Band-limited Imaging
with Undersampled
Detectors
Andy Fruchter
TIPS -- 11/16/06
Drizzle: The Pictorial
Alas -- Drizzle is not
Perfect
Relative photometry is very stable -- but
aperture correction depends on Drizzle
parameters
Exact PSF depends not only on parameters
but also sub-pixel phase of input pixels
Noise in output image is correlated
Power Spectrum of WFPC2 PSF
Telescope images are band-limited
But:
Drizzle does not use the band limit
http://www.math.ucdavis.edu/~strohmer/
Tutorial by Tobias Werther (NUHAG)
see http://www.math.ucdavis.edu/~strohmer/
The Idea
Use Drizzle instead of Voronoi approximation
Drizzle provides statistical weighting of input
points
Iteration should effectively remove
convolution with pixfrac and scale
The Result
`
Drizzle
Iteration
Iteration
Iteration
Iteration
Iteration
Iteration
1
2
3
6
12
24
Peak
Peak
Peak
Peak
Peak
Peak
Peak
Error
Error
Error
Error
Error
Error
Error
= 1494
= 519
= 289
= 183
=
97
=
76
=
73
WFPC2 + Noise
The Pros
Method can handle arbitrary dithers,
distortions and missing data (nothing new ;-)
Reconstructs images with extraordinary
fidelity
Provides a powerful new mechanism for
observationally deriving PSFs
Can be performed with a 100 line Pyraf
script.
The Cons
New method requires sufficient number of
images (and appropriate positioning) so that
the image plane is (nearly) Nyquist sampled
Speed of convergence depends on quality of
sub-pixel sampling
Output image is slightly (∼ 10%) noisier than
the Drizzled image
The “Point” of the
Exercise
In the presence of temporal or spatial
stability provides extremely powerful method
of determining point spread function.
JWST should have reasonable temporal
stability
Procedure:
Drizzle onto oversampled image
Fourier transform drizzled image and then
mask higher frequencies
Inverse FT image, add to continuing sum, and
blot back to positions of original input images
Subtract from blotted images and repeat
After iterations complete -- resample to final
?
?
?
Real Data: The UDF
Real Data II