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Related Concept Videos

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Transmission-Line Differential Equations01:26

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Base complementarity between the three base pairs of mRNA codon and the tRNA anticodon is not a failsafe mechanism. Inaccuracies can range from a single mismatch to no correct base pairing at all. The free energy difference between the correct and nearly correct base pairs can be as small as 3 kcal/ mol. With complementarity being the only proofreading step, the estimated error frequency would be one wrong amino acid in every 100 amino acids incorporated. However, error frequencies observed in...
Improving Translational Accuracy02:07

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Related Experiment Video

Updated: Jul 4, 2026

Automation of Mode Locking in a Nonlinear Polarization Rotation Fiber Laser through Output Polarization Measurements
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Published on: February 28, 2016

Phase retrieval with transverse translation diversity: a nonlinear optimization approach.

Manuel Guizar-Sicairos1, James R Fienup

  • 1The Institute of Optics, University of Rochester, Rochester, New York 14627, USA. mguizar@optics.rochester.edu

Optics Express
|June 12, 2008
PubMed
Summary

We developed a new nonlinear optimization algorithm for phase retrieval using transverse translation diversity. This method improves image reconstruction accuracy, especially with noisy or inaccurate system parameters.

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Area of Science:

  • Optics and Photonics
  • Computational Imaging
  • Image Reconstruction

Background:

  • Phase retrieval is crucial for reconstructing images from intensity measurements.
  • Existing methods can be sensitive to inaccuracies in system parameters and noise.
  • Transverse translation diversity offers a way to acquire diverse measurements.

Purpose of the Study:

  • To develop and validate a nonlinear optimization algorithm for phase retrieval.
  • To enhance reconstruction accuracy using transverse translation diversity.
  • To jointly optimize object, illumination, and translation parameters.

Main Methods:

  • Developed a nonlinear optimization algorithm.
  • Utilized transverse translation diversity for far-field intensity measurements.
  • Derived analytical gradient expressions for joint optimization.

Main Results:

  • Achieved superior image reconstructions compared to previous techniques.
  • Demonstrated improved performance with inaccurate system parameters and in noisy conditions.
  • Explored the method's applicability to samples smaller than the illumination pattern.

Conclusions:

  • The developed algorithm offers a robust solution for phase retrieval.
  • Joint optimization of parameters significantly improves reconstruction quality.
  • The method shows promise for various imaging applications, including sub-illumination-sized samples.