Closed-loop phase stepping in a calibrated fiber-optic fringe projector for shape measurement.

Active homodyne feedback control can be used to stabilize an interferometer against unwanted phase drifts introduced by, for example, temperature gradients. The technique is commonly used in fiber-optic sensors to maintain the fiber at its most sensitive (quadrature) position. We describe an extension of the technique to introduce stabilized, pi/2-rad phase steps in a full-field interferometer. The technique was implemented in a single-mode, fiber-optic interference fringe projector used for shape measurement and can be easily applied to other fiber- or bulk-optic interferometers, for example, speckle pattern and holographic interferometers. Fresnel reflections from the distal fiber ends undergo a double pass in the fibers and interfere at the fourth port of a directional coupler. The interference intensity (and hence phase) is maintained at quadrature by feedback control to a phase modulator in one of the fiber arms. Stepping between quadrature positions (separated by pi rad for light undergoing a double pass) introduces stabilized phase steps in the projected fringes (separated by pi/2 rad for a single pass). A root-mean-square phase stability of 0.61 mrad in a 50-Hz bandwidth and phase step accuracy of 1.17 mrad were measured.