Hızlı kaliteli beneklenme yapmayan bilgisyarda yaratılan faz hologramlı görüntü projeksiyonu

Computer generated holography based image projection, 3D television, head-up and near-to-eye (N2E) display systems offer unique advantages over conventional schemes and constitute a promising option for the future of display technology. Such systems provide much higher light efficiency, eliminate the need for bulky optics and provide natural 3D experience. Computer generated holograms (CGHs) are displayed on spatial light modulators (SLMs) illuminated by coherent light. Ideally, each pixel of an SLM should provide simultaneous and independent amplitude and phase modulation since CGHs are in general complex-valued functions. However, current state of the art SLM technology allows the implementation of only a constrained set of complex values depending on the device type, such as binary amplitude, binary phase, amplitude-mostly or phaseonly. Among various types, liquid crystal-on-silicon (LCoS) phase-only SLMs provide the most convenient option due to their smaller pixel pitch, higher diffraction efficiency and 8-bit modulation depth. Yet, these devices become useful only when they are combined with algorithms that encode a full-complex SLM pattern into a phase-only SLM pattern. In the context of holographic image projection, existing algorithms for phase CGH computation are iterative optimization procedures that require successive transformations with high computational costs. As higher pixel counts are attained, the computational load of iterative methods become increasingly excessive, hindering real-time video applications. Despite their high cost though, the reconstruction performance of these algorithms are only moderate, with generated images suffering significantly from speckle noise. In this thesis, two novel phase CGH computation algorithms are proposed. The first algorithm removes the iteration requirement and provides a direct solution, significantly improving the computational efficiency. The second algorithm processes a given desired image and non-iteratively calculates a phase CGH which, when used as a starting point, lets iterative algorithms to converge to almost global optimum, significantly improving reconstruction quality. The first algorithm is based on the observation that two phase-only pixels are equivalent to a full complex pixel; thus, the SLM is expected to reconstruct half of the desired image samples exactly. Simple Discrete Fourier Transform (DFT) and multirate signal processing relations are utilized to non-iteratively determine a phase CGH that exactly reconstructs the even (or odd) rows (or columns) of a given image. By requiring only a single Fast Fourier Transform (FFT) and a few additional trivial matrix operations, the algorithm offers 6 to 20 times improvement on computational efficiency compared to conventional procedures. The simulation results and proof-of-concept experiments indicate that our algorithm can provide full field-of-view (FOV), low speckle image reconstructions with maximized light efficiency when the reconstructions of 4 CGHs are averaged. High quality frames in the interlaced video format is already deliverable with 60Hz SLMs when the FOV in one direction is reduced to half. In the second algorithm, we developed a procedure for designing an image specific phase function that leads to an ideal CGH that is almost readily unit magnitude, resulting in a very low quantization error to begin with. When the phase CGH obtained in the described way is used as the starting point for existing iterative algorithms, much quicker convergence and unprecedentedly low reconstruction errors are achieved. The simulations and experiments reveal that reconstruction quality improves by about 20 times compared to iterative algorithms starting from random guesses. The reconstructions are almost speckle free, while allowing maximum light efficiency and FOV. The developed methods are particularly novel over existing approaches in that full physical as well as mathematical insight is exploited in their development. In particular, while most approaches formulate the phase CGH computation problem as a purely mathematical optimization problem, our methods recognize and utilize the correspondence between phase functions, ray directions, lenses, prisms and so forth. As a result, we can non-iteratively determine phase CGHs that are almost ready, i.e., can perform the desired reconstructions already with low error. In this way, we significantly reduce the number of iterations required, i.e., our methods require iterations just for fine-tuning, whereas in existing algorithms iterations are required for both coarse and fine tuning. Meanwhile, we can get much closer to global optimums than any other method. In this respect, we believe that this thesis also contributes significantly to the understanding of the fundamental limits of phase-only computer holography.