# Displays Based on Dynamic Phase-Only Holography
## 4 Algorithms  
Computational holography makes high demands on computational resources. Therefore, a large effort has been deployed in fine-tuning the algorithms in order to minimize the computational burden. A large reduction of computational efforts has been achieved by incorporating into the design, the limited resolution of the human visual system (HVS), and the position of the viewer (defined eye box or eye tracking device). The extra computational resources can be deployed for a high contrast, low noise image, or a display, which must be updated at video rates or faster. The following discussion tracks the advances, which have been made in reducing the computational burden and then summarizes our efforts with the production of holograms for 2D display in consumer products. The Active Tiling 3D display system of Qinetiq [9] employed a variant of the diffraction-specific (DS) algorithm [18]. The DS algorithm advanced computational holography by providing solutions in four problem areas including noise, speed, 3D object definition, and encoding. The noise problem was the appearance of the DC term in the hologram replay, which was solved by using an off-axis reference beam in Reference [1]. This solution places significant demands on the limited SBWP of SLMs and is currently not practical for dynamic holography. These DC terms are omitted in the DS algorithm. The speed of the computation was increased by a factor of over 100 by taking account of the limited resolution of the HVS. The object in Reference [1] existed in space while computer models exist as point-clouds or patch-models. Algorithms, which sum the contributions from the object elements (points or patches) in these computer models over the whole hologram, are computationally expensive. The DS algorithm improved the speed of computation by pre-computing the basis fringes for the diffraction of light in discrete directions so that the run-time computation is reduced to table look-up and multiplication by the desired replay field amplitudes. Crucially, amplitude modulated fringes allow a linear superposition while if the basis fringes were phase coded, then linear superposition is only valid for small phase modulation depth (Appendix B in ref. [18]). Amplitude modulation of the 3D holographic display has been preferred to this day [19]. The wave front-recording plane (WRP) method [19] is based on adding the contributions from the object elements over small areas on a plane close to the object. A look-up table can be adopted for increased speed in the first step. The Fresnel diffraction from the WRP to the hologram plane is calculated using the fully complex FFT algorithm so that the modulation format of the computed hologram can be chosen as amplitude, phase, or fully complex. However, the computational effort  
Figure 5: High performance, phase-only SLM. required for 3D objects still places a demonstrator as a lab project rather than a consumer item. The approach taken here is to begin the work with 2D displays in consumer products and extends the work towards 3D when consumer acceptance has improved to the extent that design of a custom ASIC can be commercially viable. The initial holographic display systems are based on phase-only holograms (or kinoforms). A phase-only hologram, which is computer-generated was announced in 1969 [20], and an iterative algorithm for the design of these kinoforms known as the GS algorithm was presented a few years later [21]. The advantage of the phase-only hologram for display is that a significant portion of the light energy arrives at the image plane. This enables a more efficient display system but comes at the expense of a significant noise floor. The GS iterative phase retrieval algorithm for calculating the kinoform produces relatively noisy images with poor contrast. This is also known as the Iterative Fourier Transform Algorithm (IFTA) [22]. We have developed a new generation of iterative phase retrieval algorithms that deliver outstanding image quality, which was exemplified in Reference [23].