Maciej Wielgus

Adaptive enhancement of optical fringe patterns by selective reconstruction using FABEMD algorithm and Hilbert spiral transform

Presented method for fringe pattern enhancement has been designed for processing and analyzing low quality fringe patterns. It uses a modified fast and adaptive bidimensional empirical mode decomposition (FABEMD) for the extraction of bidimensional intrinsic mode functions (BIMFs) from an interferogram. Fringe pattern is then selectively reconstructed (SR) taking the regions of selected BIMFs with high modulation values only. Amplitude demodulation and normalization of the reconstructed image is conducted using the spiral phase Hilbert transform (HS). It has been tested using computer generated interferograms and real data. The performance of the presented SR-FABEMD-HS method is compared with other normalization techniques. Its superiority, potential and robustness to high fringe density variations and the presence of noise, modulation and background illumination defects in analyzed fringe patterns has been corroborated.

Evaluation of amplitude encoded fringe patterns using the bidimensional empirical mode decomposition and the 2D Hilbert transform generalizations

We propose an application for a bidimensional empirical mode decomposition and a Hilbert transform algorithm (BEMD-HT) in processing amplitude modulated fringe patterns. In numerical studies we investigate the influence of parameters of the algorithm and a fringe pattern under study on the demodulation results to optimize the procedure. A spiral phase method and the angle-oriented partial Hilbert transform are introduced to the BEMD-HT and tested. A postprocessing filtration method for BEMD-HT is proposed. Results of processing experimental data, such as vibration mode patterns obtained by time-average interferometry, correspond richly with numerical findings. They compare very well with the results of our previous investigations using the temporal phase-shifting (TPS) method and the continuous wavelet transform (CWT). Not needing to perform phase-shifting represents significant simplification of the experimental procedure in comparison with the TPS method.

Denoising and extracting background from fringe patterns using midpoint-based bidimensional empirical mode decomposition

We propose a 2D generalization to the midpoint-based empirical mode decomposition algorithm (MBEMD). Unlike with the regular bidimensional empirical mode decomposition algorithm (BEMD), we do not interpolate the upper and lower envelopes, but rather directly find the mean envelope, utilizing well-defined points between two extrema of different kinds (midpoints). This approach has several advantages, such as improved spectral selectivity and better time performance over the regular BEMD process. The MBEMD algorithm is then applied to the task of the interferometric fringe pattern analysis, to identify its distinct components. This allows separating the oscillatory pattern component, which is of interest, from the background, noise, and possibly other spurious interferometric patterns. Such an enhancement is meant to aid further phase demodulation and reduce its errors. Flexibility of the adaptive method allows for processing correlation fringe patterns met in the digital speckle pattern interferometry as well as the regular interferometric fringe patterns without any special tuning of the algorithm.

Hilbert-Huang processing and analysis of complex fringe patterns

Single-frame fringe pattern processing and analysis is an important task of optical interferometry, structural illumination and moiré techniques. In this contribution we present several algorithmic solutions based on the notion of Hilbert-Huang transform consisting of empirical mode decomposition algorithm and Hilbert spectral analysis. EMD adaptively dissects a meaningful number of intrinsic mode functions from the analyzed pattern. Appropriately managing this set of functions results in a powerful fringe processing tool. We describe in detail especially tailored manners proposed to extend the EMD algorithm to 2D and perform Hilbert-transform-aided efficient fringe pattern denoising, detrending and amplitude/phase demodulation.

AFM nanomoiré technique with phase multiplication

We discuss the phenomenon of the moire fringe phase multiplication encountered under incoherent superimposition of quasiperiodic structures. Its application to increase the in-plane displacement sensitivity of the AFM nano-moire technique is demonstrated. The principle is based on the spatial beating effect between the Mth harmonic of the nonsinusoidal profile quasiperiodic specimen and the first harmonic of the reference grating. Implementations using digitally generated reference grating and resampled AFM image are described. Numerical simulations and experiments with intermediate polymer stamps used in nanoimprint lithography illustrate and corroborate the proposal.

Real-Time Image Fusion Monitoring System: Problems and Solutions

The paper presents complete real-time image fusion system intended for supervisory and monitoring purposes in mobile appliances. The system is equipped with an optoelectronic head containing two multiband image sensors: TV and IR (infrared). System structure as well as searching process of the efficient, real-time image processing algorithms are briefly described. Principally, image registration is based on the hybrid approach (edge extraction and phase correlation). The image fusion method can be chosen according to operator demands between Laplacian pyramid and FABEMD decomposition. Real-time multispectral video signals processing is performed by application of custom hardware solution based on a single FPGA chip. This allows for implementing fast paralleled and pipelined processing flow. The system hardware is also presented in this paper.

Non-local fringe image filtration: a new interferometric data filtration paradigm?

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

Comparative Analysis of Image Fusion Performance Evaluation Methods for the Real-Time Environment Monitoring System

We discuss and compare several objective measures used for image fusion algorithm performance evaluation. Subjective assessments are given as well. Many of the considered evaluation methods originate from prior literature, we also introduce measure based on Jensen-Shannon divergence and a simple gradient-based measure, particularly well fitted for the real time fusion evaluation issue. Along with several well known fusion methods we put under tests recently developed, promising algorithm based on the fast and adaptive bidimensional empirical mode decomposition.

Fast Adaptive Processing of Low Quality Fringe Patterns by Automated Selective Reconstruction and Enhanced Fast Empirical Mode Decomposition

Optical fringe pattern processing and analysis [1] plays crucial role in metrological applications (e.g., interferometry, moire and structured illumination methods). It might be often a troublesome task because of fringe pattern defects such as noise, uneven background, low modulation and generally complex fringe shapes in a wide spatial frequency range. In this paper we present adaptive optical fringe pattern processing (filtering and normalization) techniques, robust to mentioned pattern imperfections, based on the empirical mode decomposition (EMD).

Continuous wavelet transform for d-space distribution analysis in nanocrystallic materials

We present a novel application of the continuous wavelet transform (CWT) for quantitative analysis of electron diffraction fringe patterns for material science research. With this method unsupervised analysis of large data sets can be performed, to determine statistical distribution of fringe periods, corresponding to the spacing between the planes in the atomic lattice. It is more robust and less time consuming than typical manual approach. Obtained information can be further utilized for characterization and identification of the crystallographic structures present in the sample. The proposed method is applied to analysis of high resolution transmission electron microscope (HRTEM) images of Iridium-Zinc-Silicon-Oxide thin films, which reveal nanocrystallic structures dispersed in an amorphous matrix.