Transmission-virtual grating method and its applications in measuring deformed liquid surface

A novel method based upon deformed transmission-virtual grating is proposed for determination of deformed liquid surface. Mathematic relations between out-of-plane displacement of deformed liquid surface and in-plane displacement of transmission-virtual grating for the method are derived. By addressing an orthogonal grating (1~5 line/mm) under the transparent water groove and then capturing images from upset of the deformed water surface, a displacement vector of full-field which directly associates the three-dimensional (3D) deformed liquid surface then can be evaluated by processing the recorded deformed fringe pattern by using special algorithm. By substituting the displacement field to the obtained equations then the out-of-plane displacement of 3D deformed liquid surface can be calculated. Validation test to measure the deformed water surface caused by a Chinese one-cent coin has been conducted. The result agrees with the previous literature, with except a slight difference of 2%, which demonstrates the feasibility of the developed method.