Phase-map measurements by interferometry with sinusoidal phase modulation and four integrating buckets.

Phase-shifting interferometry based on the integrating-bucket technique with sinusoidal phase modulation is studied theoretically and demonstrated experimentally to obtain phase maps from double-beam interferometers. The method uses four frames obtained by integration of the time-varying intensity in an interference pattern during the four quarters of the modulation period. An optimum sinusoidal phase modulation is found to minimize the effect of the additive noise. The absolute accuracy of the phase measurements is discussed. Possible applications of the method are demonstrated with two interference microscopes with which the phase modulation is achieved by sinusoidal oscillation of a mirror attached to a piezoelectric transducer and by sinusoidal birefringence modulation with a photoelastic modulator. In both experimental arrangements, phase images can be produced in real time at a rate of several hertz. Noise measurements are reported and compared with theory.

[1]  P. J. Caber.  Interferometric profiler for rough surfaces. , 1993, Applied optics.

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

[3]  K Creath,et al.  Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry. , 1995, Applied optics.

[4]  V Loriette,et al.  Birefringence imaging with imperfect benches: application to large-scale birefringence measurements. , 2000, Applied optics.

[5]  Kenneth D. Stumpf.  Real-Time Interferometer , 1979 .

[6]  A C Boccara,et al.  Phase measurements with wide-aperture interferometers. , 2000, Applied optics.

[7]  J. Greivenkamp,et al.  Phase Shifting Interferometers , 1992 .

[8]  O. Sasaki,et al.  Sinusoidal phase modulating interferometry for surface profile measurement. , 1986, Applied optics.

[9]  Dennis C. Ghiglia,et al.  Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software , 1998 .

[10]  Mark P. Davidson,et al.  An Application Of Interference Microscopy To Integrated Circuit Inspection And Metrology , 1987, Advanced Lithography.

[11]  O. Sasaki,et al.  Analysis of measurement accuracy in sinusoidal phase modulating interferometry. , 1986, Applied optics.

[12]  G S Kino,et al.  Mirau correlation microscope. , 1990, Applied optics.

[13]  J. Schwider,et al.  New compensating four-phase algorithm for phase-shift interferometry , 1993 .

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

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

[16]  Y Surrel,et al.  Design of algorithms for phase measurements by the use of phase stepping. , 1996, Applied optics.

[17]  Bing Zhao,et al.  Phase shifting: six-sample self-calibrating algorithm insensitive to the second harmonic in the fringe signal , 1995 .

[18]  J. Schwider,et al.  IV Advanced Evaluation Techniques in Interferometry , 1990 .

[19]  Kieran G. Larkin,et al.  Design and assessment of symmetrical phase-shifting algorithms , 1992 .

[20]  J. Wyant.  Use of an ac heterodyne lateral shear interferometer with real-time wavefront correction systems. , 1975, Applied optics.

[21]  Kieran G. Larkin,et al.  Efficient nonlinear algorithm for envelope detection in white light interferometry , 1996 .

[22]  H Saint-Jalmes,et al.  Multichannel Nomarski microscope with polarization modulation: performance and applications. , 1997, Optics letters.

[23]  Y. Surrel.  Phase stepping: a new self-calibrating algorithm. , 1993, Applied optics.

[24]  B. Oreb,et al.  Design and assessment of symmetrical phase-shifting algorithms , 1992 .

[25]  Peter de Groot,et al.  Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window. , 1995, Applied optics.

[26]  D W Phillion,et al.  General methods for generating phase-shifting interferometry algorithms. , 1997, Applied optics.

[27]  O. Sasaki,et al.  Sinusoidal phase modulating interferometer using the integrating-bucket method. , 1987, Applied optics.

[28]  Chris P. Brophy,et al.  Effect of intensity error correlation on the computed phase of phase-shifting interferometry , 1990 .

[29]  A C Boccara,et al.  Real-time reflectivity and topography imagery of depth-resolved microscopic surfaces. , 1999, Optics letters.

[30]  P. Flournoy,et al.  White-light interferometric thickness gauge. , 1972, Applied optics.