JO URNAL O F T O R T HE EUR O PEAN O PTI CAL SOCI ETY R APID PUBLICATI O NS Journal of the European Optical Society - Rapid Publications 6, 11045 (2011) www.jeos.org Self calibration of sensorless adaptive optical microscopes Anisha Thayil Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, United King- dom Martin J. Booth martin.booth@eng.ox.ac.uk Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1 3PJ, United King- dom We present a self-calibrating scheme for microscopes using model-based wavefront sensorless adaptive optics. Unlike previous methods, this scheme permits the calibration of system aberration modes without the need for a separate wavefront sensor or interferometer. Basis modes are derived from the deformable mirror influence functions and an image cross-correlation method is used to remove image displacement effects from these modes. Image based measurements are used to derive an optimum modal representation from the displacement-free basis modes. These new modes are insensitive to system misalignments and the shape of the illumination profile. We demonstrate the effectiveness and robustness of these optimal modes in a third harmonic generation (THG) microscope. [DOI: http: //dx.doi.org/10.2971/jeos.2011.11045] Keywords: Adaptive optics, aberrations, microscopy 1 INTRODUCTION Aberrations frequently affect the performance of high resolu- tion microscopes. In order to overcome this problem, adaptive optics (AO) techniques have been introduced in a range of dif- ferent microscope modalities. These AO systems employ an adaptive element, such as a deformable mirror (DM) or spatial light modulator, to correct the specimen and system-induced aberrations. Unlike in conventional adaptive optics systems, most of the AO microscope implementations have been “sen- sorless”, employing indirect wavefront measurements rather than wavefront sensors. Modal methods of sensorless AO pro- vide an efficient method of indirect wavefront measurement, but require careful calibration of the adaptive element to func- tion effectively, particularly when using a DM; this calibration encodes the control signals that generate aberration modes from a suitable basis set, such as the Zernike polynomials. For this reason, systems have incorporated interferometers or wavefront sensors, which required increased complexity in the overall optical design and operation. The operation of these systems is also sensitive to the alignment of the adaptive element relative to the pupil of the objective lens [1]. The optical layout of these AO microscopes could be con- siderably simplified if the sensor or interferometer were re- moved. Further benefit would be obtained by using a cali- bration scheme that is insensitive to misalignments. In this paper, we propose a fully empirical determination of aberra- tion modes that can be implemented in any optical microscope and does not require a wave front sensor. We demonstrate this scheme in an adaptive third harmonic generation (THG) mi- croscope and show its effectiveness in the presence of system misalignments. 2 Principles of sensorless adaptive optics We outline in this section the principles of model-based sen- sorless AO schemes for use in microscopes. In particular, we explain the importance of the choice of modal expansion for the aberration representation and the relationship between image shifts and certain aberration modes. 2.1 Functional representation of aberrations The DM is controlled by a set of signals that drive the individ- ual actuators that deform the mirror surface. This produces a limited range of shapes that are determined by the mechani- cal properties of the mirror and the actuator arrangement. The influence function of an actuator is defined as the DM shape produced when a unit signal is applied to that actuator. We as- sume that the DM operates in a regime where linearised con- trol signals can be used. This means that the overall shape of the DM is determined by the linear superposition of the ac- tuator influence functions. This is a reasonable approximation for many practical systems, particularly for small aberration amplitudes. The DM aberration can then be expressed as Φ(r)= N ∑ i=1 c i ψ i (r) (1) where N is the number of actuators, c i and ψ i are respectively the control signal and the influence function for the ith actua- tor, and r is the position vector in the pupil. The set of influence functions forms a basis that can repre- sent any DM shape. However, it is usually desirable to control Received May 30, 2011; published September 07, 2011 ISSN 1990-2573