Modelling the Gaia instrument
Daniele Gardiol
D.Bonino, D.Busonero, L.Corcione, M.Gai, M.Lattanzi, D.Loreggia, A.Riva, F.Russo, J.C.Terrazas Vargas
INAF - Osservatorio Astronomico di Torino
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
1
Overview
• Gaia expected performances
• Instrument modelling approach
• Gaia: the instrument
• PSF/LSF model for simulation
• CCD Charge Transfer Inefficiency modelling
• Basic Angle Variation and Monitoring
• Astrometric error prediction for General Relativity Experiment
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
2
Gaia expected performances
Hipparcos
Gaia
Magnitude limit
Completeness
Bright limit
Number of objects
12
7.3 – 9.0
0
120 000
Effective distance
limit
Quasars
Galaxies
Accuracy
1 kpc
None
None
1 milliarcsec
Photometry
photometry
Radial
velocity
Observing
programme
2-colour (B and V)
None
Pre-selected
20 mag
20 mag
6 mag
26 million to V = 15
250 million to V = 18
1000 million to V = 20
50 kpc
5 x 105
106 – 107
7 µarcsec at V = 10
10-25 µarcsec at V = 15
300 µarcsec at V = 20
Low-res. spectra to V = 20
15 km/s to V = 16-17
Complete and unbiased
Gaia: complete, faint, accurate (from www.rssd.esa.int)
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
3
Gaia expected performances
Hipparcos
Gaia
Magnitude limit
Completeness
Bright limit
Number of objects
12
7.3 – 9.0
0
120 000
Effective distance
limit
Quasars
Galaxies
Accuracy
1 kpc
None
None
1 milliarcsec
Photometry
photometry
Radial
velocity
Observing
programme
2-colour (B and V)
None
Pre-selected
20 mag
20 mag
6 mag
26 million to V = 15
250 million to V = 18
1000 million to V = 20
50 kpc
5 x 105
106 – 107
7 µarcsec at V = 10
10-25 µarcsec at V = 15
300 µarcsec at V = 20
Low-res. spectra to V = 20
15 km/s to V = 16-17
Complete and unbiased
→ Stringent requirements also in Instrument Modelling performances
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
4
Instrument modelling approach
Design
parameters
In-flight
instrument
behaviour
forward
Analysis
backward
Daniele Gardiol – Modelling the Gaia instrument
Instrument
predicted
performances
Real
observations
LIII congresso SAIt – Pisa 4-8 maggio 2009
5
Instrument modelling approach
SIMULATIONS
Design
parameters
In-flight
instrument
behaviour
forward
Analysis
backward
Instrument
predicted
performances
Real
observations
CALIBRATIONS
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
6
DU4 - Instrument model
DU1
Management:
Management
SW system:
X.Luri
Orbit/Attitude:
Un.Barcelona
Optics:
DU3
Dispersers:
Universe
CCD:
model
PSF/LSF:
A.Robin
Obs.Besançon
BAM:
On-Board processing:
CU2 - Simulations
D.Gardiol
Oss.Torino
F.Russo
Oss.Torino
DU2
SW Engineering
J.M. Wallut
Data Generators
R.Keil
ZARM Bremen CNRS Tolosa
DU5
GASS → telemetry
D.Loreggia
Oss.Torino
E.Masana - Un. Barcelona
J.Rebordao
INETI Lisbon
DU6 GIBIS → pixel level
L.Corcione
Oss.Torino
C.Babusiaux - Obs. Meudon
D.Gardiol, D.Busonero OATo
DU7 GOG → MDB objects
Y.Isasi – Un. Barcelona
D.Gardiol
Oss. Torino
J.Portell
Daniele Gardiol – Modelling the Gaia instrument
DU4
Instrument
model
D.Gardiol
Oss.Torino
Univ. Barcelona
LIII congresso SAIt – Pisa 4-8 maggio 2009
7
Overview
• Gaia expected performances
• Instrument modelling approach
• Gaia: the instrument
• PSF/LSF model for simulation
• CCD Charge Transfer Inefficiency modelling
• Basic Angle Variation and Monitoring
• Astrometric error prediction for General Relativity Experiment
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
8
Gaia – Disegno ottico
LOS2
LOS2
Image credit: www.rssd.esa.int
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
9
Gaia – Piano focale
Image credit: www.rssd.esa.int
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
10
Overview
• Gaia expected performances
• Instrument modelling approach
• Gaia: the instrument
• PSF/LSF model for simulation
• CCD Charge Transfer Inefficiency modelling
• Basic Angle Variation and Monitoring
• Astrometric error prediction for General Relativity Experiment
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
11
PSF/LSF model for simulations
Model described in GAIA-CU2-TN-INAF-DG-011 (ESA-Gaia livelink)
The model is based on a dual representation:
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
12
PSF/LSF model for simulations
Model described in GAIA-CU2-TN-INAF-DG-011 (ESA-Gaia livelink)
