Maximum-likelihood methods in wavefront sensing: Stochastic models and likelihood functions

Harrison H. Barrett, Christopher Dainty, David Lara

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


Maximum-likelihood (ML) estimation in wavefront sensing requires careful attention to all noise sources and all factors that influence the sensor data. We present detailed probability density functions for the output of the image detector in a wavefront sensor, conditional not only on wavefront parameters but also on various nuisance parameters. Practical ways of dealing with nuisance parameters are described, and final expressions for likelihoods and Fisher information matrices are derived. The theory is illustrated by discussing Shack-Hartmann sensors, and computational requirements are discussed. Simulation results show that ML estimation can significantly increase the dynamic range of a Shack-Hartmann sensor with four detectors and that it can reduce the residual wavefront error when compared with traditional methods.

Original languageEnglish (US)
Pages (from-to)391-414
Number of pages24
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Issue number2
StatePublished - Feb 2007

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Computer Vision and Pattern Recognition


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