Displacement measurement with phosphorescent spherical marker

Measuring three-dimensional positions with images has an advantage of simultaneous and contactless measurements of multiple points in a view. One of the most useful applications of image measurements is the motion capture system that can measure a change of pose of a target object in three-dimensional space. Motion capture systems can be used for easy calibration of machine tools and parallel mechanisms if its total accuracy is improved. We have proposed phosphorescent spherical markers as optical markers for precise image measurements. The phosphorescent spherical markers can be detected in a captured image with milli-pixel precision which is about 10 times higher precision of retro-reflective markers conventionally used in motion capture systems. The milli-pixel detection is induced by two important features of phosphorescent spherical markers: (1) high sphericity, (2) high contrast between the marker and background. In this paper, we report displacement measurement with two phosphorescent spherical markers. One of these markers was fixed on a vibration isolation table. The other marker was installed on a linear stage and moved 10 mm for displacement measurement. The initial distance between these markers was 100 mm. These markers were excited by two ultraviolet lights and captured by a camera right after switching off the lights. The shooting distance was 500 mm. The three-dimensional positions of these markers were calculated from the detected marker position and diameter in the captured image. The displacement amount of the moving marker was calculated as a change of three-dimensional relative position of the moving marker against the fixed one. The displacement of the moving marker was measured 150 times for evaluating its total accuracy. The precision and total accuracy of this displacement measurement were 0.88 µm in standard deviation and 1.03 µm in RMSE respectively.