1. The New Perturbation Physics Framework in PhoSim John Peterson En-Hsin Peng Chuck Claver Andy Rasmussen Steve Kahn Nov 2012

2. Perturbation Definition  For the purpose of this talk, we are considering either the body motions and shape deformations of all optical surfaces  Every optical surface in PhoSim can be perturbed by 6 degrees of freedom (2 decenter, 1 defocus, and 3 euler angles (using x- convention (zx’z’))) and 22 zernike coefficients (up to 5 th order). The PhoSim internal coordinate system is the same as CCS. (These definitions can be easily changed if necessary)  We do not need any information about implied PSF sizes or performance or any calculation where you would do anything with light ; We are purely trying to predict where every surface is at the start of the photon simulation  We are moving from a “tolerance”-based approach to a “physics”-based approach for these perturbations

3. Importance of Perturbations Chang et al. 2012

4. Optics +Tracking +Diffraction +Det Perturbations +Lens Perturbations +Mirror Perturbations +Detector +Dome Seeing +Low Altitude +Mid Altitude +High Altitude +Pixelization Atmosphere Atmosphere Atmosphere 4 0.2”

5. Phase I: Uncompensated Perturbations

6.  Consider the 22 zernike coeff+6 degrees of freedom for every optical surface (12) = 28*12 = 336  All the degrees of freedom are either an angle or a displacement  And then only consider displacements or angular shifts from the ideal optical design  Call this:  where i is an index of all possible ~336 degrees of freedom  Now consider things that might affect each dof from the ideal (fabrication error, thermal, gravity, other environmental, and actuators) Mathematical Representation

7. Term #1: Assembly/Fabrication Errors  Consider the first form of perturbation; when the optics are fabricated and assembled there is some error that cannot be corrected  Assembly or fabrication errors are built to some tolerance and if there is an error it should be the same throughout the ~10 years (i.e. every simulation)  Mathematically, this is expressed as  where f i is the tolerance for every degree of freedom and u is a uniform random number between 0 and 1; The infinity subscript is to designate that this random number is chosen for an infinite time scale & therefore will be the same every time the simulator is run;  so dx i will be between +/- f i  Note pressure-induced perturbations on lenses might puts here

8. Term #2: Bulk Thermal  Bulk thermal changes move the optical surfaces from their ideal positions, we can represent this as  dx/dT is the derivative of the perturbations as a function of temperature which can be derived from the FEA (we are assuming this is linear for now, but if its not we can easily add a second derivative term)  T is the temperature, and T 0 is a nominal temperature (10 degrees C)  δ T is called the thermal non-uniformity parameter and represents the difficulty in controlling or knowing the temperature & would encompass hysteresis-like effects; (one could make this much more complicated and have a separate parameter for every degree of freedom)  This will become necessary to make the control system not able perfectly correct the thermal perturbations  g T is a gaussian random number with sigma of 1 and mean of 0, and will change on a thermal drift timescale; it should be sufficient for now to make this timescale more than a visit and thus have this random number changed for every simulation

9. Term #3: Gravity  Bending due to the change in gravity vector perturbs the optical elements from their ideal position  This can be expressed as:  where dx/d ϑ is the change in value per elevation ( ϑ ) and is derived from the FEA data (again we can do second derivatives if necessary)  δ ϑ is a bending non-uniformity parameter and would represent residual shaking/bending & hysteresis-like effects  Note Andy R has indicated that there is azimuthal dependence to this, which be represented by something like:

10. Term #4: Other environmental (hidden variable)  There are other possible effects that may be important in knowing where surfaces are located  Wind effects, seismic/vibrational?, and unmeasured temperature gradients (across the mirror surface, for instance)  These might be hard to model, but easier to bound with the rms value of these effects with another term like:  where h i is the rms value and g is a gaussian random number  Alternatively, we might consider implementing wind as a state variable like temperature & gravity (it mainly depends if this is going to be a variable of the LUT)

