Abstract

A novel wavelength-difference measurement scheme with a Wollaston prism is presented. By using a suitable reference wavelength, a small variation in the signal wavelength can be converted into a relatively larger change in the modulated wavelength, as a result of the so-called fringe beating effect, resulting in enhanced measurement sensitivity by use of autocorrelation and Gaussian filtering techniques. From the results of a simulation carried out, we observed a wavelength variation of 0.01 nm over 15 nm or 0.1 nm over 60 nm for a typical pair of laser diodes with wavelengths of 785 and 810 nm, and wavelength variations of 0.5 nm over 40 nm or 1 nm over 110 nm for 671 -and 785-nm wavelengths. These results were partially verified by the experimental results obtained for which a resolution of 0.01 nm over a range of 2.5 nm for the first pair and 0.5 nm over 4 nm for the second pair of laser diodes was seen. The results have applications to the determination of wavelength variations in a wavelength-division multiplexing system or measurement of the wavelength changes induced in a range of optical sensors.

© 1997 Optical Society of America

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References

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  1. E. Schrufer, E. Lindermeir, F. Palme, K. Wulbern, “Spectral measurements of exhaust gases using a Fourier transform spectrometer,” in Measurement Technology and Intelligent Instruments, L. Zhu, ed., Proc. SPIE2101, 1226–1233 (1993).
    [CrossRef]
  2. M. J. Padgett, A. R. Harvey, A. J. Duncan, W. Sibbett, “Single-pulse, Fourier-transform spectrometer having no moving parts,” Appl. Opt. 33, 6035–6040 (1994).
    [CrossRef] [PubMed]
  3. T. Okamoto, S. Kawata, S. Minami, “Fourier transform spectrometer with a self-scanning photodiode array,” Appl. Opt. 23, 269–273 (1984).
    [CrossRef] [PubMed]
  4. Miniature Fourier transform spectrometer, Manufacturer’s Data (Photonex Company, Scotland, 1995).
  5. M. J. Padgett, A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 2807–2811 (1995).
    [CrossRef]
  6. M. Francon, S. Mallick, Polarization Interferometers (Wiley Interscience, New York, 1971), Chap. 2, pp. 19–34.
  7. K. T. V. Grattan, B. T. Meggitt, Optical Fiber Sensor Technology (Chapman & Hall, London, 1995).
    [CrossRef]

1995 (1)

M. J. Padgett, A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 2807–2811 (1995).
[CrossRef]

1994 (1)

1984 (1)

Duncan, A. J.

Francon, M.

M. Francon, S. Mallick, Polarization Interferometers (Wiley Interscience, New York, 1971), Chap. 2, pp. 19–34.

Grattan, K. T. V.

K. T. V. Grattan, B. T. Meggitt, Optical Fiber Sensor Technology (Chapman & Hall, London, 1995).
[CrossRef]

Harvey, A. R.

M. J. Padgett, A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 2807–2811 (1995).
[CrossRef]

M. J. Padgett, A. R. Harvey, A. J. Duncan, W. Sibbett, “Single-pulse, Fourier-transform spectrometer having no moving parts,” Appl. Opt. 33, 6035–6040 (1994).
[CrossRef] [PubMed]

Kawata, S.

Lindermeir, E.

E. Schrufer, E. Lindermeir, F. Palme, K. Wulbern, “Spectral measurements of exhaust gases using a Fourier transform spectrometer,” in Measurement Technology and Intelligent Instruments, L. Zhu, ed., Proc. SPIE2101, 1226–1233 (1993).
[CrossRef]

Mallick, S.

M. Francon, S. Mallick, Polarization Interferometers (Wiley Interscience, New York, 1971), Chap. 2, pp. 19–34.

Meggitt, B. T.

K. T. V. Grattan, B. T. Meggitt, Optical Fiber Sensor Technology (Chapman & Hall, London, 1995).
[CrossRef]

Minami, S.

Okamoto, T.

Padgett, M. J.

M. J. Padgett, A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 2807–2811 (1995).
[CrossRef]

M. J. Padgett, A. R. Harvey, A. J. Duncan, W. Sibbett, “Single-pulse, Fourier-transform spectrometer having no moving parts,” Appl. Opt. 33, 6035–6040 (1994).
[CrossRef] [PubMed]

Palme, F.

