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Applied Optics

Applied Optics


  • Vol. 26, Iss. 18 — Sep. 15, 1987
  • pp: 3919–3928

Refraction correction in holographic interferometry and tomography of transparent objects

Ignacio H. Lira and Charles M. Vest  »View Author Affiliations

Applied Optics, Vol. 26, Issue 18, pp. 3919-3928 (1987)

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In this paper we review and extend the state of the art in the algorithms that have been developed to tomographically reconstruct 1-D and 2-D refractive-index fields in the presence of significant refraction. A perturbation approach and two iterative procedures were tested and compared in numerical simulation of holographic interferometry experiments. Due to the nonlinearity of the problem, it is very difficult to draw general conclusions with respect to the behavior of the iterative algorithms, which is divergent in the examples presented here. In contrast, the perturbation technique, which is the easiest one to implement and the fastest to run, is shown to be very powerful in reducing refraction errors.

© 1987 Optical Society of America

Original Manuscript: December 23, 1986
Published: September 15, 1987

Ignacio H. Lira and Charles M. Vest, "Refraction correction in holographic interferometry and tomography of transparent objects," Appl. Opt. 26, 3919-3928 (1987)

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  1. C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).
  2. C. M. Vest “Tomography for Properties of Materials that Bend Rays: a Tutorial,” Appl. Opt. 24, 4089 (1985). [CrossRef] [PubMed]
  3. R. J. Lytle, K. A. Dines, “Iterative Ray Tracing Between Boreholes for Underground Image Reconstruction,” IEEE Trans. Geosci. Remote Sensing GE-18, 234 (1980). [CrossRef]
  4. A. H. Andersen, A. C. Kak, “The Application of Ray Tracing Towards a Correction for Refracting Effects in Computed Tomography with Diffracting Sources,” TR-EE 84-14, School of Electrical Engineering, Purdue U. (1984).
  5. S. A. Johnson, J. F. Greenleaf, A. Chu, J. Sjostrand, B. K. Gilbert, E. H. Wood, “Reconstruction of Material Characteristics from Highly Refraction Distorted Projections by Ray Tracing,” in Technical Digest of Topical Meeting on Image Processing for 2-D and 3-D Reconstruction from Projections: Theory and Practice in Medicine and the Physical Sciences (Optical Society of America, Washington, DC, 1975), paper TuB2.
  6. M. Born, E. Wolf, Principles of Optics(Pergamon, New York, 1975).
  7. G. P. Wachtel, “Refraction Error in Interferometry of Boundary Layer in Supersonic Flow Along a Flat Plate,” Ph.D. Thesis, Princeton U. (1951).
  8. W. L. Howes, D. R. Buchele, “A Theory and Method for Applying Interferometry to the Measurement of Certain Two-Dimensional Density Fields,” NACA TN-2693 (1952).
  9. W. L. Howes, D. R. Buchele, “Generalization of Gas-Flow Interferometry Theory and Interferogram Evaluation Equations for One-Dimensional Density Fields,” NACA TN-3340 (1955).
  10. W. L. Howes, D. R. Buchele, “Practical Considerations in Specific Applications of Gas-Flow Interferometry,” NACA TN-3507 (1955).
  11. W. L. Howes, D. R. Buchele, “Optical Interferometry of Inhomogeneous Gases,” J. Opt. Soc. Am. 56, 1517 (1966). [CrossRef]
  12. E. E. Anderson, W. H. Stevenson, R. Viskanta, “Estimating the Refractive Error in Optical Measurements of Transport Phenomena,” Appl. Opt. 14, 185 (1975). [PubMed]
  13. K. W. Beach, R. H. Muller, C. W. Tobias, “Light-Deflection Effects in the Interferometry of One-Dimensional Refractive-Index Fields,” J. Opt. Soc. Am. 63, 559 (1973). [CrossRef]
  14. F. R. McLarnon, R. H. Muller, C. W. Tobias, “Derivation of One-Dimensional Refractive-Index Profiles from Interferograms,” J. Opt. Soc. Am. 65, 1011 (1975). [CrossRef]
  15. J. M. Mehta, W. Z. Black, “Errors Associated with Interferometric Measurement of Convective Heat Transfer Coefficients,” Appl. Opt. 16, 1720 (1977). [CrossRef] [PubMed]
  16. J. M. Mehta, W. M. Worek, “Analysis of Refraction Errors for Interferometric Measurements in Multicomponent Systems,” Appl. Opt. 23, 928 (1984). [CrossRef] [PubMed]
