Characterization of the 3D resolution of topometric sensors based on fringe and speckle pattern projection by a 3D transfer function

The increasing importance of optical 3D measurement techniques and the growing number of available methods and systems require a fast and simple method to characterize the measurement accuracy. However, the conventional approach of comparing measured coordinates to known reference coordinates of a test target faces two major challenges: the precise fabrication of the target and - in case of pattern projecting systems - finding the position of the reference points in the obtained point cloud. The modulation transfer function (MTF) on the other hand is an established instrument to describe the resolution characteristics of 2D imaging systems. Here, the MTF concept is applied to two different topometric systems based on fringe and speckle pattern projection to obtain a 3D transfer function. We demonstrate that in the present case fringe projection provides typically 3.5 times the 3D resolution achieved with speckle pattern projection. By combining measurements of the 3D transfer function with 2D MTF measurements the dependency of 2D and 3D resolutions are characterized. We show that the method allows for a simple comparison of the 3D resolution of two 3D sensors using a low cost test target, which is easy to manufacture.