Krzysztof Pokorski

Hilbert-Huang processing for single-exposure two-dimensional grating interferometry.

Single-shot crossed-type fringe pattern processing and analysis method called Hilbert-Huang grating interferometry (HHGI) is proposed. It consist of three main procedures: (1) crossed pattern is resolved into two fringe families using novel orthogonal empirical mode decomposition approach, (2) separated fringe sets are filtered using modified automatic selective reconstruction aided by enhanced fast empirical mode decomposition and mutual information detrending, and (3) Hilbert spiral transform is employed for fringe phase demodulation. Numerical and experimental studies corroborate the validity, versatility and robustness of the proposed HHGI technique. It can be successfully applied to multiplicative and additive type crossed patterns with sinusoidal and binary orthogonal component structures. Efficient adaptive filtering enables successful fast processing and analysis of complex and defected patterns.

Fourier domain interpretation of real and pseudo-moiré phenomena

Unified interpretation for the real and pseudo moiré phenomena using the concept of biased and unbiased frequency pairs in the Fourier spectrum is given. Intensity modulations are responsible for pseudo moiré appearance in the image plane rather than average intensity variations dominating real moiré. Detection of pseudo moiré necessitates resolving superimposed structures in the image plane. In the case of the product type superimposition generating both real and pseudo moiré, our interpretation utilizes the Fourier domain information only. The moiré pattern characteristics such as an effective carrier, modulation and bias intensity distributions can be readily predicted. We corroborate them using two-dimensional continuous wavelet transform and fast adaptive bidimensional empirical mode decomposition methods as complementary image processing tools.

Visualization of additive-type moiré and time-average fringe patterns using the continuous wavelet transform

An application of the continuous wavelet transform to modulation extraction of additive moiré fringes and time-average patterns is proposed. We present numerical studies of the influence of various parameters of the wavelet transformation itself and a fringe pattern under study on the demodulation results. To facilitate the task of demodulating a signal with zero crossing values, a two-frame approach for wavelet ridge extraction is proposed. Experimental studies of vibration mode patterns by time-average interferometry provide excellent verification of numerical findings. They compare very well with the results of our previous investigations using the temporal phase-shifting method widely considered as the most accurate one. No need of performing phase shifting represents significant simplification of the experimental procedure.

Separation of complex fringe patterns using two-dimensional continuous wavelet transform

A method for processing fringe patterns containing additively superimposed multiple fringe sets is presented. It enables to analyze different fringe families present in a single image separately. The proposed method is based on a two-dimensional continuous wavelet transform. A robust ridge extraction algorithm for a single fringe set extraction is presented. The method is fully automatic and requires no user interference. Spectral separation of fringe families is not required. Simulations are presented to verify performance and advantage of the proposed method over the Fourier transform based technique. Method validity has been confirmed using experimental images.

Examination of singular scalar light fields using wavelet processing of fork fringes.

A single frame fork fringe pattern automatic processing method for detecting optical vortices in coherent light fields using two-dimensional continuous wavelet transformation is proposed. When a vortex sign is of no importance, it is sufficient to calculate the fork interferogram modulation distribution and its normalized gradient map to establish vortex locations without resorting to complicated phase calculations. Normalization of modulation gradient maps enables unambiguous vortex discrimination from local modulation minima without phase singularity. The issue of vortex detection resolution versus carrier fringe frequency and orientation is discussed. Corroboration of simulation and experimental studies of integer and noninteger singular light beams as well as speckle fields reported in the literature and analyzed using different approaches is presented.

Processing and phase analysis of fringe patterns with contrast reversals

A method for demodulating fringe patterns containing contrast reversals is proposed. It consists of two steps. First, the absolute value of the fringe intensity distribution with its background removed is calculated. Then, two dimensional continuous wavelet transform with enhanced ridge extraction algorithm is applied to extract the fringe phase map. Proposed approach allows to dispose of phase jumps along the contrast reversal bands. The method requires only one image and has no special demands concerning the fringe pattern design. Method validity and robustness is confirmed using experimentally acquired time-averaged interferograms of vibrating silicon micromembranes.

Diffraction grating three-beam interferometry without self-imaging regime contrast modulations

Achromatic grating shearing interferometry method for wave front sensing is developed. Two Fresnel diffraction patterns formed by grating three lowest diffraction orders are recorded. The beam-splitter grating is displaced laterally by half its period between exposures. Calculating the sum of two patterns results in a two-beam interferogram free of inherent light propagation direction and observation plane contrast modulations imposed by the self-imaging phenomenon (Talbot effect). Single-frame automatic fringe pattern processing provides the interferogram phase distribution. The technique enables continuous shear variations suitable for dynamic range sensing. Experimental works corroborate enhanced capabilities of the proposed approach.

Circular–linear grating Talbot interferometry with moiré Fresnel imaging for beam collimation

The Talbot interferometer using different self-imaging structures is studied and applied for laser beam collimation. A circular-linear grating pair enables visual dynamic detection and computer moirégram analysis. Automatic single-frame processing is performed using a 2D continuous wavelet transform. Conducting moirégram imaging in the Fresnel field of a double-diffraction system is brought up to avoid using distortion-free objectives and simplify the experimental setup. Simulation and experimental results document the method properties and provide beautiful exemplification of the double-grating Fresnel diffraction theory developed earlier.

Single-shot two-channel Talbot interferometry using checker grating and Hilbert-Huang fringe pattern processing

Diffraction efficiency and image processing enhanced two-dimensional Talbot shearing interferometry providing phase object derivative information in two mutually orthogonal directions is proposed. The properties of the Talbot interferometer using amplitude checker grating are studied and its performance is compared with a common configuration based on the cross-type amplitude Ronchi grids. Besides the light output gain further setup attractiveness is related to conducting the automatic fringe pattern analysis guided by recently introduced Hilbert-Huang processing for single exposure two-dimensional grating interferometry. The checker grating self-image deformed by the object under test is resolved into two linear fringe families running in 45/135 deg directions with respect to checker grating lines. Next the separated fringe sets are filtered using automatic selective reconstruction aided by enhanced fast empirical mode decomposition and mutual information detrending. Finally the Hilbert spiral transform is implemented to retrieve phase maps representing first derivatives of the object phase distribution. Efficient adaptive digital filtering enables analysis of complex patterns without resorting to coherent spatial filtering resulting in complicated and bulky experimental setups. Numerical and experimental studies corroborate the robustness and versatility of the proposed approach.

Evaluation of optical parameters of quasi-parallel plates with single-frame interferogram analysis methods

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