Abstract

A simple single-beam technique employing radio-frequency modulation of a tunable diode laser with homodyne demodulation is demonstrated as a means of measuring optical path lengths. This technique offers a straightforward method for determining path lengths traversed through optical multipass cells or performing optical range-finding over short (i.e., tens of meters) standoff distances. The radio-frequency phase-sensitive nature of the technique permits narrow-band detection and high signal-to-noise ratios, even when range-finding measurements are made with range resolutions of ≪1 m. This compares favorably with traditional short-pulse, wide-bandwidth optical range finders.

© 1996 Optical Society of America

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References

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1995 (1)

1994 (1)

1991 (1)

1988 (1)

1987 (2)

1986 (1)

1984 (1)

1983 (1)

C. Harder, K. Vahala, A. Yariv, “Measurement of the linewidth enhancement factor α of semiconductor lasers,” Appl. Phys. Lett. 42, 328–330 (1983).
[CrossRef]

1981 (1)

G. C. Bjorklund, K. Jain, J. D. Hope, “Interferometric measurements with laser FM sidebands,” Appl. Phys. Lett. 38, 747–749 (1981).
[CrossRef]

1977 (1)

D. Nitzan, A. E. Brain, R. O. Duda, “The measurement and use of registered reflectance and range data in scene analysis,” Proc. IEEE 65, 206–220 (1977).
[CrossRef]

1973 (1)

Arecchi, F. T.

F. T. Arecchi, E. O. Schulz-Dubois, “Lasers in metrology,” in Laser Handbook (North-Holland, Amsterdam, 1976), pp. 1469–1476.

Bjorklund, G. C.

G. C. Bjorklund, K. Jain, J. D. Hope, “Interferometric measurements with laser FM sidebands,” Appl. Phys. Lett. 38, 747–749 (1981).
[CrossRef]

Brain, A. E.

D. Nitzan, A. E. Brain, R. O. Duda, “The measurement and use of registered reflectance and range data in scene analysis,” Proc. IEEE 65, 206–220 (1977).
[CrossRef]

Cooper, D. E.

Danliker, R.

de Groot, P.

Duda, R. O.

D. Nitzan, A. E. Brain, R. O. Duda, “The measurement and use of registered reflectance and range data in scene analysis,” Proc. IEEE 65, 206–220 (1977).
[CrossRef]

Greve, A.

Hamano, K.

Harder, C.

C. Harder, K. Vahala, A. Yariv, “Measurement of the linewidth enhancement factor α of semiconductor lasers,” Appl. Phys. Lett. 42, 328–330 (1983).
[CrossRef]

Harth, W.

Hope, J. D.

G. C. Bjorklund, K. Jain, J. D. Hope, “Interferometric measurements with laser FM sidebands,” Appl. Phys. Lett. 38, 747–749 (1981).
[CrossRef]

Ishii, Y.

Iwata, K.

Jain, K.

G. C. Bjorklund, K. Jain, J. D. Hope, “Interferometric measurements with laser FM sidebands,” Appl. Phys. Lett. 38, 747–749 (1981).
[CrossRef]

Kay, S. M.

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (PTR Prentice Hall, Englewood Cliffs, N.J., 1993).

Kikuta, H.

Kishner, S.

Nagata, R.

Nitzan, D.

D. Nitzan, A. E. Brain, R. O. Duda, “The measurement and use of registered reflectance and range data in scene analysis,” Proc. IEEE 65, 206–220 (1977).
[CrossRef]

Onodera, R.

Polhemus, C.

Prongue, D.

Schulz-Dubois, E. O.

F. T. Arecchi, E. O. Schulz-Dubois, “Lasers in metrology,” in Laser Handbook (North-Holland, Amsterdam, 1976), pp. 1469–1476.

Thalman, R.

Vahala, K.

C. Harder, K. Vahala, A. Yariv, “Measurement of the linewidth enhancement factor α of semiconductor lasers,” Appl. Phys. Lett. 42, 328–330 (1983).
[CrossRef]

Warren, R. E.

