Abstract

We describe a method for efficiently determining the wavelength of a monochromatic source and provide an experimental proof-of-concept. The photomeasurement efficiency for a wavemeter can be written as η(N,q)=(1+ logqN)/m, where N is the number of spectral channels, q is the number of distinguishable output levels per photodetector, and m is the actual number of photomeasurements made. An implementation is developed that achieves a theoretical efficiency of η(N,q)=1. The proof-of-concept experiment achieves efficiencies η=O(1), where the deviation from theory is attributable to well-known optical effects and should be correctable in future versions.

©2004 Optical Society of America

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References

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  1. J.J. Snider, “Laser Wavelength meters,” Laser Focus18(5), 55–61 (1982).
  2. J.J. Snyder and T.W. Hansch, “Laser wavemeters,” in Topics in Applied Physics: Dye Lasers, F.P. Schafer, ed. (Springer-Verlag, Berlin, 1990), pp.201–219.
  3. J.-P. Monchalin, M.J. Kelly, J.E. Thomas, N.A. Kurnit, A. Szoke, F. Zernike, P.H. Lee, and A. Javan, “Accurate laser wavelength measurement with a precision two-beam scanning Michelson interferometer,” Appl. Opt. 20, 736–757 (1981).
    [Crossref] [PubMed]
  4. P.J. Fox, R.E. Scholten, M.R. Walkiewicz, and R.E. Drullinger, “A reliable, compact, and low-cost Michelson wavemeter for laser wavelength measurement,” Am. J. Phys. 67, 624–630 (1999).
    [Crossref]
  5. M-L. Junttila, B. Stahlberg, E. Kyro, T. Verijola, and J. Kauppinen, “Fourier transform wavemeter,” Rev. Sci. Instrum. 58, 1180–1184 (1987)
    [Crossref]
  6. D. Steers, W. Sibbett, and M.J. Padgett, “Dual-purpose, compact spectrometer and fiber-coupled laser wavemeter based on a Wollaston prism,” Appl. Opt. 37, 5777–5781 (1998).
    [Crossref]
  7. D. Du and F. Hwang, Combinatorial group testing and its applications, vol. 12 of Series on Applied Mathematics (World Scientific, Singapore, 2000).
  8. U. Gopinathan, D.J. Brady, and N.P. Pitsianis, “Coded apertures for efficient pyroelectric motion tracking,” Opt. Express 11, 2142–2152 (2003), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-18-2142.
    [Crossref] [PubMed]
  9. D.J. Schroeder, Astronomical Optics (Academic, San Diego, Calif.1987).
  10. C. Papaliolios, P. Nisenson, and S. Ebstein, “Speckle imaging with the Papa detector,” Appl. Opt. 24, 287–292 (1985).
    [Crossref] [PubMed]

2003 (1)

1999 (1)

P.J. Fox, R.E. Scholten, M.R. Walkiewicz, and R.E. Drullinger, “A reliable, compact, and low-cost Michelson wavemeter for laser wavelength measurement,” Am. J. Phys. 67, 624–630 (1999).
[Crossref]

1998 (1)

1987 (1)

M-L. Junttila, B. Stahlberg, E. Kyro, T. Verijola, and J. Kauppinen, “Fourier transform wavemeter,” Rev. Sci. Instrum. 58, 1180–1184 (1987)
[Crossref]

1985 (1)

1981 (1)

Brady, D.J.

Drullinger, R.E.

P.J. Fox, R.E. Scholten, M.R. Walkiewicz, and R.E. Drullinger, “A reliable, compact, and low-cost Michelson wavemeter for laser wavelength measurement,” Am. J. Phys. 67, 624–630 (1999).
[Crossref]

Du, D.

D. Du and F. Hwang, Combinatorial group testing and its applications, vol. 12 of Series on Applied Mathematics (World Scientific, Singapore, 2000).

Ebstein, S.

Fox, P.J.

P.J. Fox, R.E. Scholten, M.R. Walkiewicz, and R.E. Drullinger, “A reliable, compact, and low-cost Michelson wavemeter for laser wavelength measurement,” Am. J. Phys. 67, 624–630 (1999).
[Crossref]

Gopinathan, U.

Hansch, T.W.

J.J. Snyder and T.W. Hansch, “Laser wavemeters,” in Topics in Applied Physics: Dye Lasers, F.P. Schafer, ed. (Springer-Verlag, Berlin, 1990), pp.201–219.

Hwang, F.

D. Du and F. Hwang, Combinatorial group testing and its applications, vol. 12 of Series on Applied Mathematics (World Scientific, Singapore, 2000).

Javan, A.

Junttila, M-L.

M-L. Junttila, B. Stahlberg, E. Kyro, T. Verijola, and J. Kauppinen, “Fourier transform wavemeter,” Rev. Sci. Instrum. 58, 1180–1184 (1987)
[Crossref]

Kauppinen, J.

M-L. Junttila, B. Stahlberg, E. Kyro, T. Verijola, and J. Kauppinen, “Fourier transform wavemeter,” Rev. Sci. Instrum. 58, 1180–1184 (1987)
[Crossref]

Kelly, M.J.

