Special Section Guest Editorial: Machine Learning In Optics

This guest editorial summarizes the Special Section on Machine Learning in Optics

Least-squares phase estimation with wrapped measurements and branch points

J. Opt. Soc. Am. A, Volume 30, No. 11, pp. 2225-2236 (November 2013)The article of record as published may be located at http://dx.doi.org/10.1364/JOSAA.30.002225A nonorthogonal model for 2D signals with rotational components is presented, which enables estimation of phase values from observations of its local gradients. In this research, the rotational components are caused by the presence of branch points, which indicates phase wrapping. Using the proposed model, the phase is estimated using standard least-squares or recently proposed wavelet techniques by processing a linear combination of the wrapped observed gradients and the curl generated by phase wrapping

Generalized orthogonal wavelet phase reconstruction

J. Opt. Soc. Am. A, Volume 30, No. 5, pp. 859-870 (May 2013)The article of record as published may be located at http://dx.doi.org/10.1364/JOSAA.30.000859Phase reconstruction is used for feedback control in adaptive optics systems. To achieve performance metrics for high actuator density or with limited processing capabilities on spacecraft, a wavelet signal processing technique is advantageous. Previous derivations of this technique have been limited to the Haar wavelet. This paper derives the relationship and algorithms to reconstruct phase with O n computational complexity for wavelets with the orthogonal property. This has additional benefits for performance with noise in the measurements. We also provide details on how to handle the boundary condition for telescope apertures.The authors acknowledge email communication with P. Hampton. This research was performed with the Adaptive Optics Center of Excellence in National Security, located at the Naval Postgraduate School. T. W. Axtell was funded by the Department of Defense SMART Scholarship and Space and Naval Warfare Command. Gratitude is also expressed to the anonymous reviewers for their comments, which were crucial for improving the quality of the paper

Generalized orthogonal wavelet phase reconstuction

The article of record as published may be found at http://dx.doi.org/10.1364/JOSSA.30.000859Phase reconstruction is used for feedback control in adaptive optics systems. To achieve performance metrics for high actuator density or with limited processing capabilities on spacecraft, a wavelet signal processing technique is advantageous. Previous derivations of this technique have been limited to the Haar wavelet. This paper derives the relationship and algorithms to reconstruct phase with O(n) computational complexity for wavelets with the orthogonal property. This has additional benefits for performance with noise in the measurements. We also provide details on how to handle the boundary condition for telescope apertures.Department of Defense SMART ScholarshipSpace and Naval Warfare Comman

Segmented Mirror Telescope model and simulation

The Segmented Mirror Telescope (SMT) housed at the Naval Postgraduate School is a unique, state-of-the-art optical instrument built to explore new technologies needed for future spacebased telescopes. A discrete Fourier transform wavefront reconstruction technique developed at Lawrence Livermore National Laboratory is discussed in this thesis as applied to a hexagonal aperture. A Fourier domain implementation of a spatial-frequency modal controller for a simple spring-mass model of a deformable mirror surface is provided by this thesis. This technique avoids more difficult time-domain solutions, is computationally efficient and scalable to much larger multi-input, multi-output systems than the SMT.http://archive.org/details/segmentedmirrort109455614Approved for public release; distribution is unlimited

Wavefront reconstruction and mirror surface optimization for adaptive optics

The problem of wavefront reconstruction is important in high precision optical systems, such as astronomical telescopes, where it is used to estimate the distortion of the collected light caused by the atmosphere and corrected by adaptive optics. A generalized orthogonal wavelet wavefront reconstruction algorithm is presented in this research for use with gradient measurements from a Shack- Hartmann wavefront sensor. This algorithm can be implemented using a number of different wavelets for improved performance in the presence of noise. An extension of this algorithm is also presented to provide wavefront estimation in the presence of isolated branch points where the phase is undetermined. The wavefront is obtained by augmenting the wrapped observations with a filtered curl of the vector field. The wavefront estimation can then be used for surface control of a deformable mirror. A third contribution is in deformable mirror surface control. The control signals to a deformable mirror are computed that minimize the wavefront error using constrained optimization to ensure that the hardware actuator voltage limits are satisfied. A sequence of optimal solutions is used to verify the linear model of a deformable mirror. A multigrid approach to the optimization problem is shown to improve computation efficiency.http://archive.org/details/wavefrontreconst1094542576Approved for public release; distribution is unlimited