Single shot interferogram analysis for optical metrology.

We report a novel constrained optimization method for single shot interferogram analysis. The unknown test wavefront is estimated as a minimum L2-norm squared solution whose phase is constrained to the space spanned by a finite number of Zernike polynomials. Using a single frame from standard phase shifting datasets, we demonstrate that our approach provides a phase map that matches with that generated using phase shifting algorithms to within λ/100  rms error. Our simulations and experimental results suggest the possibility of a simplified low-cost high quality optical metrology system for performing routine metrology tests involving smooth surface profiles.

[1]  J. Marroquín,et al.  General n-dimensional quadrature transform and its application to interferogram demodulation. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[2]  B. A. D. H. Brandwood A complex gradient operator and its applica-tion in adaptive array theory , 1983 .

[3]  Kedar Khare,et al.  Single shot high resolution digital holography. , 2013, Optics express.

[4]  Wolfgang Osten,et al.  Improvement of the regularized phase tracking technique for the processing of nonnormalized fringe patterns. , 2002, Applied optics.

[5]  J. Wyant,et al.  Basic Wavefront Aberration Theory for Optical Metrology , 1992 .

[6]  Mitsuo Takeda,et al.  Spatial-carrier fringe-pattern analysis and its applications to precision interferometry and profilometry: An overview , 1990 .

[7]  Christopher J. Evans,et al.  PVr—a robust amplitude parameter for optical surface specification , 2009 .

[8]  J. Marroquín,et al.  Demodulation of a single interferogram by use of a two-dimensional regularized phase-tracking technique. , 1997, Applied optics.

[9]  Katherine Creath,et al.  Choosing a phase-measurement algorithm for measurement of coated LIGO optics , 2000, SPIE Optics + Photonics.

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

[11]  Kedar Khare,et al.  Quantitative phase imaging with single shot digital holography , 2014 .

[12]  Robert E. Parks,et al.  Visualization of surface figure by the use of Zernike polynomials. , 1995, Applied optics.

[13]  Qian Kemao,et al.  Sequential demodulation of a single fringe pattern guided by local frequencies. , 2007, Optics letters.

[14]  M Servin,et al.  Regularization methods for processing fringe-pattern images. , 1999, Applied optics.

[15]  M. Servin,et al.  Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms , 2001 .

[16]  M. A. Oldfield,et al.  Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[17]  D. J. Brangaccio,et al.  Digital wavefront measuring interferometer for testing optical surfaces and lenses. , 1974, Applied optics.

[18]  Thomas Kreis,et al.  Digital holographic interference-phase measurement using the Fourier-transform method , 1986 .

[19]  Manuel Servin,et al.  Regularized quadrature and phase tracking from a single closed-fringe interferogram. , 2004, Journal of the Optical Society of America. A, Optics, image science, and vision.