# Metrology studies for high precision astrometry in Theia / HWO

Fabien Malbet, M. Lizzana, F. Pancher, S. Soler, H. Rousset, Y.

Er-Rahmaouy, Y. Bakka, A. Léger, T. Lépine, A. Sozzetti, et al.

► To cite this version:

Fabien Malbet, M. Lizzana, F. Pancher, S. Soler, H. Rousset, et al. Metrology studies for high precision astrometry in Theia / HWO. Milky Way Gaia Doctororal Network, Nic Walton, Jul 2025, Cambridge, United Kingdom. hal-05379628

HAL Id: hal-05379628

https://hal.science/hal-05379628v1

Submitted on 24 Nov 2025

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Distributed under a Creative Commons Attribution 4.0 International License
# Metrology studies
for high precision astrometry
in Theia / HWO

<figure><img src="image_2.png" /></figure>

Fabien MALBET
IPAG / Univ. Grenoble Alpes / CNRS

with M. Lizzana, F. Pancher, S. Soler, H. Rousset, Y. Er-Rahmaouy, Y. Bakka @IPAG
and A. Léger, (IAS) T. Lépine (IOGS/University. St-Etienne), A. Sozzetti (INAF Torino), L. Labadie (University. Köln)
<figure><img src="image_3.png" /><figcaption>Theia proposal for ESA M8</figcaption></figure>

<figure><img src="image_4.png" /></figure>

# Context of the studies

## High precision space astrometry in the visible domain

* Earth-mass planets orbiting in the Habitable Zone of nearby solar-type stars
=> Bright star mode with requirement

* Investigating the nature of Dark Matter through the shape of dwarf spheroidal galaxies (cored or cuspy ?), the kinematic disturbances for stars above/below Galactic plane, and the direction of proper motion for hypervelocity stars

## Two application projects

* **Theia**: 0.8-m telescope with FoV of 0.7 degrees (ESA M8)

* **HWO** 7-m telescope high resolution imager with 3'x2' FoV (NASA)

## Differential pointed astrometry

* Gaia global astrometry allows data closure over the sky but is limited in exposure time and number of visits

* Pointed astrometry allows optimization of exposure time and observing sequences, but fewer objects
# Principle : relative and precise differential astrometry

<figure><img src="image_5.png" /><figcaption>Gaia DR3 data</figcaption></figure>

* ✓ The science target is at the center of the FOV

* ✓ We measure the offset angles between the target object (in the center) and the reference stars (other stars in green)

* ✓ The single measurement is repeated several times over the mission lifetime to reach the required accuracy on the target motion

* ✓ The detector calibration is done using interferometric modulated Young's fringes

<figure><img src="image_6.png" /></figure>
# Theia expected performances

<figure><img src="image_7.png" /></figure>

- **Faint Source Mode (FSM)**: 23 times the PM precision of Gaia (10yr) and 14 times that of HST (10yr)

- **Bright Source Mode (BSM)**: Theia's 1µas precision in 1h integrations at the reference value $R = 10\text{mag}$ exceeds that of Gaia by factor of ~40-50, Roman ~10-20 and VLTI/GRAVITY by ~30-100, and other missions/instruments (e.g. HST, JWST, ELT/MICADO, Rubin) by even larger factors.
# Theia optical concept (ESA M8)

## Theia characteristics :

- 0.8-m telescope diameter

- diffraction-limited 0.5° FOV

## Proposed implementation (M8)

<figure><img src="image_8.png" /><figcaption>Three mirror anastigmat, Korsch design</figcaption></figure>

## Spot Diagram

<figure><img src="image_9.png" /><figcaption>Airy disk radius: 10.86 microns</figcaption></figure>

<figure><img src="image_10.png" /></figure>

## Distortion map 13x13

<figure><img src="image_11.png" /></figure>
# Focal plane for Theia

The Focal Plane uses 4 Pyxalis CMOS detectors
GIGA220M (in development) +1 GIGA14M:

- 4x [16640 x 13156 pixels] (4 x 218 915 840 pixels) + 1 x
  [4160 x 3256 pixels] with 4,4 um pixel pitch

- Non buttable (~10 mm on 2 sides / ~2 mm on 2 sides): 27%
  loss of area

- Focal Plane 173 mm x 136 mm
  `<=> 45.7 arcmin x 35.9 arcmin`
  `<=> 0.76°x0.60°`

