# Presentation: 004624

## TPF-C Optical Requirements 

- Stuart Shaklan
- TPF-C Architect
- Jet Propulsion Laboratory, California Institute of Technology
*with Contributions from*
*Luis Marchen, Oliver Lay, Joseph Green, Dan Ceperly, Dan  Hoppe, R. Belikov, J. Kasdin, and R. Vanderbei*
- TPF-C Coronagraph Workshop
- September 28, 2006

## Overview

- Flowdown of science requirements to engineering requirements
- Meeting the requirements: TPF-C FB-1 Error Budget
- Optical surface requirements
- Related to wave front control system and bandwidth
- Effect of uncontrolled spatial frequencies (frequency folding)
- Related to finite size of the star
- Image plane mask surface roughness requirements
- Thermal/Dynamics requirements
- Sensitivity of different coronagraphs to low-order aberrations
- System requirements

## High-Level Requirements

- _SCIENCE:_ Detect 30 potentially habitable planets assuming earth =1.
- Also measure orbital semi-major axis, perform spectro-photometry, detect photons from 0.5 – 1.1 um, perform spectroscopy.
- Ongoing _MISSION STUDIES_ have been used to derive engineering requirements from science requirements.
- For the Flight Baseline 1 (FB-1) study, emphasis was first placed on the *detection* requirement.
- _ENGINEERING:_ The Mission Studies reveal that the detection requirement is satisfied with IWA = ~65 mas and  SNR=5 at mag = 25.5 (Contrast = 6.3e-11), using a100 nm wide channel.
- Orbit, spectro-photometry, and spectroscopy requirements will likely drive us to a deeper contrast requirement.
- _FLOWDOWN:_
- Control Scattered light to below Zodi + ExoZodi, ~ 1e-10
- Measure, estimate, or subtract speckles to 5x below mag = 25.5 or 1.2e-11
- Work at 4 /D with D=8 m (equiv to 2 /D for D=4 m).

## Speckle Floor, Stability

*I**s* = Static Contrast
- Wave Front Sensing
- Wave Front Control
- Gravity Sag Prediction
- Print Through
- Coating Uniformity
- Polarization
- Mask Transmission
- Stray Light
- Micrometeoroids
- Contamination

*I**d* = Dynamic Contrast
- Pointing Stability
- Thermal and Jitter
-    Motion of optics
-      Beam Walk
-      Aberrations
-    Bending of optics

- Contrast = *I**s* + <*I**d*>
- Stability = sqrt(2*I**s*<*I**d*> + <*I**d**2*>)

## Static vs. Dynamic

- Speckle variability exceeds requirement in this region.

## System Static Error Budget

## System Thermal/Dynamic Error Budget

## Where do TPF-C surface requirements come from?

- Axiom:  Given a pair of ideal DMs, a stable telescope, and monochromatic light, all energy in the dark hole can be completely removed.

- - Independent of the wave front quality of the optics.

- What happens in broad-band light?

## Michelson Wave Front Control

- y

- z

**

- D

- P

- Incoming Light

- =4s/

- To Coronagraph

- DM

- DM

- Pupil Conjugate

- Phase control: 1/
- Ampl. Control: 1/2

## Sequential WFC

- D

- Incoming Light

- To Coronagraph

- DMp

- zDM

- Pupil Image

- Two DMs are separated by distance *z**DM*.  One is at the pupil.  The pupil DM controls phase.  The non-pupil DM adjusts its phase, which propagates to the pupil and becomes wavelength-independent amplitude.

- DMnp

- Phase control: 1/
- Ampl. Control: independent

## Visible Nuller

- Phase control: 1/
- Ampl. Control: 1/2

- A segmented-DM is matched to a lenslet array that couples light into a single-mode fiber optic.  DM-element tilt adjusts the coupling efficiency, resulting in a change in the output light level.

## Propagation Kernel

## Direct and Propagated Terms

## TPF-C Layout

- Image-space images of the optics

- Final beam is collimated at the exit pupil.  All optics appear to have the same diameter as seen from the exit pupil.

## Surface Height Requirementsfor R=6.3 and C = 1e-12 per optic

- Secondary

- DMcol =50 nm

- M4

- DMcol

- DMcol
- =200 nm

- EUV

- Secondary

- DMcol =50 nm

- M4

- DMcol

- DMcol
- =200 nm

- EUV

- Surface  Requirement
- Michelson and Visible Nuller

- Surface  Requirement
- Sequential

- Surface Height Requirementsfor R=6.3 and C = 1e-12 per optic

## Reflectivity Uniformity Requirementfor R=6.3, C=1e-12

- Reflectivity Uniformity Requirementfor R=6.3, C=1e-12

- Control limit for
- 30 nm piston, DM is 3 m from pupil

- Limited by direct reflectivity.

