LSST Integrated Model & Performance LSST2014

1. LSST Integrated Model & Performance LSST2014 Bo Xin Systems Analysis Scientist

2. Outline • This talk is mostly about how we • assess the performance of LSST (image size, ellipticity) • by means of integrated modeling. • Simulation Architecture • Perturbation Model • Telescope (M1M3 as example) • Camera • Atmosphere • Estimator and Controller • Simulation Results LSST2014 • Phoenix, Arizona • August 13, 2014

3. Simulation Architecture Temperature, Elevation, Camera Rotation, Thermal Gradients Atmosphere* Image Quality (FWHM & ellipticity) Camera Internal Optics x2 x Telescope Mirror Figures and Rigid Body Positions Residual after Look-Up Table Correction ZEMAX Model Wavefront Sensor Estimator Wavefront Error Wavefront Sensor Feedback x: controlled variables x2: uncontrolled variables, including camera internal distortions and M1M3 relative position etc. *Atmosphere is assumed to be uncorrelated between exposures Controller LSST2014 • Phoenix, Arizona • August 13, 2014

4. System Perturbations Green: has been implemented • Uncontrolled DOFs: • M1M3: • M1M3polishing errors • gravity print through • thermal induced errors • M3 position relative to M1 • M2: • polishing errors • gravity print through • thermal induced errors • Camera internal distortions: • rigid body motions of L1/L2/Filter/L3/FPA (gravitational & thermal) • surface distortions of L1/L2/L3 (gravitational & thermal) • Lens polishing errors • Lens and filter Installation errors • Detector installation errors • For a complete list of perturbation we plan to implement, see document-16234, or the system perturbations confluence page • https://confluence.lsstcorp.org/display/SIM/System+Perturbations • DOFs controlled by AOS • M2hexapod rigid body positions (5) • Camera hexapod rigid body positions (5) • M1M3 bending modes (20) • M2 bending modes (20) LSST2014 • Phoenix, Arizona • August 13, 2014

5. System Image Quality Budget Numbers that should be compared to current simulations Ellipticity mean < 0.04 No more than 5% larger than 0.07 LSST2014 • Phoenix, Arizona • August 13, 2014

6. M1M3 Gravitational Print Through • Elevation angle is drawn randomly from distribution provided by Opsim. • For any given zenith angle the actuator forces are optimized for achieving the optimal mirror surface shape. • As a very conservative estimate, we add 5% noise on the actuator forces for imperfect repeatability. LSST OpSim Distribution of elevation angle M1M3 Print through M1M3 shape with 5% actuator noise Elevation angle =44o LSST2014 • Phoenix, Arizona • August 13, 2014

7. M1M3 Thermal Induced Errors From M1M3 Finite Element Analysis M1M3 thermal control maintains the mirror bulk temperature and the thermal gradient: Bulk (relative to ambient) : 0.8 oC Z-direction 0.1 oC Radial 0.1 oC X- and Y- direction 0.4 oC Use Gaussian random numbers in simulations, where [-σ,σ] covers the range defined by the numbers on the left. LSST2014 • Phoenix, Arizona • August 13, 2014

8. M1M3 Polishing Error From SOML, data taken 04/10/2014 before bending mode correction M1: 139 nm rms M3: 0 nm rms After 20 bending mode correction Structure function meets specs M1: 23 nm rms (constrained to limit the effect on M3) LSST2014 • Phoenix, Arizona • August 13, 2014

9. State Estimator M2 Cam M2 bending M1M3 bending Singular values of A-matrix Log scale! • Without estimating the state covariance and the noise covariance, the estimator is the pseudo-inverse of the sensitivity matrix • Matrix is near-degenerate. • 5 smallest singular values are truncated • Rigid body motion scaled by factor of 100 for clarity LSST2014 • Phoenix, Arizona • August 13, 2014

10. Optimal Control • Optimize both the IQ across the field and the motions of the control variable • ρ and the diagonal elements of H define the weights of the control motions relative to the FWHM. • The current choices are • The weight on each bending mode is proportional to the force it requires • 1N RMS actuator force = 1um piston or decenter on M2 or camera = 1arcsec tilt on M2 or camera = 0.1mas of FWHM Drift due to environmental conditionand operation parameters not implemented in current simulations Control motion for iteration k+1 Control gain, use α<1 to integrate atmosphere over longer time. LSST2014 • Phoenix, Arizona • August 13, 2014

11. Linear Analysis: gain=0.3 232mas LSST2014 • Phoenix, Arizona • August 13, 2014

12. Linear Analysis, gain=1 LSST2014 • Phoenix, Arizona • August 13, 2014

13. Non-linear Simulation, gain=1 FWHM ellipticity LSST2014 • Phoenix, Arizona • August 13, 2014

14. Summary & Future Work • System is near-degenerate, therefore sensitive to sensor noise (dominated by atmosphere, not algorithm) • Truncation of the influence matrix (removing small singular values) • Optimal control to penalize large commands • Reduced gain (roughly equivalent to increased integration time) • Both the linear and nonlinear simulations show acceptable performance (FWHM and ellipticity) • Simulations will be useful in future requirement validations, system verifications, design trade studies, and commissioning. • Future work: • Observability analysis (which bending modes to control and what Zernikes to measure) • Optimize control weights • Optimal estimator • Update the input perturbation data as they become available LSST2014 • Phoenix, Arizona • August 13, 2014

15. End of Presentation