Interferometric measurements beyond the coherence length of the laser source

Interferometric measurements beyond the coherence length of the laser are investigated theoretically and experimentally in this paper. Thanks to a high-bandwidth detection, high-speed digitizers and a fast digital signal processing, we have demonstrated that the limit of the coherence length can be overcome. Theoretically, the maximal measurable displacement is infinite provided that the sampling rate is sufficiently short to prevent any phase unwrapping error. We could verify experimentally this concept using a miniature interferometer prototype, based on a frequency stabilized vertical cavity surface emitting laser. Displacement measurements at optical path differences up to 36 m could be realized with a relative stability better than 0.1 ppm, although the coherence length estimated from the linewidth and frequency noise measurements do not exceed 6.6 m. OCIS codes: (030.0030) Coherence and statistical optics; (120.3180) Interferometry; (120.5050) Phase measurement. References and links 1. Y. Kotaki and H. Ishikawa, “Wavelength tunable DFB and DBR lasers for coherent optical fibre communications,” IEE Proc., J Optoelectron. 138(2), 171–177 (1991). 2. R. Michalzik, VCSELs: Fundamentals, Technology and Applications of Vertical-Cavity Surface-Emitting Lasers (Springer, 2012) 3. U. Hofbauer, E. Dalhoff, and H. Tiziani, “Double-heterodyne-interferometry with delay-lines larger than coherence length of the laser light used,” Opt. Commun. 162(1-3), 112–120 (1999). 4. E. Fischer, E. Dalhoff, and H. Tiziani, “Overcoming coherence length limitation in two wavelength interferometry an experimental verification,” Opt. Commun. 123(4–6), 465–472 (1996). 5. M. Rohner and T. Jensen, “Phase noise compensation for interferometric absolute rangefinders,” US patent no US7619719 B2, 2009. 6. X. Fan, Y. Koshikiya, and F. Ito, “Phase-noise-compensated optical frequency domain reflectometry with measurement range beyond laser coherence length realized using concatenative reference method,” Opt. Lett. 32(22), 3227–3229 (2007). 7. Z. Ding, X. S. Yao, T. Liu, Y. Du, K. Liu, Q. Han, Z. Meng, J. Jiang, and H. Chen Ding, “Long Measurement Range OFDR Beyond Laser Coherence Length,” IEEE Photonics Technol. Lett. 25(2), 202–205 (2013). 8. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 1984) 9. L. Mandel and E. Wolf, “Coherence Properties of Optical Fields,” Rev. Mod. Phys. 37(2), 231–287 (1965). 10. J. W. Goodman, Statistical Optics (Wiley, 1985), Chap. 5. 11. K. Petermann, Laser Diode Modulation and Noise (Kluwer Academic, 1988), Chap. 7. 12. Y. Salvadé and R. Dändliker, “Limitations of interferometry due to the flicker noise of laser diodes,” J. Opt. Soc. Am. A 17(5), 927–932 (2000). 13. Y. Petremand, C. Affolderbach, R. Straessle, M. Pellaton, D. Briand, G. Mileti, and N. F. de Rooij, “Microfabricated rubidium vapour cell with a thick glass core for small-scale atomic clock applications,” J. Micromech. Microeng. 22(2), 025013 (2012). Published in Optics Express 24, issue 19, 21729-21743, 2016 which should be used for any reference to this work 1