Abstract

The information capacity of an image in the atmosphere, ocean, or biological media does not grow indefinitely with increasing light power but has well defined limits. Here, the exact effects of the propagation of light in random inhomogeneous media are elucidated and upper bounds to the capacity of image pixels to represent a corresponding point in the object are described.

© 2013 Optical Society of America

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References

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  1. C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).
  2. J. A. O’Sullivan, R. E. Blahut, and D. L. Snyder, IEEE Trans. Inf. Theory 44, 2094 (1998).
    [CrossRef]
  3. G. T. di Francia, J. Opt. Soc. Am. 59, 799 (1969).
    [CrossRef]
  4. E. Biglieri, J. Proakis, and S. Shamai, IEEE Trans. Inf. Theory 44, 2619 (1998).
    [CrossRef]
  5. A. Belmonte and J. M. Kahn, Opt. Express 16, 14151 (2008).
    [CrossRef]
  6. J. W. Goodman, Speckle Phenomena in Optics. Theory and Applications (Ben Roberts, 2007).
  7. L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media, 2nd ed. (SPIE, 2005).

2008 (1)

1998 (2)

J. A. O’Sullivan, R. E. Blahut, and D. L. Snyder, IEEE Trans. Inf. Theory 44, 2094 (1998).
[CrossRef]

E. Biglieri, J. Proakis, and S. Shamai, IEEE Trans. Inf. Theory 44, 2619 (1998).
[CrossRef]

1969 (1)

1948 (1)

C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).

Andrews, L. C.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media, 2nd ed. (SPIE, 2005).

Belmonte, A.

Biglieri, E.

E. Biglieri, J. Proakis, and S. Shamai, IEEE Trans. Inf. Theory 44, 2619 (1998).
[CrossRef]

Blahut, R. E.

J. A. O’Sullivan, R. E. Blahut, and D. L. Snyder, IEEE Trans. Inf. Theory 44, 2094 (1998).
[CrossRef]

di Francia, G. T.

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics. Theory and Applications (Ben Roberts, 2007).

Kahn, J. M.

O’Sullivan, J. A.

J. A. O’Sullivan, R. E. Blahut, and D. L. Snyder, IEEE Trans. Inf. Theory 44, 2094 (1998).
[CrossRef]

Phillips, R. L.

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media, 2nd ed. (SPIE, 2005).

Proakis, J.

E. Biglieri, J. Proakis, and S. Shamai, IEEE Trans. Inf. Theory 44, 2619 (1998).
[CrossRef]

Shamai, S.

E. Biglieri, J. Proakis, and S. Shamai, IEEE Trans. Inf. Theory 44, 2619 (1998).
[CrossRef]

Shannon, C. E.

C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).

Snyder, D. L.

J. A. O’Sullivan, R. E. Blahut, and D. L. Snyder, IEEE Trans. Inf. Theory 44, 2094 (1998).
[CrossRef]

Bell Syst. Tech. J. (1)

C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).

IEEE Trans. Inf. Theory (2)

J. A. O’Sullivan, R. E. Blahut, and D. L. Snyder, IEEE Trans. Inf. Theory 44, 2094 (1998).
[CrossRef]

E. Biglieri, J. Proakis, and S. Shamai, IEEE Trans. Inf. Theory 44, 2619 (1998).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Express (1)

Other (2)

J. W. Goodman, Speckle Phenomena in Optics. Theory and Applications (Ben Roberts, 2007).

L. C. Andrews and R. L. Phillips, Laser Beam Propagation Through Random Media, 2nd ed. (SPIE, 2005).

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Figures (2)

Fig. 1.
Fig. 1.

Upper bounds to the outage pixel spectral efficiency for imaging in a random medium. Probability of outage versus image capacity per unit bandwidth and pixel for heterodyne detection (solid lines) and direct detection (dashed lines) are considered using Eqs. (3) and (4), respectively. The trade-off between the outage probability and the maximum achievable pixel spectral efficiency is analyzed for both fast image integration time (in blue) and slow integration times (in red) leading to the ergodic limit (vertical lines). In all cases, we assume the number of photons per pixel γ0 equals 100 (i.e., 20 dB SNR). Random-media effects on the phase wavefront are characterized by a moderate phase coherence length r0 such that four coherent regions are within the aperture, i.e., D/r0=2. Wavefront amplitude fluctuations are considered by assuming σγ2=1/3.

Fig. 2.
Fig. 2.

Curves represent upper bounds to the outage and ergodic pixel spectral efficiency for imaging in a random media as a function of the lens aperture diameter normalized to the wavefront coherent diameter r0. For heterodyne detection (solid lines) and direct detection (dashed lines), pixel spectral efficiency bounds are analyzed for both fast (in blue, lower dashed line and bottom 3 curves) and slow (in red, top curve and top dashed line) integration times leading to the outage and ergodic limits, respectively. Outage probability levels of 0, 1/100 and 1/10 are considered. For the smallest aperture considered, we assume γ0 is equal to 100 photons-per-pixel. For any other aperture diameter, the value of γ0 is proportional to D2. Wavefront amplitude fluctuations consider σγ2=1/3.

Tables (1)

Tables Icon

Table 1. We Investigate Various Pixel Representational Capacity Definitions of Imaging in Random Media for Direct and Heterodyne Detection Optical Receivers

Equations (4)

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Fγ(γ)=1Q1(2r,2(1+r)rγ/γ¯),
Fγ(γ)=Q(loge(γ/γ0)/σβ+σβ/2),
γεγ¯/2(1+r)[2loge(1ε)+2r]2.
γεγ0exp[σβ2/2+2σβ2loge(2ε)].

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