Benjamin W. Frazier

Theory and operation of a robust controller for a compact adaptive optics system

We describe the design and operation of a high-speed adaptive optics system using a robust H ∞ controller. The system is also general purpose—it can be used in almost any application with minimal modifications and can be set up and operated by a minimally trained operator. The demonstrated system uses a wavefront sensor camera operating at 955 frames/s, a Xinetics 37-channel deformable mirror, and a dual processor computer to perform computations. The system exhibits control of up to 5 waves of focus, a closed-loop bandwidth of ~50 Hz, with a residual error of λ/75 rms.

Microelectromechanical system programmable aberration generator for adaptive optics

Adaptive optics systems and control algorithms can be tested in the laboratory with controlled disturbances. We have a micromachined deformable mirror that we use as a programmable aberration generator. We present a method of programming the actuator amplitudes so that the wave front reflecting from the surface will simulate atmospheric turbulence. We present experimental results that show that we can simulate the Kolmogorov spatial spectrum within the constraints of the useful region of the deformable mirror.

Design and operation of an integrated wavefront corrector (IWC)

Typical adaptive optics systems require a deformable mirror to provide high spatial frequency wavefront correction and a separate tip-tilt mirror so that the deformable mirror’s dynamic range is not exhausted on low order aberrations. Having two correction devices requires additional optical relays to be incorporated in the system, which in turn translates into more cost, size and complexity. If the two devices were combined into an integrated wavefront corrector (IWC), the cost, size and complexity of an adaptive optics system could be drastically reduced. This paper outlines the design and operation of an electro-ceramic driven tip tilt stage that has been designed specifically for a 37 channel deformable mirror. The tip tilt system can deliver more than 500 μradians of tilt, 20 microns of piston, and has natural frequencies greater than 400 hertz. The tip-tilt stage has a fast response time and the axis of rotation is centered at the optical surface. This prevents translation and wavefront shear associated with typical tip-tilt mirrors for which the axis of rotation is centered behind the surface of the mirror. The 37 channel deformable mirror has a 7mm actuator spacing and is designed with high temperature and low outgassing materials which are compatible with high temperature coatings. The IWC may be retrofitted with Xinetics actuators to operate at cryogenic temperatures. We also describe the use of this device in a closed loop adaptive optics system and outline its benefits.

Closed-loop results of a compact high-speed adaptive optics system with H∞

We report on the results of experiments that demonstrate a robust control system for a general-purpose adaptive optics system and provide robust stability analysis for such a system. Using a commercially available high-speed CCD camera in the Shack-Hartmann wavefront sensor and a 37-actuator Xinetics deformable mirror, we are able to achieve closed-loop performance sufficient for many astronomical, vision science, or laser communications applications. The control system must be robust for the various applications and the entire system must be easily set-up, calibrated, and run by a minimally-trained operator. An H-infinity controller, which optimizes the closed-loop stability of a system, is implemented and analyzed.

Performance of a compact adaptive-optics system

The design of an adaptive-optics system for correction of a beam propagating through high-speed, unpredictable optical turbulence required the use of a robust controller rather than a conventional least-squares controller. We describe the 37-channel, 50-Hz adaptive-optical system and its performance (lambda/75 rms).

Robust control system for a compact modular adaptive optics system

Buiding a compact general-purpse adaptive optics system presents new challenges. By “compact” we mean a complete system less than 0.05 m3 in volume that contains all optics and processing electronics. By “general-purpose” we mean a system that can be used in astronomy, in laser communications, and in commercial and military applications with only minimal modifications specific to the application. This necssarily requires a robust control system that can be easily set-up, calibrated, and run by a minimally-trained operator. Knowing that transport or installation of such a system can misalign some components, we built a control system to accommodate those errors in a fast reconstructor reconfiguruing algorithm. A robust H-infinity control is implemented for closed-loop operation. Results of computer simulations and a series of laboratory demonstrations are presented.

Shack-Hartmann Wavefront Sensor and Error

This excerpt gives a succinct explanation of the Shack-Hartmann Wavefront Sensor and Error.

The Strehl Ratio: Laser Beam Propagation to the Far Field with Wavefront Error

This excerpt gives a succinct explanation of The Strehl Ratio—Laser-Beam Propagation to the Far Field with Wavefront Error.

Effect of Sampling Rate on Achievable Bandwidth

This excerpt gives a succinct explanation of the Effect of Sampling Rate on Achievable Bandwidth.

Angle of Arrival Fluctuations (Image Motion)

This excerpt gives a succinct explanation of the Angle of Arrival Fluctuations (Image Motion).