Abstract

A method for measuring absolute distance by the wavelength shift of laser diode light has previously been proposed. In this work three serious systematic error sources for the method are discussed and some of the discussion is confirmed by experiment. The error sources are optical feedback effect, longitudinal mode distribution of laser light, and unwanted light reflected from optical devices (coherent noise). The optical feedback effect influences the wavelength shift of the emitted light. The mode distribution causes the periodic error dependent on the measured distance, and the maximum error is determined by the change in the intensity ratio of the submodes to the main mode. Coherent noise causes the periodic error also dependent on the distance, and the maximum error is determined by the amplitude ratio of the measuring lightwave to the noise. These systematic errors are observed in some demonstrative experiments.

© 1987 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. M. Born, E. Wolf, “The Method of Excess Fractions,” in Principles of Optics, M. Born, E. Wolf, Eds. (Pergamon, Oxford, 1965), p. 291.
  4. M. Yonemura, “Wavelength-Change Characteristics of Semiconductor Lasers and Their Application to Holographic Contouring,” Opt. Lett. 10, 1 (1985).
    [CrossRef] [PubMed]
  5. H. Kikuta, K. Iwata, R. Nagata, “Distance Measurement by the Wavelength Shift of Laser Diode Light,” Appl. Opt. 25, 2976 (1986).
    [CrossRef] [PubMed]
  6. R. Lang, K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. QE-16, 347 (1980).
    [CrossRef]
  7. L. Goldberg, H. F. Taylor, A. Dandridge, J. F. Weller, R. O. Miles, “Spectral Characteristics of Semiconductor Lasers with Optical Feedback,” IEEE J. Quantum Electron. QE-18, 555 (1982).
    [CrossRef]
  8. I. G. Goncharov, A. P. Grachev, K. B. Dedushenko, M. V. Zverkov, A. N. Mamaev, “Influence of an External Mirror on the Characteristics of Semiconductor Laser Radiation,” Sov. J. Quantum Electron. 15, 259 (1985).
    [CrossRef]
  9. S. Matsui et al., “Low Noise Characteristics of V-Channeled Substrate Inner Stripe Laser in Single-Longitudinal-Mode Operation,” Appl. Opt. 23, 4001 (1984).
    [CrossRef] [PubMed]
  10. J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, K. Merkel, “Digital Wave-Front Measuring Interferometry: Some Systematic Error Sources,” Appl. Opt. 22, 3421 (1983).
    [CrossRef] [PubMed]

1986 (1)

1985 (2)

I. G. Goncharov, A. P. Grachev, K. B. Dedushenko, M. V. Zverkov, A. N. Mamaev, “Influence of an External Mirror on the Characteristics of Semiconductor Laser Radiation,” Sov. J. Quantum Electron. 15, 259 (1985).
[CrossRef]

M. Yonemura, “Wavelength-Change Characteristics of Semiconductor Lasers and Their Application to Holographic Contouring,” Opt. Lett. 10, 1 (1985).
[CrossRef] [PubMed]

1984 (2)

1983 (1)

1982 (1)

L. Goldberg, H. F. Taylor, A. Dandridge, J. F. Weller, R. O. Miles, “Spectral Characteristics of Semiconductor Lasers with Optical Feedback,” IEEE J. Quantum Electron. QE-18, 555 (1982).
[CrossRef]

1981 (1)

1980 (1)

R. Lang, K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

Born, M.

M. Born, E. Wolf, “The Method of Excess Fractions,” in Principles of Optics, M. Born, E. Wolf, Eds. (Pergamon, Oxford, 1965), p. 291.

Burow, R.

Dandridge, A.

L. Goldberg, H. F. Taylor, A. Dandridge, J. F. Weller, R. O. Miles, “Spectral Characteristics of Semiconductor Lasers with Optical Feedback,” IEEE J. Quantum Electron. QE-18, 555 (1982).
[CrossRef]

Dedushenko, K. B.

I. G. Goncharov, A. P. Grachev, K. B. Dedushenko, M. V. Zverkov, A. N. Mamaev, “Influence of an External Mirror on the Characteristics of Semiconductor Laser Radiation,” Sov. J. Quantum Electron. 15, 259 (1985).
[CrossRef]

Elssner, K.-E.

Goldberg, L.

