Simulated Adaptive-Optic Correction of a Weakly-Compressible Shear Layer using Phase-Lock-Loop Control 20 th Annual Aerospace and Mechanical Engineering Graduate Student Conference 19 October, 2006 Alice Nightingale Advisors: Bill Goodwine and Eric Jumper Center for Flow Physics and Control Department of Aerospace and Mechanical Engineering University of Notre Dame Supported by: Air Force Office of Scientific Research, Air Force Research Laboratory, and the Directed Energy Professional Society

Outline Background / Motivation Research Objective Optical Characterization of Shear Layer Regularization Results Adaptive-Optic Corrections –Phase-lock-loop control approach –Simulation results Future Research

Optical Aberrations Density variations are related to index-of-refraction by the Gladstone- Dale constant Original planar wavefront Emerging aberrated wavefront Optical path length and optical path difference typically used to measure a beams optical aberrations θ Optical Wavefront Small Aperture Laser beam Jitter Angle Huygens’ Principle states that a small aperture beam will emerge normal to the outgoing wavefront

System Performance Reduction Aberrations on optical wavefronts degrade the far-field irradiance pattern and significantly reduce the performance of airborne optical systems by reducing the laser beams intensity on target. Aberrated wavefront I Planar wavefront IoIo Far-field irradiance pattern and Strehl ratio are often used to measure the optical system’s performance.

Field-of-Regard Restrictions Boundary Layer Transonic Region & Shock Separated (Free) Shear Layer Coherent Structures Inside Projected Laser Beam Edge Field-of-regard restrictions imposed by aero-optic effects

Conventional Adaptive-Optic Approach AO Systems Sense, construct, and apply conjugate corrective waveforms at regular time intervals Contain Wavefront Sensors (WFS), Reconstructors, and Deformable Mirrors (DM) Limited by real-time processing issues WFSReconstructor Amplifier DM Outgoing Laser Probe Beam HEL Beam Current DM Figure Residual Error 1/10 th Error - + Planar wavefront Aberrated wavefront Conjugate wavefront Planar wavefront

Research Objective A priori knowledge of the shear layers aberrating wavefront would reduce bandwidth requirements placed on the AO control system. –Use flow control to regularize shear layer structures and their corresponding optical wavefronts –Determine relationship between flow control and the emerging wavefront –Perform AO corrections using a phase-lock-loop control approach y x Low Speed Flow High Speed Flow Planar Wavefront Aberrated Wavefront Low Speed Flow High Speed Flow y x Planar Wavefront Aberrated Wavefront

Optical Characterization Free shear layers contain a range of natural optical frequencies Low Speed Flow High Speed Flow y x Natural optical frequency is related to optical coherence length through the convection velocity

Regularization Results Forcing a shear layer at its origin regularizes its large-scale coherent structures upstream from the point where the forcing frequency equals the unforced natural optical frequency

Aberrated Wavefront Planar Wavefront Forcing Frequency DM θ sl AslAsl Mixing Circuit Feedback Circuitry SMSM  Quarter Wave Lag Filter β sl Position Sensing Device 2 Lens L (θ sl - θ DM ) +- θ DM Position Sensing Device 1 L Lens Feedforward Circuitry Automated AO Control System Deformable Mirror (DM) applies conjugate correction Regularized shear layer provides ‘predictable’ waveform: DM jitter signal is multiplied with the phase shifted shear layer jitter signal producing: Mixing signal filtered to recover D.C. bias, phase error signal: Position sensing devices used to measure and determine shear layer jitter signal and DM jitter signal:

Phase Locked Loop (PLL) Transfer Function: Double integral action assures asymptotic response to step and ramp changes in phase with zero tracking error Minimum phase zero assures feedback system’s closed loop stability Reference Source Low Pass Filter, F(s) Loop Filter, L F (s) X Phase-Locked Signal

PLL Controller Simulation Convection velocity (U c ) of m/s and forcing frequency (f f ) of 900 Hz

Strehl Ratio Results Case 1:Shear Layer Parameters:Ma 1 ~ 0.7, Ma 2 ~ 0.2 Flow Control Parameters: f = 900 Hz, A = 5 mm Case 2:Shear Layer Parameters:Ma 1 ~ 0.55, Ma 2 ~ 0.17 Flow Control Parameters: f = 1100 Hz, A = 1 mm

System Response Step change in phase Ramp change in phase (frequency error) Alterations to control parameters used to produce a more desirable system response.Alterations to control parameters used to produce a more desirable system response. Tip/tilt removal used to further increase Strehl ratio after AO corrections are performed.Tip/tilt removal used to further increase Strehl ratio after AO corrections are performed.

Simulated Far-Field Irradiance with and without AO Corrections Simulated irradiance pattern for a beam propagating through a Mach 0.7 forced shear layer (900 Hz) 0.35 meters downstream from the splitter plate given an aperture of 0.18 meters and wavelength of 0.63 μm.

Future Research System identification of control system components Further analysis of control system response and robustness Build alternative AO controller Apply real-time AO corrections to heated jet experiment Apply real-time AO corrections to high-speed shear layer experiment

Acknowledgements US Air Force Directed Energy Professional Society Advisors: Bill Goodwine and Eric Jumper Michael Lemmon (EE Professor)Thanks