Abstract

The performance of spectral imagers is customarily described by several characteristics including resolution, noise, and coregistration. These must be traded off against each other in a practical imager design. This paper proposes a way to use the information capacity, in an information-theoretic sense, as a figure of merit for spectral imagers. In particular, it is shown how a metric [Opt. Express 20, 918 (2012)] can be used to incorporate coregistration performance in a definition of total noise, which in turn can be used in the definition of information capacity. As an example, it is shown how the information capacity can be used to optimize the pixel size in a simple case that can be treated analytically. Generally, the information capacity is attractive as a fundamental, application-independent figure of merit for spectral imager optimization and benchmarking.

© 2013 Optical Society of America

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References

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  5. C.-L. Tisse, F. Guichard, and F. Cao, “Does resolution really increase image quality?” Proc. SPIE 6817, 68170Q (2008).
    [CrossRef]
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    [CrossRef]
  7. P. Mouroulis, D. A. Thomas, T. G. Chrien, V. Duval, R. O. Green, J. J. Simmonds, and A. H. Vaughan, Trade Studies in Multi/Hyperspectral Imaging Systems—Final Report (NASA Jet Propulsion Laboratory, 1998).
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    [CrossRef]
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    [CrossRef]
  14. S. Arimoto, “An algorithm for computing the capacity of arbitrary discrete memoryless channels,” IEEE Trans. Inf. Theory 18, 14–20 (1972).
    [CrossRef]

2012 (2)

T. Skauli, “An upper-bound metric for characterizing spectral and spatial coregistration errors in spectral imaging,” Opt. Express 20, 918–933 (2012).
[CrossRef]

A. Lapidoth, “Capacity results of an optical intensity channel with input-dependent channel noise,” IEEE Trans. Inf. Theory 58, 207–223 (2012).
[CrossRef]

2011 (1)

T. Skauli, “Quantifying coregistration errors in spectral imaging,” Proc. SPIE 8158, 81580A (2011).
[CrossRef]

2010 (1)

F. Cao, F. Guichard, and H. Hornung, “Information capacity: a measure of potential image quality of a digital camera,” Proc. SPIE 7537, 75370F (2010).
[CrossRef]

2009 (1)

A. Lapidoth, and S. M. Moser, “On the capacity of the discrete-time Poisson channel,” IEEE Trans. Inf. Theory 55, 303–322 (2009).
[CrossRef]

2008 (1)

C.-L. Tisse, F. Guichard, and F. Cao, “Does resolution really increase image quality?” Proc. SPIE 6817, 68170Q (2008).
[CrossRef]

2007 (1)

2000 (1)

1987 (1)

1986 (1)

1984 (1)

1972 (1)

S. Arimoto, “An algorithm for computing the capacity of arbitrary discrete memoryless channels,” IEEE Trans. Inf. Theory 18, 14–20 (1972).
[CrossRef]

1955 (1)

P. B. Fellgett and E. H. Linfoot, “On the assessment of optical images,” Phil. Trans. R. Soc. A 247, 369–407 (1955).
[CrossRef]

Arimoto, S.

S. Arimoto, “An algorithm for computing the capacity of arbitrary discrete memoryless channels,” IEEE Trans. Inf. Theory 18, 14–20 (1972).
[CrossRef]

Burton, G. J.

Cao, F.

F. Cao, F. Guichard, and H. Hornung, “Information capacity: a measure of potential image quality of a digital camera,” Proc. SPIE 7537, 75370F (2010).
[CrossRef]

C.-L. Tisse, F. Guichard, and F. Cao, “Does resolution really increase image quality?” Proc. SPIE 6817, 68170Q (2008).
[CrossRef]

Chrien, T. G.

P. Mouroulis, D. A. Thomas, T. G. Chrien, V. Duval, R. O. Green, J. J. Simmonds, and A. H. Vaughan, Trade Studies in Multi/Hyperspectral Imaging Systems—Final Report (NASA Jet Propulsion Laboratory, 1998).

