OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 26 — Dec. 25, 2006
  • pp: 12751–12759

Theory of two beam interference with arbitrary spectra

Zhilin Hu and Andrew M. Rollins  »View Author Affiliations

Optics Express, Vol. 14, Issue 26, pp. 12751-12759 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (256 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A new formulation describing the interference term of a two beam interferometer with unequal Gaussian spectra propagating in different dispersive media is provided by defining a composite standard deviation and a composite center frequency of the interfering spectra. This formulation is generalized to arbitrary spectra by decomposing each spectrum into a linear composition of Gaussian distributions. The effective phase and group delays indicate the effect of the unequal spectral distributions and the dispersive media. An effective coherence length is derived, different than the coherence lengths of the interfering fields. The accuracy of the new formulation is proven experimentally by using optical coherence tomography systems.

© 2006 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(110.4500) Imaging systems : Optical coherence tomography
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(170.3890) Medical optics and biotechnology : Medical optics instrumentation

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: October 4, 2006
Revised Manuscript: December 14, 2006
Manuscript Accepted: December 14, 2006
Published: December 22, 2006

Virtual Issues
Vol. 2, Iss. 1 Virtual Journal for Biomedical Optics

Zhilin Hu and Andrew M. Rollins, "Theory of two beam interference with arbitrary spectra," Opt. Express 14, 12751-12759 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. A. Michelson, "Interferometer," Am. J. Sci. 3, 120 (1881).
  2. R. S. Shankland, S. W. McCuskey, F. C. Leone, and G. Kuerti, "New analysis of the interferometer obervations of Dayton C. Miller," Rev. Mod. Phys. 27, 167-178 (1955). [CrossRef]
  3. R. P. Patten, "Michelson interferometer as a remote gauge," Appl. Opt. 10, 2717-2721 (1971). [CrossRef] [PubMed]
  4. P. Becker, K. Dorenwendt, G. Ebeling, R. Lauer, W. Lucas, R. Probst, H.-J. Rademacher, G. Reim, P. Seyfried, and H. Siegert, "Absolute measurement of the (200) lattice plane spacing in a Silicon Crystal," Phys. Rev. Lett. 46, 1540-1543 (1981). [CrossRef]
  5. M. S. Chapman, C. R. Ekstrom, T. D. Hammond, R. A. Rubenstein, J. Schmiedmayer, S. Wehinger, and D. E. Pritchard, "Optics and interferometry with Na2 Molecules," Phys. Rev. Lett. 74, 4783-4786 (1995). [CrossRef] [PubMed]
  6. T. Fuji, M. Arakawa, T. Hattori, and H. Nakatsukaa, "A white-light Michelson interferometer in the visible and near infrared regions," Rev. Sci. Instrum. 69, 2854-2858 (1998). [CrossRef]
  7. K. McKenzie, D. A. Shaddock, D. E. McClelland, B. C. Buchler, and P. K. Lam, "Experimental demonstration of a squeezing-enhanced power-recycled Michelson interferometer for gravitational wave detection," Phys. Rev. Lett. 88, 231102-231101 (2002). [CrossRef] [PubMed]
  8. W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, "Towards Quantum superpositions of a mirror," Phys. Rev. Lett. 91, 130401-130404 (2003). [CrossRef] [PubMed]
  9. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical Coherence Tomography," Science 254, 1178-1181 (1991). [CrossRef] [PubMed]
  10. M. C. Booth, G. D. Giuseppe, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, "Polarization-sensitive quantum-optical coherence tomography," Phys. Rev. A 69, 043815- (2004). [CrossRef]
  11. D. J. Faber, M. C. G. Aalders, E. G. Mik, B. A. Hooper, M. J. C. v. Gemert, and T. G. v. Leeuwen, "Oxygen saturation-dependent absorption and scattering of blood," Phys. Rev. Lett. 93, 028102 (2004). [CrossRef] [PubMed]
  12. D. L. Marks, and S. A. Boppart, "Nonlinear interferometric vibrational imaging," Phys. Rev. Lett. 92, 123905 (2004). [CrossRef] [PubMed]
  13. R. A. Leitgeb, L. Schmetterer, C. K. Hitzenberger, A. F. Fercher, F. Berisha, M. Wojtkowski, and T. Bajraszewski, "Real-time measurement of in vitro flow by Fourier-domain color Doppler optical coherence tomography," Opt. Lett. 29, 171-173 (2004). [CrossRef] [PubMed]
  14. J. Zhang, J. S. Nelson, and Z. Chen, "Removal of a mirror image and enhancement of the signal-to-noise ratio in Fourier-domain optical coherence tomography using an electro-optic phase modulator," Opt. Lett. 30, 147-149 (2005). [CrossRef] [PubMed]
  15. A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, "Optical coherence tomography—principles and applications," Rep. Prog. Phys. 66, 239-303 (2003). [CrossRef]
  16. W. Drexler, U. Morgner, R. K. Ghanta, F. X. Kartner, J. S. Schuman, and J. G. Fujimoto, "Ultrahigh-resolution ophthalmic optical coherence tomography," Nat. Med. 7, 502-507 (2001). [CrossRef] [PubMed]
  17. I. Hartl, X. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, "Ultrahigh-resolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber," Opt. Lett. 26, 608-610 (2001). [CrossRef]
  18. Y. Wang, Y. Zhao, J. S. Nelson, Z. Chen, and R. S. Windeler, "Ultrahigh-resolution optical coherence tomography by broadband continuum generation from a photonic crystal fiber," Opt. Lett. 28, 182-184 (2003). [CrossRef] [PubMed]
  19. N. Nishizawa, Y. Chen, P. Hsiung, E. P. Ippen, and J. G. Fujimoto, "Real-time, ultrahigh-resolution, optical coherence tomography with an all-fiber, femtosecond fiber laser continuum at 1.5 mm," Opt. Lett. 29, 2846-2848 (2004). [CrossRef]
  20. R. L. Forward, "Wideband laser-interferometer gravitational-radiation experiment," Phys. Rev. D 17, 379-390 (1978). [CrossRef]
  21. W. Koechner, Solid-State Laser Engineering (Springer, New York, 1999).
  22. K. J. Kuhn, Laser Engeering (Prentice-Hall, Inc., Upper Saddle River, 1998).
  23. A. Puglisi, V. Loreto, U. M. B. Marconi, A. Petri, and A. Vulpiani, "Clustering and non-Gaussian behavior in granular matter," Phys. Rev. Lett. 81, 3848-3851 (1998). [CrossRef]
  24. J. S. Olafsen, and J. S. Urbach, "Velocity distributions and density fluctuations in a granular gas," Phys. Rev. E 60, 2468-2471 (1999). [CrossRef]
  25. A. E. Siegman, Laser (1986).
  26. B. E. Bouma, and G. J. Tearney, Handbook of optical coherence tomography (Marcel Dekker, New York, 2002).
  27. A. M. Rollins, M. D. Kulkarni, S. Yazdanfar, R. Un-Arunyawee, and J. A. Izatt, "In vivo video rate optical coherence tomography," Opt. Express 3, 219-229 (1998). [CrossRef] [PubMed]
  28. Z. Hu, and A. M. Rollins, "Quasi-telecentric optical design of a microscope-compatible OCT scanner," Opt. Express 13, 6407-6415 (2005). [CrossRef] [PubMed]

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

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited