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

Applied Optics, Vol. 39, Issue 1, pp. 108-113 (2000)

http://dx.doi.org/10.1364/AO.39.000108

Enhanced HTML Acrobat PDF (118 KB)

### 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(2π*f*_{
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 =
1/2*f*_{
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 2^{16}, 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: Year | Journal | Reset

### References

- D. Malacara, Optical Shop Testing (Wiley, New York, 1975).
- P. Hariharan, “Optical interferometry,” Rep. Prog. Phys. 54, 339–390 (1990). [CrossRef]
- J. Chamberlain, The Principles of Interferometric Spectroscopy (Wiley, New York, 1979).
- P. Griffiths, Chemical Infrared Fourier Transform Spectroscopy (Wiley, New York, 1975).
- P. Grangier, J. Levenson, J. Poizat, “Quantum non-demolition measurements in optics,” Nature 396, 537–542 (1998). [CrossRef]
- 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]
- V. Daria, C. Saloma, “Bandwidth and detection limit in crossing-based spectrum analyzer,” Rev. Sci. Instrum. 68, 240–242 (1997). [CrossRef]
- M. Lim, C. Saloma, “Direct signal recovery from threshold crossings,” Phys. Rev. E 58, 6759–6765 (1998). [CrossRef]
- J. Proakis, D. Manolakis, Introduction to Digital Processing (Maxwell-Macmillan, 1989, New York), pp. 111–123.
- 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]
- C. Saloma, “Computational complexity and observation of physical signals,” J. Appl. Phys. 74, 5314–5319 (1993). [CrossRef]
- C. Saloma, P. Haeberli, “Optical spectrum analysis from zero crossings,” Opt. Lett. 16, 1535–1537 (1991). [CrossRef] [PubMed]
- 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]
- 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]
- M. Litong, C. Saloma, “Detection of sub-threshold oscillations by sinusoid-crossing sampling,” Phys. Rev. E 57, 3579–3588 (1998). [CrossRef]
- 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.
- M. Demler, High-Speed Analog-to-Digital Conversion (Academic, New York, 1991).
- J. Candy, “A use of double integration in delta signal modulation,” IEEE Trans. Commun. COM-33, 249–258 (1985). [CrossRef]
- 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]
- 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.

« Previous Article | Next Article »

OSA is a member of CrossRef.