OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 39, Iss. 1 — Jan. 1, 2000
  • pp: 108–113

High-accuracy Fourier transform interferometry, without oversampling, with a 1-bit analog-to-digital converter

Vincent Ricardo Daria and Caesar Saloma  »View Author Affiliations


Applied Optics, Vol. 39, Issue 1, pp. 108-113 (2000)
http://dx.doi.org/10.1364/AO.39.000108


View Full Text Article

Enhanced HTML    Acrobat PDF (118 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We demonstrate a new technique for performing accurate Fourier transform interferometry with a 1-bit analog-to-digital (AD) converter that does not require oversampling of the interferogram, unlike in other 1-bit coding schemes that rely on delta-sigma modulation. Sampling aims at locating the intersections {z i } of the modulation term s(z) of the interferogram and a reference sinusoid r(z) = A cos(2πf r z), where z is the optical path difference. A new autocorrelation-based procedure that includes the accurate recovery of the equally sampled amplitude representation {s(k)} of s(z) from {z i } is utilized to calculate the square of the emission spectrum of the light source (sample). The procedure is suitable for interferograms that are corrupted with additive noise. Sinusoid-crossing sampling satisfies the Nyquist sampling criterion, and a z i exists within each sampling interval Δ = 1/2f r , if A ≥ |s(z)| for all z, and f r f c , where f c is the highest frequency component of s(z). By locating a crossing at an accuracy of 1 part in 216, we determine the multimode spectrum of an argon-ion laser with a 1-bit AD converter that performs like a 13-bit amplitude-sampling AD converter.

© 2000 Optical Society of America

OCIS Codes
(070.4790) Fourier optics and signal processing : Spectrum analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.6200) Instrumentation, measurement, and metrology : Spectrometers and spectroscopic instrumentation

History
Original Manuscript: June 14, 1999
Revised Manuscript: August 23, 1999
Published: January 1, 2000

Citation
Vincent Ricardo Daria and Caesar Saloma, "High-accuracy Fourier transform interferometry, without oversampling, with a 1-bit analog-to-digital converter," Appl. Opt. 39, 108-113 (2000)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-1-108


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. D. Malacara, Optical Shop Testing (Wiley, New York, 1975).
  2. P. Hariharan, “Optical interferometry,” Rep. Prog. Phys. 54, 339–390 (1990). [CrossRef]
  3. J. Chamberlain, The Principles of Interferometric Spectroscopy (Wiley, New York, 1979).
  4. P. Griffiths, Chemical Infrared Fourier Transform Spectroscopy (Wiley, New York, 1975).
  5. P. Grangier, J. Levenson, J. Poizat, “Quantum non-demolition measurements in optics,” Nature 396, 537–542 (1998). [CrossRef]
  6. G. Hazel, F. Bucholtz, I. Aggarwal, “Characterization and modeling of drift noise in Fourier transform spectroscopy: implications for signal processing and detection limits,” Appl. Opt. 36, 6751–6759 (1993). [CrossRef]
  7. V. Daria, C. Saloma, “Bandwidth and detection limit in crossing-based spectrum analyzer,” Rev. Sci. Instrum. 68, 240–242 (1997). [CrossRef]
  8. M. Lim, C. Saloma, “Direct signal recovery from threshold crossings,” Phys. Rev. E 58, 6759–6765 (1998). [CrossRef]
  9. J. Proakis, D. Manolakis, Introduction to Digital Processing (Maxwell-Macmillan, 1989, New York), pp. 111–123.
  10. K. Minami, S. Kawata, “Dynamic range enhancement of Fourier transform infrared spectrum measurement using delta sigma modulation,” Appl. Opt. 32, 4822–4827 (1993). [CrossRef] [PubMed]
  11. C. Saloma, “Computational complexity and observation of physical signals,” J. Appl. Phys. 74, 5314–5319 (1993). [CrossRef]
  12. C. Saloma, P. Haeberli, “Optical spectrum analysis from zero crossings,” Opt. Lett. 16, 1535–1537 (1991). [CrossRef] [PubMed]
  13. C. M. Blanca, V. Daria, C. Saloma, “Spectral recovery by analytic continuation in crossing-based spectral analysis,” Appl. Opt. 35, 6417–6422 (1996). [CrossRef] [PubMed]
  14. M. A. Nazario, C. Saloma, “Signal recovery in sinusoid-crossing sampling by use of the minimum-negativity constraint,” Appl. Opt. 37, 2953–2964 (1998). [CrossRef]
  15. M. Litong, C. Saloma, “Detection of sub-threshold oscillations by sinusoid-crossing sampling,” Phys. Rev. E 57, 3579–3588 (1998). [CrossRef]
  16. G. Pfeifer, “Modulators, demodulators and converters,” in Electronics Engineers Handbook, D. Fink, D. Christiansen, eds., (McGraw-Hill, New York, 1982), Section 14, pp. 14-24–14-45.
  17. M. Demler, High-Speed Analog-to-Digital Conversion (Academic, New York, 1991).
  18. J. Candy, “A use of double integration in delta signal modulation,” IEEE Trans. Commun. COM-33, 249–258 (1985). [CrossRef]
  19. Y. Matsuya, K. Uchimura, A. Iwata, T. Kobayashi, M. Ishikawa, T. Yoshitome, “A 16-bit oversampling A-to-D conversion technology using triple integration noise shaping,” IEEE J. Solid-State Circuits SC-22, 921–929 (1987). [CrossRef]
  20. K. C. Chao, S. H. Lee, C. G. Sodini, “A high order topology for interpolative modulators for oversampling A/D converter,” IEEE Trans. Circuits Sys. 37, 309–318 (1990). [CrossRef]

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.

Figures

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

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited