Temporal Phase Stepping Research Articles

A Robust Data Evaluation Method for the DCMIX Microgravity Experiments

Measurements of non-isothermal diffusion in ternary mixtures under microgravity conditions are performed in the framework of the DCMIX (Diffusion and thermodiffusion Coefficient Measurements in ternary mIXtures) project aboard the ISS by means of the SODI instrument. Its digital Mach-Zehnder interferometer permits the time resolved determination of the 2d-refractive index profile within a Soret cell at two different detection wavelengths of 670 and 935 nm. The operation of the interferometer is based on temporal phase stepping, where five consecutive images with a phase shift of π/2 are combined to an image stack. We present a robust method for the evaluation of these interferometric data by mapping the time evolution of the phase gradient in the center of the cell to an equivalent two-color optical beam deflection (2-OBD) experiment. It allows to extract transients of the central phase gradient even in occasional situations where temporal phase stepping breaks down due to laser instabilities. For this purpose, only a single image from every image stack, instead of five images with well controlled π/2-phase stepping, is required. Our results demonstrate the sound design and the robustness of the SODI instrument, which still yields fully valid data even in the event of unexpected laser phase instabilities.

Silicon microelement vibration testing using conventional and heterodyned time-average interferometry with automated temporal and spatial phase stepping

This paper focuses on the applicability of the temporal (TPS) and spatial carrier (SCPS) phase-shifting techniques to the time-average interferogram intensity modulation distribution determination. Both techniques use the same mathematical formulae, but in different domains: temporal and spatial ones. They are sensitive to different types of errors. The influence of main experimental errors: phase-step miscalibration, spatial carrier miscalibration, average intensity changes and intensity noise in both the presented techniques on the fringe function determination (| J 0| or J 0 2 in case of sinusoidal vibrations), is discussed. The techniques are compared to find the most appropriate one. The time-average technique with heterodyning for small vibration–amplitude measurements is also discussed. The application of the SCPS method to this technique is shown for the first time.

Surface strain measurement using multi-component shearography with coherent fibre-optic imaging bundles

Shearography is a full-field interferometric speckle technique used to determine displacement derivatives. Measurement of surface strain is possible using shearography if six components of displacement gradient are calculated. This can be achieved using shearography instrumentation that incorporates at least three measurement channels combined with two orthogonal shear directions. This paper presents a laser shearography instrument that utilizes coherent imaging fibre bundles to port four spatially multiplexed speckle images to a single CCD camera via a shearing Michelson interferometer. The four images are spatially multiplexed onto the sensor of a CCD camera. Wrapped phase maps are derived from the recorded speckle interferograms using temporal phase stepping. The unwrapped phase maps are combined with the measurement channel sensitivity vectors using a matrix operation to determine the required displacement derivatives. Results from an out-of-plane displacement of a flat aluminium plate are presented and compared with a computational model. Results from a second test object that show in-plane and out-of-plane strain components are also shown.

Interferogram intensity modulation calculations using temporal phase shifting: error analysis

The phase shifting method is an effective tool to determine the intensity modulation distribution of a two-beam interferogram. We present numerical studies of the influence of two experimental errors on the results obtained using temporal phase stepping, i.e., the phase step miscalibration and average intensity changes between the component interferograms. Experimental studies of vibration mode patterns by time-average interferometry provide excellent verification of numerical findings. Comparative analysis of interferogram contrast and intensity modulation determination is included.