The New Perturbation Physics Framework

in PhoSimJohn PetersonEn-Hsin PengChuck Claver

Andy RasmussenSteve Kahn

Nov 2012

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 5th 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

Importance of Perturbations

Chang et al. 2012

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”

Phase I: Uncompensated Perturbations

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

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 fi 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 dxi will be between +/- fi

Note pressure-induced perturbations on lenses might puts here

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 T0 is a nominal temperature (10 degrees C)

δT 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

gT 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

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/dϑ is the change in value per elevation (ϑ) and is derived from the FEA data (again we can do second derivatives if necessary)

δϑ 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:

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 hi 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)

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 δa that keeps the control from being perfect

aj 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

All Perturbation Terms:One equation for every angle, displacement,and surface deformation coefficient

Project-provided PhoSim input Comes from feedback model or phosim input

Fabricationerror

Bulkthermalderivativefrom FEA

Temperature Thermalnon-uniformityparameter (would be 0if 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 distanceor force (key to feedbackis deciding this value;last slides)

Compensationerror

Actuator matrix

“Hidden variable” errorIncludes unmeasured thermalderivatives, wind fluctuations?,and seismic?Probably will include 2nd derivatives

depending on FEA data

Needed Inputs

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 Tbulk=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 Tbulk=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?

Implementation

Base Catalog(Universe)

OperationsSimulator

Run

Loop over chipsLoop over visits

Loop over exposures

Static Physics & Design Data (Under version control)(Files editable locally for experiments)

data/lsst: LSST camera, telescope, & site specific filesdata/subaru: Subaru camera, telescope, & site specific filesdata/SEDs: SEDs of Universe (not under version ctrl)data/sky: sky background/moon datadata/cosmic_rays: cosmic ray templatesdata/atmosphere: Earth-specific atmosphere data

Physics command

override files(optional)

Project Inputs:ZEMAX fileCamera filesCoating desc.misc inputs

IntegrationValidation

Tests(validation/)

OperationCommands

AstroCatalog

User

Amplifierimages

Extra Outputs:eimage

Centroid filesSurface throughput

filesEvent files

User Catalog

Electron->ADC

(source/e2adc)

Photon Raytrace

(source/raytrace)

Atmosphere Creator(source/

atmosphere)

Instrument Config(source/instrum

ent)

Trim (source/tri

m)

Phosim script

(./phosim)

CatalogGenerato

r

Operations

Simulator

Code

Data

Instance Catalog“Trim file”

12

3

4

5

6

7

8

PhoSim

CatSim

OpSim

Sys EngUser

Base Catalog(Universe)

OperationsSimulator

Run

Loop over chipsLoop over visits

Loop over exposures

Static Physics & Design Data (Under version control)(Files editable locally for experiments)

data/lsst: LSST camera, telescope, & site specific filesdata/subaru: Subaru camera, telescope, & site specific filesdata/SEDs: SEDs of Universe (not under version ctrl)data/sky: sky background/moon datadata/cosmic_rays: cosmic ray templatesdata/atmosphere: Earth-specific atmosphere data

Physics command

override files(optional)

Project Inputs:ZEMAX fileCamera filesCoating desc.misc inputs

IntegrationValidation

Tests(validation/)

OperationCommands

AstroCatalog

User

Amplifierimages

Extra Outputs:eimage

Centroid filesSurface throughput

filesEvent files

User Catalog

Electron->ADC

(source/e2adc)

Photon Raytrace

(source/raytrace)

Atmosphere Creator(source/

atmosphere)

Instrument Config(source/instrum

ent)

Trim (source/tri

m)

Phosim script

(./phosim)

CatalogGenerato

r

Operations

Simulator

Code

Data

Instance Catalog“Trim file”

12

3

4

5

6

7

8

PhoSim

CatSim

OpSim

Sys EngUser

Perturbation Calculation Code:Uncompensated perturbations module & Compensation module

Static Perturbation Data:Thermal/ Gravity DerivativesActuator MatrixCompensation ErrorsFabrication TolerancesHidden variable estimates

http://dev.lsstcorp.org/cgit/LSST/sims/phosim.git/tree/data/lsst?h=dev

User Control:TemperatureAlt, AZdT, dAltControl System SwitchesActuator positions (optional)

Perturbation Validation:Task 1F, Task 2B, & more

Perturbations applied to photons

Physics Override:Can override any perturbation in command files

Phase II: Compensated Perturbations

Feedback Correction: Have to decide on aj’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 aj’s given temperature and elevation) and simulate wavefrontimages apply wavefront reconstruction algorithm and choose compensation aj’s

Split driving termsinto predictable (non-random &random long time-scales) and unpredictable (random short time-scales)

Then guess howLUT & WFS willwork

LUT WFS