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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 28, Iss. 3 — Mar. 1, 2011
  • pp: 296–306

Information content of the near field: three-dimensional samples

David G. Fischer, Richard A. Frazin, Marius Asipauskas, and P. Scott Carney  »View Author Affiliations

JOSA A, Vol. 28, Issue 3, pp. 296-306 (2011)

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We present an analysis of the accuracy and information content of three-dimensional reconstructions of the dielectric susceptibility of a sample from noisy, near-field holographic measurements, such as those made in scanning probe microscopy. Holographic measurements are related to the dielectric susceptibility via a linear operator within the accuracy of the first Born approximation. The maximum-likelihood reconstruction of the dielectric susceptibility is expressed as a linear combination of basis functions determined by singular value decomposition of the weighted measurement operator. Maximum a posteriori estimates based on prior information are also discussed. Semianalytical expressions are given for the likely error due to measurement noise in the basis function coefficients, resulting in effective resolution limits in all three dimensions. These results are illustrated by numerical examples.

© 2011 Optical Society of America

OCIS Codes
(070.6020) Fourier optics and signal processing : Continuous optical signal processing
(110.0180) Imaging systems : Microscopy
(110.3000) Imaging systems : Image quality assessment
(180.5810) Microscopy : Scanning microscopy
(290.3200) Scattering : Inverse scattering
(110.3010) Imaging systems : Image reconstruction techniques

ToC Category:
Imaging Systems

Original Manuscript: October 8, 2010
Manuscript Accepted: November 20, 2010
Published: February 7, 2011

Virtual Issues
Vol. 6, Iss. 4 Virtual Journal for Biomedical Optics

David G. Fischer, Richard A. Frazin, Marius Asipauskas, and P. Scott Carney, "Information content of the near field: three-dimensional samples," J. Opt. Soc. Am. A 28, 296-306 (2011)

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