- **0.46 deg² total for 0.33 deg²**
  effective (881 Mpx), i.e. 27% loss

<figure><img src="image_12.png" /></figure>

pyxalis
Your Image Sensor Solution

<figure><img src="image_13.png" /></figure>

Field around 1 Per (V = 4.05 mag, d = 10.58 pc, G0V)

<figure><img src="image_14.png" /></figure>

0.76 deg / 46 arcmin
<figure><img src="image_15.png" /><figcaption># Astrometric error budget for bright targets with Theia and HWO</figcaption></figure>
# The accuracy of target position increases with number of reference stars

Uncertainties on reference position increases with flux, mostly limited by photon noise at the bright end and detector noise at the faint end.

<figure><img src="image_16.png" /></figure>

Accuracy of Gaia position for after 20 years is not sufficient, but this can be solved by using multiple reference stars and decrease with the number of references.

But number of reference stars increases exponentially. The final accuracy of the reference frame using Gaia data depends on each direction. However, the final precision will depend on the current mission accuracy.

<figure><img src="image_17.png" /></figure>
# Telescope calibration : using reference stars to monitor the distortion

Distortion can be corrected by fitting the transformation (Sky -> Detector) as calculated by Ray-tracing (Zemax) by a 2D polynomial

<figure><img src="image_18.png" /><figcaption>Simulated field-dependent distortion and fitted position</figcaption></figure>

<figure><img src="image_19.png" /></figure>
<figure><img src="image_20.png" /></figure>

# Current lab tests at IPAG
## (FOCUS & CNES R&T)
# Detector radiometric performance measurements

## GIGAPYX 4600

46 Megapixel, BSI Rolling Shutter
High Speed HDR CMOS image sensor

<figure><img src="image_21.png" /></figure>

Ultimate video image quality

pyxalis
Your Image Sensor Solution

<figure><img src="image_22.png" /></figure>

<figure><img src="image_23.png" /></figure>

<figure><img src="image_24.png" /></figure>

<figure><img src="image_25.png" /></figure>

## Key Performances

<table><thead><tr><th>Parameter</th><th>Typical Value</th></tr></thead><tbody><tr><td>Saturation Charge (linear), HG/LG</td><td>5 ke-/50 ke-</td></tr><tr><td>Temporal Noise in darkness (HG) <sup>(1)</sup></td><td>1.5 e- rms</td></tr><tr><td>Linearity Error, 5-95% QSAT<sub>LIN</sub></td><td>&lt; 3%</td></tr><tr><td>Dynamic Range, HG <sup>(1)</sup></td><td>70 dB</td></tr><tr><td>Dynamic Range, HDR <sup>(1)</sup></td><td>90 dB</td></tr><tr><td>SNR at blending point in HDR</td><td>37 dB</td></tr><tr><td>Peak QE x FF, at 445 nm (mono)</td><td>80 %</td></tr><tr><td>Relative Illumination, up to ± 25°</td><td>&gt; 90%</td></tr><tr><td>Dark-Current <sup>(1)</sup></td><td>24 e-/s rms (@35°C)</td></tr><tr><td>Fixed-Pattern Noise <sup>(2)</sup></td><td>14 DN</td></tr><tr><td>Photo-Response Non-Uniformity <sup>(2)</sup></td><td>&lt; 2%</td></tr><tr><td>Frame-rate, FF, 12 bits, HG/LG</td><td>152 FPS</td></tr><tr><td>Frame-rate, 8K, 12 bits, HG/LG</td><td>192 FPS</td></tr><tr><td>Frame-rate, FF, 13 bits, HDR</td><td>54 FPS</td></tr><tr><td>Frame-rate, 8K, 13 bits, HDR</td><td>63 FPS</td></tr><tr><td>Power-consumption, standby</td><td>&lt; 150 mW</td></tr><tr><td>Power-consumption, full operation <sup>(3)</sup></td><td>&lt; 4.1W</td></tr></tbody></table>

## Our measurements

median_bias_(ADU): 377.0
std_bias_(ADU): 60.9961
medianDark_current_(ADU/ms): 0.0387
stdDark_current_interpx_(ADU/ms): 0.011
stdDark_current_1px_(ADU/ms): 0.0002
linearity_error_(%): 0.5154
median_roq_noise_(ADU): 0.7798
std_roq_noise_(ADU): 0.2203
median gain_(ADU/e-): 0.7105
std gain_(ADU/e-): 0.0359
PRNU Tot_(%): 2.2207
PRNU Center_(%): 1.7011
PRNU HF_(%): 2.7931

