Temporal Phase Unwrapping for High-Speed Holographic Shape Measurements of Geometrically Discontinuous Objects

Abstract

We are developing a High-speed Digital Holographic (HDH) system capable of performing near-simultaneous measurements of nanometer-scale displacement and micrometer-scale shape within a fraction of a second during uncontrolled environmental and physiological disturbances, suitable for industrial and life science applications. However, for some applications where time-dependent variations introduce geometrical discontinuities, optical phase measurements become a challenge. In this paper, we present methodologies that overcome these geometrical discontinuities while enabling different levels of measuring resolution. The HDH shape measurements are based on Multiple Wavelength Holographic Interferometry (MWHI). In MWHI the wavelength of the laser is rapidly varied between a series of exposures resulting in micro to millimeter scale synthetic wavelengths. In the holographic recording step, during a single laser tuning ramp, tens of rapid optical phase samplings are acquired, each describing the phase of the object with slightly varied illumination wavelengths (i.e., <0.1 nm). In the holographic reconstruction step, a database consisting of hundreds of phase maps with different synthetic wavelengths is constructed by recovering the shape from any two non-repeated combinations of the phase samplings. A custom temporal phase unwrapping method is developed that resolves and unwraps the depth uncertainties of high-resolution phase maps using the collection of low-fringe density wrapped phase maps from the database that are immune to surface discontinuities. Measurements on National Institute of Standard and Technology (NIST) traceable gauges and discontinuous samples demonstrate the performance of the method. A use of the method in a specific biomedical application is presented.