Dariusz Wojnowski

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.

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.

Surface profilometry with binary axicon-vortex and lens-vortex optical elements.

We report on the interesting effect observed with the diffractive binary element, which matches the property of an axicon and vortex lens. Binary phase coding simplifies the manufacturing process and gives additional advantages for metrology purposes. Under laser beam illumination, our element produces two waves: converging and diverging. Both waves carry a single optical vortex. We show that this special diffractive element can be used to set up a simple surface profilometer.

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.

Digital holography with self-imaging by a two-step phase element

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

Utilization of an LCoS spatial light modulator's phase flicker for improving diffractive efficiency

This work presents the observation, measurement and utilization of phase modulation in-time flickering, on a high-end Liquid Crystal on Silicon (LCoS) Spatial Light Modulator (SLM). The flicker due to binary driving electronics is a negative effect. However, this drawback can be minimized by appropriate adjustment of phase modulation depth, which results in a time-synchronization of peak efficiencies for selected wavelengths. In this paper optimal parameters for three wavelengths of primary RGB colors are investigated. The result is optimal performance of the SLM for full-color dynamic holography.

Modelling of the space invariant optical systems with a spatially incoherent illumination

A study of imaging in an isoplanatic optical setup with a spatially incoherent illumination is presented. In such optical setups a light intensity distribution in an image plane can be calculated by a convolution of an input field with a Point Spread Function (PSF). Additionally a numerical simulation of incoherent monochromatic illumination is done by an integration of intensity images obtained with different random initial phase distributions (equivalent to a long exposure with a rotating diffuser in an optical setup). When an optical system is non space-invariant the point source image changes in various regions of the image plane and imaging simulation becomes complicated. Method with a simple convolution with PSF distribution cannot be applied because there is no one well defined PSF for the whole optical setup. This second method needs a bigger computational effort but can provide imaging modelling for both isoplanatic and non space invariant situations. In this contribution we compare the two mentioned methods in terms of imaging quality and its agreement with theoretical expectations. We give some statistical analysis of a contrast and noise level of the obtained pictures. We discuss the advantages and limitations of both modelling techniques for typical greyscale test patterns.

Holographic color projection with additional phase factor to suppress zero diffractive order

A method of color projection of 2D images utilizing red, green and blue laser sources and Fourier holograms addressed on a single phase modulator has been reported. High quality rich-colored images were achieved, although the main difficulty in reaching the TV-quality is the presence of a 0th diffractive order. It is inevitably created due to a limited fill factor and phase modulation nonlinearity of the used Spatial Light Modulator (SLM) device. However, in certain conFigureurations the light energy contributing to the spurious diffractive order can be focused in a single point in space and absorbed with an amplitude filter. In this work we present the experimental results of a color projection with the non-diffracted peak shifted outside the viewing range in both transverse directions and along the optical axis.

Speckless head-up display on two spatial light modulators

There is a continuous demand for the computer generated holograms to give an almost perfect reconstruction with a reasonable cost of manufacturing. One method of improving the image quality is to illuminate a Fourier hologram with a quasi-random, but well known, light field phase distribution. It can be achieved with a lithographically produced phase mask. Up to date, the implementation of the lithographic technique is relatively complex and time and money consuming, which is why we have decided to use two Spatial Light Modulators (SLM). For the correctly adjusted light polarization a SLM acts as a pure phase modulator with 256 adjustable phase levels between 0 and 2π. The two modulators give us an opportunity to use the whole surface of the device and to reduce the size of the experimental system. The optical system with one SLM can also be used but it requires dividing the active surface into halves (one for the Fourier hologram and the second for the quasi-random diffuser), which implies a more complicated optical setup. A larger surface allows to display three Fourier holograms, each for one primary colour: red, green and blue. This allows to reconstruct almost noiseless colourful dynamic images. In this work we present the results of numerical simulations of image reconstructions with the use of two SLM displays.