Optical reconstruction of three-dimensional object from digital holograms using phase information calculated by continuous wavelet transform

2011 ◽  
Author(s):  
Zehra Saraç ◽  
Duygu Önal Tayyar ◽  
F. Necati Ecevit
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Three Dimensional ◽  
Continuous Wavelet ◽  
Phase Information ◽  
Digital Holograms ◽  
Optical Reconstruction ◽  
Dimensional Object

Study on the extraction and reconstruction of arbitrary frequency topography from precision machined surfaces

2018 ◽  
Vol 233 (7) ◽  
pp. 1772-1780 ◽  
Author(s):  
Qilong Pang ◽  
Liangjie Kuang ◽  
Youlin Xu ◽  
Xiang Dai
Keyword(s):  
Wavelet Transform ◽  
Surface Topography ◽  
Continuous Wavelet Transform ◽  
Three Dimensional ◽  
Reconstruction Method ◽  
Continuous Wavelet ◽  
Two Dimensional ◽  
Arbitrary Frequency ◽  
Frequency Features ◽  
Machined Surfaces

This article presents an extraction and reconstruction method for arbitrary two-dimensional and three-dimensional frequency features in precision machined surfaces. A combination of power spectrum density and continuous wavelet transform is used to analyze the potassium dihydrogen phosphate crystal surface topography. All frequencies involved in sampling area of measuring instrument are distinguished by power spectrum density method. Compared to discrete wavelet transform used to decompose frequency features, continuous wavelet transform method can extract and reconstruct two-dimensional profile and three-dimensional topography of arbitrary frequency features from original precision machined surfaces. Analysis results show that amplitude and distribution of different frequency features in two-dimensional profile or three-dimensional surface topography are fully restored by continuous wavelet transform. The effects of different factors in machining process on precision machined surface topography may be discovered. Furthermore, the extraction and reconstruction method is generally applicable for the analysis of all precision machined surfaces.

Flow field around a vibrating cantilever: coherent structure eduction by continuous wavelet transform and proper orthogonal decomposition

2011 ◽  
Vol 669 ◽  
pp. 584-606 ◽  
Author(s):  
Y.-H. KIM ◽  
C. CIERPKA ◽  
S. T. WERELEY
Keyword(s):  
Wavelet Transform ◽  
Proper Orthogonal Decomposition ◽  
Continuous Wavelet Transform ◽  
Vector Fields ◽  
Three Dimensional ◽  
Orthogonal Decomposition ◽  
Continuous Wavelet ◽  
Vortical Structures ◽  
Flow Features ◽  
Proper Orthogonal

The velocity field around a vibrating cantilever plate was experimentally investigated using phase-locked particle image velocimetry. Experiments were performed at Reynolds numbers of Reh = 101, 126 and 146 based on the tip amplitude and the speed of the cantilever. The averaged vector fields indicate a pseudo-jet flow, which is dominated by vortical structures. These vortical structures are identified and characterized using the continuous wavelet transform. Three-dimensional flow features are also clearly revealed by this technique. Furthermore, proper orthogonal decomposition was used to investigate regions of vortex production and breakdown. The results show clearly that the investigation of phase-averaged data hides several key flow features. Careful data post-processing is therefore necessary to investigate the flow around the vibrating cantilever and similar highly transient periodic flows.

scholarly journals Continuous Wavelet Transform of Schwartz Distributions in DL2′(Rn), n ≥ 1

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1106
Author(s):  
Jagdish N. Pandey
Keyword(s):  
Wavelet Transform ◽  
Function Space ◽  
Continuous Wavelet Transform ◽  
Inversion Formula ◽  
Continuous Wavelet ◽  
The Real ◽  
Schwartz Distributions ◽  
Distributional Sense ◽  
Wavelet Inversion

We define a testing function space DL2(Rn) consisting of a class of C∞ functions defined on Rn, n≥1 whose every derivtive is L2(Rn) integrable and equip it with a topology generated by a separating collection of seminorms {γk}|k|=0∞ on DL2(Rn), where |k|=0,1,2,… and γk(ϕ)=∥ϕ(k)∥2,ϕ∈DL2(Rn). We then extend the continuous wavelet transform to distributions in DL2′(Rn), n≥1 and derive the corresponding wavelet inversion formula interpreting convergence in the weak distributional sense. The kernel of our wavelet transform is defined by an element ψ(x) of DL2(Rn)∩DL1(Rn), n≥1 which, when integrated along each of the real axes X1,X2,…Xn vanishes, but none of its moments ∫Rnxmψ(x)dx is zero; here xm=x1m1x2m2⋯xnmn, dx=dx1dx2⋯dxn and m=(m1,m2,…mn) and each of m1,m2,…mn is ≥1. The set of such wavelets will be denoted by DM(Rn).

Sign in / Sign up

Export Citation Format

Share Document