Abstract

New modulation codes are presented for a random modulation cw lidar. One characteristic of these modulation codes is that for very noisy background conditions, the signal-to-noise ratio is improved by using these new sequences, and is better than for the maximum-length sequence (the M-sequence) which is commonly used as the modulation code. Another characteristic of these modulation codes is that there is no correlation between them. This fact will be useful for the simultaneous multitransmitter of the differential absorption lidar. These two characteristics of the new modulation codes were confirmed experimentally.

© 1990 Optical Society of America

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References

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  1. N. Takeuchi, N. Sugimoto, H. Baba, K. Sakurai, “Random Modulation CW Lidar,” Appl. Opt. 22, 1382–1386 (1983).
    [Crossref] [PubMed]
  2. N. Takeuchi, H. Baba, K. Sakurai, T. Ueno, “Diode-Laser Random-Modulation CW Lidar,” Appl. Opt. 25, 63–67 (1986).
    [Crossref] [PubMed]
  3. I. Sato, “Pseudorandom Sequence,” Correlation Function and Spectrum, T. Isobe, Ed. (U. of Tokyo, 1968), p.179, (in Japanese).
  4. M. Abo, C. Nagasawa, T. Kaneki, O. Uchino, “Diode-Laser Pulse-Modulation Laser Radar System,” Mem. Fac. of Tech. Tokyo Metropolitan U. 38, 3935–3942 (1988).

1988 (1)

M. Abo, C. Nagasawa, T. Kaneki, O. Uchino, “Diode-Laser Pulse-Modulation Laser Radar System,” Mem. Fac. of Tech. Tokyo Metropolitan U. 38, 3935–3942 (1988).

1986 (1)

1983 (1)

Abo, M.

M. Abo, C. Nagasawa, T. Kaneki, O. Uchino, “Diode-Laser Pulse-Modulation Laser Radar System,” Mem. Fac. of Tech. Tokyo Metropolitan U. 38, 3935–3942 (1988).

Baba, H.

Kaneki, T.

M. Abo, C. Nagasawa, T. Kaneki, O. Uchino, “Diode-Laser Pulse-Modulation Laser Radar System,” Mem. Fac. of Tech. Tokyo Metropolitan U. 38, 3935–3942 (1988).

Nagasawa, C.

M. Abo, C. Nagasawa, T. Kaneki, O. Uchino, “Diode-Laser Pulse-Modulation Laser Radar System,” Mem. Fac. of Tech. Tokyo Metropolitan U. 38, 3935–3942 (1988).

Sakurai, K.

Sato, I.

I. Sato, “Pseudorandom Sequence,” Correlation Function and Spectrum, T. Isobe, Ed. (U. of Tokyo, 1968), p.179, (in Japanese).

Sugimoto, N.

Takeuchi, N.

Uchino, O.

M. Abo, C. Nagasawa, T. Kaneki, O. Uchino, “Diode-Laser Pulse-Modulation Laser Radar System,” Mem. Fac. of Tech. Tokyo Metropolitan U. 38, 3935–3942 (1988).

Ueno, T.

Appl. Opt. (2)

Mem. Fac. of Tech. Tokyo Metropolitan U. (1)

M. Abo, C. Nagasawa, T. Kaneki, O. Uchino, “Diode-Laser Pulse-Modulation Laser Radar System,” Mem. Fac. of Tech. Tokyo Metropolitan U. 38, 3935–3942 (1988).

Other (1)

I. Sato, “Pseudorandom Sequence,” Correlation Function and Spectrum, T. Isobe, Ed. (U. of Tokyo, 1968), p.179, (in Japanese).

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Figures (4)

Fig. 1
Fig. 1

Cross-correlation function of (a) ai and a i (M-sequence), (b) a i * and a i * (A1-sequence) and (c) a i * * and a i * * (A2-sequence).

Fig. 2
Fig. 2

Block diagram of the experimental setup.

