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Erika Odlund, Caroline Kulcsár, Henri-François Raynaud, Xavier Levecq, Adrian G. Podoleanu; The Use Of LQ Control To Optimize The Dynamic Behavior Of An Electromagnetic Deformable Mirror For Ophthalmic Applications. Invest. Ophthalmol. Vis. Sci. 2011;52(14):4057.
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© ARVO (1962-2015); The Authors (2016-present)
The purpose of this study is to design and validate a linear quadratic (LQ) control to improve the temporal performance of a deformable mirror (DM) used in ophthalmic applications, such as retinal imaging. The control is developed using a high speed adaptive optics (AO) test bench with a sampling frequency of 10 kHz. In previous work, the same test bench has successfully been used to develop a reference model for the control of a single DM actuator.
The membrane motion of the electromagnetic mirao52-e DM (Imagine Eyes, France) was measured using a high-speed, open-loop adaptive optics (AO) test bench with a variable sampling frequency up to 10 kHz, whilst using a wavefront sensor (WFS) whose acquisition rate is approximately 60 Hz, HASO-eye WFS (Imagine Optic, France). The high sampling frequency was made possible through repetitive application of DM signals and stroboscopic wavefront measurements. The actuators were classified in distinct groups depending on their placement on the mirror’s pupil. The step response of the mirror membrane expressed in wavefront root mean square (RMS) error was studied for each group and system identification methods were used to create state-space models of the actuators’ responses. Based on these models, LQ controls with varied criteria for optimality were developed using Simulink software, and evaluated with the high-speed test bench.
The LQ control were implemented for the distinct groups of actuators separately, and when correcting for current ocular aberrations such as astigmatism and defocus. An important gain in terms of stability was observed relative to operation without LQ control. The most efficient strategy proved to be discrete time LQ control, where the continuous-time state-space models were made discrete to respect the characteristics of the DM electronics.
The proposed method enabled dynamic characterization of a DM using a WFS capable of measuring large aberrations with high accuracy. Detailed knowledge of the system allowed accurate modeling of the DMs’ dynamic behavior. Powerful controls were implemented to adjust the temporal performance of the DM.Such a dynamic DM model can also be integrated in a complete AO closed loop model in order to optimize the global performance of an AO system.
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