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A lenslet array measures light distributions by sampling a smoothed Wigner distribution function (SWDF). This study rigorously connects lenslet measurements to wave optics for partially coherent beams, analyzing factors affecting measurement fidelity.

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Area of Science:

  • Optical physics
  • Wave optics
  • Metrology

Background:

  • Traditional geometrical-optical explanations for lenslet array measurements of spatial and spatial frequency light distributions.
  • Need for a rigorous wave-optical derivation for partially coherent beams.

Purpose of the Study:

  • To rigorously derive the connection between lenslet array intensity measurements and wave-optical light distributions.
  • To analyze the measurement of the smoothed Wigner distribution function (SWDF) by lenslet arrays.
  • To investigate the impact of lenslet geometry and beam coherence on measurement accuracy.

Main Methods:

  • Utilized the Wigner distribution function (WDF) for wave-optical analysis.
  • Derived the relationship between measured intensity and the SWDF.
  • Analyzed lenslet geometry and beam coherence properties.
  • Derived an expression for cross-talk between lenslets.

Main Results:

  • Demonstrated that a lenslet array samples a smoothed version of the Wigner distribution function (SWDF).
  • Quantified the effect of lenslet geometry and beam coherence on the SWDF measurement.
  • Derived an expression for cross-talk, a key source of measurement error.
  • Investigated conditions for high-fidelity SWDF measurement and discrepancies with the WDF for Schell-model beams.

Conclusions:

  • The lenslet array's measurement is rigorously described as sampling the SWDF, not the full WDF.
  • Understanding cross-talk and coherence is crucial for accurate optical beam characterization.
  • Provides a wave-optical framework for interpreting lenslet array measurements of partially coherent light.