Fig. 3
Fig. 3

Lidar echo signal from a tower with (a) the M-sequence and (b) the A2-sequence for severe noise conditions.

Fig. 4
Fig. 4

Lidar echos from aerosol (a) with a single transmitter modulated by the A2-sequence and recovered by the A2-sequence, (b) with multitransmitters modulated by the A1-sequence and the A2-sequence and recovered by the A2-sequence.

Tables (1)

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Table I Specifications of the experimental setup

Equations (22)

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y i = j = 0 N - 1 x i - j G j + b i             i = 0 , 1 , 2 , , N - 1 ,
ϕ a a ( k ) = i = 0 N - 1 a i a i + k .
ϕ a a ( k ) = { ( N + 1 ) / 2 k = 0 ( mod N ) 0 k 0 ( mod N ) .
S l = i = 0 N - 1 y i a i - l .
S l = i = 0 N - 1 { i = 0 N - 1 x i - j G j + b i } a i - l = P o j = 0 N - 1 ϕ a a ( j - l ) G j + i = 0 N - 1 a i - l b i .
E [ S l ] = N + 1 2 P o G l + b ¯ ,
SNR = M ξ P o ( N + 1 ) G l / 2 N μ { P o ( N + 1 ) G ¯ / 2 + b ¯ } ,
a i * = ( - 1 ) i a i             i = 0 , 1 , , 2 N - 1.
a i * * = { a i ( i = 4 m , 4 m + 1 ) - a i ( i = 4 m + 2 , 4 m + 3 )             m = 0 , 1 , , N - 1 ,
ϕ a * a * ( k ) = { N k = 0 ( mod 2 N ) 1 k = 2 n - 1 ( mod N ) - 1 k = 2 n ( mod N ) - N k = N ( mod 2 N )             n = 1 , 2 , , ( N - 1 ) / 2 ,
ϕ a * * a * * ( k ) = { 2 N k = 0 ( mod 4 N ) 2 k = 4 n - 2 ( mod 2 N ) 0 k = 2 n - 1 ( mod 2 N ) - 2 k = 4 n ( mod 2 N ) - 2 N k = 2 N ( mod 4 N )             n = 1 , 2 , , ( N - 1 ) / 2.
S l * = P o j = 0 2 N - 1 ϕ a * a * ( j - l ) G j + i = 0 2 N - 1 a i - l * b i .
E [ S l * ] = N P o G l - N P o G l + N + P o n = 1 ( N - 1 ) / 2 ( G 2 n - 1 + l + G 2 n - 1 + l + N ) - P o n = 1 ( N - 1 ) / 2 ( G 2 n + l + G 2 n + l + N ) + i = 0 2 N - 1 a i - l * b i N P o G l .
S i * * = P o j = 0 4 N - 1 ϕ a * * a * * ( j - l ) G j + i = 0 4 N - 1 a i - l * * b i .
E [ S l * * ] = 2 N P o G l - 2 N P o G l + 2 N + 2 P o n = 1 ( N - 1 ) / 2 ( G 4 n - 2 + l + G 4 n - 2 + l + 2 N ) - 2 P o n = 1 ( N - 1 ) / 2 ( G 4 n + l + G 4 n + l + 2 N ) + i = 0 4 N - 1 a i - l * * b i 2 N P o G l .
i = 0 2 N - 1 a i * = 0
i = 0 4 N - 1 a i * * = 0.
ϕ a * a * * ( k ) = 0
ϕ a * * a * ( k ) = 0.
y A B i = j = 0 4 N - 1 x A i - j G A j + j = 0 4 N - 1 x B i - j + b i ,
S A l = i = 0 4 N - 1 y A B i a i - l * = P A j = 0 4 N - 1 ϕ a * a * ( j - l ) G A j + P B j = 0 4 N - 1 ϕ a * * a * ( j - l ) G B j + i = 0 4 N - 1 a i - l * b i .
E [ S A l ] 2 N P A G A l .

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