# Enhancing the Quality of Sampled Phase-Only Hologram (SPOH) Based on Time-Division Comb Filtering
## 1 Introduction  
A three-dimensional (3-D) digital object image, or a computer graphic model, can be represented by a two-dimensional (2-D) digital complex-valued hologram that is comprised of a pair of components (e.g., a magnitude component and a phase component). To date, there are many modern methods for generating digital holograms, a process that is commonly referred to as computer generated holography (CGH). A good review on the state-of-the-art can be found in [1, 2]. To reconstruct the 3-D image of a digital hologram to an observer, each component is displayed with a spatial light modulator (SLM) through a meticulous optical setup [3, 4]. It has been demonstrated that a single SLM can be used to display the pair of hologram components [5, 6]. Despite the success, the optical setup is rather complicated. A more practical approach is to convert a complex-valued hologram into a phase-only hologram, so that it can be displayed with a single phase-only SLM. Digital Fresnel phase-only hologram has two major advantages over a complex-valued hologram. First, it can be displayed directly with a single phase-only spatial light modulator, leading to significant simplification in the optical setup. Second, the optical efficiency is higher, resulting in brighter reconstructed images. However, when a phase-only hologram is obtained simply by removing the magnitude component of a complex-valued hologram, the quality of the reconstructed image will be heavily degraded. In the past 2 decades there are numerous solutions to address this problem. The Gerchberg Saxton algorithm (GSA) [7] is one of the earliest and popular frameworks for generating a phase-only hologram. Based on the GSA, the iterative Fourier transform and the iterative Fresneltransform algorithms [8; 9] (both methods also referred to as IFTA) have been developed to generate Fourier and Fresnel phase-only holograms. Starting from a hologram with random phase values, repetitive rounds of iterations are conducted to adjust the phase of the hologram pixels so that the reconstructed image will be rendered towards a target image. Reconstructed image of a hologram generated with IFTA is generally similar in appearance to the target, but contaminated with considerable amount of noise. The computation loading is also intensive as multiple rounds of iterations are needed to obtain the hologram. Although the noise problem can be reduced through averaging the reconstructed images of multiple holograms, or the mixed region methods [10], the computation time will be further increased. Another iterative approach, known as direct binary search (DBS) [11; 12], works on similar principles as the GSA. In comparison with the latter, DBS results in reconstructed images of higher quality, but the computational efficiency is substantially lowered. Non-iterative methods have also been developed to reduce the time for generating phase-only holograms. The complex amplitude modulation (CAM) [13; 14] and the double phase methods [15; 16; 17] are effective for generating phase-only holograms. However, both methods required some kind of optical filtering to remove unwanted signals from the reconstructed images. A less complicated way, known as noise addition method, adds random phase noise to the intensity image of a three-dimensional (3-D) object. The random noise acts like a diffuser, so that the diffracted waves of the object are close to homogeneous on the hologram plane. The magnitude component, therefore, can be approximated as a constant throughout the entire hologram. Similar to IFTA, reconstructed images of phase-only holograms generated with this method are heavily masked with random noise. Although the degradation of the lines and edges can be improved by restricting the noise addition to the smooth regions of the intensity image [18], the noise level of the shaded areas are still significant. A method to suppress the noise in the reconstructed image, known as one step phase retrieval (OSPR), is proposed in [19; 20].