Kurnit, N.A.

Kyro, E.

M-L. Junttila, B. Stahlberg, E. Kyro, T. Verijola, and J. Kauppinen, “Fourier transform wavemeter,” Rev. Sci. Instrum. 58, 1180–1184 (1987)
[Crossref]

Lee, P.H.

Monchalin, J.-P.

Nisenson, P.

Padgett, M.J.

Papaliolios, C.

Pitsianis, N.P.

Scholten, R.E.

P.J. Fox, R.E. Scholten, M.R. Walkiewicz, and R.E. Drullinger, “A reliable, compact, and low-cost Michelson wavemeter for laser wavelength measurement,” Am. J. Phys. 67, 624–630 (1999).
[Crossref]

Schroeder, D.J.

D.J. Schroeder, Astronomical Optics (Academic, San Diego, Calif.1987).

Sibbett, W.

Snider, J.J.

J.J. Snider, “Laser Wavelength meters,” Laser Focus18(5), 55–61 (1982).

Snyder, J.J.

J.J. Snyder and T.W. Hansch, “Laser wavemeters,” in Topics in Applied Physics: Dye Lasers, F.P. Schafer, ed. (Springer-Verlag, Berlin, 1990), pp.201–219.

Stahlberg, B.

M-L. Junttila, B. Stahlberg, E. Kyro, T. Verijola, and J. Kauppinen, “Fourier transform wavemeter,” Rev. Sci. Instrum. 58, 1180–1184 (1987)
[Crossref]

Steers, D.

Szoke, A.

Thomas, J.E.

Verijola, T.

M-L. Junttila, B. Stahlberg, E. Kyro, T. Verijola, and J. Kauppinen, “Fourier transform wavemeter,” Rev. Sci. Instrum. 58, 1180–1184 (1987)
[Crossref]

Walkiewicz, M.R.

P.J. Fox, R.E. Scholten, M.R. Walkiewicz, and R.E. Drullinger, “A reliable, compact, and low-cost Michelson wavemeter for laser wavelength measurement,” Am. J. Phys. 67, 624–630 (1999).
[Crossref]

Zernike, F.

Am. J. Phys. (1)

P.J. Fox, R.E. Scholten, M.R. Walkiewicz, and R.E. Drullinger, “A reliable, compact, and low-cost Michelson wavemeter for laser wavelength measurement,” Am. J. Phys. 67, 624–630 (1999).
[Crossref]

Appl. Opt. (3)

Opt. Express (1)

Rev. Sci. Instrum. (1)

M-L. Junttila, B. Stahlberg, E. Kyro, T. Verijola, and J. Kauppinen, “Fourier transform wavemeter,” Rev. Sci. Instrum. 58, 1180–1184 (1987)
[Crossref]

Other (4)

D. Du and F. Hwang, Combinatorial group testing and its applications, vol. 12 of Series on Applied Mathematics (World Scientific, Singapore, 2000).

D.J. Schroeder, Astronomical Optics (Academic, San Diego, Calif.1987).

J.J. Snider, “Laser Wavelength meters,” Laser Focus18(5), 55–61 (1982).

J.J. Snyder and T.W. Hansch, “Laser wavemeters,” in Topics in Applied Physics: Dye Lasers, F.P. Schafer, ed. (Springer-Verlag, Berlin, 1990), pp.201–219.

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Figures (10)

Fig. 1.
Fig. 1. Physical layout of the wavemeter system.
Fig. 2.
Fig. 2. Mask pattern for binary (q=2) detectors.
Fig. 3.
Fig. 3. Mask pattern for quaternary (q=4) detectors.
Fig. 4.
Fig. 4. Detection of the bit-pattern 10001100.
Fig. 5.
Fig. 5. Expected bit patterns for the binary mask. White indicates “1”, black indicates “0.”
Fig. 6.
Fig. 6. Measured bit patterns for the binary mask. White indicates “1”, black indicates “0.”
Fig. 7.
Fig. 7. Bit errors (theory minus measured) for the binary mask. White indicates “1”, gray indicates “0”, and black indicates “-1.”
Fig. 8.
Fig. 8. Expected quaternary digit patterns for the quaternary (q=4) mask. Values are indicated by the colorbar. The calibration row has been suppressed in this image.
Fig. 9.
Fig. 9. Measured quaternary digit patterns for the quaternary (q=4) mask. Values are indicated by the colorbar. The calibration row has been suppressed in this image.
Fig. 10.
Fig. 10. Errors (theory minus measured) for the quaternary (q=4) mask. Values are indicated by the colorbar. The calibration row has been suppressed in this image.

Equations (12)

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η ( N , q ) = χ ( N , q ) m .
d 1 = j 2 ( mod 2 )
d 2 = j 2 2 ( mod 2 )
d 3 = j 2 3 ( mod 2 )
d m = j 2 m ( mod 2 ) ,
d 1 = j q ( mod q )
d 2 = j q 2 ( mod q )
d 3 = j q 3 ( mod q )
d m = j q m ( mod q ) ,
η ( N , q ) = 1 + log q ( N ) m .

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