Abstract

The relative performance of an optical heterodyne receiver and a photon-counting receiver are compared. These conditions under which the two types of systems perform equally well are defined. Background noise is shown to be an almost negligible consideration. Detector noise is seen to be a much more severe problem. It is concluded that for wavelengths below 1 μ, photon-counting reception is preferred because of the availability of photoemissive detectors. For wavelengths greater than 3 μ, detector noise considerations are so severe that it is unlikely that photon counting will be competitive with heterodyne detection. The type of detection preferred in the 1–3 μ range is shown to be a matter of detector development.

© 1967 Optical Society of America

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References

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  1. B. M. Oliver, Proc. Inst. Radio Engrs. 49, 1960 (1961).
  2. H. A. Haus, C. H. Townes, Proc. Inst. Radio Engrs. 50, 1544 (1962).
  3. S. Gardner, IEEE International Convention Record(1964), Part 6, p. 337.
  4. D. L. Fried, Proc. IEEE, 55, No. 1 (1967).
    [CrossRef]
  5. R. C. Jones, Proc. Inst. Radio Engrs. 47, 1498 (1959).
  6. At least one manufacturer finds it convenient to specify the capability of his filters in terms of a percentage bandwidth for filters covering a wide range of wavelengths. [δ= 10−3for 0.32 μ< λ < 15.5 μ; Spectrum Systems, Inc., Appl. Opt. 5, No. 5, A7 (1966).]
  7. E. E. Bell, L. Eisner, J. Young, R. A. Oetjen, J. Opt. Soc. Am. 50, 1313 (1960).
    [CrossRef]
  8. N. Ginsburg, W. R. Fredrickson, R. Paulson, J. Opt. Soc. Am. 50, 1176 (1960).
    [CrossRef]
  9. F. Moller, Appl. Opt. 3, 157 (1964).
    [CrossRef]
  10. D. S. Bayley has computed sky spectral brightness based on Allen’s data (C. W. Allen, “Astrophysical Quantities”, Univ. of London, London, 1955) for transmission of a clear atmosphere and the assumptions that the sun is a blackbody at 5700°K, and, with the sun at the zenith, the sky’s spectral radiance is uniform over the hemisphere. Details will be found in ASTIA Document No. AD261583, Table 5-I.
  11. This type of fine tracking can be achieved in the obvious manner for a photon-counting system by using an image dissector. It has been shown [W. S. Read, D. L. Fried, Proc. IEEE 51, 1787 (1963)] that an image dissector can be used for the same purpose in an optical heterodyne receiver.
    [CrossRef]
  12. E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley Publishing Co., Inc., Reading, Mass., 1963), p. 87.
  13. D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).
    [CrossRef]

1967 (1)

D. L. Fried, Proc. IEEE, 55, No. 1 (1967).
[CrossRef]

1966 (2)

At least one manufacturer finds it convenient to specify the capability of his filters in terms of a percentage bandwidth for filters covering a wide range of wavelengths. [δ= 10−3for 0.32 μ< λ < 15.5 μ; Spectrum Systems, Inc., Appl. Opt. 5, No. 5, A7 (1966).]

D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).
[CrossRef]

1964 (2)

F. Moller, Appl. Opt. 3, 157 (1964).
[CrossRef]

S. Gardner, IEEE International Convention Record(1964), Part 6, p. 337.

1963 (1)

This type of fine tracking can be achieved in the obvious manner for a photon-counting system by using an image dissector. It has been shown [W. S. Read, D. L. Fried, Proc. IEEE 51, 1787 (1963)] that an image dissector can be used for the same purpose in an optical heterodyne receiver.
[CrossRef]

1962 (1)

H. A. Haus, C. H. Townes, Proc. Inst. Radio Engrs. 50, 1544 (1962).

1961 (1)

B. M. Oliver, Proc. Inst. Radio Engrs. 49, 1960 (1961).

1960 (2)

1959 (1)

R. C. Jones, Proc. Inst. Radio Engrs. 47, 1498 (1959).

Allen, C. W.

D. S. Bayley has computed sky spectral brightness based on Allen’s data (C. W. Allen, “Astrophysical Quantities”, Univ. of London, London, 1955) for transmission of a clear atmosphere and the assumptions that the sun is a blackbody at 5700°K, and, with the sun at the zenith, the sky’s spectral radiance is uniform over the hemisphere. Details will be found in ASTIA Document No. AD261583, Table 5-I.

Bell, E. E.

Eisner, L.

Fredrickson, W. R.

Fried, D. L.

D. L. Fried, Proc. IEEE, 55, No. 1 (1967).
[CrossRef]

D. L. Fried, J. Opt. Soc. Am. 56, 1372 (1966).
[CrossRef]

This type of fine tracking can be achieved in the obvious manner for a photon-counting system by using an image dissector. It has been shown [W. S. Read, D. L. Fried, Proc. IEEE 51, 1787 (1963)] that an image dissector can be used for the same purpose in an optical heterodyne receiver.
[CrossRef]

Gardner, S.

S. Gardner, IEEE International Convention Record(1964), Part 6, p. 337.

Ginsburg, N.

Haus, H. A.

H. A. Haus, C. H. Townes, Proc. Inst. Radio Engrs. 50, 1544 (1962).

Jones, R. C.

R. C. Jones, Proc. Inst. Radio Engrs. 47, 1498 (1959).

Moller, F.

O’Neill, E. L.

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley Publishing Co., Inc., Reading, Mass., 1963), p. 87.

Oetjen, R. A.

Oliver, B. M.

