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One of the simplest implementations of adaptive optics requires an adaptive correction element and a single pinhole photodetector. Aberration measurement is performed by the sequential application of chosen aberrations using the correction element and appropriate processing of the corresponding photodetector intensity measurements in order to maximise the detector signal. These wave front sensorless adaptive optics systems have been demonstrated in many applications, which have included confocal microscopy, intra-cavity aberration correction for lasers, fibre coupling and optical trapping. The maximisation procedure, the choice of the applied aberrations and the processing of the intensity measurements must be optimised if the system is to work efficiently. In many practical systems aberrations can be accurately represented by a small number of orthogonal modes. We present a model of such systems and show that they have properties that facilitate algorithm design, in particular a well defined maximum and spherical symmetry. Through mathematical reasoning these properties can be used to calculate optimum parameters, rather than obtaining them in an empirical manner. The model leads to a direct maximisation algorithm that has much better convergence properties than search algorithms and permits the measurement of N modes with only N + 1 intensity measurements. We also describe a general scheme for such wave front sensorless algorithms and relate various methods to this general scheme.

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