Multiple-Wavelength Holographic Interferometry with Tunable Laser Diodes

Abstract

Two-wavelength holographic interferometry is an effective technique to generate a contour map of a diffusely reflecting surface (Friesem & Levy (1976); Heflinger & Wuerker (1969); Hildebrand & Haines (1967); Yonemura (1985)). In this technique, two holograms are recorded with two wavelengths. An interference fringe pattern is generated by superposing two object images reconstructed from the holograms. In digital holography, a hologram is recorded by an image sensor and saved into a computer. An object image can be reconstructed by numerical calculation. Several reconstruction methods were reported. Some of these have adjustablity of position and scale of a reconstruction image (Yu & Kim (2006); Zhang et al. (2004)). An object phase distribution can be obtained by the numerical reconstruction of digital holograms. Therefore, two-wavelength digital holographic interferometry makes it possible to generate a contour map by numerical extraction of a phase difference between two reconstructed images (Gass et al. (2003); Parshall & Kim (2006); Wagner et al. (2000; 1999); Yamaguchi (2001); Yamaguchi et al. (2006)). A phase difference extracted from reconstructed object images is wrapped into a half-open interval (−π,π]. If a measured object height was largewith respect to a synthetic wavelength, 2π ambiguities of the phase difference should be eliminated for retrieving the object profile. Common phase unwrapping algorithms (Asundi & Wensen (1998); Servin et al. (1998)) which use phase information of neighbor pixels can be applied when an object structure has no discontinuity. However the algorithms can not work correctly for an object profile having isolated region surrounded by discontinuous step. An object profile with discontinuous structure can be measured by two-wavelength interferometry with a sufficiently large synthetic wavelength. For example, two-wavelength holographic interferometry with a ruby laser and a synthetic wavelength of ∼ 2 cm was reported (Heflinger & Wuerker (1969); Pedrini et al. (1999)). Nevertheless the measurement error tends to be amplified linearly with an increase in the synthetic wavelength since most of the error sources are the product of the synthetic wavelength and an error of the extracted phase difference (Cheng & Wyant (1984)). A technique which eliminates 2π ambiguities by using a phase difference with a large synthetic wavelength was reported (Cheng & Wyant (1985); de Groot (1991); Wagner et al. (2000)). This technique makes it possible to measure a large step-height with high depth resolution. Wagner et. al. reported multiple-wavelength holographic interferometry using a dye laser. They combined three phase differences with synthetic wavelengths of 3.04 mm, 3