlling the amplitude distribution of the hologram plane and imaging plane [42; 43]. In general, the iteration algorithm is the most widely used method for phase-only CGH calculation and has achieved considerable success in less convergence time and clear reconstruction. In this article, we propose a multiplexing scheme to increase information capacity. CGHs of different images are generated by different reference light waves and encoded into one MCGH.