OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 6 — Mar. 14, 2011
  • pp: 5350–5356

Isotropic edge-enhancement by the Hilbert-transform in optical tomography of phase objects

Areli Montes-Perez, Cruz Meneses-Fabian, and Gustavo Rodriguez-Zurita  »View Author Affiliations

Optics Express, Vol. 19, Issue 6, pp. 5350-5356 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (1196 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



In optical tomography, isotropic edge-enhancement of phase-object slices under the refractionless limit approximation can be reconstructed using spatial filtering techniques. The optical Hilbert-transform of the transmittance function leaving the object at projection angles ϕ ( 0 0 , 360 0 ) , is one of these techniques with some advantages. The corresponding irradiance of the so modified transmittance is considered as projection data, and is proved that they share two properties with the Radon transform: its symmetry property and its zeroth-moment conservation. Accordingly, a modified sinogram able to reconstruct edge-enhanced phase slices is obtained. In this paper, the theoretical model is amply discussed and illustrated both with numerical and experimental results.

© 2011 OSA

OCIS Codes
(070.1170) Fourier optics and signal processing : Analog optical signal processing
(100.2980) Image processing : Image enhancement
(100.6950) Image processing : Tomographic image processing
(070.2615) Fourier optics and signal processing : Frequency filtering

ToC Category:
Image Processing

Original Manuscript: November 29, 2010
Revised Manuscript: January 20, 2011
Manuscript Accepted: January 21, 2011
Published: March 7, 2011

Virtual Issues
Vol. 6, Iss. 4 Virtual Journal for Biomedical Optics

Areli Montes-Perez, Cruz Meneses-Fabian, and Gustavo Rodriguez-Zurita, "Isotropic edge-enhancement by the Hilbert-transform in optical tomography of phase objects," Opt. Express 19, 5350-5356 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. S. R. Deans, “The Radon Transform and Some of its Applications,” (Wiley, New York. 1983).
  2. A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography—principles and applications,” Rep. Prog. Phys. 66(2), 239–303 (2003). [CrossRef]
  3. G. P. Montgomery and D. L. Reuss, “Effects of refraction on axisymmetric flame temperatures measured by holographic interferometry,” Appl. Opt. 21(8), 1373–1380 (1982). [CrossRef] [PubMed]
  4. J. M. Mehta and W. Z. Black, “Errors associated with interferometric measurement of convective heat transfer coefficients,” Appl. Opt. 16(6), 1720–1726 (1977). [CrossRef] [PubMed]
  5. J. M. Mehta and W. M. Worek, “Analysis of refraction errors for interferometric measurements in multicomponent systems,” Appl. Opt. 23(6), 928–933 (1984). [CrossRef] [PubMed]
  6. S. Cha and C. M. Vest, “Tomographic reconstruction of strongly refracting fields and its application to interferometric measurement of boundary layers,” Appl. Opt. 20(16), 2787–2794 (1981). [CrossRef] [PubMed]
  7. C. Meneses-Fabian, G. Rodriguez-Zurita, and V. Arrizón, “Optical tomography of transparent objects with phase-shifting interferometry and stepwise-shifted Ronchi ruling,” J. Opt. Soc. Am. A 23(2), 298–305 (2006). [CrossRef]
  8. C. Meneses-Fabian, G. Rodriguez-Zurita, R. Rodriguez-Vera, and F. Jose, “Optical tomography with parallel projection differences and Electronic Speckle Pattern Interferometry,” Opt. Commun. 228(4-6), 201–210 (2003). [CrossRef]
  9. G. Rodríguez-Zurita, C. Meneses-Fabián, J.-S. Pérez-Huerta, and J.-F. Vázquez-Castillo, ““Tomographic directional derivative of phase objects slices using 1-D derivative spatial filtering of fractional order ½,” ICO20,” Proc. SPIE 6027, 410–416 (2006).
  10. J. A. Davis, D. E. McNamara, and D. M. Cottrell, “Analysis of the fractional hilbert transform,” Appl. Opt. 37(29), 6911–6913 (1998). [CrossRef]
  11. J. A. Davis, D. E. McNamara, D. M. Cottrell, and J. Campos, “Image processing with the radial Hilbert transform: theory and experiments,” Opt. Lett. 25(2), 99–101 (2000). [CrossRef]
  12. J. A. Davis and M. D. Nowak, “Selective edge enhancement of images with an acousto-optic light modulator,” Appl. Opt. 41(23), 4835–4839 (2002). [CrossRef] [PubMed]
  13. J. Hsieh, “Computed Tomography: principles, design, artifacts, and recent advances,” (SPIE PRESS, Bellingham, Washington USA, 2003).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited