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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 15, Iss. 2 — Feb. 1, 1998
  • pp: 359–366

Optimum linear combination strategy for an N-channel polarization-sensitive imaging or vision system

J. S. Tyo  »View Author Affiliations

JOSA A, Vol. 15, Issue 2, pp. 359-366 (1998)

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The optimum linear combination channels for an N-receptor polarization-sensitive imaging or vision system are found by using a principal-components analysis. The channels that are derived are optimum in the sense that their information contents are uncorrelated when considered over the ensemble of possible polarization signals. For a two-receptor system, the optimum channels are shown to be the sum and the difference of the outputs of the individual receptors. As a corollary, the optimal arrangement of the two receptors is shown to be a mosaic of identical, orthogonally aligned linear polarization analyzers. The implications of these results on the development of a representational scheme for polarization information are discussed.

© 1998 Optical Society of America

OCIS Codes
(110.0110) Imaging systems : Imaging systems
(230.5440) Optical devices : Polarization-selective devices
(260.5430) Physical optics : Polarization

Original Manuscript: April 9, 1997
Revised Manuscript: September 8, 1997
Manuscript Accepted: September 16, 1997
Published: February 1, 1998

J. S. Tyo, "Optimum linear combination strategy for an N-channel polarization-sensitive imaging or vision system," J. Opt. Soc. Am. A 15, 359-366 (1998)

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  26. The four Stokes parameters can be determined (up to an ambiguity in sign of one of the parameters) with only three intensity measurements for monochromatic radiation.22 Because circular polarization and unpolarized light are indistinguishable with a system that detects only linear polarization states, their effects on the final representation should be similar, and partially circularly polarized monochromatic radiation is analyzed here for mathematical clarity.
  27. This representation of the incident field is exact up to the choice of a constant. Although the linearly polarized portion of the radiation is constrained to have unit amplitude here, in general it can have arbitrary amplitude. In the general case, A is the ratio between the amplitudes of the circularly polarized and linearly polarized portions of the incident radiation.
  28. Nonbirefringent, nonoptically active photoreceptors are considered for simplicity, since most linear polarization analyzers satisfy this requirement. In a biological PVS, the photoreceptors may in fact be birefringent or optically active, but this can be accounted for by adding appropriate phase delay terms to the P and Q matrices (birefringence) or adding off-diagonal terms to these matrices (optical activity). As mentioned in Section 2, to sense the complete state of polarization, at least one birefringent receptor is needed either to yield the intensity of a circular polarization state or to give a relative phase value.
  29. G. Buchsbaum, J. L. Goldstein. “Optimum probabilistic processing in colour perception. II. Colour vision as template matching,” Proc. R. Soc. London, Ser. B 205, 249–266 (1979). [CrossRef]
  30. The matrix given by Eq. (19) [as well as Eq. (10)] is real symmetric and therefore an example of a self-adjoint matrix. Self-adjoint M×M matrices always produce M orthogonal eigenvectors that span the vector space operated on by the matrix.20 Correlation matrices like the ones treated here are always self-adjoint, even if the random variables are complex.16 The fact that any M×M correlation matrix necessarily spawns M orthogonal eigenvectors is the basis of principal-components analysis.18
  31. In their study Bernard and Wehner13 assumed that the output of the individual receptors was proportional to the logarithm of the input. In this investigation the receptors are assumed to respond linearly within a particular range of intensities.
  32. J. S. Tyo, “Polarization-difference imaging: a means for seeing through scattering media,” Ph.D. dissertation (University of Pennsylvania, Philadelphia, 1997).

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