Convolving data models with PSF models
[Tiny Tim Page]

Convolving Data Models with PSF Models

Computer models of objects (galaxies, circumstellar disks, etc.) are often generated to compare with observed images. A crucial part of the process is the inclusion of instrumental artifacts which could significantly alter the model. For comparisons with ground-based images, it is usually necessary to include seeing effects by convolving the model with an estimated seeing profile function.

When comparing models to WFPC2 images, it is often forgotten that the instrumental PSF can have a very significant effect. The core of the PSF has a finite width, and the wings contain a considerable amount of light. Also, the undersampling of the WFPC2 cameras makes the model image very sensitive to subpixel alignment.

Here is an example of work on modelling the protostellar disk of HH30. We (the WFPC2 IDT) observed it on the WFPC2 Wide Field Camera, which has a resolution of 0.1 arcsec/pixel. The disk itself is about 35 pixels across and is separated in two by a dark band of obscuring dust which is only a couple of pixels thick. The small size of the object meant that both sampling and PSF effects were important.

The observed image is shown in the left panel of Figure 1, with a seventh-root stretch. The intensity across the disk falls off rapidly, with large changes across the width of a pixel. The three-dimensional models of the dust distribution were computed at a finer resolution than the detector sampling. This allowed for accurate alignment of the model with the observed image.

Before rebinning the disk model to the detector's sampling, it was convolved with a Tiny Tim model PSF, which itself was subsampled by the same amount. This spread out the light from the disk, simulating the effects of the telescope's optics. Some light ended up in the dark lane, while the brighter peaks were reduced. The resulting subsampled, PSF-convolved model was shifted and then rebinned to detector-sized pixels. The final step was to convolve the result with the pixel scattering kernel (which is not applied to subsampled PSFs by Tiny Tim).

The cross-sectional plot in Figure 2 demonstrates the necessity of convolving the model with the PSF.

Tiny Tim model PSFs have advantages over observed ones in this case because they can be subsampled and are noiseless.

Figure 1. (Left) WFPC2 WFC F814W image of HH30 (0.1 arcsec/pixel); (Middle) Model of HH30 disk; (Right) Model of HH30 disk convolved with a Tiny Tim model PSF.

Figure 2. Vertical cross-section through the disk axis. The observed data (yellow) has an anomalous "bar" of material towards the lower edge of the disk, which causes the bulge on the left side of the graph.

Another instance where PSF effects were important in modelling an object was Supernova 1987a. An initial look at the outer rings might lead one to think that they are caused by limb brightening of an hourglass-shaped shell surrounding the supernova. Models of such shells were computed, but it was nearly impossible to reproduce the high contrast between the rings and the ring interiors. Some papers were published which tried to show that such models might be able to do it, but they left out an important detail. The PSF will redistribute light from the rings into the interior, but that light is not seen - it is in the noise. This means that the ring-to-interior contrast is even greater than that implied by the raw image. If the authors of those papers had convolved their models with PSFs, they would have found that out (plus they were comparing the models to GIF images, which is a BAD IDEA).

Web page and image processing by John Krist