Closed-loop phase stabilizing and phase stepping methods for fiber-optic projected-fringe digital interferometry

Abstract

Closed-loop active homodyne control can be used to make an interferometer steady against phase fluctuating followed by, for example, temperature gradients. This technology is introduced to stabilize π/2 -rad phase steps in a full-field interferometer. Two beams emitted from a fiber-optic coupler are combined to form an interference fringe pattern on a diffusely reflecting object. Fresnel reflections from the distal fiber ends undergo a double pass in the fibers and interference at the fourth port of the coupler which formed a Michelson interferometer. We suggested two means of ac phase tracking (PTAC) and dc phase tracking (PTDC) to maintain the interference intensity at quadrature by feedback control. Stepping between quadrature positions forces a π/2 -rad phase step. A method based on the ratio of harmonic of the interference signal was proposed to estimate phase step accuracy. A root-mean-square phase stability of 1.5 mrad and phase step accuracy of 2.6 mrad were measured with PTAC and a root-mean-square phase stability of 2 mrad and phase step accuracy of 13.8 mrad were measured with PTDC for the fiber-optic projected-fringe digital interferometry following the same condition. It worked well in two hours without resetting the integrator.