Phase shifting profilometry (PSP) is considered as an effective method for 3D shape measurement based onfringe projection. However, PSP is not suitable for dynamic measurement, as it requires that the object be keptstill. Movement of the object during the cause of projection of multiple fringe patterns may lead to significanterror in the measurement of the 3D shape. A number of approaches were proposed to combat this problemconsisting of two steps: Capturing of the movement and then compensation (or correction) of fringe patterns.However, such compensation is only valid for the cases where the object moves or rotates in the way that allpoints on the object surface change by the same amount. In other words, there is still not a method effective formeasuring objects moving in a free 3D space. In this paper, a new method is proposed to combat the problem.Firstly, movement of the object is capturing by means of existing methods, yielding rotation matrix andtranslation vector, able to characterize arbitrary movement in a 3D space. Secondly, variation of the fringepatterns by the movement is analyzed and formulated, leading to the expressions of phase maps. Based on theseexpressions, a new method is proposed to compensate the variance on height map, with which PSP can be usedto yield improved measurement performance. Computer simulations is carried out to verify the effectiveness ofthe proposed method.
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