- Limited by ampl.-to- phase prop.

- Michelson and Visible Nuller Requirement

- We believe that the state-of-the-art in large optics coatings is about 0.5% r.m.s., with a 1/f3 PSD. This leads to ~ 1e-11 contrast at 4 cycles/aperture (worse at 2 cycles/aperture).

## Finite Size Source

- D

- Incoming Light

- To Coronagraph

- DMp

- zDM

- Pupil Image

- Two DMs are separated by distance *z**DM*.  One is at the pupil.  The pupil DM controls phase.  The non-pupil DM adjusts its phase, which propagates to the pupil and becomes wavelength-independent amplitude.

- DMnp

- DM compensation is sheared for an off-axis element of the target.

## Contrast Due to Finite Size Source 

- C = Contrast
** = r.m.s. wavefront (radians)
-        or r.m.s. (reflectivity/2)
***x* = beam shear
*N* = cycles/aperture
*D *= beam diameter

- a = Source radius
- z = effective distance of optic
-       from pupil
*D**p** *= pupil diameter
*D**b** *= beam diameter

## Surface Height Requirementsfor Finite Size Star (1.7 mas diam.),  C = 1e-12 per optic

- Secondary

- DMcol =50 nm

- M4

- DMcol

- DMcol
- =200 nm

- EUV

- Secondary

- DMcol =50 nm

- M4

- DMcol

- DMcol
- =200 nm

- EUV

- Surface  Requirement
- Michelson and Visible Nuller

- Surface  Requirement
- Sequential

- Surface Height Requirementsfor Finite Size Star (1.7 mas diam.),  C = 1e-12 per optic

## Reflectivity Uniformity Requirementfor Finite Size Star (1.7 mas diam.),  C = 1e-12 per optic

- Reflectivity Uniformity Requirementfor Finite Size Star (1.7 mas diam.),  C = 1e-12 per optic

- Control limit for
- 30 nm piston, DM is 3 m from pupil

- Michelson and Visible Nuller Requirement

## Preferred DM Configuration

- DMp

- DMnp,2

- DMnp,1

- M2

- M1

- CDM

- Collim.

- f1=2.5

- f2=2.5

- 1

*z**DM*=3

*z**DM*=3

- 1

- Cass. Focus

**3-DM fully redundant system**. This diagram depicts an unfolded layout that provides for 2 non-pupil DMs placed *z**DM*=3 m from the pupil DMp.  A unity magnification telescope images the coarse DM pupil plane CDM to DMp (dashed line). The design provides 1 m between CDM-M1 and M2-DMnp,1 to fold the beams at a shallow angle.

## LESSON 1

**Use a sequential wave front controller. **
- Relaxes optical surface requirements
- Increases the useful size of the dark hole
- Allows a wider optical bandwidth
- Relaxes coating requirements on PM and SM to within state-of-the-art
- Provides redundancy
- A Michelson controller, and fiber spatial-filter amplitude controller make broad-band amplitude control very challenging.
- Pushes Silver coating beyond state-of-the-art
- Is Aluminum coating uniformity sufficient?
- Aluminum is desired on PM, SM, and M3 to enable general astrophysics.

## Frequency Folding: Uncontrolled High Spatial Frequencies Appear in the Dark Hole

- The previous charts addressed controllable spatial frequencies – those below the DM Nyquist frequency.

- Give’on has shown that frequency folding terms scatter light into the dark hole.

## Frequency Folding Residual

- The Michelson controller has 1/2 amplitude dependence and completely
- 	removes the light.

- The Visible Nuller fiber array does not pass spatial frequencies above N/2.  The 	frequency folding problem is eliminated.

