Defect Isolation from Whole to Local Field Separation in Complex Interferometry Fringe Patterns through Development of Weighted Least-Squares Algorithm

In this paper, based on Gaussian 1σ-criterion and histogram segmentation, a weighted least-squares algorithm is applied and validated on digital holographic speckle pattern interferometric data to perform phase separation on the complex interference fields. The direct structural diagnosis tool is used to investigate defects and their impact on a complex antique wall painting of Giotto. The interferometry data is acquired with a portable off-axis interferometer set-up with a phase-shifted reference beam coupled with the object beam in front of the digital photosensitive medium. A digital holographic speckle pattern interferometry (DHSPI) system is used to register digital recordings of interferogram sequences over time. The surface is monitored for as long as it deforms prior to returning to its initial reference equilibrium state prior to excitation. The attempt to separate the whole vs. local defect complex amplitudes from the interferometric data is presented. The main aim is to achieve isolation and visualization of each defect’s impact amplitude in order to obtain detailed documentation of each defect and its structural impact on the surface for structural diagnosis purposes.