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.

[1]  Alejandro Federico,et al.  Normalization of fringe patterns using the bidimensional empirical mode decomposition and the Hilbert transform. , 2009, Applied optics.

[2]  Olof Bryngdahl,et al.  Moiré and higher grating harmonics , 1975 .

[3]  Jean Claude Nunes,et al.  Image analysis by bidimensional empirical mode decomposition , 2003, Image Vis. Comput..

[4]  Olof Bryngdahl,et al.  Characteristics of superposed patterns in optics , 1976 .

[5]  Xu Guanlei,et al.  Improved bi-dimensional EMD and Hilbert spectrum for the analysis of textures , 2009 .

[6]  Alejandro Federico,et al.  Noise reduction in digital speckle pattern interferometry using bidimensional empirical mode decomposition. , 2008, Applied optics.

[7]  Jesmin F. Khan,et al.  A novel approach of fast and adaptive bidimensional empirical mode decomposition , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[8]  Olof Bryngdahl,et al.  Moiré: Formation and interpretation , 1974 .

[9]  Alejandro Federico,et al.  Phase measurement in temporal speckle pattern interferometry signals presenting low-modulated regions by means of the bidimensional empirical mode decomposition. , 2011, Applied optics.

[10]  Reiner Eschbach,et al.  Generation of moiré by nonlinear transfer characteristics , 1988 .

[11]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[12]  Christophe Damerval,et al.  A fast algorithm for bidimensional EMD , 2005, IEEE Signal Processing Letters.

[13]  Krzysztof Patorski,et al.  Examination of singular scalar light fields using wavelet processing of fork fringes. , 2011, Applied optics.

[14]  Roger D. Hersch,et al.  The role of Fourier theory and of modulation in the prediction of visible moiré effects , 2009 .

[15]  Krzysztof Patorski,et al.  Visualization of additive-type moiré and time-average fringe patterns using the continuous wavelet transform. , 2010, Applied optics.

[16]  Huanfeng Ma,et al.  Advanced continuous wavelet transform algorithm for digital interferogram analysis and processing , 2006 .

[17]  Jesmin F. Khan,et al.  Fast and Adaptive Bidimensional Empirical Mode Decomposition Using Order-Statistics Filter Based Envelope Estimation , 2008, EURASIP J. Adv. Signal Process..

[18]  Munther A Gdeisat,et al.  Spatial carrier fringe pattern demodulation by use of a two-dimensional continuous wavelet transform. , 2006, Applied optics.

[19]  David P. Dobkin,et al.  The quickhull algorithm for convex hulls , 1996, TOMS.

[20]  K. Patorski,et al.  Evaluation of amplitude encoded fringe patterns using the bidimensional empirical mode decomposition and the 2D Hilbert transform generalizations. , 2011, Applied optics.

[21]  Krzysztof Patorski,et al.  Moiré Profile Prediction by Using Fourier Series Formalism , 1976 .

[22]  Markku Renfors,et al.  Code Tracking Algorithms for Mitigating Multipath Effects in Fading Channels for Satellite-Based Positioning , 2008, EURASIP J. Adv. Signal Process..