Abstract

We present an information-based analysis of three candidate imagers: a conventional lens system, a cubic phase mask system, and a random phase mask system. For source volumes comprising relatively few equal-intensity point sources we compare both the axial and lateral information content of detector intensity measurements. We include the effect of additive white Gaussian noise. Single and distributed aperture imaging is studied. A single detector in each of two apertures using conventional lenses can yield 36% of the available scene information when the source volume contains only single point source. The addition of cubic phase masks yields nearly 74% of the scene information. An identical configuration using random phase masks offers the best performance with 89% scene information available in the detector intensity measurements.

© 2003 Optical Society of America

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References

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Appl. Opt. (2)

JOSA A (1)

S. Prasad, �??Statistical-information-based performance criteria for Richardson-Lucy image deblurring�?? JOSA A, 19, 1286-1296, (2002).
[CrossRef] [PubMed]

Opt. Comm (1)

S. Prasad, �??Information capacity of a seeing-limited imaging system�?? Opt. Comm., 177, 119-134, (2000).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

S. Reichenbach, Y. Xiong, R. Narayanan, and L. Cao, �??Information theoretic assessment and design of hyperspectral imaging system�?? Visual Information Processing, Proc. SPIE, 3716, 100-104, (1999).

Visual Information Processing (2)

J. van der Gracht and G. W. Euliss, �??Information optimized extended depth-of-field imaging systems,�?? Visual Information Processing X, 103-112, (2001).

M. A. Neifeld, �??Information-optimized imaging systems design,�?? Visual Information Processing X, 113-116(2001).

Other (4)

J. Goodman, �??Introduction of Fourier Optics�?? (Mc-Graw Hill, New York, 1996).

M. Born and E. Wolf, �??Principles of Optics: Electromagnetic theory of propogation inteference and diffraction�?? (Cambridge University Press, 1999).

E. R. Dowski, �??An Information Theory Approach to Incoherent Information Processing Systems,<a href="http://www.colorado.edu/isl/papers/info/paper.html">http://www.colorado.edu/isl/papers/info/paper.html</a>

T. Cover and J. Thomas, �??Elements of Information Theory�?? (John Wiley and Sons, New York, 1991).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

Imaging system layout: (a) Single aperture system (b) Distributed aperture system.

Fig. 2.
Fig. 2.

(a) Cubic phase profile and (b) Random phase profile.

Fig. 3.
Fig. 3.

Single detector imager (a) Total/axial/lateral IMI ratio (b) Total IMI ratio for multiple point sources with (D=3cm) (c) Optimal detector size and (d) Optimal detector position.

Fig. 4.
Fig. 4.

Detector intensity maps (a), (b) and (c) and detector intensity log-pdf (d), (e) and (f) for conventional lens, cubic phase mask and random phase imagers respectively with D=3cm.

Fig. 5.
Fig. 5.

Single aperture two detector imager (a) Total/axial/lateral IMI ratio (b) Total IMI ratio for multiple point sources with (D=3cm) (c) Optimal detector sizes and (d) Optimal detector positions.

Fig. 6.
Fig. 6.

Distributed aperture two detector imager (a) Total/axial/lateral IMI ratio for single point source (b) Total IMI ratio for multiple point sources (D=3cm) (c) Optimal detector sizes and (d) Optimal detector positions (θ=90°).

Tables (1)

Tables Icon

Table 1. Total/axial/lateral IMI ratio of three imagers for various angles (D=3cm).

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