While the coronagraph suppresses the diffracted light from the central star, the scattered light still overwhelms faint, nearby sources. It is possible to subtract most of the remaining halo using an image of another occulted star. PSF subtraction has been successfully used with images taken by other HST cameras, with and without a coronagraph. The quality of the subtraction depends critically on how well the target and reference PSFs match.
As mentioned above, for any pair of target and reference PSF observations, there is likely to be a difference of 5 to 20 milliarcseconds between the positions of the stars. Because the scattered light background is largely insensitive to small errors in star-to-spot alignment (it is produced before the coronagraph), most of it can be subtracted if the two stars are precisely registered and normalized. Due to the numerous sharp, thin streaks that form the scattered light background, subtraction quality is visually sensitive to registration errors as small as 0.03 pixels (0.75 milliarcseconds). To achieve this level of accuracy, the reference PSF may be iteratively shifted and subtracted from the target until an offset is found where the streaks are minimized. This method relies on the judgment of the observer, as any circumstellar material could unexpectedly bias a registration optimization algorithm. A higher-order sampling method, such as cubic convolution interpolation, should be used to shift the reference PSF by subpixel amounts; simpler schemes such as bilinear interpolation degrade the fine PSF structure too much to provide good subtractions.
Normalization errors as small as 1% to 4% between the target and reference stars may also create significant residuals. However, derivation of the normalization factors from direct photometry is often not possible. Bright, unocculted stars will be saturated in medium or broadband filters at the shortest exposure time (0.1 seconds). An indirect method uses the ratio of saturated pixels in unocculted images (the accuracy will improve with greater numbers of saturated pixels). A last-ditch effort would rely on the judgment of the observer to iteratively subtract the PSFs while varying the normalization factor.
In addition to registration offsets, positional differences can alter the diffraction patterns near the spots' edges. The shape and intensity of these rings are very sensitive to the location of the star relative to the spot. They cannot be subtracted by simply adjusting the registration or normalization. These errors are especially frustrating because they increase the diameter of the central region where the data are unreliable. The only solution to this problem is to observe the target and reference PSF star in adjacent orbits without flipping the masks out of the beam between objects.
Color differences between the target and reference PSF can be controlled by choosing an appropriate reference star. As wavelength increases, the speckles that make up the streaks in the halo move away from the center while their intensity decreases ( Figure 6.7). The diffraction rings near the spot edges will expand as well. These effects can be seen in images through wideband filters - a red star will appear to have a slightly larger PSF than a blue one. Thus, an M-type star should be subtracted using a similarly red star - an A-type would result in significant residuals. Even the small color difference between A0 V and B8 V stars, for example, may be enough to introduce bothersome errors ( Figure 6.9).
Figure 6.9: Predicted absolute mean subtraction residual levels for cases where the target and reference stars have color mismatches.
A focus change can also alter the distribution of light in the PSF. The telescope focus changes over time scales of minutes to months. Within an orbit, the separation between the primary and secondary mirrors varies on average by 3 µm (resulting in 1/28 wave rms of defocus @ = 5000 Ċ) - an effect called breathing. This is caused by the occultation of the telescope's field of view by the warm Earth, which typically occurs during half of each 96-minute orbit. This heats HST's interior structure, which expands. After occultation the telescope gradually shrinks. Changes relative to the sun (mostly anti-sun pointings) cause contraction (not expansion) of the telescope, which gradually expands to "normal" size after a few orbits. The main result of these small focus changes is the redistribution of light in the wings ( Figure 6.10).
Plots of the azimuthal median radial profiles after PSF subtraction are shown in Figure 6.8. In these cases, images of Arcturus were subtracted from others of itself taken a day later. The images were registered as previously described. Combined with PSF subtraction, the coronagraph reduces the median background level by 250x to 2500x, depending on the radius and filter. An example of a PSF subtraction is shown in Figure 6.11. The mean of the residuals is not zero. Because of PSF mismatches, one image will typically be slightly brighter than the other over a portion of the field (such as shown in Figure 6.12). The pixel-to-pixel residuals can be more than 10x greater than the median level ( Figure 6.13). Note that these profiles would be worse if there were color differences between the target and reference PSFs.
One way to get around both the color and normalization problems is to take images of the central source at different orientations, and subtract one from the other (roll subtraction). This can be done by either requesting a roll of the telescope about the optical axis (up to 30º total) between orbits or by revisiting the object at a later date when the default orientation of the telescope is different. This technique only works when the nearby object of interest is not azimuthally extended. It is the best method for detecting point source companions or imaging strictly edge-on disks (e.g. Beta Pictoris). This method can also be used to reduce the pixel-to-pixel variations in the subtraction residuals by rotating and co-adding the images taken at different orientations (this works for extended sources if another PSF star is used). Ideally, the subtraction errors will decrease as the square root of the number of orientations.
The large sizes of the occulting spots severely limit how close to the central source one can image. It may be useful to combine coronagraphic imaging with direct observations of the target, allowing the central columns to saturate (additional observations at other rolls would help). PSF subtraction can then be used to remove the diffracted and scattered light.
Figure 6.11: Residual errors from the subtraction of one image of Arcturus from another taken in a different visit (filter = F435W, D = 1.8 arcseconds spot).
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