OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editor: Gregory W. Faris
  • Vol. 3, Iss. 12 — Dec. 1, 2008

Application of maximum likelihood estimator in nano-scale optical path length measurement using spectral-domain optical coherence phase microscopy

S. M. R. Motaghian Nezam, C. Joo, G. J. Tearney, and J. F. de Boer  »View Author Affiliations

Optics Express, Vol. 16, Issue 22, pp. 17186-17195 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (332 KB) Open Access

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Spectral-domain optical coherence phase microscopy (SD-OCPM) measures minute phase changes in transparent biological specimens using a common path interferometer and a spectrometer based optical coherence tomography system. The Fourier transform of the acquired interference spectrum in spectral-domain optical coherence tomography (SD-OCT) is complex and the phase is affected by contributions from inherent random noise. To reduce this phase noise, knowledge of the probability density function (PDF) of data becomes essential. In the present work, the intensity and phase PDFs of the complex interference signal are theoretically derived and the optical path length (OPL) PDF is experimentally validated. The full knowledge of the PDFs is exploited for optimal estimation (Maximum Likelihood estimation) of the intensity, phase, and signal-to-noise ratio (SNR) in SD-OCPM. Maximum likelihood (ML) estimates of the intensity, SNR, and OPL images are presented for two different scan modes using Bovine Pulmonary Artery Endothelial (BPAE) cells. To investigate the phase accuracy of SD-OCPM, we experimentally calculate and compare the cumulative distribution functions (CDFs) of the OPL standard deviation and the square root of the Cramér- Rao lower bound 1 2 SNR over 100 BPAE images for two different scan modes. The correction to the OPL measurement by applying ML estimation to SD-OCPM for BPAE cells is demonstrated.

© 2008 Optical Society of America

OCIS Codes
(110.0180) Imaging systems : Microscopy
(110.4500) Imaging systems : Optical coherence tomography
(170.0110) Medical optics and biotechnology : Imaging systems
(180.3170) Microscopy : Interference microscopy

ToC Category:

Original Manuscript: April 22, 2008
Revised Manuscript: August 20, 2008
Manuscript Accepted: October 6, 2008
Published: October 13, 2008

Virtual Issues
Vol. 3, Iss. 12 Virtual Journal for Biomedical Optics

S. M. R. Motaghian Nezam, C. Joo, G. J. Tearney, and J. F. de Boer, "Application of maximum likelihood estimator in nano-scale optical path length measurement using spectral-domain optical coherence phase microscopy," Opt. Express 16, 17186-17195 (2008)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. K. Svoboda, C. F. Schmidt, B. J. Schnapp, S. M. Block, “Direct observation of kinesin stepping by optical trapping interferometry,”Nature 365, 721–727 (1993). [CrossRef] [PubMed]
  2. J. Farinas, A. S. Verkman, “Cell volume and plasma membrane osmotic water permeability in epithelial cell layers measured by interferometry,” Biophys. J. 71, 3511–3522 (1996). [CrossRef] [PubMed]
  3. C. Yang, A. Wax, M. S. Hahn, K. Badizadegan, R. R. Dasari, M. S. Feld, “Phase-referenced interferometer with subwavelength and subhertz sensitivity applied to the study of cell membrane dynamics,” Opt. Lett. 26, 1271–1273 (2001). [CrossRef]
  4. A. Barty, K. A. Nugent, D. Paganin, A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23, 817–819 (1998). [CrossRef]
  5. P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30, 468–470 (2005). [CrossRef] [PubMed]
  6. G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. 29, 2503–2505 (2004). [CrossRef] [PubMed]
  7. S. Kostianovski, S. G. Lipson, E. N. Ribak, “Interference microscopy and Fourier fringe analysis applied to measuring the spatial refractive-index distribution,” Appl. Opt. 32, 4744- (1993). [CrossRef] [PubMed]
  8. T. Ikeda, G. Popescu, R. R. Dasari, M. S. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. 30, 1165–1167 (2005). [CrossRef] [PubMed]
  9. M. A. Choma, A. K. Ellerbee, C. Yang, T. L. Creazzo, J. A. Izatt, “Spectral-domain phase microscopy,”Opt. Lett. 30, 1162–1164 (2005). [CrossRef] [PubMed]
  10. C. Joo, T. Akkin, B. Cense, B. H. Park, J. F. de Boer, “Spectral-domain optical coherence phase microscopy for quantitative phase-contrast imaging,” Opt. Lett. 30, 2131–2133 (2005). [CrossRef] [PubMed]
  11. D. C. Adler, R. Huber, J. G. Fujimoto, “Phase-sensitive optical coherence tomography at up to 370,000 lines per second using buffered Fourier domain mode-locked lasers,” Opt. Lett. 32, 626–628 (2007). [CrossRef] [PubMed]
  12. B. White, M. Pierce, N. Nassif, B. Cense, B. Park, G. Tearney, B. Bouma, T. Chen, J. de Boer, “In vivo dynamic human retinal blood flow imaging using ultra-high-speed spectral domain optical coherence tomography,” Opt. Express 11, 3490–3497 (2003). [CrossRef] [PubMed]
  13. S. Yazdanfar, C. Yang, M. Sarunic, J. Izatt, “Frequency estimation precision in Doppler optical coherence tomography using the Cramer-Rao lower bound,” Opt. Express 13, 410–416 (2005). [CrossRef] [PubMed]
  14. B. Park, M. C. Pierce, B. Cense, S. H. Yun, M. Mujat, G. Tearney, B. Bouma, J. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 µm,” Opt. Express 13, 3931–3944 (2005). [CrossRef] [PubMed]
  15. A. Papoulis, S. U. Pillai, Probability, Random Variables and Stochastic Processes, (McGraw-Hill, 2002) 4th edition.
  16. A. J. Miller, P. M. Joseph, “The use of power images to perform quantitative analysis on low SNR MR images,” Magn. Reson. Imaging 11, 1051–1056 (1993). [CrossRef] [PubMed]
  17. G. McGibney, M. R. Smith, “An unbiased signal-to-noise ratio measure for magnetic resonance images,” Med Phys. 20, 1077–1078 (1993). [CrossRef] [PubMed]
  18. B. A. van den, Handbook of Measurement Science, (Wiley, Chichester, England, 1982) Vol. 1, pp. 331–377.

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited