A Comparison between wavelet fringe analysis algorithms By: Abdulbasit Abid
Outline • Fringe Analysis. • Wavelet Transform (WT). • Wavelet fringe analysis algorithms • Computer simulated & real fringes. • Comparison
CCD Camera Fringe Analysis: Fringes Object Fringe pattern • A structured light fringe pattern is projected onto the object’s surface. • The projected fringe pattern is phase modulated by the object heights. • The image of the deformed fringe pattern is captured by a CCD camera and stored in the computer.
Wavelet Wavelet: • Means a small wave of limited duration (with zero average and finite energy). • It could be real or complex. Examples of wavelets: Morlet Mexican hat Gaussian
Wavelet transform A modulated signal The result is a time-scale plot
Wavelet fringe analysis algorithms Frequency estimation Phase estimation Estimates the instantaneous frequencies, which are integrated to estimate the phase Estimates the phase Suffers from 2π discontinuities Phase unwrapping is not required Phase unwrapping is required Employs complex and real wavelet Employs complex wavelet
Simulated fringes Fringe Analysis: Phase estimation 2. The result is 1. Apply WT to the first row of the fringes (using complex Morlet wavelet). 2D Complex Array 64 512
3. Find the maximum value in each column of the Modulus array. 4. Find the corresponding angle from the Phase array.
5. If we repeat the previous process for all the 512 rows, we will get a wrapped phase. 6. Therefore, an unwrapping algorithm is needed
Simulated fringes Fringe Analysis: Frequency estimation 2. The result is 1. Apply WT to the first row of the fringes (using complex Morlet wavelet). 2D Complex Array 64 512
3. Find the maximum value in each column of the Modulus array. 4. Find the corresponding scale values at these maximum values Scales 5. Find the instantaneous frequency by:
6. Finally, the phase distribution can be found by integrating the estimated frequencies. Therefore phase unwrapping is not required
Real fringes Fringe Analysis: Phase estimation
Real fringes Fringe Analysis: Frequency estimation