L. Goldberg, H. F. Taylor, A. Dandridge, J. F. Weller, R. O. Miles, “Spectral Characteristics of Semiconductor Lasers with Optical Feedback,” IEEE J. Quantum Electron. QE-18, 555 (1982).
[CrossRef]

Goncharov, I. G.

I. G. Goncharov, A. P. Grachev, K. B. Dedushenko, M. V. Zverkov, A. N. Mamaev, “Influence of an External Mirror on the Characteristics of Semiconductor Laser Radiation,” Sov. J. Quantum Electron. 15, 259 (1985).
[CrossRef]

Grachev, A. P.

I. G. Goncharov, A. P. Grachev, K. B. Dedushenko, M. V. Zverkov, A. N. Mamaev, “Influence of an External Mirror on the Characteristics of Semiconductor Laser Radiation,” Sov. J. Quantum Electron. 15, 259 (1985).
[CrossRef]

Grzanna, J.

Iwata, K.

Kikuta, H.

Kobayashi, K.

R. Lang, K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

Lang, R.

R. Lang, K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

Mamaev, A. N.

I. G. Goncharov, A. P. Grachev, K. B. Dedushenko, M. V. Zverkov, A. N. Mamaev, “Influence of an External Mirror on the Characteristics of Semiconductor Laser Radiation,” Sov. J. Quantum Electron. 15, 259 (1985).
[CrossRef]

Matsui, S.

Matsumoto, H.

Merkel, K.

Miles, R. O.

L. Goldberg, H. F. Taylor, A. Dandridge, J. F. Weller, R. O. Miles, “Spectral Characteristics of Semiconductor Lasers with Optical Feedback,” IEEE J. Quantum Electron. QE-18, 555 (1982).
[CrossRef]

Nagata, R.

Schwider, J.

Spolaczyk, R.

Taylor, H. F.

L. Goldberg, H. F. Taylor, A. Dandridge, J. F. Weller, R. O. Miles, “Spectral Characteristics of Semiconductor Lasers with Optical Feedback,” IEEE J. Quantum Electron. QE-18, 555 (1982).
[CrossRef]

Weller, J. F.

L. Goldberg, H. F. Taylor, A. Dandridge, J. F. Weller, R. O. Miles, “Spectral Characteristics of Semiconductor Lasers with Optical Feedback,” IEEE J. Quantum Electron. QE-18, 555 (1982).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, “The Method of Excess Fractions,” in Principles of Optics, M. Born, E. Wolf, Eds. (Pergamon, Oxford, 1965), p. 291.

Yonemura, M.

Zverkov, M. V.

I. G. Goncharov, A. P. Grachev, K. B. Dedushenko, M. V. Zverkov, A. N. Mamaev, “Influence of an External Mirror on the Characteristics of Semiconductor Laser Radiation,” Sov. J. Quantum Electron. 15, 259 (1985).
[CrossRef]

Appl. Opt. (5)

IEEE J. Quantum Electron. (2)

R. Lang, K. Kobayashi, “External Optical Feedback Effects on Semiconductor Injection Laser Properties,” IEEE J. Quantum Electron. QE-16, 347 (1980).
[CrossRef]

L. Goldberg, H. F. Taylor, A. Dandridge, J. F. Weller, R. O. Miles, “Spectral Characteristics of Semiconductor Lasers with Optical Feedback,” IEEE J. Quantum Electron. QE-18, 555 (1982).
[CrossRef]

Opt. Lett. (1)

Sov. J. Quantum Electron. (1)

I. G. Goncharov, A. P. Grachev, K. B. Dedushenko, M. V. Zverkov, A. N. Mamaev, “Influence of an External Mirror on the Characteristics of Semiconductor Laser Radiation,” Sov. J. Quantum Electron. 15, 259 (1985).
[CrossRef]

Other (1)

M. Born, E. Wolf, “The Method of Excess Fractions,” in Principles of Optics, M. Born, E. Wolf, Eds. (Pergamon, Oxford, 1965), p. 291.

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Figures (10)

Fig. 1
Fig. 1

Optical/electrical system for the experiment; the current modulation frequency is 1 kHz: LD, laser diode; CL, collimating lens; AOM1,2, acoustooptical modulators (driving frequency, 40.455 and 40.000 MHz); PD, photodiode.

