Comparative analysis of nanometric inspection methods in fringeless speckle pattern interferometry

In digital speckle pattern interferometry, fringeless speckle pattern interferograms are obtained when the object field deformation is insufficient to produce local phase variations higher than 2π. Therefore, the use of the well-known phase recovery algorithms based on fringe processing is not adequate. In this work, distinct algorithms based on the application of a straightforward arccosine function to a filtered interferogram and the correlation of intensity images and implicit smoothing splines are proposed, analyzed, and compared for the fast inspection of nanometric displacement fields, avoiding the acquisition of several images. In addition, three different methods for the normalization of fringeless speckle pattern interferograms are proposed. The Structural Similarity Index is used to assess the performance of the tested methods by means of numerical simulations under different illuminations, signal-to-noise ratios, phase excursions, and mean speckle size conditions. The analysis shows that the phase recovered by the methods based on the arccosine function and correlation are appropriate for a fast inspection solution. The implicit smoothing spline outperforms other methods in almost all conditions.