<table><thead><tr><th rowspan="2"></th><th>PYXALIS</th><th colspan="2">IPAG measurements</th></tr><tr><th>(e-)</th><th>(ADU)</th><th>(e-)</th></tr></thead><tbody><tr><td>Conversion factor (ADU/e-)</td><td>0.7</td><td>-</td><td>0.71</td></tr><tr><td>Read-out noise</td><td>1.6</td><td></td><td></td></tr><tr><td>Dark current (/ms)</td><td>24</td><td>39</td><td>27</td></tr><tr><td>PNRU</td><td>&lt;2%</td><td></td><td>2.2%</td></tr></tbody></table>
First fring measurements on a 46MP detector

<figure><img src="image_26.png" /></figure>

<figure><img src="image_27.png" /></figure>

<figure><img src="image_28.png" /></figure>

<figure><img src="image_29.png" /></figure>
# Temporal correlation of the interferometric signal

<figure><img src="image_30.png" /></figure>

<figure><img src="image_31.png" /></figure>
# Retrieving pixel positions at sub-millipixel accuracy

$$I_{ij}(t) = B(t) \ell_{ij} + A(t) \alpha_{ij} \sin \left[ i K_x(t) + j K_y(t) + \phi(t) + \delta_{x,ij} K_x(t) + \delta_{y,ij} K_y(t) \right]$$

<table><thead><tr><th>Notation</th><th>Name</th><th>Absorbed noises</th></tr></thead><tbody><tr><td>B(t)</td><td>Average intensity</td><td>Laser flux, offset fluctuations</td></tr><tr><td>l<sub>ij</sub></td><td>Intensity carrier</td><td>Photo response non uniformity (PNRU)</td></tr><tr><td>A(t)</td><td>Average fringe amplitude</td><td>Laser flux, polarisation fluctuations</td></tr><tr><td>α<sub>ij</sub></td><td>Fringe relative amplitude</td><td>Photo response non uniformity (PNRU)</td></tr><tr><td>K<sub>x</sub>(t), K<sub>y</sub>(t)</td><td>Metrology wavevector</td><td>Laser freq. fluctuation, thermal expansion</td></tr><tr><td>φ(t)</td><td>Differential phase</td><td>Phase jitter (thermal and mechanical)</td></tr><tr><td>δ<sub>x,ij</sub>, δ<sub>y,ij</sub></td><td>Pixel offsets (x and y directions)</td><td>-</td></tr></tbody></table>

<figure><img src="image_32.png" /></figure>
# Detector interferometric measurements

<figure><img src="image_33.png" /></figure>

<figure><img src="image_34.png" /></figure>

## Best results so far:

- IPAG/CNES: 6 $10^{-5}$ pixels (Crouzier et al. 2016, A&A 595, A108)

- JPL/VESTA: 3 $10^{-5}$ pixels (Shao et al. 2023, PASP 135, 074502)
Optical calibration in the lab

<figure><img src="image_35.png" /></figure>

On the OLED
micro-display

<figure><img src="image_36.png" /></figure>

<figure><img src="image_37.png" /></figure>

<figure><img src="image_38.png" /></figure>

<figure><img src="image_39.png" /></figure>

On the GigaPyx
46MP detector

<figure><img src="image_40.png" /></figure>
Image data processing

Gaussian fit barycenter

Image d'origine - barycentres (avant / après ajustement)

<figure><img src="image_41.png" /></figure>

Classic barycenter

<figure><img src="image_42.png" /></figure>

FWHM ~ 3.3 px

<figure><img src="image_43.png" /></figure>

Accuracy ~ 6e-2 px

Quite promising ! We need to make sure that we are meeting the flux requirement.
# Conclusion and perspectives

* We have shown that the CMOS 46MP Gigapyx should be a viable technology for high precision astrometry

* The lab measurements are reaching the company announced performance

* The test bench in the lab is operational

* We are measuring fringes and temporal modulation, but we are not yet at the pixel position calibration

* The lab simulation of optical distortion correction is working at 1e-2 level, but not yet reaching 1e-4 pixel;

* For GaiaNIR, the detector technology is different but the process is the same with other materials.