Measuring the complex amplitude of wave fields by means of shear interferometry.

This paper presents a treatise on the determination of the complex amplitude of a monochromatic wave field from measurements obtained by a lateral shear interferometer. Both amplitude and phase distributions are recovered from the same set of measurements. Special consideration is given to the case of measurements with large shear. Here, the state of the art in the reconstruction of discontinuous wavefronts is extended by introducing a two-step process. In the first step, the phasors of the underlying wavefront are reconstructed across specific subsets of the measurement grid. In the second step, the individual reconstructions are combined by a novel (to the best of the author's knowledge) convolution approach in the Fourier domain, called residual phasor separation.

[1]  D. Youla,et al.  Image Restoration by the Method of Convex Projections: Part 1ߞTheory , 1982, IEEE Transactions on Medical Imaging.

[2]  R. Prim.  Shortest connection networks and some generalizations , 1957 .

[3]  Y. Y. Hung,et al.  Image-shearing camera for direct measurement of surface strains. , 1979, Applied optics.

[4]  J C Wyant,et al.  Two-wavelength phase shifting interferometry. , 1984, Applied optics.

[5]  C. Falldorf,et al.  Compact Lateral Shearing Interferometer to Determine Continuous Wave Fronts , 2007, 2007 3DTV Conference.

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

[7]  Lianxiang Yang,et al.  Digital Shearography for Nondestructive Testing: Potentials, Limitations, and Applications , 2004 .

[8]  Claas Falldorf,et al.  Efficient reconstruction of spatially limited phase distributions from their sheared representation. , 2007, Applied optics.

[9]  David L. Fried,et al.  Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements , 1977 .

[10]  K. Creath.  Phase-Shifting Speckle Interferometry , 1985, Optics & Photonics.

[11]  Petra Aswendt,et al.  ESPI solution for non-contacting MEMS-on-wafer testing , 2003 .

[12]  John F Nye,et al.  The elliptic umbilic diffraction catastrophe , 1979, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[13]  Thomas M. Kreis,et al.  Automatic Evaluation Of Holographic Interferograms By Reference Beam Phase Shifting , 1983, Other Conferences.

[14]  M Cywiak,et al.  Extreme shearing interferometry: theoretical limits with practical consequences. , 2007, Optics express.

[15]  Wolfgang Osten,et al.  Shearography system for the testing of large-scale aircraft components taking into account noncooperative surfaces , 2000, SPIE Optics + Photonics.

[16]  I. Yamaguchi,et al.  Phase-shifting digital holography. , 1997, Optics letters.

[17]  Chris L. Koliopoulos,et al.  Modal estimation of a wave front from difference measurements using the discrete Fourier transform , 1986 .

[18]  David L. Fried,et al.  Adaptive optics wave function reconstruction and phase unwrapping when branch points are present , 2001 .

[19]  J C Wyant,et al.  Evaluation of large aberrations using a lateral-shear interferometer having variable shear. , 1975, Applied optics.

[20]  C. Elster,et al.  Solution to the shearing problem. , 1999, Applied optics.

[21]  Jean-François Vandenrijt,et al.  Electronic speckle pattern interferometry and digital holographic interferometry with microbolometer arrays at 10.6 μm. , 2010, Applied optics.

[22]  J L Marroquin,et al.  Wave-front recovery from two orthogonal sheared interferograms. , 1996, Applied optics.

[23]  David L Fried,et al.  Evaluation of the performance of a shearing interferometer in strong scintillation in the absence of additive measurement noise. , 2002, Applied optics.

[24]  Claas Falldorf,et al.  Shearing interferometer based on the birefringent properties of a spatial light modulator. , 2009, Optics letters.

[25]  H van Brug.  Zernike polynomials as a basis for wave-front fitting in lateral shearing interferometry. , 1997, Applied optics.

[26]  R. Hudgin.  Wave-front reconstruction for compensated imaging , 1977 .

[27]  S. Loheide,et al.  Innovative evaluation method for shearing interferograms , 1997 .

[28]  R Kowarschik,et al.  Testing of refractive silicon microlenses by use of a lateral shearing interferometer in transmission. , 1998, Applied optics.

[29]  Ole Lekberg.  Electronic speckle pattern interferometry , 1980 .

[30]  Isaac Freund,et al.  Optical dislocation networks in highly random media , 1993 .

[31]  U. Schnars,et al.  Direct recording of holograms by a CCD target and numerical reconstruction. , 1994, Applied optics.

[32]  Ervin Kolenovic,et al.  Speckle shearography using a multiband light source , 2003 .

[33]  Ole Lekberg,et al.  Electronic speckle pattern interferometry , 1980 .

[34]  W. J. Bates.  A wavefront shearing interferometer , 1947 .

[35]  Peiying Liang,et al.  Two-dimensional wave-front reconstruction from lateral shearing interferograms. , 2006, Optics express.

[36]  A. V. Mamaev,et al.  Wave-front dislocations: topological limitations for adaptive systems with phase conjugation , 1983 .