Dynamic out-of-plane displacement measurement using the instantaneous analysis phase-shifting method

This paper presents an instantaneous analysis shadow moire method for dynamic out-of-plane displacement measurement. The shadow moire method is widely applied to the measurement of the out-of-plane displacement, such as the deformation or warpage on the surface of the objects. Generally, the method of phase shifting is used to analyze the phases of the shadow moire fringes and to obtain the out-of-plane displacement. To generate accurate phase shifting, the grating must be moved step by step precisely. However, the step motion provided by the conventional mechanical device is neither accurate nor prompt. In this study, a novel stair-structured plate consisting of a series of 4-step-height sets is designed to produce shadow moire fringes with the quadrature phase. The quadrature-phase fringes are utilized to extract instantaneously the shadow moire phase for measurement of the dynamic out-of-plane displacement of an object. Experiments show that our method can effectively detect the dynamic out-of-plane displacement with a micrometric scale resolution and is capable of suppressing the discrepancy of displacement to 0.83 $$\%$$ . The proposed measurement method of the out-plane displacement is suitable for the pressure sensing or application of the tactile sensor.