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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 29, Iss. 10 — Oct. 1, 2012
  • pp: 2104–2109

Experimental validation of phase using Nomarski microscopy with an extended Fried algorithm

Scott A. Prahl, Amanda Dayton, Kyle Juedes, Erik J. Sánchez, Rafael Páez López, and Donald D. Duncan  »View Author Affiliations

JOSA A, Vol. 29, Issue 10, pp. 2104-2109 (2012)

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Reconstruction of an image (or shape or wavefront) from measurements of the derivatives of the image in two orthogonal directions is a common problem. We demonstrate how a particular reconstructor, commonly referred to as the Fried algorithm, can be used with megapixel derivative images to recover the original image. Large datasets are handled by breaking the derivative images into smaller tiles, applying the Fried algorithm and stitching the tiles back together. The performance of the algorithm is demonstrated using differential interference contrast microscopy on a known test object.

© 2012 Optical Society of America

OCIS Codes
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(180.3170) Microscopy : Interference microscopy
(170.6935) Medical optics and biotechnology : Tissue characterization

ToC Category:

Original Manuscript: May 4, 2012
Revised Manuscript: August 24, 2012
Manuscript Accepted: August 25, 2012
Published: September 12, 2012

Scott A. Prahl, Amanda Dayton, Kyle Juedes, Erik J. Sánchez, Rafael Páez López, and Donald D. Duncan, "Experimental validation of phase using Nomarski microscopy with an extended Fried algorithm," J. Opt. Soc. Am. A 29, 2104-2109 (2012)

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  1. S. S. Kou, L. Waller, G. Barbastathis, and C. J. R. Sheppard, “Transport-of-intensity approach to differential interference contrast (TI-DIC) microscopy for quantitative phase imaging,” Opt. Lett. 35, 447–449 (2010). [CrossRef]
  2. M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. 73, 1434–1441 (1983). [CrossRef]
  3. C. Preza, S. V. King, and C. J. Cogswell, “Algorithms for extracting true phase from rotationally-diverse and phase-shifted DIC images,” Proc. SPIE 6090, 60900E (2006). [CrossRef]
  4. M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7–12 (2004). [CrossRef]
  5. M. Shribak and S. Inoué, “Orientation-independent differential interference contrast microscopy,” Appl. Opt. 45, 460–469 (2006). [CrossRef]
  6. K. J. Dana, “Three dimensional reconstruction of the tectorial membrane: an image processing method using Nomarski differential interference contrast microscopy,” Master’s thesis (Massachusetts Institute of Technology, 1992).
  7. D. D. Duncan, D. G. Fischer, A. Dayton, and S. A. Prahl, “Quantitative Carré differential interference contrast microscopy to assess phase and amplitude,” J. Opt. Soc. Am. A 28, 1297–1306(2011). [CrossRef]
  8. D. L. Fried, “Least-square fitting a wave-front distortion estimate to an array of phase-difference measurements,” J. Opt. Soc. Am. 67, 370–375 (1977). [CrossRef]
  9. D. L. Fried, “Branch point problem in adaptive optics,” J. Opt. Soc. Am. A 15, 2759–2768 (1998). [CrossRef]
  10. D. L. Fried, “Adaptive optics wave function reconstruction and phase unwrapping when branch points are present,” Opt. Commun. 200, 43–72 (2001). [CrossRef]
  11. W. J. Tropf, M. E. Thomas, and T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, Volume II: Devices, Measurements, & Properties, 2nd ed. (McGraw-Hill, 1995), Chap. 33, pp. 33.3–33.101.
  12. D. D. Duncan, D. G. Fischer, M. Daneshbod, and S. A. Prahl, “Differential interference contrast microscopy for the quantitative assessment of tissue organization,” Proc. SPIE 7570, 75700C (2010). [CrossRef]
  13. R. H. Hudgin, “Wave-front reconstruction for compensated imaging,” J. Opt. Soc. Am. 67, 375–378 (1977). [CrossRef]
  14. R. J. Noll, “Phase estimates from slope-type wavefront sensors,” J. Opt. Soc. Am. 68, 139–140 (1978). [CrossRef]
  15. W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980). [CrossRef]
  16. D. J. Cuccia, F. Bevilacqua, A. J. Durkin, and B. J. Tromberg, “Modulated imaging: quantitative analysis and tomography of turbid media in the spatial-frequency domain,” Opt. Lett. 30, 1354–1356 (2005). [CrossRef]
  17. D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. 14, 024012 (2009). [CrossRef]

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