Sensitivity improvement in phase-shifted moire´ interferometry using 1-D continuous wavelet transform image processing

2003 ◽  
Vol 42 (9) ◽  
pp. 2646 ◽  
Author(s):  
Heng Liu
Keyword(s):  
Image Processing ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Moiré Interferometry ◽  
Moire Interferometry ◽  
Continuous Wavelet ◽  
Sensitivity Improvement

scholarly journals Seismic entangled patterns analyzed via multiresolution decomposition

2009 ◽  
Vol 16 (2) ◽  
pp. 211-217 ◽  
Author(s):  
F. E. A. Leite ◽  
R. Montagne ◽  
G. Corso ◽  
L. S. Lucena
Keyword(s):  
Image Processing ◽  
Wavelet Transform ◽  
Coherent Structures ◽  
Continuous Wavelet Transform ◽  
Original Data ◽  
Continuous Wavelet ◽  
Original Image ◽  
Generating Set ◽  
Multiresolution Decomposition ◽  
Ground Roll

Abstract. This article explores a method for distinguishing entangled coherent structures embedded in geophysical images. The original image is decomposed in a series of j-scale-images using multiresolution decomposition. To improve the image processing analysis each j-image is divided in l-spacial regions generating set of (j, l)-regions. At each (j, l)-region we apply a continuous wavelet transform to evaluate Eν, the spectrum of energy. Eν has two maxima in the original data. Otherwise, at each scale Eν hast typically one peak. The localization of the peaks changes according to the (j, l)-region. The intensity of the peaks is linked with the presence of coherent structures, or patterns, at the respective (j, l)-region. The method is successfully applied to distinguish, in scale and region, the ground roll noise from the relevant geologic information in the signal.

Continuous Wavelet Transform Based Nanoscale Strain Field Measurement Using Moire´ Interferometry With Phase Shifting

2009 ◽  
Author(s):  
Bicheng Chen ◽  
Cemal Basaran
Keyword(s):  
Wavelet Transform ◽  
Spatial Resolution ◽  
Continuous Wavelet Transform ◽  
Field Measurement ◽  
Strain Field ◽  
Phase Shifting ◽  
Moire Interferometry ◽  
Continuous Wavelet ◽  
Phase Calculation ◽  
Strain Field Measurement

Moire´ Interferometry (MI) provides real-time full strain field measurement for the structure under the dynamic loading. It has been successfully applied to the reliability testing of the electronic packaging under different loadings (e.g. thermal cycling, electrical current stressing and etc). The miniaturization of the microelectronic packaging calls for the operation of MI at a level with higher sensitivity and better resolution. The proposed operation of MI combines two novel methods in the interferometry, phase shifting (PS) and continuous wavelet transform (CWT) to achieve a 164 nm/pixel spatial resolution. The entire operation procedure is completed automatically by computer programs. A two-level zooming system is designed and implemented in MI to give a high spatial resolution. The idea of combination of CWT and PS here is to put both spatial phase calculation and temporal phase calculation together. By introducing both the spatial and temporal redundancy, the authors show that the hybrid methods take the advantages from both of them. Furthermore, the direct calculation of the spontaneous spatial frequency of the interferogram is carried out using the property of the maximum power ridge of CWT. This method doesn’t require unwrapping and differentiation, which avoid the possible numerical noise introduced in these two steps. In the proposed system, pixel by pixel in-plane strain tensors can be calculated from the intensity map of interferograms using phase-based method for MI in contrast with the traditional fringe counting. The resulting strain tensor can be used to model constitutive relationship or compare with finite element analysis results. A thermal experiment on BGA packaging is used to demonstrate the advantages of the proposed new design.

The continuous wavelet transform in n-dimensions

2016 ◽  
Vol 14 (05) ◽  
pp. 1650037 ◽  
Author(s):  
J. N. Pandey ◽  
N. K. Jha ◽  
O. P. Singh
Keyword(s):  
Image Processing ◽  
Wavelet Transform ◽  
Real Number ◽  
Continuous Wavelet Transform ◽  
Inversion Formula ◽  
Spherically Symmetric ◽  
Continuous Wavelet ◽  
Wavelet Inversion ◽  
Translation Parameter

Daubechies obtained the [Formula: see text]-dimensional inversion formula for the continuous wavelet transform of spherically symmetric wavelets in [Formula: see text] with convergence interpreted in the [Formula: see text]-norm. From the wavelet [Formula: see text], Daubechies generated a doubly indexed family of wavelets [Formula: see text] by restricting the dilation parameter [Formula: see text] to be a real number greater than zero and the translation parameter [Formula: see text] belonging to [Formula: see text]. We show that [Formula: see text] can be chosen to be in [Formula: see text] with none of the components [Formula: see text] vanishing. Further, we prove that if [Formula: see text] and [Formula: see text] are continuous in [Formula: see text], then the convergence besides being in [Formula: see text] is also pointwise in [Formula: see text]. We advance our theory further to the case when [Formula: see text] and [Formula: see text] both belong to [Formula: see text] then convergence of the wavelet inversion formula is pointwise at all points of continuity of [Formula: see text]. This result significantly enhances the applicability of the wavelet inversion formula to the image processing.

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