Yamaguchi, I.

Yariv, A.

C. Harder, K. Vahala, A. Yariv, “Measurement of the linewidth enhancement factor α of semiconductor lasers,” Appl. Phys. Lett. 42, 328–330 (1983).
[CrossRef]

Appl. Opt. (6)

Appl. Phys. Lett. (2)

C. Harder, K. Vahala, A. Yariv, “Measurement of the linewidth enhancement factor α of semiconductor lasers,” Appl. Phys. Lett. 42, 328–330 (1983).
[CrossRef]

G. C. Bjorklund, K. Jain, J. D. Hope, “Interferometric measurements with laser FM sidebands,” Appl. Phys. Lett. 38, 747–749 (1981).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (2)

Proc. IEEE (1)

D. Nitzan, A. E. Brain, R. O. Duda, “The measurement and use of registered reflectance and range data in scene analysis,” Proc. IEEE 65, 206–220 (1977).
[CrossRef]

Other (2)

F. T. Arecchi, E. O. Schulz-Dubois, “Lasers in metrology,” in Laser Handbook (North-Holland, Amsterdam, 1976), pp. 1469–1476.

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (PTR Prentice Hall, Englewood Cliffs, N.J., 1993).

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Figures (6)

Fig. 1
Fig. 1

Experimental setup used to demonstrate optical path-length estimation.

Fig. 2
Fig. 2

Schematic illustration of RF paths experienced by signal and local oscillator RF channels.

Fig. 3
Fig. 3

Waveform recorded with a frequency sweep of 100 MHz and an optical path length of 103.3 m.

Fig. 4
Fig. 4

Waveform recorded with a frequency sweep of 100 MHz and an optical path length of 21.4 m.

Fig. 5
Fig. 5

Experimental setup used for range-finding experiments.

Fig. 6
Fig. 6

Waveform recorded with the range-finder setup and a frequency sweep of 200 MHz.

Equations (15)

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E 1 ( t ) = E 0 ( t ) [ 1 + M sin ( 2 π ν t + ψ ) ] exp ( i β sin 2 π ν t )
I 1 ( t ) = | E 0 ( t z / c ) | 2 n { r n r ¯ n + 1 exp [ i 2 π ν ( t z / c ) ] + r n r ¯ n 1 exp [ i 2 π ν ( t z / c ) ] } = 2 M | E 0 ( t z / c ) | 2 sin [ 2 π ν ( t z / c ) + ψ ] ,
I 1 = M | E 0 ( t z / c ) | 2 cos ( 2 π ν z z 0 c + ψ )
P ( ν ) = ε 0 A r P 0 σ π z 2 M cos ( 2 π ν z z 0 c + ψ ) ,
ν k = ν 0 + k ( ν 1 ν 0 ) N 1 , 0 k N 1 ,
P k = A cos ( 4 π ν k z z 0 c + ψ ) + n k ,
A ε 0 A r P 0 σ π z 2 M ,
σ z 2 3 c 2 ( N 1 ) 4 π 2 η N ( N + 1 ) ( ν 1 ν 0 ) 2 ,
η A 2 2 σ 2
A M P 0 T 0 .
σ SN = ( 2 e B P 0 R ) 1 / 2 = 2 . 8 n W, σ JN = 4 K T B = 5 . 5 n W, η = ( M ) 2 P 0 2 T 0 2 R 2 e B P 0 = M 2 P 0 T 0 2 R 2 e B .
f ( P A , z , ψ ) k = 0 N 1 ( 2 πσ 2 ) 1 / 2 × exp { 1 2 σ 2 [ P k A cos ( 2 π ν k z z 0 c + ψ ) ] 2 }
J k = 0 N 1 ( P k α 1 C k α 2 S k ) 2 ,
z ˆ = arg { min z k = 0 N 1 [ P k α ˆ 1 C k ( z ) α ˆ 2 S k ( z ) ] 2 } + z 0 .
Q ( z ) ( P T H ) ( H T H ) 1 H T P

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