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Controlling Light Transmission Through Highly Scattering Media Using Semi-Definite Programming as a Phase Retrieval

Moussa N'Gom1, Miao-Bin Lien2, Nooshin M Estakhri2

  • 1Department of Electrical & Computer Engineering, University of Michigan Ann Arbor, Ann Arbor, MI, 48109, USA. mngom@umich.edu.

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Complex Semi-Definite Programming (SDP) enables phase retrieval for light control through scattering media. This method computes the transmission matrix from intensity measurements, allowing precise focusing without iterations.

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Area of Science:

  • Optics and Photonics
  • Computational Physics
  • Wavefront Engineering

Background:

  • Controlling light transmission through scattering media is challenging due to complex wave interactions.
  • Traditional methods often require iterative measurements or reference beams for phase retrieval.

Purpose of the Study:

  • To introduce Complex Semi-Definite Programming (SDP) as a novel method for phase retrieval and light control in scattering media.
  • To demonstrate wavefront shaping for precise focusing without iterative measurements.

Main Methods:

  • Utilizing a spatial light modulator to generate phase-modulated wavefronts.
  • Acquiring intensity speckle patterns of transmitted light using a camera.
  • Applying Complex Semi-Definite Programming (SDP) to compute the system's complex transmission matrix from intensity-only measurements.

Main Results:

  • The SDP algorithm successfully computed the complex transmission matrix without a reference beam.
  • Optimal wavefronts were computed to focus light to desired positions beyond the scattering medium.
  • Focusing was achieved without requiring subsequent measurements or wavefront shaping iterations.

Conclusions:

  • Complex Semi-Definite Programming (SDP) offers an efficient and direct approach to phase retrieval for controlling light in scattering media.
  • The method enables precise wavefront shaping for targeted light delivery, with performance dependent on spatial light modulator pixel count.