Wave front sensor-less adaptive optics: a model-based approach using sphere packings

Martin J. Booth

Certain adaptive optics systems do not employ a wave front

sensor but rather maximise a photodetector signal by appropriate control

of an adaptive element. The maximisation procedure must be optimised if

the system is to work efficiently. Such optimisation is often implemented

empirically, but further insight can be obtained by using an appropriate

mathematical model. In many practical systems aberrations can be accurately

represented by a small number of modes of an orthogonal basis,

such as the Zernike polynomials. By heuristic reasoning we develop a

model for the operation of such systems and demonstrate a link with the

geometrical problems of sphere packings and coverings. This approach aids

the optimisation of control algorithms and is illustrated by application to

direct search and hill climbing algorithms. We develop an efficient scheme

using a direct maximisation calculation that permits the measurement of N

Zernike modes with only N +1 intensity measurements.

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