Abstract

It is shown how to use a lenticular fringe detector as a complex homodyne receiver working ratiometrically in a photon counting mode. While analog outputs for both quadrature components are available simultaneously it is argued that recursive digital filtering confers the benefits of photon antibunching. A successful hardware implementation of the polar innovations form of such a digital filter is also demonstrated.

© 1988 Optical Society of America

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References

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  1. L. Mertz, “Complex Interferometry,” Appl. Opt. 22, 1530 (1983).
    [CrossRef] [PubMed]
  2. L. Mertz, “Phase Estimation with Few Photons,” Appl. Opt. 23, 1638 (1984).
    [CrossRef] [PubMed]
  3. L. Mertz, “Innovations in the Phasor Diagram that Give Lower Ultimate Quantum Noise,” in Technical Digest, Topical Meeting on Quantum-Limited Imaging and Image Processing (Optical Society of America, Washington, DC, 1986), paper MD1.
  4. J. F. Walkup, J. W. Goodman, “Limitations of Fringe-Parameter Estimation at Low Light Levels,” J. Opt. Soc. Am. 63, 399 (1973).
    [CrossRef]
  5. N. G. Walker, “Quantum Theory of Multiport Optical Homodyning,” J. Mod. Opt. 34, 15 (1987).
    [CrossRef]
  6. P. Young, Recursive Estimation and Time-Series Analysis (Springer-Verlag, New York, 1984).
    [CrossRef]

1987 (1)

N. G. Walker, “Quantum Theory of Multiport Optical Homodyning,” J. Mod. Opt. 34, 15 (1987).
[CrossRef]

1984 (1)

1983 (1)

1973 (1)

Goodman, J. W.

Mertz, L.

L. Mertz, “Phase Estimation with Few Photons,” Appl. Opt. 23, 1638 (1984).
[CrossRef] [PubMed]

L. Mertz, “Complex Interferometry,” Appl. Opt. 22, 1530 (1983).
[CrossRef] [PubMed]

L. Mertz, “Innovations in the Phasor Diagram that Give Lower Ultimate Quantum Noise,” in Technical Digest, Topical Meeting on Quantum-Limited Imaging and Image Processing (Optical Society of America, Washington, DC, 1986), paper MD1.

Walker, N. G.

N. G. Walker, “Quantum Theory of Multiport Optical Homodyning,” J. Mod. Opt. 34, 15 (1987).
[CrossRef]

Walkup, J. F.

Young, P.

P. Young, Recursive Estimation and Time-Series Analysis (Springer-Verlag, New York, 1984).
[CrossRef]

Appl. Opt. (2)

J. Mod. Opt. (1)

N. G. Walker, “Quantum Theory of Multiport Optical Homodyning,” J. Mod. Opt. 34, 15 (1987).
[CrossRef]

J. Opt. Soc. Am. (1)

Other (2)

P. Young, Recursive Estimation and Time-Series Analysis (Springer-Verlag, New York, 1984).
[CrossRef]

L. Mertz, “Innovations in the Phasor Diagram that Give Lower Ultimate Quantum Noise,” in Technical Digest, Topical Meeting on Quantum-Limited Imaging and Image Processing (Optical Society of America, Washington, DC, 1986), paper MD1.

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Figures (7)

Fig. 1
Fig. 1

Circuit for pulse detection from photons.

Fig. 2
Fig. 2

Complex homodyne receiver.

Fig. 3
Fig. 3

Interferometer test configurations.

Fig. 4
Fig. 4

Ratiometric phasor display circuitry.

Fig. 5
Fig. 5

Ratiometric phasor display: (A) elliptical trace while scanning fringes bright enough to give many photons per time constant and triangular trace while most of the light is blocked to give only an occasional photon per time constant; (B) not scanning fringes and with time constant reduced to include only ~4 photons per time constant.

Fig. 6
Fig. 6

Circuitry for recursive polar innovations filter.

Fig. 7
Fig. 7

Analog quadrature vs polar innovations output: (A) two cycles selected range; (B) eight cycles selected range.

Equations (4)

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S t + 1 = S t - N - 1 ( S t - s t ) ,
Q t + 1 = Q t - N - 1 ( Q t - sin ϕ t ) , I t + 1 = I t - N - 1 ( I t - cos ϕ t ) ,
Φ t = arctan ( Q t / I t ) + K t ( 360 ° ) , V t = ( Q t 2 + I t 2 ) 1 / 2 ,
Φ t + 1 = Φ t - N - 1 ( Φ t - ϕ t ) R , V t + 1 = V t - N - 1 [ V t - cos ( Φ t - ϕ t ) ] ,

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