  17. F. W. Schmidt, M. E. Newell, “Evaluation of Refraction Errors in Interferometric Heat Transfer Studies,” Rev. Sci. Instrum. 39, 592 (1968). [CrossRef]
  18. H. Svensson, “The Second-Order Aberrations in the Interferometric Measurement of Concentration Gradients,” Opt. Acta 1, 25 (1954). [CrossRef]
  19. W. L. Howes, “Rainbow Schlieren vs Mach-Zehnder Interferometer: a Comparison,” Appl. Opt. 24, 816 (1985). [CrossRef] [PubMed]
  20. G. D. Kahl, D. C. Mylin, “Refractive Deviation Errors of Interferograms,” J. Opt. Soc. Am. 55, 364 (1965). [CrossRef]
  21. C. M. Vest, “Interferometry of Strongly Refracting Axisymmetric Phase Objects,” Appl. Opt. 14, 1601 (1975). [CrossRef] [PubMed]
  22. G. Gillman, “Interferometer Focussing Accuracy and the Effect on Interferograms for Density Measurements of Laser Produced Plasmas,” Opt. Commun. 35, 127 (1980). [CrossRef]
  23. G. P. Montogomery, D. L. Reuss, “Effects of Refraction on Axisymmetric Flame Temperatures Measured by Holographic Interferometry,” Appl. Opt. 21, 1373 (1982). [CrossRef]
  24. D. W. Sweeney, D. T. Attwood, L. W. Coleman, “Interferometric Probing of Laser Produced Plasmas,” Appl. Opt. 15, 1126 (1976). [CrossRef] [PubMed]
  25. Y. Maruyama, K. Iwata, R. Nagata, “A Method for Measuring Axially Symmetrical Refractive Index Distribution Using Eikonal Approximation,” Jpn. J. Appl. Phys. 15, 1921 (1976). [CrossRef]
  26. V. D. Zimin, P. G. Frik, “Strong Refraction by Axisymmetric Optical Inhomogeneities,” Sov. Phys. Tech. Phys. 21, 233 (1976).
  27. Y. Maruyama, K. Iwata, R. Nagata, “Determination of Axially Symmetrical Refractive Index Distribution from Directions of Emerging Rays,” Appl. Opt. 16, 2500 (1977). [CrossRef] [PubMed]
  28. A. M. Hunter, P. W. Schreiber, “Mach-Zehnder Interferometer Data Reduction Method for Refractively Inhomogeneous Test Objects,” Appl. Opt. 14, 634 (1975). [CrossRef]
  29. S. Cha, C. M. Vest, “Tomographic Reconstruction of Strongly Refracting Fields and Its Application to Interferometric Measurement of Boundary Layers,” Appl. Opt. 20, 2787 (1981). [CrossRef] [PubMed]
  30. I. H. Lira, C. M. Vest, “Perturbation Correction for Refraction in Interferometric Tomography,” Appl. Opt. 26, 774 (1987). [CrossRef] [PubMed]
  31. H. Schomberg, “An Improved Approach to Reconstructive Ultrasound Tomography,” J. Phys. D 11, L181 (1978). [CrossRef]
  32. R. D. Radcliff, C. A. Balanis, “Electromagnetic Geophysical Imaging Incorporating Refraction and Reflection,” IEEE Trans. Antennas Propag. AP-29, 288 (1981). [CrossRef]
  33. R. H. T. Bates, G. C. McKinnon, “Towards Improving Images in Ultrasonic Transmission Tomography,” Australas. Phys. Sci. Med. 2–3, 134 (1979).
  34. G. C. McKinnon, R. H. T. Bates, “A Limitation on Ultrasonic Transmission Tomography,” Ultrasonic Imaging 2, 48 (1980). [CrossRef] [PubMed]
  35. A. H. Anderson, A. C. Kak, “Digital Ray Tracing in Two-Dimensional Refractive Fields,” J. Acoust. Soc. Am. 72, 1593 (1982). [CrossRef]
  36. S. J. Norton, M. Linzer, “Correcting for Ray Refraction in Velocity and Attenuation Tomography: a Perturbation Approach,” Ultrasonic Imaging 4, 201 (1982). [CrossRef] [PubMed]
  37. I. H. Lira, “Correcting for Refraction Effects in Holographic Interferometry of Transparent Objects,” Ph.D. Thesis, U. Michigan (1987).
  38. Y. Censor, “Finite Series-Expansion Reconstruction Methods,” IEEE Proc. 71, 409 (1983). [CrossRef]
  39. G. N. Ramachandran, A. V. Lakshminarayanan, “Three Dimensional Reconstruction from Radiographs and Electron Micrographs: Application of Convolution instead of Fourier Transforms,” Proc. Natl. Acad. Sci. U.S.A. 68, 2236 (1971). [CrossRef] [PubMed]
  40. L. A. Shepp, B. F. Logan, “The Fourier Reconstruction of a Head Section,” IEEE Trans. Nucl. Sci. NS-21, 21 (1974).
  41. A. H. Andersen, A. C. Kak, “Simultaneous Algebraic Reconstruction Technique (SART): a Superior Implementation of the ART Algorithm,” Ultrasonic Imaging 6, 81 (1984). [CrossRef] [PubMed]
  42. B. Gebhart, L. Pera, “The Nature of Vertical Natural Convection Flows Resulting from the Combined Buoyancy Effects on Thermal Mass Difussion,” Int. J. Heat Mass Transfer 14, 2025 (1971). [CrossRef]

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