## Frequency Folding Contrastfor R=6.3, Sequential DMs (96 x 96)

## LESSON 2

**Uncontrolled high-spatial frequencies look manageable.**
- Existing optics lead to acceptable frequency folding
- What happens when we light-weight the PM???
- Requires large format DM
- Becomes an issue for bandwidth >> 100 nm

## Image Plane Mask errors

- Static contrast

- Mask error

- Random

- Systematic

- Spatially random variations in mask transmission amp and phase

- Variations in mask transmission amp and phase that are correlated with mask pattern

- Unaberrated input field with mask errors

## Gaussian error, monochromatic

- Unaberrated sombrero function *E*0
- Gaussian mask error *M *at ~ 4** / D

- Angular offset / rad

- 550 nm

- E field

- E field

- E field

- E field error exiting mask = *E*0*M*

- Diffracted by Lyot stop
*E*0*M ***L*
- Perfect DM correction (dotted line)

## Gaussian error, broadband

- Two wavelengths to illustrate broadband case
- Blue sombrero function is compressed

- Angular offset / rad

- 550 nm + 510 nm

- E field

- E field

- E field

- E field at mask exit is quite different at 510 nm

- DM correction still perfect for 550 nm, but compressed for 510 nm
- DM correction is completely inappropriate for 510 nm

- 510 nm after DM ‘correction’

- DM ‘correction’@ 510 nm

- 510 nm error beforeDM correction

- 550 nm errorand correction

## Dependence on error spatial scalefor a 100 nm bandpass 500-600 nm, evaluated at 4 /D

| Mask errorscale size (FWHM) |  | Rms mask errorfor 10-11 contrast |
| --- | --- | --- |
| f / D | F/60 |  |
| 2 | 60 m | 91 pm |
| 1 | 30 m | 31 pm |
| 1/2 | 15 m | 24 pm |
| 1/4 | 7.5 m | 27 pm |
| 1/8 | 4 m | 38 pm |
| 1/16 | 2 m | 50 pm |

- Large

- Small

- Simple 1-D analysis used to predictcontrast in image plane from a grid ofrandom Gaussian mask errors

- Light scattered from both verysmall features is blocked by Lyot stop
- Large scale errors are effectively controlled over a broad band.

- Most sensitive to scalescomparable to sidelobes ofsombrero function:

## Mask error PSD requirement

- Each component has different characteristic spatial scale
- Each represents 10-11 contrast
- Overall contrast can be suballocated to different scales to match actual PSD of mask errors

- Norequirement

- 91 pm rms (60 um scale size)

- 31 pm rms

- 24 pm rms (15 um scale size))

- 27 pm rms

- 38 pm rms

- 50 pm rms (2 um scale size)

- Period = 30 m

- Period = 100 m

- sum

- Overall surface r.m.s. ~ 1 A for scales 2 – 60 um.

## LESSON 3

**If you’re going to put a transmissive mask in the image plane, it should have <1 A rms for spatial scales up to 2 ********F#**
- Due to inherent scaling of spatial frequency with wavelength in the image plane
- A mask-leakage error looks like a planet – it does not scale with wavelength.
- Calibrate by rotating the mask, but still requires 1 A rms to keep scattered light level near 1e-11.

## Thermal/Dynamics Error Budget

- Observing Scenario
- Coronagraph sensitivity to Low-Order Aberrations
- Control systems
- Key Requirements

## Observing Scenario

## Aberration Sensitivity 1Mask Throughput

## Aberration Sensitivity 2Contrast Sensitivity Curves

- Evaluated at 4 /D

- Focus, 4 /D

- Coma, 4 /D

- Focus, 4 /D

- Coma, 4 /D

- Linear dual-shear VNC aberration sensitivity and Lyot throughput are identical to a linear 4th order mask of the form T = 1-cos(x). Sensitivity is almost identical to 1-sinc2(x).

## Aberration Sensitivity 3Allowed WFE

## Aberration Sensitivity 4Pupil Mapping Sensitivity Curves

## Aberration Sensitivity 5Pupil Mapping Sensitivity Curves

- Pupil Mapping, 4 lambda/D

- BL4, VNC
- 4 lambda/D

- BL8,
-    4 lambda/D

- Pupil Mapping, 2 lambda/D

- Shaped Pupil,
-    4 lambda/D

## Open-Loop Aberration Sensitivity Summary

- The 8th-order null of a properly built BL8 provides orders-of-magnitude reduction to low-order aberrations.
- Working at 4 /D, the mask sensitivity to aberrations increases in order:
- BL8, Shaped pupil, Pupil Mapping, BL4/VNC
- BL4/VNC is 100 x more sensitive to aberrations than BL8 (C=1e-12)
- OVCn behaves like 2nth null (OVC4 = 8th order null). Still studying the tradeoff between sensitivity and throughput.
- Working at 3 /D increases aberration sensitivity by an order of magnitude.
- 3x tighter WF tolerance to work at 3 /D with BL8
- Working at **2 ********/D is harder yet** – BL8 throughput too low, so must go to BL4/VNC, OVC2 or OVC4 (?), or pupil mapping.
**This is 1000x more sensitive to aberration than BL8 at 4 ********/D.**