B. M. Oliver, Proc. Inst. Radio Engrs. 49, 1960 (1961).

Paulson, R.

Read, W. S.

This type of fine tracking can be achieved in the obvious manner for a photon-counting system by using an image dissector. It has been shown [W. S. Read, D. L. Fried, Proc. IEEE 51, 1787 (1963)] that an image dissector can be used for the same purpose in an optical heterodyne receiver.
[CrossRef]

Townes, C. H.

H. A. Haus, C. H. Townes, Proc. Inst. Radio Engrs. 50, 1544 (1962).

Young, J.

Appl. Opt. (2)

At least one manufacturer finds it convenient to specify the capability of his filters in terms of a percentage bandwidth for filters covering a wide range of wavelengths. [δ= 10−3for 0.32 μ< λ < 15.5 μ; Spectrum Systems, Inc., Appl. Opt. 5, No. 5, A7 (1966).]

F. Moller, Appl. Opt. 3, 157 (1964).
[CrossRef]

IEEE International Convention Record (1)

S. Gardner, IEEE International Convention Record(1964), Part 6, p. 337.

J. Opt. Soc. Am. (3)

Proc. IEEE (2)

D. L. Fried, Proc. IEEE, 55, No. 1 (1967).
[CrossRef]

This type of fine tracking can be achieved in the obvious manner for a photon-counting system by using an image dissector. It has been shown [W. S. Read, D. L. Fried, Proc. IEEE 51, 1787 (1963)] that an image dissector can be used for the same purpose in an optical heterodyne receiver.
[CrossRef]

Proc. Inst. Radio Engrs. (3)

R. C. Jones, Proc. Inst. Radio Engrs. 47, 1498 (1959).

B. M. Oliver, Proc. Inst. Radio Engrs. 49, 1960 (1961).

H. A. Haus, C. H. Townes, Proc. Inst. Radio Engrs. 50, 1544 (1962).

Other (2)

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley Publishing Co., Inc., Reading, Mass., 1963), p. 87.

D. S. Bayley has computed sky spectral brightness based on Allen’s data (C. W. Allen, “Astrophysical Quantities”, Univ. of London, London, 1955) for transmission of a clear atmosphere and the assumptions that the sun is a blackbody at 5700°K, and, with the sun at the zenith, the sky’s spectral radiance is uniform over the hemisphere. Details will be found in ASTIA Document No. AD261583, Table 5-I.

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Figures (4)

Fig. 1
Fig. 1

Optical schematic of a photon-counting receiver. All optics are shown as refractive but could be reflective equally well. The field stop, used to define the field of view although shown as distinct from the detector, could be combined with the detector.

Fig. 2
Fig. 2

Daytime sky spectral radiance index Ñλ vs measurement wavelength λ. (The spectral radiance index is equal to the spectral radiance, with dimensions of W cm−2 sr−1 Å−1, times the wavelength.) The source data is Bayley6 (— — —), Bell et al. (— … —)7, Ginsburg et al.8 (— . — . —), and Moller9 (——) The heavy curve is our estimated fit to this data.

Fig. 3
Fig. 3

αmax, the allowed increase in a photon-counting receiver’s field of view over an (equal collector diameter) heterodyne receiver’s field of view vs wavelength of operation. Results are based on the daytime sky radiance data of Fig. 2. Calculations are carried out for two different quantum efficiencies, η = 0.1 and η = 0.5, an assumed optical filter bandwidth δ = Δλ/λ = 0.002, and the indicated range of values of (S/N)* Δf, the products of signal-to-noise power ratio and information bandwidth which the collected signal flux could sustain in the absence of any noise other than the quantum noise of the signal flux. The allowed field of view is based on the requirement that the photon-counting receiver be background quasi-ideal, i.e., that the system result in no more quantization noise than the amount due to the signal flux.

Fig. 4
Fig. 4

(D*)min the minimum acceptable detector D* vs the normalized detector size, αf, for various wavelengths, quantum efficiencies and for a range of values of (S/N)* Δf, the product of signal-to-noise power ratio and information bandwidth which the collected signal flux could sustain in the absence of any noise other than the quantum noise of the signal flux. The detector diameter is αfλ. Since fλ is the minimum allowable detector size (f is the f number of the condenser lens in Fig. 1), α′ is the relaxation of detector size over the minimum allowable. The minimum acceptable detector D* is evaluated on the basis that the photon-counting receiver be detector quasi-ideal, i.e., that the intrinsic detector noise be no more than the noise due to the quantized nature of the signal flux.

Equations (13)

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N * = 2 I S e Δ f ,             e = 1.602 × 10 - 19 coulomb .
( S / N ) * = I S / 2 e Δ f .
N * = ( 2 e Δ f ) 2 ( S / N ) * .
N ˜ λ = λ N λ .
I B = η ( e λ / h c ) ( π / 4 ) D 2 N ˜ λ Ω δ ,
Ω 8 h c ( S / N ) * Δ f / η λ π D 2 N ˜ λ δ ,
Ω = ( α λ / D ) 2 ,
α max = ( 2 / λ ) [ 2 h c ( S / N ) * Δ f / η λ π N ˜ λ δ ] ½ .
D * = ( A Δ f ) ½ / ( NEP ) .
( NEP ) * = ( h c / η e λ ) ( N * ) ½ = ( 2 h c Δ f / η λ ) [ ( S / N ) * ] ½ .
( D * ) min = ( η λ / 2 h c ) [ A / Δ f ( S / N ) * ] 1 / 2 .
A = ( α f λ ) 2 .
( D * ) min = η λ 2 α f / 2 h c [ Δ f ( S / N ) * ] ½ .

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