Abstract

We present a generalized frequency selection method for N-frequency interferometry to form an optimum geometric series at synthetic wavelengths. The absolute range that is measurable is bounded by the number of beat frequency operations, phase noise, and the number of wavelengths used to form the geometric series of synthetic wavelengths. Theoretical predictions are compared with experimental results from a full-field fringe projector. A comparison of this technique with the method of excess fractions shows orders-of-magnitude faster processing with similar measurement reliability.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. Fabry and A. Perot, Astrophys. J. 15, 73 (1902).
    [CrossRef]
  2. F. H. Rolt, Engineering 144, 162 (1937).
  3. A. Lewis, Meas. Sci. Technol. 5, 694 (1994).
    [CrossRef]
  4. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, England, 2002).
  5. A. Pfoertner and J. Schwider, Appl. Opt. 42, 667 (2003).
    [CrossRef]
  6. Y. Cheng and J. Wyant, Appl. Opt. 24, 804 (1985).
    [CrossRef]
  7. C. Creath, in Interferogram Analysis, D. W. Robinson and G. T. Reid, eds. (Institute of Physics, London, 1993), p. 94.
  8. H. Zhao, W. Chen, and Y. Tan, Appl. Opt. 33, 4497 (1994).
    [CrossRef] [PubMed]
  9. C. E. Towers, D. P. Towers, and J. D. C. Jones, Opt. Lett. 28, 887 (2003).
    [CrossRef] [PubMed]
  10. R. Dandliker, Y. Salvade, and E. Zimmermann, J. Opt. 29, 105 (1998).
    [CrossRef]

2003 (2)

1998 (1)

R. Dandliker, Y. Salvade, and E. Zimmermann, J. Opt. 29, 105 (1998).
[CrossRef]

1994 (2)

1985 (1)

1937 (1)

F. H. Rolt, Engineering 144, 162 (1937).

1902 (1)

C. Fabry and A. Perot, Astrophys. J. 15, 73 (1902).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, England, 2002).

Chen, W.

Cheng, Y.

Creath, C.

C. Creath, in Interferogram Analysis, D. W. Robinson and G. T. Reid, eds. (Institute of Physics, London, 1993), p. 94.

Dandliker, R.

R. Dandliker, Y. Salvade, and E. Zimmermann, J. Opt. 29, 105 (1998).
[CrossRef]

Fabry, C.

C. Fabry and A. Perot, Astrophys. J. 15, 73 (1902).
[CrossRef]

Jones, J. D. C.

Lewis, A.

A. Lewis, Meas. Sci. Technol. 5, 694 (1994).
[CrossRef]

Perot, A.

C. Fabry and A. Perot, Astrophys. J. 15, 73 (1902).
[CrossRef]

Pfoertner, A.

Rolt, F. H.

F. H. Rolt, Engineering 144, 162 (1937).

Salvade, Y.

R. Dandliker, Y. Salvade, and E. Zimmermann, J. Opt. 29, 105 (1998).
[CrossRef]

Schwider, J.

Tan, Y.

Towers, C. E.

Towers, D. P.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, England, 2002).

Wyant, J.

Zhao, H.

Zimmermann, E.

R. Dandliker, Y. Salvade, and E. Zimmermann, J. Opt. 29, 105 (1998).
[CrossRef]

Appl. Opt. (3)

Astrophys. J. (1)

C. Fabry and A. Perot, Astrophys. J. 15, 73 (1902).
[CrossRef]

Engineering (1)

F. H. Rolt, Engineering 144, 162 (1937).

J. Opt. (1)

R. Dandliker, Y. Salvade, and E. Zimmermann, J. Opt. 29, 105 (1998).
[CrossRef]

Meas. Sci. Technol. (1)

A. Lewis, Meas. Sci. Technol. 5, 694 (1994).
[CrossRef]

Opt. Lett. (1)

Other (2)

C. Creath, in Interferogram Analysis, D. W. Robinson and G. T. Reid, eds. (Institute of Physics, London, 1993), p. 94.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, Cambridge, England, 2002).

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 (2)

Fig. 1
Fig. 1

Theoretical performance of the GOMF interferometry approach, shown as log10 of the unambiguously measurable maximum fringe order.

Fig. 2
Fig. 2

Comparison of the theoretical and experimental performance of the GOMF interferometry. Curves, theoretical predictions; symbols, experimental measurements.

Tables (1)

Tables Icon

Table 1 Comparison of the Method of EFs and the GOMF Interferometry Approacha

Equations (8)

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

{L/λi,L/λjZ+|L/λ0>>L/λn-1,L/λi,L/λj=1 for one of i,j=0,n-1,ij},
ϕuk=2πmk+ϕwk,    k=1,,s,
ϕuk×Λk=ϕul×Λl.
2πmk+ϕwkΛk=2πml+ϕwlΛl.
ml=NINTΛkΛlmk+ϕwk2π-ϕwl2π,
-π<errorΛkΛl2πmk+ϕwk-ϕwl<π.
σe=σΛk/Λl2rk+1+rl+11/2.
p=1σe-ππexp-x2/2σe2dx.

Metrics