Dynamic fringe analysis using GPU assisted root-MUSIC method

Abstract

Estimation of phase and its derivatives from fringe patterns, commonly referred to as fringe analysis is an important step in many non-destructive optical measurement techniques such as Fringe projection, Electronic speckle pattern interferometry (ESPI) and Digital holographic interferometry (DHI). Some of the applications of these techniques include deformation analysis, stress analysis, profilometry and defect detection. Here, the quantities of interest like displacement, stress and refractive index are encoded in the form of phase and phase derivatives in the recorded fringe patterns. In dynamic systems, large number of such fringe patterns are recorded necessitating the use of reliable and fast methods for fringe analysis. In this work, we proposed a GPU assisted subspace based method called multiple signal classification (MUSIC) for estimating both the phase and its derivatives. The method relies on noise subspace to calculate a polynomial equation whose roots are computed numerically. Both the phase and its derivatives are computed by selecting a relevant root according to the stability conditions. The performance of the proposed method was tested using 250 simulated fringe patterns with gradually increasing phase at signal to noise ratio of 5 dB. Collective processing of all 250 fringe patterns using Python’s Numpy library took approximately 14535 seconds whereas the graphics processing unit (GPU) had taken only 260 seconds, thus resulting in substantial reduction in execution time. These results show that the proposed method is robust against noise and the use of GPU makes it computationally very efficient.