The model is based on a dual representation:
• numerical library for GIBIS. The starting point is a numerical library
(discrete sampling) where the elements are generated from the optical
design of the instrument (CodeV generated WFEs) plus some ad-hoc
effects.
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
13
PSF/LSF model for simulations
Model described in GAIA-CU2-TN-INAF-DG-011 (ESA-Gaia livelink)
The model is based on a dual representation:
• numerical library for GIBIS. The starting point is a numerical library
(discrete sampling) where the elements are generated from the optical
design of the instrument (CodeV generated WFEs) plus some ad-hoc
effects.
• analytical library for GASS/GOG. The elements of the library are
generated from fittings of suitable functions to the elements of the
numerical library. Interpolation may be used when appropriate. Detailed
in GAIA-CU3-TN-INAF-DB-007 (ESA-Gaia livelink)
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
14
Advantages of such a model
• many effects can be introduced at the level of the numerical
library and they will automatically be present in the analytical
representation (no need to develop specific models for GASS
and GOG) → homogeneity of simulations
• the analytical representation requires a minimised number of
computations in GASS/GOG → good compromise between realism
and efficiency
• nonetheless, many effects are not usefully described by means
of precomputed libraries (CTI, noise, magnitude, non-linearity/
saturation, …) and have to be treated separately
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
15
Analytical model – example (AF)
•S1R1T1 vs. S1R7T1 (V-I = 0.0)
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
16
Overview
• Gaia expected performances
• Instrument modelling approach
• Gaia: the instrument
• PSF/LSF model for simulation
• CCD Charge Transfer Inefficiency modelling
• Basic Angle Variation and Monitoring
• Astrometric error prediction for General Relativity Experiment
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
17
CCD – modelling radiation damage and CTI
• high energy solar radiation creates traps
into the semiconductor lattice that
capture photoelectrons and release them
after some time
• this increases the CTI of the CCD
• as a result, the charge packet is
displaced (retarded) wrt the source
Image credit: www.rssd.esa.int
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
18
Radiation damage - test campaign
• Three CCD zones: No irradiated,
transition, Irradiated (end-ofmission dose)
• Three irradiated sessions with
different diffuse optical background
(DOB): 0, 5, and 10 e-/pixel
• Different brightness levels
corresponding to nominal 60000,
7000, 2000, 650, 400, and 200
integrated eJ.C.Terrazas Vargas, L.Corcione, M.Gai, M.Lattanzi (OATo)
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
19
Photometry – charge loss
Not irradiated zone
Transition zone
Irradiated zone
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
20
Astrometry – centroid bias
Centroids relative to the linear best fit from stars A to C in the non-irradiate zone
Non irradiated
zone
Transition
zone
Irradiated
zone
not compensated for the mask bias
Daniele Gardiol – Modelling the Gaia instrument
mask bias subtracted
LIII congresso SAIt – Pisa 4-8 maggio 2009
21
21
Radiation test campaign and Simulations
Test
campaign
Microscopic
model
Raw test
data
Montecarlo
Model
simulations
verification
Test data
analysis
Models
verification
Daniele Gardiol – Modelling the Gaia instrument
Macroscopic
models
GASS
(CDM1)
GIBIS
(CDM1&2)
Simulated
datasets
LIII congresso SAIt – Pisa 4-8 maggio 2009
22
Overview
• Gaia expected performances
• Instrument modelling approach
• Gaia: the instrument
• PSF/LSF model for simulation
• CCD Charge Transfer Inefficiency modelling
• Basic Angle Variation and Monitoring
• Astrometric error prediction for General Relativity Experiment
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
23
Basic Angle Variation and Monitoring
LOS 1
LOS 2
Image credit: Meijer et al., SPIE 7010
Daniele Gardiol – Modelling the Gaia instrument
D.Gardiol, A.Riva, F.Russo (OATo)
LIII congresso SAIt – Pisa 4-8 maggio 2009
24
Basic Angle Variation
Sinusoidal behaviour
expected (P = 6 hours)
Thermal perturbation
(M1#1 – M2#2)
~ 200 µK peak to peak
BA response
~ 1200 µas

