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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 14 — Jul. 6, 2009
  • pp: 11673–11689

Improvement of matrix condition of Hybrid, space variant optics by the means of Parallel Optics design

Iftach Klapp and David Mendlovic  »View Author Affiliations

Optics Express, Vol. 17, Issue 14, pp. 11673-11689 (2009)

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The problem of image restoration of space variant blur is common and important. One of the most useful descriptions of this problem is in its algebraic form I=H∗O, where O is the object represented as a column vector, I is the blur image represented as a column vector and H is the PSF matrix that represents the optical system. When inverting the problem to restore the geometric object from the blurred image and the known system matrix, restoration is limited in speed and quality by the system condition. Current optical design methods focus on image quality, therefore if additional image processing is needed the matrix condition is taken “as is”. In this paper we would like to present a new optical approach which aims to improve the system condition by proper optical design. In this new method we use Singular Value Decomposition (SVD) to define the weak parts of the matrix condition. We design a second optical system based on those weak SVD parts and then we add the second system parallel to the first one. The original and second systems together work as an improved parallel optics system. Following that, we present a method for designing such a “parallel filter” for systems with a spread SVD pattern. Finally we present a study case in which by using our new method we improve a space variant image system with an initial condition number of 8.76e4, down to a condition number of 2.29e3. We use matrix inversion to simulate image restoration. Results show that the new parallel optics immunity to Additive White Gaussian Noise (AWGN) is much better then that of the original simple lens. Comparing the original and the parallel optics systems, the parallel optics system crosses the MSEIF=0 [db] limit in SNR value which is more than 50db lower then the SNR value in the case of the original simple lens. The new parallel optics system performance is also compared to another method based on the MTF approach.

© 2009 Optical Society of America

OCIS Codes
(070.6110) Fourier optics and signal processing : Spatial filtering
(080.1010) Geometric optics : Aberrations (global)
(100.3190) Image processing : Inverse problems
(110.3010) Imaging systems : Image reconstruction techniques

ToC Category:
Image Processing

Original Manuscript: October 2, 2008
Revised Manuscript: April 1, 2009
Manuscript Accepted: April 12, 2009
Published: June 26, 2009

Iftach Klapp and David Mendlovic, "Improvement of matrix condition of Hybrid, space variant optics by the means of Parallel Optics design," Opt. Express 17, 11673-11689 (2009)

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