The technique used for object detection follows that outlined in Ginski et al. (2012), in which the image is convolved with a 2D Gaussian kernel and then subtracted from the original image. This method approximates the ‘difference of Gaussians’ technique used for feature enhancement and detection in computer vision (e.g. Gonzalez & Woods 2002), in which a source image is convolved with two Gaussian kernels of differing FWHM, and the results of one convolution subtracted from the other. For the case of astronomical images, the observed image corresponds to a series of unresolved, point source stars, which have been convolved with the (approximately Gaussian) PSF. The convolution of a Gaussian-convolved image with a second Gaussian kernel is equivalent to a single Gaussian convolution of the original point sources. The standard deviation of the convolving Gaussian was set at 4.0 pixels, corresponding to an FWHM of 11.7 pixels or an 1.0400on the sky, and hence approximately twice the FWHM of the observed
images.
The difference of Gaussians image was then analysed to determine the averaged radial profile of the image around the target star. Under the assumption that the stellar PSF is circularly symmetric, any deviation from this symmetry would indicate the presence of a separate object. This has the inherent advantage of revealing stars that are not fully resolved, as compared to a simple peak-finding algorithm which would struggle to find close companions against the ‘background’ of the bright target star. The position of the target star was typically determined as the brightest pixel within the central 50×50 pixels of the image, although separate coordinates or window sizes were specified for cases where the target star was not the brightest object or significantly offset from the image centre. The radial profile was then determined in steps of 0.25 pixels, including the counts from all pixels with radii within 0.5px of the current step radius. The sub-pixel size for step radius was chosen to avoid artefacts near the target star caused by the background varying significantly across wider steps, whilst the inclusion of pixels more than a single ‘step’ away was motivated by the need to include a sufficiently large number of pixels, especially at small radii. A sigma
clipping routine was used to remove pixels with counts more than 3σ from the mean in each bin (typically those pixels representing stars), after which the mean and standard deviation of the remaining pixel counts were determined. Any pixel located within the 0.25px step (including those rejected by sigma clipping) with counts more than 1.7σ from the bin mean in each bin was then flagged as a ‘detection’. The 1.7σ cutoff was found to provide the best compromise between false positive detections (typically due to PSF asymmetries) and the loss in completeness for faint objects.
The detection process was repeated for seven different lucky imaging selection criteria from 1% to 90%, as is possible with the reduced TCI data. A master detection list was created by counting the number of times a given pixel was flagged in these seven iterations and retaining only those pixels that were flagged two or more times. Adjacent pixels were grouped together into a single object detection, the location of which was set as the mean position of the grouped pixels. These detections were subsequently manually validated, which was found to be necessary in order to remove false positive detections, often caused by asymmetries in the target star PSF. This step additionally allowed the user to manually correct of close pairs of companion stars that were grouped into a single detection, as well as identification of other unusual companions or image features – for example, a number of companion stars were visually identified as galaxies or nebulae. To facilitate the manual inspection an interactive program was developed, displaying the detections on top the observed data. The user is able to view different images of the same target, including the simultaneously obtained Vis data where available, in addition to changing the lucky imaging selection fraction and the colour scale. It is possible for the user to inspect the difference of Gaussians image, or instead to see the number of separate detections registered for each pixel. The automated detections can be confirmed as is, or instead the user may specify new detections (e.g. splitting merged detections of two stars), with the possibility of adding notes to each detection.
Figure 3.13: Optical ghosts in TCI images. This TCI Vis camera image of WASP-131 shows two clear features other than WASP-131, located to the left and right of the target, indicated with black lines. The ring-shaped source on the right is seen with both the Red camera and Vis camera, but is brighter relative to the target stars in Vis camera images. It resembles the defocused PSF of the TCI instrument, suggestive of it being caused by reflections within the optical system with a slightly different path length to the main starlight. The point-like source on the left is often bright in Vis camera data, but often undetectable in Red camera images.
2015-04-29 2015-05-15
Figure 3.14: False companions caused by atmospheric dispersion. Both images show TCI Red camera observations the WASP-85AB system, a wide binary with the two components aligned nearly vertically on these images. Marked on each image are the false companions caused by the dichroic leak at 410nm and the effects of atmospheric dispersion, with both of the real stars having an associated ‘companion’. The red line in each image indicates the direction of dispersion, which varies depending on telescope azimuth, with the lines drawn so as to pass through the centre of WASP-85A’s PSF. Evans et al., A&A, 610, A20, 2018, reproduced with permission c ESO