Abstract

In many interferometers, two fringe signals can be generated in quadrature. The relative phase of the two fringe signals depends on whether the optical path length is increasing or decreasing. A system is developed in which two quadrature fringe signals are digitized and analyzed in real time with a digital signal processor to yield a linear, high-resolution, wide-dynamic-range displacement transducer. The resolution in a simple Michelson interferometer with inexpensive components is 5 × 10-13 m Hz-1/2 at 2 Hz.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. A. Zumberge, J. Berger, M. A. H. Hedlin, E. Husmann, S. Nooner, R. Hilt, R. Widmer-Schnidrig, “An optical fiber infrasound sensor: a new lower limit on atmospheric pressure noise between 1 and 10 Hz,” J. Acoust. Soc. Am. 113, 2474–2479 (2003).
    [CrossRef] [PubMed]
  2. T. Eom, J. Y. Kim, K. Jeong, “The dynamic compensation of nonlinearity in a homodyne laser interferometer,” Meas. Sci. Technol. 12, 1734–1738 (2001).
    [CrossRef]
  3. P. L. M. Heydemann, “Determination and correction of quadrature fringe measurement errors in interferometers,” Appl. Opt. 20, 3382–3384 (1981).
    [CrossRef] [PubMed]
  4. C. L. Lawson, R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J., 1974), Chap. 18, pp. 107–120.

2003 (1)

M. A. Zumberge, J. Berger, M. A. H. Hedlin, E. Husmann, S. Nooner, R. Hilt, R. Widmer-Schnidrig, “An optical fiber infrasound sensor: a new lower limit on atmospheric pressure noise between 1 and 10 Hz,” J. Acoust. Soc. Am. 113, 2474–2479 (2003).
[CrossRef] [PubMed]

2001 (1)

T. Eom, J. Y. Kim, K. Jeong, “The dynamic compensation of nonlinearity in a homodyne laser interferometer,” Meas. Sci. Technol. 12, 1734–1738 (2001).
[CrossRef]

1981 (1)

Berger, J.

M. A. Zumberge, J. Berger, M. A. H. Hedlin, E. Husmann, S. Nooner, R. Hilt, R. Widmer-Schnidrig, “An optical fiber infrasound sensor: a new lower limit on atmospheric pressure noise between 1 and 10 Hz,” J. Acoust. Soc. Am. 113, 2474–2479 (2003).
[CrossRef] [PubMed]

Eom, T.

T. Eom, J. Y. Kim, K. Jeong, “The dynamic compensation of nonlinearity in a homodyne laser interferometer,” Meas. Sci. Technol. 12, 1734–1738 (2001).
[CrossRef]

Hanson, R. J.

C. L. Lawson, R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J., 1974), Chap. 18, pp. 107–120.

Hedlin, M. A. H.

M. A. Zumberge, J. Berger, M. A. H. Hedlin, E. Husmann, S. Nooner, R. Hilt, R. Widmer-Schnidrig, “An optical fiber infrasound sensor: a new lower limit on atmospheric pressure noise between 1 and 10 Hz,” J. Acoust. Soc. Am. 113, 2474–2479 (2003).
[CrossRef] [PubMed]

Heydemann, P. L. M.

Hilt, R.

M. A. Zumberge, J. Berger, M. A. H. Hedlin, E. Husmann, S. Nooner, R. Hilt, R. Widmer-Schnidrig, “An optical fiber infrasound sensor: a new lower limit on atmospheric pressure noise between 1 and 10 Hz,” J. Acoust. Soc. Am. 113, 2474–2479 (2003).
[CrossRef] [PubMed]

Husmann, E.

M. A. Zumberge, J. Berger, M. A. H. Hedlin, E. Husmann, S. Nooner, R. Hilt, R. Widmer-Schnidrig, “An optical fiber infrasound sensor: a new lower limit on atmospheric pressure noise between 1 and 10 Hz,” J. Acoust. Soc. Am. 113, 2474–2479 (2003).
[CrossRef] [PubMed]

Jeong, K.

T. Eom, J. Y. Kim, K. Jeong, “The dynamic compensation of nonlinearity in a homodyne laser interferometer,” Meas. Sci. Technol. 12, 1734–1738 (2001).
[CrossRef]

Kim, J. Y.

T. Eom, J. Y. Kim, K. Jeong, “The dynamic compensation of nonlinearity in a homodyne laser interferometer,” Meas. Sci. Technol. 12, 1734–1738 (2001).
[CrossRef]

Lawson, C. L.

C. L. Lawson, R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J., 1974), Chap. 18, pp. 107–120.

Nooner, S.