11. Term #5: Actuators  Finally, the surfaces obviously move them if you intentionally move them with either the mirror actuators, M2 hexapod actuators, or Camera hexapod actuators; The thinking was that it is better to put these on the same mathematical footing as the environmental variables  It is likely that you would describe this in terms of either a displacement or force for every compensator degree of freedom  It turns out PhoSim doesn’t need to know the units of this  In general, we need a matrix with columns equal to the surface degrees of freedom and rows equal to the possible actuator degrees of freedom (hopefully this is mostly diagonal); The elements would then be derivatives dx/da where a is the actuator force or distance  We also would need the actuator error δ a that keeps the control from being perfect  a j would then either be predicted from the compensation algorithm (phase II) or controlled by the user; g would be a gaussian random number changed every visit

12. All Perturbation Terms: One equation for every angle, displacement, and surface deformation coefficient Project-provided PhoSim input Comes from feedback model or phosim input Fabrication error Bulk thermal derivative from FEA Temperature Thermal non-uniformity parameter (would be 0 if in perfect thermal equilibrium; this could be higher near twilight) Elevation derivative (bending) from FEA “Shaking/Twisting” parameter (would be 0 if didn’t ever move the telescope; could be larger if more recent motion) Elevation Actuator distance or force (key to feedback is deciding this value; last slides) Compensation error Actuator matrix “Hidden variable” error Includes unmeasured thermal derivatives, wind fluctuations?, and seismic? Probably will include 2 nd derivatives depending on FEA data

13. Needed Inputs

14.  Camera Team  Brief Description of conventions of how displacements/angles/surface deformations are described in the camera team  FEA: Displacements/Angles/Surface deformations from nominal of all camera optics at T bulk =0,10,20 °C  FEA: Displacements/Angles/Surface deformations from nominal of all camera optics at elevation=0,45,90°  FEA: Displacements/Angles/Surface deformations from nominal of all camera optics for each hexapod actuator at +/- extreme values (of either force or position)  Positional or force error for each hexapod actuator  Fabrication/Assembly displacement/angle/surface deformations tolerances for all camera optics  Telescope Team  Brief Description of conventions of how displacements/angles/surface deformations are described in the telescope team  FEA: Displacements/Angles/Surface deformations from nominal for both mirrors at T bulk =0,10,20 °C  FEA: Displacements/Angles/Surface deformations from nominal for both mirrors at elevation=0,45,90°  FEA: Displacements/Angles/Surface deformations from nominal for both mirrors for each actuator group & M2 hexapod actuators at +/- extreme values (of either force or position)  Positional or force error for each actuator group and M2 hexapod actuators  Fabrication/Assembly displacement/angle/surface deformations tolerances for both mirrors  Expected rms displacement/angle/surface deformations for each mirror due to unmeasured temperature gradients  Expected rms displacement/angle/surface deformations for each mirror due to wind flow  Does mirror move measurably in bulk direction due to wind vector or is it only differential motion?

15. Implementation

16. Instance Catalog “Trim file” 1 2 3 4 5 6 7 8

17. Instance Catalog “Trim file” 1 2 3 4 5 6 7 8 Perturbation Calculation Code: Uncompensated perturbations module & Compensation module Static Perturbation Data: Thermal/ Gravity Derivatives Actuator Matrix Compensation Errors Fabrication Tolerances Hidden variable estimates http://dev.lsstcorp.org/cgit/LSST/sims/phosim.git/tree/data/lsst?h=dev User Control: Temperature Alt, AZ dT, dAlt Control System Switches Actuator positions (optional) Perturbation Validation: Task 1F, Task 2B, & more Perturbations applied to photons Physics Override: Can override any perturbation in command files

18. Phase II: Compensated Perturbations

19. Feedback Correction: Have to decide on a j ’s given the other perturbations We will probably pursue two methods as we test phase I. We don’t have to decide this now, and may even have multiple modules. 1) Develop heuristic model for how we think the feedback might behave 2) Take a more literal approach where we run simulations to “accumulate” the look up table (get a j ’s given temperature and elevation) and simulate wavefront images apply wavefront reconstruction algorithm and choose compensation a j ’s Split driving terms into predictable (non- random & random long time-scales) and unpredictable (random short time-scales) Then guess how LUT & WFS will work LUT WFS