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Imaging Biological Samples with Optical Microscopy

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Related Experiment Video

Updated: Jul 4, 2026

Digital Inline Holographic Microscopy (DIHM) of Weakly-scattering Subjects
10:16

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Published on: February 8, 2014

Numerical reconstruction of optical surfaces.

Jayoung Nam1, Jacob Rubinstein

  • 1Mathematics Department, Indiana University, Bloomington, Indiana 47405, USA.

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|July 3, 2008
PubMed
Summary

Numerical methods for optical surface reconstruction are compared. An approximate direct integration method offers a stable, accurate solution, even with noisy data, outperforming direct integration techniques.

Area of Science:

  • Optics and Photonics
  • Computational Science

Background:

  • Surface reconstruction is crucial in optics for components like lenses and reflectors.
  • Reconstruction problems often yield systems of first-order differential equations.

Purpose of the Study:

  • To compare numerical methods for integrating differential equations in surface reconstruction.
  • To identify robust and accurate integration techniques for optical applications.

Main Methods:

  • Evaluation of direct integration methods for differential equations.
  • Analysis of an approximate direct integration technique.
  • Exploration of minimization-based approaches derived from the original equations.

Main Results:

  • Direct integration methods frequently fail in practical surface reconstruction scenarios.

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  • The approximate direct integration method demonstrates consistent convergence.
  • This method provides stable and accurate surface reconstruction, robust to measurement noise.

    • Conclusions:

    • Approximate direct integration is a reliable method for optical surface reconstruction.
    • Minimization-based methods offer alternative approaches to consider.