E. Schrufer, E. Lindermeir, F. Palme, K. Wulbern, “Spectral measurements of exhaust gases using a Fourier transform spectrometer,” in Measurement Technology and Intelligent Instruments, L. Zhu, ed., Proc. SPIE2101, 1226–1233 (1993).
[CrossRef]

Schrufer, E.

E. Schrufer, E. Lindermeir, F. Palme, K. Wulbern, “Spectral measurements of exhaust gases using a Fourier transform spectrometer,” in Measurement Technology and Intelligent Instruments, L. Zhu, ed., Proc. SPIE2101, 1226–1233 (1993).
[CrossRef]

Sibbett, W.

Wulbern, K.

E. Schrufer, E. Lindermeir, F. Palme, K. Wulbern, “Spectral measurements of exhaust gases using a Fourier transform spectrometer,” in Measurement Technology and Intelligent Instruments, L. Zhu, ed., Proc. SPIE2101, 1226–1233 (1993).
[CrossRef]

Appl. Opt. (2)

Rev. Sci. Instrum. (1)

M. J. Padgett, A. R. Harvey, “A static Fourier-transform spectrometer based on Wollaston prisms,” Rev. Sci. Instrum. 66, 2807–2811 (1995).
[CrossRef]

Other (4)

M. Francon, S. Mallick, Polarization Interferometers (Wiley Interscience, New York, 1971), Chap. 2, pp. 19–34.

K. T. V. Grattan, B. T. Meggitt, Optical Fiber Sensor Technology (Chapman & Hall, London, 1995).
[CrossRef]

Miniature Fourier transform spectrometer, Manufacturer’s Data (Photonex Company, Scotland, 1995).

E. Schrufer, E. Lindermeir, F. Palme, K. Wulbern, “Spectral measurements of exhaust gases using a Fourier transform spectrometer,” in Measurement Technology and Intelligent Instruments, L. Zhu, ed., Proc. SPIE2101, 1226–1233 (1993).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Configuration of the Wollaston interferometer that we used in this study: x, displacement from the center of the Wollaston prism; θ, the internal angle of the prism; DSA, digital storage adapter.

Fig. 2
Fig. 2

Simulated results of the variation of modulated wavelength as a function of signal wavelength: (a) reference wavelength λ1 is 785 nm and the signal wavelength λ2 is changed from 810 to 910 nm, (b) the reference wavelength λ1 is 671 nm and the signal wavelength λ2 is changed from 785 to 895 nm.

Fig. 3
Fig. 3

Experimental interferograms obtained from the system shown in Fig. 1 from (a) the first pair of laser diodes and (b) the second pair of laser diodes.

Fig. 4
Fig. 4

Modulated waveforms obtained experimentally with the use of (a) the first pair of laser diodes, (b) the second pair of laser diodes.

Fig. 5
Fig. 5

Experimental results showing the variation of the modulated wavelength for different driving currents of the laser diodes from (a) the first pair of laser diodes and (b) the second pair of laser diodes.

Fig. 6
Fig. 6

Experimental results of the variation of the signal wavelength for different modulated wavelengths from (a) the first pair of laser diodes and (b) the second pair of laser diodes.

Equations (7)

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ΔL1x=2xneλ1-noλ1tanθ,ΔL2x=2xneλ2-noλ2tanθ,
Ix=12I01x2+exp-4neλ1-noλ1tanθΔL1xLc12cos2πΔL1xλ1+I02x2+exp- 4neλ2-noλ2tanθΔL2xLc22cos2πΔL2xλ2,
exp-8xneλ1-noλ12tan2θLc2 exp-8xneλ2-noλ22tan2θLc2.
Ix=12Iox4+2 exp-8xneλ1-noλ12tan2θLc2cos4πxλmcos4πxλa,
λm=2λ1λ2neλ1 -noλ1λ2-neλ2-noλ2λ1tanθ,
λa=2λ1λ2neλ1 -noλ1λ2+neλ2-noλ2λ1tanθ,
pk=144k-1δp144k+1δp Ixdx,

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