M. A. Zumberge, J. Berger, M. A. H. Hedlin, E. Husmann, S. Nooner, R. Hilt, R. Widmer-Schnidrig, “An optical fiber infrasound sensor: a new lower limit on atmospheric pressure noise between 1 and 10 Hz,” J. Acoust. Soc. Am. 113, 2474–2479 (2003).
[CrossRef] [PubMed]

Widmer-Schnidrig, R.

M. A. Zumberge, J. Berger, M. A. H. Hedlin, E. Husmann, S. Nooner, R. Hilt, R. Widmer-Schnidrig, “An optical fiber infrasound sensor: a new lower limit on atmospheric pressure noise between 1 and 10 Hz,” J. Acoust. Soc. Am. 113, 2474–2479 (2003).
[CrossRef] [PubMed]

Zumberge, M. A.

M. A. Zumberge, J. Berger, M. A. H. Hedlin, E. Husmann, S. Nooner, R. Hilt, R. Widmer-Schnidrig, “An optical fiber infrasound sensor: a new lower limit on atmospheric pressure noise between 1 and 10 Hz,” J. Acoust. Soc. Am. 113, 2474–2479 (2003).
[CrossRef] [PubMed]

Appl. Opt. (1)

J. Acoust. Soc. Am. (1)

M. A. Zumberge, J. Berger, M. A. H. Hedlin, E. Husmann, S. Nooner, R. Hilt, R. Widmer-Schnidrig, “An optical fiber infrasound sensor: a new lower limit on atmospheric pressure noise between 1 and 10 Hz,” J. Acoust. Soc. Am. 113, 2474–2479 (2003).
[CrossRef] [PubMed]

Meas. Sci. Technol. (1)

T. Eom, J. Y. Kim, K. Jeong, “The dynamic compensation of nonlinearity in a homodyne laser interferometer,” Meas. Sci. Technol. 12, 1734–1738 (2001).
[CrossRef]

Other (1)

C. L. Lawson, R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J., 1974), Chap. 18, pp. 107–120.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Michelson interferometer in which one of the arms is lengthened by a quarter of a wavelength for one polarizations state. A polarizing beam splitter separates the two fringe signals yielding a quadrature output.

Fig. 2
Fig. 2

Mach-Zehnder interferometer formed with optical fibers. In this case a quadrature output is generated with analog electronics by differentiating the fringe signal with a lock-in amplifier. To facilitate this, a split piezoelectric transducer modulates the two arm lengths 180° out of phase with each other.

Fig. 3
Fig. 3

(a) Example of quadrature fringe signals as described in Eqs. (1) and (2) plotted for a simulated case in which x 0 = y 0 = 3, a = 1.7, b = 2.6, and p 0 = 30°. (b) Plotted against each other, quadrature fringe signals trace out an ellipse. At any instant the optical phase p can be found from the position on the ellipse of an xy voltage pair. This position and the value in degrees are indicated for several values of p. The DSP continually least squares fits a recent collection of xy pairs for the five ellipse parameters and uses them to compute p from each new xy pair.

Fig. 4
Fig. 4

Plot of the power spectral density of the displacement record from DSP processing for an equal-arm free-space Michelson interferometer illuminated with a 0.5-mW He-Ne laser. The corner cubes and beam splitter are attached to a small fixture held in a partial vacuum. For 7 h, data were sampled at 200 samples/s. To display this clearly, we smoothed the spectrum below 1 Hz into approximately 1/3 octave bands. Above 1 Hz we smoothed the spectrum with a fixed 0.75-Hz Gaussian window.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

y  xL.
x=x0+a sinp+p0,
y=y0+b cos p.
x2a2+ y2b2- 2xy sin p0ab-2xx0a2- y0 sin p0ab-2yy0b2- x0 sin p0ab=cos2 p0-x02a2+ y02b2- 2x0y0 sin p0ab.
α1x2+α2y2+ α3xy+α4x+ α5y=α6.
j αj2=1,
c1+c2y2+c3xy+c4x+c5y=x2,
a2α6-ab2y2+2absin p0xy+2x0-y0ab×sin p0x+2y0ab2-x0absin p0y=x2,
ra/b= -c2,
sin p0= c32r.
x0-r sin p0y0= c42, -r sin p0x0+r2y0= c52,
y0= rc4 sin p0+c52r2 cos2 p0,
x0= c42+y0r sin p0.
c1=a2 cos2 p0-x02+r2y02-2x0y0r sin p0,
a=c1+x02+r2y02-2x0y0r sin p01/2cos p0
cos p= y-y0b, sin p= x-x0a cos p0-cos p tan p0.

Metrics