Daniele Gardiol – Modelling the Gaia instrument
dBA/dT ~ 6 µas / µK
(Gardiol et al., SPIE 5497)
LIII congresso SAIt – Pisa 4-8 maggio 2009
25
BAM fringes simulation
BAM detailed optical design (Zemax) available to us only since
last week.
 Analytical model implemented, based on ideal BAM instrument
 For each telescope the fringe pattern is given by:

D  
 2B

xi  x0  
fp(i, j )  k  Airy  rij   1  V cos 
 f  
 f

where
 xi  R(i  i0 )  2  LOS  f

 y j  R( j  j0 )
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
26
Physical window on the CCD:
Size is 360 x 120 pixels =
3.6 x 3.6 mm²
Fringe image
Logical window size is
360 pixels x 60 samples
(binning x 2 AC scan)
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
27
BAM optical layout
Image credit: Meijer et al., SPIE 7010
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
28
Overview
• Gaia expected performances
• Instrument modelling approach
• Gaia: the instrument
• PSF/LSF model for simulation
• CCD Charge Transfer Inefficiency modelling
• Basic Angle Variation and Monitoring
• Astrometric error prediction for General Relativity Experiment
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
29
Astrometric error prediction near Jupiter
for the GAia Relativity Experiment
Crosta & Mignard, 2006
GAREX aims at testing General Relativity with Eddington-like differential
measurements. Right: light deflection due to the quadrupole of Jupiter predicted by
GR, but never actually measured (240 µas at limb)
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
30
Astrometric error prediction near Jupiter
for the GAia Relativity Experiment
•
•
•
•
•
Analytical law derived from Montecarlo simulations
Dependence on star magnitude and distance from Jupiter limb
partial-to-full saturation of CCD pixels taken into account
background level due to Jupiter's stray-light
Error refers to a single CCD transit (differential measurement)
Note that the actual values of the errors depend on several assumptions, e.g.:
• a specific location algorithm (least-square);
• a specific measurement process, depending on the read-out procedure actually foreseen
for Gaia
• nominal CCD performances (e.g. no CTI)
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
31
Astrometric error prediction near Jupiter
for the GAia Relativity Experiment
 CCD  10 g ( m,r )
g (m, r )  A(r )  m  B(r )  m 2  C (r )  m  D(r )  E (r )
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
32
GRAZIE PER L’ATTENZIONE
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
33
Backup slides
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
34
Current version of the model
Numerical library: The starting point is the current library of effective
PSFs generated by PSFmaker 2.1
http://gibispc.obspm.fr/~gibis/data-V4.0/psf/Gaia3/AF/effective/
Analytical library:
• Fitting functs: Bi-quartic B-Spline (L.Lindegren, GAIA-C2-TN-LU-LL-066)
• 31 knots equally spaced (spacing = 0.5 pixels AL)
• Result: Analytical function giving pixel readout for any (continuous) AL
position:
LSF ( x)   Ak  p1 ,, pn Bk x 
k
• Details of the analytical library coeffs calculation in GAIA-CU3-TN-INAFDB007 (ESA-Gaia livelink)
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
35
Parameter space domain
Parameter
SM
AF
BP
RP
RVS
Telescopes
2
2
2
2
2
FoV
7
62
7
7
12
12
12
16
18
15
Source spectrum
168 + 1488 +
224 + 252 + 360 = 2492
Size (numerical, GB)
0.672
5.952
0.244 0.252
0.360 = 7.5 GB
Size (analytical, MB)
0.148
1.333
0.196
0.316 = 2.2 MB
Daniele Gardiol – Modelling the Gaia instrument
0.211
LIII congresso SAIt – Pisa 4-8 maggio 2009
36
Current version of the model
SM/AF
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
37
Current version of the model
BP/RP/RVS
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
38
Analytical model – example (AF)
•FoV domain (coeff n. 15, V-I=0):
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
39
Analytical model – example (AF)
Source colour domain (S1R1T1):
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
40
Analytical model - AF (example)
Sub-pixel AC-shift (S1R1T1, coeff. N. 15, V-I = 0.0):
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
41
Analytical model for AF – Relative weights of effects
PSF shape variation wrt given domain estimated using BQ coeff
dispersion (coeff N15):
RWeight  100 
Max  Min
Max  Min
BQ-coeff values dispersion as a function of
• FoV position:
30% (0.36 – 0.67 peak to peak)
• Colour variation:
13% (0.45 – 0.58 peak to peak)
• sub-pixel AC position 0.1% (0.5647-0.5663 peak to peak)
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
42
Radiation campaign data analysis results
Photometry
Astrometry
•The charge loss due to trap
presence affects the star signal
mostly at the first transit
•The average amount of charge loss
is highly correlated to the signal
intensity
•Charge loss measurements are in
good agreement with a power law.
•The adopted levels of DOB
contribute in partially mitigating the
radiation
damage
(particularly
evident at the faintest signals)
•Mechanical uncertainties (mask
position jitter, mask yaw)
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
• At high signal regimes (S>=2000),
centroid bias is correlated with the
signal level and DOB apparently
mitigates the CTI effects
•At low signal levels (S<= 600), the
centroid bias is largely affected by
mask positioning uncertainties for
definitive conclusions
43
Charge loss - summary
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
44
Cose che vado a dire
• gaia expected performances-> consequences on instrument modelling (for- and back-wards)
• accenno a CU2/DU4 (forward analysis) vs. CU3/AVU (backward analysis)
• Struttura di CU2: IM,UM + GIBIS/GASS/GOG e Struttura di DU4
• Disegno ottico / Piano focale di Gaia (2)
• PSF/LSF library (5)
• CCDs - Radiation damage (5)
• BAM simulation (2)
• BAV (spie 2004?)
• Prediction of astrometric accuracy Near very bright objects (GAREX -> A&A)
Daniele Gardiol – Modelling the Gaia instrument
LIII congresso SAIt – Pisa 4-8 maggio 2009
45