Andrzej Siemion

Color image projection based on Fourier holograms

A method of color image projection is experimentally validated. It assumes a simultaneous illumination of a spatial light modulator (SLM) with three laser beams converging in a common point on a projection screen. The beams are masked with amplitude filters so that each one illuminates one third of the area of the SLM. A Fourier hologram of a chosen color component of an input image is calculated, and its phase pattern is addressed on a corresponding part of the SLM area. A full-color flat image is formed on the screen as a result of color mixing. Additional techniques of image optimization are applied: time-integral speckle averaging and an off-axis shift of a zero-order peak. Static and animated experimental results of such a color holographic projection with a good image quality are presented.

Experimental evaluation of a full-color compact lensless holographic display

An iterative phase retrieval method for a lensless color holographic display using a single light modulator is experimentally validated. The technique involves iterative calculation of a three-plane synthetic hologram which is displayed on a SLM simultaneously lit with three laser beams providing an RGB illumination. Static and animated two-dimensional flicker-free full color images are reconstructed at a fixed position and captured using a high resolution CMOS sensor. The image finesse, color fidelity, contrast ratio and influence of speckles are evaluated and compared with other techniques of holographic color image encoding. The results indicate the technique superior in a case of full-color real-life pictures which are correctly displayed by this ultra-compact and simple projection setup.

Highly efficient broadband double-sided Fresnel lens for THz range

Modern passive THz setups require effective optical elements with a large numerical aperture. Here we propose a new type of the optical element for THz applications, which is a broadband double-sided Fresnel-like lens with an optimized thickness. The optimization is performed to obtain a very low attenuation, low material cost, and small weight in the element media. It also provides achromatic properties for the assumed wavelength range. The experimental evaluation of the proposed diffractive lens by means of time-domain spectroscopy is presented and discussed.

Efficient image projection by Fourier electroholography.

An improved efficient projection of color images is presented. It uses a phase spatial light modulator with three iteratively optimized Fourier holograms displayed simultaneously--each for one primary color. This spatial division instead of time division provides stable images. A pixelated structure of the modulator and fluctuations of liquid crystal molecules cause a zeroth-order peak, eliminated by additional wavelength-dependent phase factors shifting it before the image plane, where it is blocked with a matched filter. Speckles are suppressed by time integration of variable speckle patterns generated by additional randomizations of an initial phase and minor changes of the signal.

Off-axis metallic diffractive lens for terahertz beams

A diffractive optical element for off-axis focusing of terahertz radiation is presented. It was designed in a nonparaxial regime and manufactured in a metal slab by laser cutting of curved stripes. The optical function of the structure includes focusing and deflecting the illuminating beam of a chosen frequency in a particular place. Therefore, the element acts as both a spatial and a spectral filter; hence it is especially suitable for separating the terahertz signal from a broadband thermal load in passive detection devices. The experimental evaluation of the proposed diffractive lens by means of time-domain spectroscopy is presented and discussed.

Diffuserless holographic projection working on twin spatial light modulators

An improved efficient projection of holographic images is presented. It uses two phase spatial light modulators (SLMs) with two iteratively optimized Fresnel holograms displayed simultaneously--each for one modulator. The phase distribution on the second modulator is taking into account the light distribution coming from the first one. A pixelated structure of the modulator and fluctuations of liquid-crystal molecules cause a zero-order peak that was separated in experiment. Use of two SLMs gives clear and containing almost no speckles images. Thanks to the compensation of phase distribution from the first modulator, we can abandon diffusers in the iterative process and that is why we can control both amplitude and phase distribution in the image plane independently.

One-exposure phase-shifting digital holography based on the self-imaging effect

A diffractive optical element with self-imaging capabilities is used to make a phase-shifting digital holography optical system simpler and cheaper. Sequential phase-shifting requires multiple exposures, and parallel phase-shifting demands a more complicated optical system. As opposed to typical phase-shifting methods, using the self-imaging diffractive optical element requires only one exposure on a low-cost CMOS matrix, and due to the small number of needed elements, the optical system is very compact. Instead of the approximation and interpolation methods, the properties of the self-imaging effect are utilized in the recording process and in the numerical reconstruction process.

THz Beam Shaping Based on Paper Diffractive Optics

Fast and intensive development of terahertz (THz) technology requires designing dedicated optical elements. Here, we generated complicated THz field distribution thanks to simple binary diffractive optical elements (DOEs) made from paper. The paper fabricated structures are lightweight, inexpensive, feasible for fast-prototyping purposes and they have high transparency in the THz range. Structures were designed and simulated in nonparaxial approach which suppresses the influence of geometrical aberrations and enables large apertures in comparison with their focal lengths. Such DOEs can be used in THz tomography, scanners, radiation sources collimation, focusing and gathering the radiation on the detector.

