Geometric phase analysis method using a subpixel displacement match algorithm

The geometrical phase analysis (GPA) method, which is an efficient and powerful noncontact method to obtain the strain field, has already been widely applied in deformation measurement in micro- and nano-scale. It is easy to get the strain field accurately; however, the displacement field is unreliable in some cases. Therefore, a subpixel displacement match method hereby is applied in the GPA method for the first time, to the best of our knowledge, to overcome this defect. The presented algorithm’s limit error of 0.01 pixel under ideal conditions can match two corresponding local areas in reference and deformation image, and, thus, the displacement with subpixel precision of this point can be established. Owing to the continuity of the displacement field, the displacements of other points can be obtained subsequently. The error that is associated with the existing method will be dealt with in detail and verified by simulation further. Combined with simulation, the performance of the presented method is demonstrated; furthermore, the noise introduced by the imaging system is taken into consideration. Finally, a typical bending test was performed, and the result agrees well with the theoretical analysis. Both the simulation and experiment results prove that the presented method is effective and robust.