Cox, I. J.

Duval, V.

P. Mouroulis, D. A. Thomas, T. G. Chrien, V. Duval, R. O. Green, J. J. Simmonds, and A. H. Vaughan, Trade Studies in Multi/Hyperspectral Imaging Systems—Final Report (NASA Jet Propulsion Laboratory, 1998).

Fales, C. L.

Fellgett, P. B.

P. B. Fellgett and E. H. Linfoot, “On the assessment of optical images,” Phil. Trans. R. Soc. A 247, 369–407 (1955).
[CrossRef]

Green, R. O.

P. Mouroulis, D. A. Thomas, T. G. Chrien, V. Duval, R. O. Green, J. J. Simmonds, and A. H. Vaughan, Trade Studies in Multi/Hyperspectral Imaging Systems—Final Report (NASA Jet Propulsion Laboratory, 1998).

Guichard, F.

F. Cao, F. Guichard, and H. Hornung, “Information capacity: a measure of potential image quality of a digital camera,” Proc. SPIE 7537, 75370F (2010).
[CrossRef]

C.-L. Tisse, F. Guichard, and F. Cao, “Does resolution really increase image quality?” Proc. SPIE 6817, 68170Q (2008).
[CrossRef]

Hornung, H.

F. Cao, F. Guichard, and H. Hornung, “Information capacity: a measure of potential image quality of a digital camera,” Proc. SPIE 7537, 75370F (2010).
[CrossRef]

Huck, F. O.

Lapidoth, A.

A. Lapidoth, “Capacity results of an optical intensity channel with input-dependent channel noise,” IEEE Trans. Inf. Theory 58, 207–223 (2012).
[CrossRef]

A. Lapidoth, and S. M. Moser, “On the capacity of the discrete-time Poisson channel,” IEEE Trans. Inf. Theory 55, 303–322 (2009).
[CrossRef]

Linfoot, E. H.

P. B. Fellgett and E. H. Linfoot, “On the assessment of optical images,” Phil. Trans. R. Soc. A 247, 369–407 (1955).
[CrossRef]

Martinez, A.

Miller, D. A. B.

Moorhead, I. R.

Moser, S. M.

A. Lapidoth, and S. M. Moser, “On the capacity of the discrete-time Poisson channel,” IEEE Trans. Inf. Theory 55, 303–322 (2009).
[CrossRef]

Mouroulis, P.

P. Mouroulis, D. A. Thomas, T. G. Chrien, V. Duval, R. O. Green, J. J. Simmonds, and A. H. Vaughan, Trade Studies in Multi/Hyperspectral Imaging Systems—Final Report (NASA Jet Propulsion Laboratory, 1998).

Piestun, R.

Samms, R. W.

Sheppard, C. J. R.

Simmonds, J. J.

P. Mouroulis, D. A. Thomas, T. G. Chrien, V. Duval, R. O. Green, J. J. Simmonds, and A. H. Vaughan, Trade Studies in Multi/Hyperspectral Imaging Systems—Final Report (NASA Jet Propulsion Laboratory, 1998).

Skauli, T.

Thomas, D. A.

P. Mouroulis, D. A. Thomas, T. G. Chrien, V. Duval, R. O. Green, J. J. Simmonds, and A. H. Vaughan, Trade Studies in Multi/Hyperspectral Imaging Systems—Final Report (NASA Jet Propulsion Laboratory, 1998).

Tisse, C.-L.

C.-L. Tisse, F. Guichard, and F. Cao, “Does resolution really increase image quality?” Proc. SPIE 6817, 68170Q (2008).
[CrossRef]

Vaughan, A. H.

P. Mouroulis, D. A. Thomas, T. G. Chrien, V. Duval, R. O. Green, J. J. Simmonds, and A. H. Vaughan, Trade Studies in Multi/Hyperspectral Imaging Systems—Final Report (NASA Jet Propulsion Laboratory, 1998).