## Thermal/Dynamic Error Budget

- Low-order aberrations arise by
- Thermal deformation and misalignment of optics
- Jitter induced deformation and misalignment of optics
*The BL8 mask at 4 lambda/D is quite insensitive to these.*
*BL4/VNC are the most sensitive*
- Beam Walk (shearing of spatial frequencies) is the *same for all coronagraphs.*
- If planet light is transmitted at x lambda/D, then a spatial frequency of x cycles/aperture is also transmitted.
- Beam walk is mitigated by
- Control of optics positions: secondary mirror + FSM
- Quality of optics
- Beam walk drives the optical surface quality at a few cycles/aperture.

## Control Systems

- 3-tiered pointing control
- Rigid body pointing using reaction wheels or Disturbance-Free Payload
- Secondary mirror tip/tilt (~ 1 Hz)
- Fine-guiding mirror (several Hz)
- PM-SM Laser Metrology and Hexapod
- Measures and compensates for thermal motion of secondary relative to primary.

## Key Dynamics Requirements

- 4 mas rigid body pointing

- Fold mirror 1:
- rms static surf =0.85nm
- Thermal: 10nrad, 100 nm
- Jitter: 10 nrad, 10 nm

- PM shape: (Thermal and Jitter)
- z4=z5=z6=z8=z10=0.4 nm
- z7=0.2 nm, z11=z12=5 pm

- Mask centration:
- offset=0.3 mas
- amplitude=0.3mas

- Secondary:
- Thermal: x=65 nm, z=26 nm,
- tilt=30 nrad
- Jitter: 20x smaller

- Laser metrology:
- L=25nm
- f/f=1x10-9

- Coronagraph optics motion:
- Thermal:10nrad, 100nm
- Jitter: 10 nrad, 10 nm

- Figure 5. We identify the major engineering  requirements to meet the dynamic error budget.  Thermally induced translations lead to beam walk that is partially compensated by the secondary mirror.  Jitter is partially compensated by the fine guiding mirror.

- Mask error = 5e-4 at 4 /D

- z

## Changes from Baseline

- Baseline design assumes BL8 mask.
- Relatively insensitive to low-order aberrations.
- Baseline observing scenario is:
- Difference two images made at 30 deg LOS ‘dither’ positions
- No DM reset for several hours during this time
- If we switch to BL4, VNC (and to a lesser extent pupil mapping and shaped pupil), and if we keep the same observing scenario
- We *can NOT move secondary mirror* to compensate tip-tilt because moving the secondary introduces significant low-order aberration
- We must therefore *maintain very strict pointing accuracy – sub milli-arcsec – on the telescope*
- We also *tighten primary mirror bending stability by orders of magnitude*.
- Going to 2 lambda/D with pupil mapping requires even tighter tolerances.

## LESSON 4

**Working at 2 or 3 ********/D is much, much harder than 4 ********/D.  Breakthroughs in wave front control, optical surface quality, and  a change in observing paradigm are needed.**
- Single-digit picometer wave front control for low-order aberrations
- Sub-pm control of spherical aberration and higher order terms
- Wave front control that is faster than the rigid body pointing errors
- Or, require extremely tight rigid-body pointing
- Hopefully we will hear some ideas on how to do this tonight and tomorrow.

## Summary

- Design Reference Mission modeling provides flow down of science requirements to engineering requirements.
- Optical Surface Requirements
- We have a good handle on surface height and reflectivity uniformity requirements through the system.
- The requirements are imposed by
- Wavelength-dependence of scatter vs. compensation
- Finite size of the star
- Thermal/Dynamic beam walk
- High-spatial frequency errors on large mirrors appear to be acceptable for 100 nm bandwidth
- Correction beyond ~ 25 cycles/aperture does not look feasible (but maybe can live with reduced performance at large working angles).
- Image plane mask requirements
- We have a good handle on the PSD of random mask transmission errors.
- Superpolish surfaces (<1 Angstrom r.m.s.) are probably adequate.
- Stability Requirements
- Thermal and jitter requirements are well understood.
- Modeling described in the FB-1 report and STDT report shows that the required stability can be achieved assuming an 8th-order band limited mask at 4 /D.
- Smaller IWA using masks that are more sensitive to aberrations requires a new approach to WFS/C, one that meets picometer stability requirements and 1e-11 calibration of speckles.

## Pointing Control

## Contrast Roll Up