Shearography is an interferometric technique capable of measuring the gradient of the displacement field. Shearography has also been used to determine out-of-plane displacement fields. In the latter case, conventional integration procedures are not the ideal method for determining the displacement field, as they are more susceptible to error propagation. In this work, two integration techniques are presented, the deconvolution technique and a new procedure called analytical integration, both are capable of determining the complete out-of-plane displacement. For the deconvolution technique, an appropriate kernel is proposed to process the sum of two shearography images with orthogonal shear directions. The analytical integration technique makes use of a weighted combination of two shearography images with different shear directions. The proposed techniques were applied to simulated and experimental shearography images obtained in a controlled experiment using a circular aluminum sample. Both techniques showed results with errors lower than 6% compared to the reference displacements.

剪切成像是一种能够测量位移场梯度的干涉技术。剪切成像也被用于确定平面外位移场。在后一种情况下，传统的积分程序不是确定位移场的理想方法，因为它们更容易受到误差传播的影响。在这项工作中，提出了两种积分技术，即解卷积技术和一种称为分析积分的新程序，两者都能够确定完整的平面外位移。对于解卷积技术，提出了一个合适的内核来处理两个具有正交剪切方向的剪切图像的总和。分析积分技术利用具有不同剪切方向的两个剪切图像的加权组合。将所提出的技术应用于在使用圆形铝样品的受控实验中获得的模拟和实验剪切图像。与参考位移相比，这两种技术的结果误差均低于 6%。