Utilization of the phase flicker of a LCoS Spatial Light Modulator for improved diffractive efficiency

The paper presents the way that colour can serve solving the problem of calibration points indexing in a camera geometrical calibration process. We propose a technique in which indexes of calibration points in a black-and-white chessboard are represented as sets of colour regions in the neighbourhood of calibration points. We provide some general rules for designing a colour calibration chessboard and provide a method of calibration image analysis. We show that this approach leads to obtaining better results than in the case of widely used methods employing information about already indexed points to compute indexes. We also report constraints concerning the technique. Nowadays we are witnessing an increasing need for camera geometrical calibration systems. They are vital for such applications as 3D modelling, 3D reconstruction, assembly control systems, etc. Wherever possible, calibration objects placed in the scene are used in a camera geometrical calibration process. This approach significantly increases accuracy of calibration results and makes the calibration data extraction process easier and universal. There are many geometrical camera calibration techniques for a known calibration scene [1]. A great number of them use as an input calibration points which are localised and indexed in the scene. In this paper we propose the technique of calibration points indexing which uses a colour chessboard. The presented technique was developed by solving problems we encountered during experiments with our earlier methods of camera calibration scene analysis [2]-[3]. In particular, the proposed technique increases the number of indexed points points in case of local lack of calibration points detection. At the beginning of the paper we present a way of designing a chessboard pattern. Then we describe a calibration point indexing method, and finally we show experimental results. A black-and-white chessboard is widely used in order to obtain sub-pixel accuracy of calibration points localisation [1]. Calibration points are defined as corners of chessboard squares. Assuming the availability of rough localisation of these points, the points can be indexed. Noting that differences in distances between neighbouring points in calibration scene images differ slightly, one of the local searching methods can be employed (e.g. [2]). Methods of this type search for a calibration point to be indexed, using a window of a certain size. The position of the window is determined by a vector representing the distance between two previously indexed points in the same row or column. However, experiments show that this approach has its disadvantages, as described below. * E-mail: A.Nowakowski@ire.pw.edu.pl Firstly, there is a danger of omitting some points during indexing in case of local lack of calibration points detection in a neighbourhood (e.g. caused by the presence of non-homogeneous light in the calibration scene). A particularly unfavourable situation is when the local lack of detection effects in the appearance of separated regions of detected calibration points. It is worth saying that such situations are likely to happen for calibration points situated near image borders. Such points are very important for the analysis of optical nonlinearities, and a lack of them can significantly influence the accuracy of distortion modelling. Secondly, such methods may give wrong results in the case of optical distortion with strong nonlinearities when getting information about the neighbouring index is not an easy task. Beside this, the methods are very sensitive to a single false localisation of a calibration point. Such a single false localisation can even result in false indexing of a big set of calibration points. To avoid the above-mentioned problems, we propose using a black-and-white chessboard which contains the coded index of a calibration point in the form of colour squares situated in the nearest neighbourhood of each point. The index of a certain calibration point is determined by colours of four nearest neighbouring squares (Fig.1). An order of squares in such foursome is important. Because the size of a colour square is determined only by the possibility of correct colour detection, the size of a colour square can be smaller than the size of a black or white square. The larger size of a black or white square is determined by the requirements of the exact localisation step which follows the indexing of calibration points [3]. In this step, edge information is extracted from a blackand-white chessboard. This edge information needs larger Artur Nowakowski, Wladyslaw Skarbek Institute of Radioelectronics, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warszawa, A.Nowakowski@ire.pw.edu.pl Received February 10, 2009; accepted March 27, 2009; published March 31, 2009 http://www.photonics.pl/PLP

3D imaging with the light sword optical element and deconvolution of distance-dependent point spread functions

The experimental demonstration of a blind deconvolution method on an imaging system with a Light Sword optical element (LSOE) used instead of a lens. Try-and-error deconvolution of known Point Spread Functions (PSF) from an input image captured on a single CCD camera is done. By establishing the optimal PSF providing the optimal contrast of optotypes seen in a frame, one can know the defocus parameter and hence the object distance. Therefore with a single exposure on a standard CCD camera we gain information on the depth of a 3-D scene. Exemplary results for a simple scene containing three optotypes at three distances from the imaging element are presented.