Pose Measurement at Small Scale by Spectral Analysis of Periodic Patterns

The retrieval of an observed object's pose is an essential computer vision problem. The challenge arises in many different fields, among them robotics control, contactless metrology, or augmented reality. When the observed object shrinks from the macroscopic scale to the microscopic, pose estimation is further complicated by the weaker perspective of imaging macroscale lenses down to the quasi-orthographic projection inherent to microscope objectives. This paper tackles this issue of microscale pose estimation in two complementary steps that rely on the use of planar periodic targets. We first consider the orthographic projection case as a means of presenting the theory of the method and showing how the pose of periodic patterns can be directly retrieved from the Fourier frequency spectrum of a given image. We then address the perspective case with long focal lengths, in which the full six-degrees of freedom (6-DOF) pose can be retrieved without ambiguities by following the same theoretical background. In addition to theoretically justifying pose retrieval via Fourier analysis of acquired images, this paper demonstrates the method's actual performance. Both simulations and experimentation are conducted to validate the method and confirm an experimental resolution lower than 1/1000th of a pixel for translations. For orientation measurement, resolutions below 1 mu rad. for in-plane orientation, and below 100 mu rad. for off-axis orientations can be achieved.