A model-based approach to wave front sensorless adaptive optics

In some adaptive optics systems the aberration is determined not using a wave front sensor but by sequential optimization of the adaptive correction element. Efficient schemes for the control of such systems are essential if they are to be effective. One of the simplest implementations of adaptive optics requires an adaptive correction element and a single photodetector. Aberration measurement is performed by the sequential application of chosen aberrations 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. We develop appropriate mathematical models that lead to direct maximisation algorithms with good convergence properties and that permit the measurement of N modes with only N + 1 measurements. A scheme is introduced that permits the efficient measurement of large amplitude wavefront aberrations. This scheme uses an optimization metric based upon root-mean-square spot radius and an aberration expansion using polynomials suited to the representation of lateral aberrations. The geometrical optics basis means that the scheme can be extended to arbitrarily large aberrations. We also describe a general scheme for such wave front sensorless algorithms and relate various methods to this general scheme.