A short introduction to
Angular Differential Imaging
Max Planck Institute for Astronomy, Heidelberg, Germany
Angular differential imaging (ADI) is a powerful method for the detection of faint point-sources such as extrasolar planets in close separation from their stars. The technique yields a contrast performance matching that achieved with spectral differential imaging (SDI), but is simpler to perform, does not require any specialized optics, and can be applied to a much wider range of target objects (no spectral features required).
One of the most exciting challenges in present-day astronomy is to take images of planets outside of our Solar System (orbiting other stars). The task can be compared to seeing the glow of a firefly circling a 300-Watt floodlight from a distance of several kilometers. First of all, the small apparent separation between the lightsources requires the resolving power of the largest currently available telescopes (8 – 10 meters in diameter) as well as state-of-the-art adaptive optics to counteract the blurring effect of the Earth's atmosphere. The VLT/NACO and Subaru/HiCIAO facilities, for instance, offer such capabilities.
Even with the best available hardware and clear, an image of the target star will look like this:
Figure 1: A raw image of the star GJ 758. The color scale from black over red to white simply represents brightness, not actual color (the image is taken in the infrared at a wavelength 1.6 micrometers, outside of the range visible to the human eye). The black spots in the center are areas that were too bright for the camera to measure (in technical terms, the these detector pixels are saturated). The white beams are diffraction artifacts caused by the so-called "spider", i.e. the support structure that fixes the telescope's secondary mirror in front of the primary mirror. (Image: MPIA/Subaru)
There are two planet candidates around this star, but there is no way to tell from this image. The halo of diffracted and scattered starlight floods the camera and utterly overwhelms the planet signal. The starlight must be subtracted out of the image as well as possible to reveal the planets. But how to distinguish the real planets from the starlight?
One cause of the stray light halo around the target star is the fact that the lightwaves from the astronomical object must pass through Earth's turbulent atmosphere before arriving at the telescope, which distorts and buckles the planar wavefronts. Due to high wind speeds, these wavefront errors (aberrations) change on a time scale of tens of milliseconds. Thus, the resulting stray light pattern will average itself out into a smooth symmetric halo over the course of the observation. Adaptive optics can reduce but not eliminate this background light contribution.
A more problematic of aberrations are the imperfections of the telescope mirrors and the mechanical support structure holding the secondary mirror in place (the spider). Unlike atmospheric turbulence, these factors evolve very slowly during the observation due to shifting telescope temperature, weather conditions, moving optics (e.g. the Nasmyth mirror), sagging of the telescope structure under its weight etc., and therefore result in a quasi-static stray light halo strewn with planet-like but spurious speckles.
Figure 2: Schematic of the main components of a large telescope. (Image: C. Thalmann.)
The night sky can be thought of as an infinitely large sphere surrounding Earth onto which the stars are projected. As Earth spins around its axis, the celestial sphere appears to rotate, completing a full cycle every 24 hours. During an astronomical observation, the telescope must therefore track the target across the sky. For this purpose, it is mounted on a mobile platform similar to a gun turret. To point the telescope at a given star, it is tilted vertically to match the target's elevation angle between the horizon and zenith, as well as swiveled horizontally to a match its azimuth angle measured along the horizon. Due to this construction, the telescope pupil (where the spider is located) always remains upright, oriented towards zenith. On the other hand, the observed piece of sky (the field) is fixed to celestial sphere, remaining oriented towards the celestial poles.
Figure 3: A sketch illustrating field rotation, from the viewpoint of an observer standing next to the telescope, looking South. The black square with stars stands for the sky field that the telescope is tracking across the sky, whereas the black "spiders" show the orientation of the telescope pupil. (Image: C. Thalmann)
The angle between a celestial pole, the target, and zenith is called the parallactic angle. It changes monotonously during a night, though the rate of change varies. The field rotation is fastest when the target passes the highest point of its trajectory, i.e. when it transits the local meridian. The rate of field rotation around transit furthermore depends on the declination of the target. It is greatest for targets transiting close to zenith, i.e. whose declination is close to the geographic latitude of the telescope.
Angular differential imaging exploits the fact that the field and the pupil rotate with respect to each other during the observation to distinguish the star's halo from real on-sky sources.
In conventional astronomical observations, the field orientation is kept constant on the camera. This allows the different exposures in a series to be added together conveniently. In ADI observations, the orientation of the pupil is kept constant instead. Since the major sources of quasi-static speckles (spider, telescope mirrors) are locked to the pupil orientation, the resulting speckle halo around the target star remains as stable as possible. The field, on the other hand, will rotate around the target star over the course of the observation.
Figure 4 illustrates how the series of images taken in ADI-mode (Ai) are then processed. First the pixel-wise median (B) of the image stack is calculated. All structures that appear consistent throughout the observation show up in the median, whereas a planet will move along an arc and leave no significant trace in the median. The median is then subtracted from each raw frame, yielding a series of new frames Ci = Ai – B containing only the planet, photon shot noise, and the uncorrelated component of the quasi-static speckle noise. Now the frames can be derotated into the coordinate system of the sky field (Di) and median-combined into a final output image (E). The planet signals from each frame will add up, whereas the remaining spurious background structures will further average down.
Figure 4: Schematic representation of the ADI image combination technique as described in the text. In the series of raw frames taken in pupil-stabilized observing mode (Ai), the quasi-static speckle halo sketched in gray and the rotating planet signal highlighted in red. (Image: C. Thalmann)
Figure 5 illustrates the result of the angular differential imaging technique applied to the observation from which Figure 1 is taken. While the method cannot remove the star's speckle halo entirely (because it is not entirely static), it is greatly attenuated, allowing the detection of high-contrast sources near the star. The two faint objects B and C are detected at short separations (1.9" and 1.2", respectively) from the half a million times brighter star GJ 758 (published in Thalmann et al., 2009, ApJ Letters).
Figure 5 : Final output image from the ADI observations of GJ 758, revealing previously unknown high-contrast objects nearby. B hast been identified as a bound substellar companion, possibly a planet, whereas the status of C is currently still unconfirmed. The scale bars provide a size comparison with members of our Solar System. (Image: MPIA/Subaru, Thalmann et al. 2009 ApJ Letters)
ADI observations should be taken when the target is at its highest in the sky, where the field rotation is at its fastest.
The previous section describes the simplest way to combine images taken with the ADI observing mode. A more sophisticated way to perform the data combination is known as LOCI (Locally Optimized Combination of Images). The algorithm resembles the basic ADI technique, but instead of subtracting one median background from all images in the series, an optimized background is constructed for each individual image on the basis of the other images. Furthermore, the images are divided into concentric ring segments, and the optimization is calculated for each segment separately. This allows for better exploitation of the closely correlated speckle patterns in images taken shortly one after the other, and yields a greater contrast improvement than basic ADI does. The algorithm is explained in detail in Lafrenière et al. 2007, ApJ. The ADI image in Figure 5 has been prepared using LOCI.
Angular differential imaging: Marois et al. 2006, ApJ
GJ 758 and companions: Thalmann et al. 2009, ApJ Letters