Tomographic reconstruction of three-dimensional refractive index fields by use of a regularized phase-tracking technique and a polynomial approximation method.

We present a complete data-processing procedure for quantitative reconstruction of three-dimensional (3D) refractive index fields from limited multidirectional interferometric data. The proposed procedure includes two parts: (1) extraction of the projection data from limited multidirectional interferograms by a regularized phase-tracking technique and wavefront fitting and (2) reconstruction of the 3D refractive index fields by a modified polynomial approximation method. It has been shown that the procedure gives a satisfactory solution to the reconstruction issue in interferometric tomography, from the initial projection data extraction to the final image reconstruction. Computer simulation and experimental results are both presented.

[1]  D Verhoeven,et al.  Limited-data computed tomography algorithms for the physical sciences. , 1993, Applied optics.

[2]  Dong Liu,et al.  Regularized frequency-stabilizing method for single closed-fringe interferogram demodulation. , 2010, Optics letters.

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

[4]  P. Middendorf,et al.  Interferometric tomography for flow visualization of density fields in supersonic jets and convective flow. , 1994, Applied optics.

[5]  Robert D. Matulka,et al.  Determination of Three‐Dimensional Density Fields from Holographic Interferograms , 1971 .

[6]  Yao Wei,et al.  Comparison of results of interferometric phase extraction algorithms for three-dimensional flow-field tomography , 1999 .

[7]  Juan Antonio Quiroga Mellado,et al.  Algorithm for fringe pattern normalization , 2001 .

[8]  G. Herman,et al.  Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and x-ray photography. , 1970, Journal of theoretical biology.

[9]  Chandra Shakher,et al.  A review on refractive index and temperature profile measurements using laser-based interferometric techniques , 1999 .

[10]  José A. Gómez-Pedrero,et al.  Algorithm for fringe pattern normalization , 2001 .

[11]  Dong Liu,et al.  Demodulation of a single complex fringe interferogram with a path-independent regularized phase-tracking technique. , 2010, Applied optics.

[12]  T. Kreis.  Handbook of Holographic Interferometry: Optical and Digital Methods , 2004 .

[13]  J A Liburdy,et al.  Three-dimensional image reconstruction using interferometric data from a limited field of view with noise. , 1991, Applied optics.

[14]  C M Vest,et al.  Reconstruction of three-dimensional refractive index fields from multidirectional interferometric data. , 1973, Applied optics.

[15]  J. Y. Wang,et al.  Wave-front interpretation with Zernike polynomials. , 1980, Applied optics.

[16]  Yongying Yang,et al.  Polynomial approximation method for tomographic reconstruction of three-dimensional refractive index fields with limited data , 2012 .

[17]  R. Noll.  Zernike polynomials and atmospheric turbulence , 1976 .

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

[19]  S S Cha,et al.  Tomography for reconstructing continuous fields from ill-posed multidirectional interferometric data. , 1990, Applied optics.

[20]  G. Ruff,et al.  Reconstruction of refractive index fields by using relative fringe data. , 1993, Applied optics.

[21]  A. He,et al.  Algebraic iterative algorithm for deflection tomography and its application to density flow fields in a hypersonic wind tunnel. , 2006, Applied optics.

[22]  Yung H. Yu,et al.  Digital Fringe Reduction Techniques Applied To The Measurement Of Three-Dimensional Transonic Flow Fields , 1985 .

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

[24]  Vishwanath Prasad,et al.  Performance evaluation of iterative tomography algorithms for incomplete projection data. , 2004, Applied optics.

[25]  Avinash C. Kak,et al.  Principles of computerized tomographic imaging , 2001, Classics in applied mathematics.

[26]  S. Deans.  The Radon Transform and Some of Its Applications , 1983 .

[27]  Kai Li,et al.  Frequency guided methods for demodulation of a single fringe pattern with quadratic phase matching , 2011 .