Maximum-likelihood methods in wavefront sensing: stochastic models and likelihood functions.

Harrison H Barrett; Christopher Dainty; David Lara

doi:10.1364/josaa.24.000391

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Maximum-likelihood methods in wavefront sensing: stochastic models and likelihood functions.

Harrison H Barrett·Christopher Dainty·David Lara

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Abstract

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.

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Electrons Likelihood Functions Models, Statistical Models, Theoretical Normal Distribution Optics and Photonics Photons Poisson Distribution Probability Refraction, Ocular Refractive Errors Software Stochastic Processes Journal Article Research Support, N.I.H., Extramural Research Support, Non-U.S. Gov't

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Harrison H Barrett, Christopher Dainty, David Lara. 2007. Maximum-likelihood methods in wavefront sensing: stochastic models and likelihood functions.. https://doi.org/10.1364/josaa.24.000391

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