Abstract

Heterodyne efficiency is discussed for a partially coherent signal and a coherent local oscillator beam. Both fileds are assumed to have Gaussian amplitude distributions. An input aperture is used to reduce the background noise. As the coherence of the signal decreases, the efficiency also decreases. However, there is a simple relation between the beam parameters and the detector dimensions to maintain optimum efficiency. The effect of the offset of the signal from the detector axis is also discussed, assuming the Gaussian probability of the deviation. In this case, the optimum parameters that give the maximum efficiency change with the average deviation.

© 1992 Optical Society of America

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References

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  1. A. L. Migdall, B. Roop, Y. C. Zheng, J. E. Hardis, Gu Jun Xia, “Use of heterodyne detection to measure optical transmittance over a wide range,” Appl. Opt. 29, 5136–5144 (1990).
    [CrossRef] [PubMed]
  2. K. Tanaka, N. Ohta, “Effects of tilt and offset of signal field on heterodyne efficiency,” Appl. Opt. 26, 627–632 (1987).
    [CrossRef] [PubMed]
  3. R. H. Kingston, Detection of Optical and Infrared Radiation (Springer-Verlag, Berlin, 1978), chap. 3.
  4. D. Fink, “Coherent detection signal-to-noise ratio,” Appl. Opt. 14, 689–690 (1975).
    [CrossRef] [PubMed]
  5. T. Takenaka, N. Saga, O. Fukumitsu, “Heterodyne detection of partially coherent optical signal,” Trans. Inst. Electron. Inform. Commun. Eng. Jpn. J64-C, 553–559 (1981).

1990 (1)

1987 (1)

1981 (1)

T. Takenaka, N. Saga, O. Fukumitsu, “Heterodyne detection of partially coherent optical signal,” Trans. Inst. Electron. Inform. Commun. Eng. Jpn. J64-C, 553–559 (1981).

1975 (1)

Fink, D.

Fukumitsu, O.

T. Takenaka, N. Saga, O. Fukumitsu, “Heterodyne detection of partially coherent optical signal,” Trans. Inst. Electron. Inform. Commun. Eng. Jpn. J64-C, 553–559 (1981).

Hardis, J. E.

Kingston, R. H.

R. H. Kingston, Detection of Optical and Infrared Radiation (Springer-Verlag, Berlin, 1978), chap. 3.

Migdall, A. L.

Ohta, N.

Roop, B.

Saga, N.

T. Takenaka, N. Saga, O. Fukumitsu, “Heterodyne detection of partially coherent optical signal,” Trans. Inst. Electron. Inform. Commun. Eng. Jpn. J64-C, 553–559 (1981).

Takenaka, T.

T. Takenaka, N. Saga, O. Fukumitsu, “Heterodyne detection of partially coherent optical signal,” Trans. Inst. Electron. Inform. Commun. Eng. Jpn. J64-C, 553–559 (1981).

Tanaka, K.

Xia, Gu Jun

Zheng, Y. C.

Appl. Opt. (3)

Trans. Inst. Electron. Inform. Commun. Eng. Jpn. (1)

T. Takenaka, N. Saga, O. Fukumitsu, “Heterodyne detection of partially coherent optical signal,” Trans. Inst. Electron. Inform. Commun. Eng. Jpn. J64-C, 553–559 (1981).

Other (1)

R. H. Kingston, Detection of Optical and Infrared Radiation (Springer-Verlag, Berlin, 1978), chap. 3.

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Figures (5)

Fig. 1
Fig. 1

Contours of the constant heterodyne efficiency for a coherent signal: (a) ws/wl = 0.8; (b) ws/wl = 1.0; (c) ws/wl = 1.2.

Fig. 2
Fig. 2

Contours of the constant heterodyne efficiency for a partially coherent signal. The coherence length is equal to the side of the input aperture (a1 = l).

Fig. 3
Fig. 3

Heterodyne efficiency as a function of a2/wl or a1/ws for various values of coherence length.

Fig. 4
Fig. 4

Heterodyne efficiency for a partially coherent signal with or without axial offset: solid curves, δ/a1 = 0.0; dashed curves, δ/a1 = 0.1.

Fig. 5
Fig. 5

Average heterodyne efficiency for a partially coherent signal with an offset that has a Gaussian probability distribution.

Equations (7)

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γ = | S 2 U s U l * d S 2 | 2 U s 2 d S 2 S 2 U l 2 d S 2 ,
P i f = ( k / 2 π ) 2 S 2 S 2 [ U l * ( x 2 , y 2 , z 2 ) × U l ( x 2 , y 2 , z 2 ) ] d S 2 d S 2 S 1 S 1 < U s * ( x 1 , y 1 ) U s ( x 1 , y 1 ) > G ( x 1 , y 1 ; x 2 , y 2 ) × G * ( x 1 , y 1 ; x 2 , y 2 ) d S 1 d S 1 ,
G ( x 1 , y 1 ; x 2 , y 2 ) = 1 ( z 2 - z 1 ) exp { - j k ( z 2 - z 1 ) - j k [ ( x 2 - x 1 ) 2 + ( y 2 - y 1 ) 2 ( z 2 - z 1 ) ] } .
U s * ( x 1 , y 1 ) U s ( x 1 , y 1 ) = γ c [ I ( x 1 , y 1 ) I ( x 1 , y 1 ) ] 1 / 2 .
I ( x 1 , y 1 ) = exp [ - 2 ( x 1 - δ ) 2 + 2 y 1 2 w s 0 2 ] .
γ c ( x 1 , y 1 ; x 1 , y 1 ) = exp [ - ( x 1 - x 1 ) 2 + ( y 1 - y 1 ) 2 l 2 ] ,
P ( δ ) = 1 π σ exp ( - δ 2 / σ 2 )

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