Browsing by Author "Ulusoy, Erdem"

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Open Access
Analysis of the complex light field generated by a deflectable mirror array device
(SPIE, 2006) Ulusoy, Erdem; Onural, Levent; Özaktaş, Haldun M.
An exact analysis of the scalar coherent monochromatic light field produced by a deflectable mirror array device is presented. The three-dimensional light field is related to the tilt angles of the mirrors. The first Rayleigh-Sommerfeld diffraction formula is used to model the diffraction. The analysis is carried out based on the assumption that the mirrors can be tilted with continuously varying angles, so the field produced by a finite (discrete) set of possible tilt angles is included as a special case.
Open Access
Signal processing based solutions for holographic displays that use binary spatial light modulators
(2012) Ulusoy, Erdem
Holography is a promising method to realize satisfactory quality threedimensional (3D) video displays. Spatial light modulators (SLM) are used in holographic video displays. Usually SLMs with higher dynamic ranges are preferred. But currently existing multilevel SLMs have important drawbacks. Some of the associated problems can be avoided by using binary SLMs, if their low dynamic range is compensated for by using appropriate signal processing techniques. In the first solution, the complex-valued gray level SLM patterns that synthesize light fields specified in the non-far-field range are halftoned into binary SLM patterns by solving two decoupled real-valued constrained halftoning problems. As the synthesis region, a sufficiently small sub-region of the central diffraction order region of the SLM is chosen such that the halftoning error is acceptable. The light fields are synthesized merely after free space propagation from the SLM plane and no other complicated optical setups are needed. In this respect, the theory of halftoning for ordinary real-valued gray scale images is extended to complex-valued holograms. Simulation results indicate that light fields that are given either on a plane or within a volume can be successfully synthesized by our approach. In the second solution, a new full complex-valued combined SLM is effectively created by forming a properly weighted superposition of a number of binary SLMs where the superposition weights can be complex-valued. The method is a generalization of the well known concepts of bit plane decomposition and representation for ordinary images and actually involves a trade-off between dynamic range and pixel count. The coverage of the complex plane by the complex values that can be generated is much more satisfactory than that is achieved by those methods available in the literature. The design is also easy to customize for any operation wavelength. As a result, we show that binary SLMs, with their robust nature, can be used for holographic video display designs
Open Access
Signal processing for three-dimensional holographic television displays that use binary spatial light modulators
(IEEE, 2010) Ulusoy, Erdem; Onural, Levent; Özaktaş, Haldun M.
One of the important techniques used for three dimensional television (3DTV) is holography. In holographic 3DTV, spatial light modulators (SLM) are used as the display device. SLMs that provide the most limited modulation are the binary SLMs, since only two different values can be assigned to their pixels. An important signal processing problem arising here is the determination of the binary signal to be written on the SLM among the possible ones such that the desired light field is generated to the best extent. Many of the proposed methods do not produce satisfactory results in terms of error rate, computational performance or light efficiency. We propose an optical setup to be placed in front of the binary SLM and the associated signal processing algorithm. The proposed system uses a 4-f setup and a periodic mask is placed to the Fourier plane. As a result, the binary SLM is convolved with a series of regularly spaced impulse functions and we get a new SLM which is smaller in pixel count compared to binary SLM but which can provide 16-bit full complex modulation. It becomes easier to generate the desired light field with this new SLM. Also, the required computations are carried out in a fast manner to enable real-time operation. ©2010 IEEE.
Open Access
Three-dimensional monochromatic light field synthesis with a deflectable mirror array device
(SPIE, 2006) Ulusoy, Erdem; Uzunov, V.; Onural, Levent; Özaktaş, Haldun M.; Gotchev, A.
We investigated the problem of complex scalar monochromatic light field synthesis with a deflectable mirror array device (DMAD). First, an analysis of the diffraction field produced by the device upon certain configurations is given assuming Fresnel diffraction. Specifically, we derived expressions for the diffraction field given the parameters of the illumination wave and the tilt angles of the mirrors. The results of the analysis are used in later stages of the work to compute the samples of light fields produced by mirrors at certain points in space. Second, the light field synthesis problem is formulated as a linear constrained optimization problem assuming that mirrors of the DMAD can be tilted among a finite number of different tilt angles. The formulation is initially developed in the analog domain. Transformation to digital domain is carried out assuming that desired fields are originating from spatially bounded objects. In particular, we arrived at a Dp = b type of problem with some constraints on p, where D and b are known, and p will be solved for and will determine the configuration of the device. This final form is directly amenable to digital processing. Finally, we adapt and apply matching pursuit and simulated annealing algorithms to this digital problem. Simulations are carried out to illustrate the results. Simulated annealing performs successful synthesis when supplied with good initial conditions. However, we should come up with systematic approaches for providing good initial conditions to the algorithm. We do not have an appropriate strategy currently. Our results also suggest that simulated annealing achieves better results than MP. However, if only a part of the mirrors can be used, and the rest can be turned off, the performance of MP is acceptable and it turns out to be stable for different types of fields.