Theory, development and testing of a novel six degree of freedom sensor using optical interferometry

This thesis describes the design, development and testing of a novel sensor based on optical interferometry that measures displacement to 6 degree of freedom (DoF). It starts with an in-depth mathematical analysis of the behaviour of the radiant flux over the active area of a rectangular photodetector under varying mirror tilt angle, width of photodetector active area, distance of photodetector from beam centre, distance of the photo-detector from the optical origin and light source wavelength. Findings not evident in the literature are presented, such as flux behaviour beyond the first modulation amplitude zero and the effect of fringe contraction and expansion on the flux at varying distance from beam centre and optical origin. The outcome of the analysis was crucial for deciding to use image sensors rather than photodetectors for this displacement sensor. Obtaining tilt and rotation information from the interferogram is discussed as well as the orthogonal design of the sensor. The mathematics for deriving the position vectors of displaced mirrors from the fringe analysis is given in detail. An experiment rig was built to test the sensor that included an XYZ translation stage as well as a Tilt/Rotation stage, which together provided a means of displacing the interferometer cube mirror to 6 DoF. The experiment rig integrated a 3 DoF tilt/rotation optical lever system designed specifically to accurately measure pitch, roll and yaw of the 6 DoF displacement sensor. Experimental data showed the optical lever system and 6 DoF sensor to have better than 0.01° correlation for pitch, roll and yaw over the test range of ±0.5° angular displacements. The accuracy and resolution of measuring linear displacement using optical interferometry is already well known, therefore this research adds a novel way of including angular displacement to that capability to provide displacement measurement to 6 DoF using 3 interferometers.