Fig. 2
Fig. 2

Dependence of wavelength on active region temperature for a laser diode with optical feedback: (a) when reflectivity of the output facet is 0.35 and that of the external mirror is 0.002. Here δλ is the external cavity mode separation. The dashed curve corresponds to the nonfeedback case. (b) Thick curve shows the case when external cavity length decreases by one-eighth of a wavelength. The arror shows the shift direction. The fine curve is the same as in (a).

Fig. 3
Fig. 3

Influence of feedback light. Dependence of phase variation on (a) the distance between the laser and the collimating lens, (b) laser bias current, and (c) temperature; (d) the combined effect of bias current and temperature. The path difference is (a) 2.0 mm; (b) 0.0, 1.0, and 2.0 mm; (c) 2.0 mm; and (d) 2.0 mm. The bias current is 64 mA in (a) and (c). The modulation current is 1 mA in (a)–(d). The temperature is 23.0°C in (a) and (b).

Fig. 4
Fig. 4

Example of mode distribution of the single-mode laser diode used in the experiment: laser injection current, 60 mA; temperature, 20.0°C.

Fig. 5
Fig. 5

Phase diagram showing the effect of a single submode. Observed phase variation is Δψ; the correct one is Δϕ.

Fig. 6
Fig. 6

Experimental results showing the influence of submodes. Bias current and modulation current are 60 and 1 mA, respectively. Temperatures are (a) 19.75°C and (b) 19.50°C.

Fig. 7
Fig. 7

Two typical cases of coherent noise in optical heterodyning. G is an optical surface such as a glass plate, which causes the noise. Case A shows that the noise is not frequency shifted; case B shows the frequency shifted noise.

Fig. 8
Fig. 8

Optical system to investigate the influence of coherent noise. Mirror Mr causes the coherent noise; A is the density filter that attenuates the noise.

Fig. 9
Fig. 9

Influence of coherent noise. Amplitude ratio of probe light to noise light is 20:1. Measured path difference L is ~2 mm, and noise path difference la is ~26 mm. Bias current, modulation current, and temperature are 60 mA, 1 mA, and 20.0°C.

Fig. 10
Fig. 10

Results of measurements; path difference vs phase variation. (a) For large path difference up to a few centimeters and (b) for small path difference within ten micrometers: bias current is 60 mA in (a) and (b); modulation current is (a) 1 mA and (b) 6 mA; temperature is 20.0°C in (a) and (b).

Equations (9)

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1 Λ = 1 λ - 1 λ + Δ λ Δ λ λ 2 ,
Δ ϕ = 2 π L / Λ .
tan ( ψ ) = I o sin ( ϕ 0 ) + I s sin ( ϕ s ) I o cos ( ϕ 0 ) + I s cos ( ϕ s ) ,
tan ( ψ ) = ( I o + Δ I o ) sin ( ϕ 0 ) + ( I s + Δ I s ) sin ( ϕ s ) ( I o + Δ I o ) cos ( ϕ 0 ) + ( I s + Δ I s ) cos ( ϕ s ) ,
α = ϕ 0 - ϕ s .
( I s + Δ I s ) / ( I o + Δ I o ) - I s / I o rad .
tan ( ψ a ) = sin ( ϕ ) + n a sin ( ϕ a ) cos ( ϕ ) + n a cos ( ϕ a ) ,
tan ( Δ ψ a ) = sin ( Δ ϕ ) + 2 n a cos [ ( ϕ - ϕ a ) - ( Δ ϕ - Δ ϕ a ) / 2 ] sin [ ( Δ ϕ + Δ ϕ a ) / 2 ] + n a 2 sin ( Δ ϕ a ) cos ( Δ ϕ ) + 2 n a cos [ ( ϕ - ϕ a ) - ( Δ ϕ - Δ ϕ a ) / 2 ] cos [ ( Δ ϕ + Δ ϕ a ) / 2 ] + n a 2 cos ( Δ ϕ a ) ,
tan ( Δ ψ b ) = sin ( Δ ϕ ) + 2 n b cos ( ϕ b - Δ ϕ b / 2 ) sin ( Δ ϕ - Δ ϕ b / 2 ) + n b 2 sin ( Δ ϕ - Δ ϕ b ) cos ( Δ ϕ ) + 2 n b cos ( ϕ b - Δ ϕ b / 2 ) cos ( Δ ϕ - Δ ϕ b / 2 ) + n b 2 cos ( Δ ϕ - Δ ϕ b ) ,

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