Two-dimensional multiscale windowed Fourier transform based on two-dimensional wavelet transform for fringe pattern demodulation

2011 ◽  
Vol 43 (1) ◽  
pp. 72-81 ◽  
Author(s):  
Hai Li ◽  
Chuping Yang
1993 ◽  
Vol 47 (7) ◽  
pp. 863-868 ◽  
Author(s):  
Satoshi Takahashi ◽  
Jeung Sun Ahn ◽  
Shuji Asaka ◽  
Teizo Kitagawa

A system for multichannel Fourier transform spectroscopy was constructed by using a CCD detector and an interferometer consisting of Savart plate held between two polarizers, and practical problems associated with its application to Raman experiments were investigated. The novel idea of the present system lies in avoiding the aliasing distortion, seen in the spectrum measured with a one-dimensional multichannel detector, by arranging the principal axis of the sensitized plane of the CCD detector so that it is not coincident with the direction of the fringe pattern of the interferogram. The observed interferogram suffered geometrical distortion due to incompleteness of the Savart plate. In order to circumvent this problem, an algorithm for correcting this distortion by referring to the interferogram of appropriate monochromatic light was successfully developed. The resolution of a Raman spectrum obtained for indene was ∼40 cm−1, in agreement with the theoretical value expected for this system.


Author(s):  
Mawardi Bahri ◽  
Ryuichi Ashino ◽  
Rémi Vaillancourt

A two-dimensional (2D) quaternion Fourier transform (QFT) defined with the kernel [Formula: see text] is proposed. Some fundamental properties, such as convolution, Plancherel and vector differential theorems, are established. The heat equation in quaternion algebra is presented as an example of the application of the QFT to partial differential equations. The wavelet transform is extended to quaternion algebra using the kernel of the QFT.


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