Frequency modulation interpretation of fringes and computation of strains

Phase modulation is a traditional model for the interpretation of fringe patterns that provide displacement information, moiré, holographic interferometry, and speckle techniques. An alternative interpretation of the fringes is to consider them as frequency modulated signals. This change of interpretation has profound practical consequences if the space-frequency representation of signals is applied. The utilization of the energy representation of a signal in the coordinates-frequency space provides powerful procedures to retrieve strains distributions directly, from fringe patterns without resorting to differentiation of the displacements. This approach also simplifies the determination of displacements replacing unwrapping procedures by integration of the strains, a robust operation in the presence of noise. The Gabor transform, wavelet transforms, and quadratic representations of the energy of signals are tools that are available to carry out the practical implementation of this approach to fringe processing. This paper extends to two dimensions the methodology developed for one dimension in a previous paper.

[1]  Mohamed Afifi,et al.  Paul wavelet-based algorithm for optical phase distribution evaluation , 2002 .

[2]  Cesar A. Sciammarella,et al.  Detection of Fringe Pattern Information Using a Computer Based Method , 1986 .

[3]  Cesar A. Sciammarella.  A Numerical Technique Of Data Retrieval From Moire Or Photoelastic Patterns , 1969, Other Conferences.

[4]  M. Takeda,et al.  Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry , 1982 .

[5]  C. Sciammarella.  Basic optical law in the interpretation of moiré patterns applied to the analysis of strains—part 1 , 1965 .

[6]  Alejandro Federico,et al.  Phase retrieval in digital speckle pattern interferometry by use of a smoothed space-frequency distribution. , 2003, Applied optics.

[7]  Cesar A. Sciammarella,et al.  Determination of strains from fringe patterns using space-frequency representations , 2003 .

[8]  Cesar A. Sciammarella,et al.  Strain measurements in the nanometer range in a particulate composite using computer-aided moiré , 2003 .

[9]  C. Sciammarella,et al.  The determination of the components of the strain tensor in holographic interferometry , 1984 .

[10]  L R Watkins,et al.  Determination of interferometer phase distributions by use of wavelets. , 1999, Optics letters.

[11]  Cesar A. Sciammarella,et al.  Computer-assisted techniques to evaluate fringe patterns , 1992, Other Conferences.

[12]  C. A. Sciammarella,et al.  Effect of photographic-film nonlinearities on the processing of moiré-fringe data , 1967 .

[13]  X. C. D. Lega.  Processing of non-stationary interference patterns , 1997 .

[14]  C. A. Sciammarella,et al.  Digital-filtering techniques applied to the interpolation of Moiré-fringes data , 1967 .