In situ measurement of MEMS topography based on phase-shifting interferometry

Abstract. Currently, phase-shifting interferometry is widely used in MEMS (micro-electro-mechanical system) microsurface topography measurements, and an expensive and high-precision piezoelectric transducer (PZT) is often necessary to realize phase-shift operation. Because of the feature of a MEMS structure which always has a flat substrate, a practical algorithm to calculate phase shifts by fast Fourier transformation (FFT) from gathered interference fringes of the substrate is presented, then microsurface topography can be reconstructed according to the obtained phase shifts. By means of the presented algorithm, an expensive and high-precision PZT is unnecessary and the phase-shift operation can even be carried out by rotating the fine focus adjustment knob. The accuracy and feasibility of the method have been verified by experiments. Experiments indicated that the presented method can satisfy the needs of in situ MEMS topography measurements and is very simple.

[1]  J. Schwider,et al.  Digital wave-front measuring interferometry: some systematic error sources. , 1983, Applied optics.

[2]  D. Lucca,et al.  Surfaces in Precision Engineering, Microengineering and Nanotechnology , 2003 .

[3]  John E. Greivenkamp,et al.  Generalized Data Reduction For Heterodyne Interferometry , 1984 .

[4]  Hongwei Guo,et al.  Least-squares algorithm for phase-stepping interferometry with an unknown relative step. , 2005, Applied optics.

[5]  Rafael C. González,et al.  Digital image processing using MATLAB , 2006 .

[6]  Liang-Chia Chen,et al.  3-D micro surface profilometry employing novel Mirau-based lateral scanning interferometry , 2014 .

[7]  C. J. Morgan.  Least-squares estimation in phase-measurement interferometry. , 1982, Optics letters.

[8]  James C. Wyant,et al.  White light interferometry , 2002, SPIE Defense + Commercial Sensing.

[9]  B. Bhushan,et al.  Measurement of surface topography of magnetic tapes by Mirau interferometry. , 1985, Applied optics.

[10]  M. Takeda,et al.  Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry , 1982 .

[11]  Yu Fu,et al.  Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography , 2009 .

[12]  In-Bok Kong,et al.  General algorithm of phase-shifting interferometry by iterative least-squares fitting , 1995 .

[13]  James C Wyant,et al.  Computerized interferometric surface measurements [Invited]. , 2013, Applied optics.

[14]  Duncan T. Moore,et al.  Phase-Locked Interferometry , 1979 .

[15]  T. Eiju,et al.  Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm. , 1987, Applied optics.

[16]  P. Carré.  Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures , 1966 .

[17]  Martin Gohlke,et al.  Picometre and nanoradian heterodyne interferometry and its application in dilatometry and surface metrology , 2012 .

[18]  Y Surrel,et al.  Additive noise effect in digital phase detection. , 1997, Applied optics.

[19]  Ki-Nam Joo,et al.  Minimization of spectral phase errors in spectrally resolved white light interferometry by the iterative least-squared phase-shifting method , 2012 .

[20]  Wen Chen,et al.  Quantitative phase retrieval of a complex-valued object using variable function orders in the fractional Fourier domain. , 2010, Optics express.

[21]  Duncan T. Moore,et al.  Phase-Locked Interferometry , 1977, Optics & Photonics.

[22]  Pramod Rastogi,et al.  Statistical study of generalized nonlinear phase step estimation methods in phase-shifting interferometry. , 2007, Applied optics.

[23]  G. Stoilov,et al.  Phase-stepping interferometry: Five-frame algorithm with an arbitrary step , 1997 .

[24]  J. Bokor,et al.  Fourier-transform method of phase-shift determination. , 2001, Applied optics.