Astrometric
Calibration for WFPC2
Vera Platais
WFPC2: 5 pix! (Holtzman et.al. 1995)
Distorted coordinates
Un-distorted coordinates
Xg=a1+a2X+a3Y+a4X2+a5XY+a6Y2+a7X3+a8X2Y+a9XY2+a10Y3
Yg=b1+b2X+b3Y+b4X2+b5XY+b6Y2+b7X3+b8X2Y+b9XY2+b10Y3
Data Set: (CAL 6941 – 1997)
- rich globular cluster ω Centauri.
F555W
F814W
F300W
Same pointing
Same orientation
Offsets:
±35 ", ±15 ", ±0.25"
Data Set: (CAL 6941 – 1997)
- rich globular cluster ω Centauri.
F555W
F814W
F300W
Same pointing
Same orientation
Offsets:
±35 ", ±15 ", ±0.25"
First Solution –
Analytical PSF fitting (IRAF/PSF) – standard error in positions
F300W - 0.08; F555W - 0.05; F814W - 0.06 pix
Metachip solution – (Holtzman-Casertano formalism):
x,y of WF cameras transformed into global coordinate system
with orientation and scale of PC1
x´=xcos -ysin + xoffset
y´=xsin +ycos + yoffset
X=x´scale
Y=y´scale
Measured
positions in each
filter, in the global
coordinate system
of PC1.
Transformed coordinates X,Y were used for least square minimization of cubic distortion solution.
A full set of coefficients aj,bj was derived.
The Problem:
Meta-chip distortion solution propagates
distortion errors of one chip into the other chips.
The residuals after
correction show
different amplitude and
phase of distortion for
each of WFPC2
cameras.
The precision of meta-chip solution is about 0.3 pix
Quo vadis?
NOVUS VIA
(A new approach)
New approach:
e_PSF (Anderson & King, 2000) measurement of stars
positions with accuracy of 0.02 pix
Astrometric flat-field (Anderson & King,2003) in F555W,
improved the geometry distortion solution with accuracy
0.01 pix in WF and  0.02 pix in PC1.
Anderson-King formalism includes four independent
distortion corrections, one for each chip.
A third order polynomial was used to represent the cubic
distortion.
Histogram – under-sampled stellar profile;
Solid curve – Gaussian model;
Dotted curve – combination of Gaussian and
Lorentzian models
Effective_PSF (Anderson & King 2000)
e_PSF is entirely empirical;
e_PSF is derived from observed pixel values;
e_PSF is fitted to the pixel values by simple evaluation and
scaling without any integration.
The accuracy of e_PSF measurement of stars positions is
0.02 pixels for F555W, F814W and F300W filters.
x,y
x,y
F555W
x,y
F814W
F300W
The residuals between the
‘astrometric flat field’ –
F555W positions and star
positions in F300W filter,
applying only a linear
transformation, for each
chip independently.
Astrometric flat-field (Anderson & King, 2003), the
coordinates free of distortion (Xg, Yg) in F555W were
used to derive geometric distortion corrections in X,Y
positions for F814W and F300W filters.
X=(x-425)/375
x,y
XgYg
x,y
XgYg
x,y
Xg=a1+a2X+a3Y+a4X2+…+a10Y3
Yg=b1+b2X+b3Y+b4X2+…+b10Y3
XgYx,y
g
XgYg
Y=(y-425)/375
10 set of aj bj for each chip & filter
XgYg
x,y
aj ,bj  for each chip & filter
After applying the bicubicpolynomial, the residuals are
essentially flat.
The differences in the distortion correction are in the sense
“F555W-F300W”. The average increase of distortion is ~3%
in F300W and 1% in F814W.
Residuals are
scaled by a factor
of 300.
The max length for
PC is 0.18pix
The max length for
WFs is 0.25 pix
Conclusion
The precision of the geometric distortion solution
for the WFPC2 cameras depends on:
centering technique in measuring positions of
stars with under-sampled PSF;
the independent chip-to-chip solution, rather
than the meta-chip solution, excludes the error
propagation from one chip to another;
the amount of geometric distortion is a function
of wavelength.
Acknowledgements
Gabriel Brammer for help
with PowerPoint.
Anton Koekemoer and Jay
Anderson.
Colin Cox and Richard
Hook with IDCTAB .
Imants Platais for helpful
comments and suggestions
at various stages of this
project.