Motion tracking through moiré images of fork gratings

A highly sensitive passive motion sensing technique is presented. This strategy is reliant on two fundamental components: the generation of moiré images and the use of fork gratings as the imaged pattern. The moiré phenomenon is well known and has been used in the past for measuring small changes in position or topography due to the large scale changes in the moiré pattern relative to the change in the system. This research effort is unique in the pairing of the moiré effect with a particular pattern known as a fork grating. Fork gratings differ from Ronchi gratings, the typical pattern used in moiré experiments, in that the central fringe splits into one or more additional line pairs at the center of the pattern. This is responsible for many unique properties of the grating. Namely, the 2-D spatial Fourier Transform produces diffraction orders which carry orbital angular momentum. This research combines the unique features of both moiré pattern generation and the fork grating in order to make motion measurements of range, lateral motion, and rotation which are more sensitive than other single-aperture passive, motion sensing techniques. The fork grating introduces a handedness to the system not present in Ronchi grating systems, and the moiré imaging process creates low spatial frequency duplicates of highly sensitive, high spatial frequency diffraction orders of the fork grating. Analysis of these fork grating moiré images are analyzed in frequency space by leveraging orbital angular momentum, a conserved quantity, which allows the ambiguity of both sign and magnitude of higher order diffraction patterns present within the moiré image to be resolved. It is shown that making sensitive measurements is dependent on detection of higher diffraction order moiré patterns, and contrast enhancement techniques are developed for more reliable detection of these inherently weaker diffraction orders. Simulations and experimental data are presented as well as limitations. This new means of motion detection provides a readily available, passive system which has potential for dynamic platforms or stationary position monitoring applications.