Abstract
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.
Highlights
A conventional adaptive optics system employs a wave front sensor to measure aberrations, an adaptive correction element to remove the aberrations, and a control system that processes the sensor signals in order to drive the correction element [1]
Such wave front sensorless adaptive systems have been implemented in confocal fluorescence and reflection microscopy [2, 3], two-photon fluorescence microscopy [4, 5], maximisation of second harmonic generation [6], intracavity aberration correction in lasers [7], optical tweezers[8], coupling laser light into an optical fibre [9] and for the characterisation of adaptive optical systems citeVorontsov2002,Booth2005
The results show that deterministic, non-adaptive algorithms can be effective in controlling wave front sensorless adaptive optics systems, if they are suitably formulated
Summary
A conventional adaptive optics system employs a wave front sensor to measure aberrations, an adaptive correction element to remove the aberrations, and a control system that processes the sensor signals in order to drive the correction element [1]. Such wave front sensorless adaptive systems have been implemented in confocal fluorescence and reflection microscopy [2, 3], two-photon fluorescence microscopy [4, 5], maximisation of second harmonic generation [6], intracavity aberration correction in lasers [7], optical tweezers[8], coupling laser light into an optical fibre [9] and for the characterisation of adaptive optical systems citeVorontsov2002,Booth2005 These applications have employed different schemes for optimisation of the correction element based upon genetic algorithms [3, 4, 5, 6, 9], hill climbing algorithms [3, 5, 7, 8, 9], stochastic gradient descent The results show that deterministic, non-adaptive algorithms can be effective in controlling wave front sensorless adaptive optics systems, if they are suitably formulated
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