Appl. Opt. (2)

IEEE Trans. Inf. Theory (3)

A. Lapidoth, and S. M. Moser, “On the capacity of the discrete-time Poisson channel,” IEEE Trans. Inf. Theory 55, 303–322 (2009).
[CrossRef]

A. Lapidoth, “Capacity results of an optical intensity channel with input-dependent channel noise,” IEEE Trans. Inf. Theory 58, 207–223 (2012).
[CrossRef]

S. Arimoto, “An algorithm for computing the capacity of arbitrary discrete memoryless channels,” IEEE Trans. Inf. Theory 18, 14–20 (1972).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (1)

Opt. Express (1)

Phil. Trans. R. Soc. A (1)

P. B. Fellgett and E. H. Linfoot, “On the assessment of optical images,” Phil. Trans. R. Soc. A 247, 369–407 (1955).
[CrossRef]

Proc. SPIE (3)

T. Skauli, “Quantifying coregistration errors in spectral imaging,” Proc. SPIE 8158, 81580A (2011).
[CrossRef]

C.-L. Tisse, F. Guichard, and F. Cao, “Does resolution really increase image quality?” Proc. SPIE 6817, 68170Q (2008).
[CrossRef]

F. Cao, F. Guichard, and H. Hornung, “Information capacity: a measure of potential image quality of a digital camera,” Proc. SPIE 7537, 75370F (2010).
[CrossRef]

Other (1)

P. Mouroulis, D. A. Thomas, T. G. Chrien, V. Duval, R. O. Green, J. J. Simmonds, and A. H. Vaughan, Trade Studies in Multi/Hyperspectral Imaging Systems—Final Report (NASA Jet Propulsion Laboratory, 1998).

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Figures (2)

Fig. 1.
Fig. 1.

Illustration of the trade-off between coregistration error and pixel count. The figure illustrates the pixel footprint for two bands, shown as red and blue rectangles, for two cases. There is a fixed amount of spatial distortion, caused by the imaging optics or other imperfections in the imaging process. On the left is a case with small pixels and a spatial coregistration error that is a large fraction of the pixel size. On the right is a case with larger but fewer pixels. Then the relative amount of distortion is reduced, and also the signal-to-noise ratio improves. The scene is assumed to contain contrasts on a wide range of spatial scales, illustrated here by an urban landscape. Here it is not obvious how to make the important trade-off between coregistration and spatial resolution in spectral imaging. This paper proposes information capacity as a relevant figure of merit.

Fig. 2.
Fig. 2.

Information capacity for one band of a spectral imager, with varying sizes of the detector pixels. This illustrates how information-theoretic considerations can be used to determine the optimal spatial resolution in a spectral imager by optimizing the information capacity. Different curves represent different degrees of coregistration error in the imaging optics. The difference between the curves illustrates the large information loss that can result from imperfect coregistration. The plot uses the approximate capacity model [Eq. (6)] and assumes the following parameter values at b=1: N¯=20,000, α=0.15, P=1000.

Equations (13)

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N=LηtAωΔλλhc.
Ntot=PL¯ηtAωΔλλhc.
N¯=NtotP.
ΔNphotN¯.
εs,ijp=12x,y|fjp(x,y)fip(x,y)|dxdy.
ΔNcoregε¯sαN¯.
ω=ΩP.
Plim=Pε¯s,
ΔNcoreg=ε¯sαN¯=PαN¯Plim=αNtotPlim.
ΔNcoregΔNphot=PPlimαN¯=αPNtotPlim.
C(N0,b)=P0bC(bN¯0,ε¯s0b).
C(N¯,εs)12logN¯ε¯sαπN¯2,
C(N0,b,s)=P0bB0sC(bsN¯0,(ε¯s0b)2+β(ε¯λ0s)2),

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