Systematic Error Correction

The last decade of planet hunting has been very prosperous. However, even today, it is still in its infancy. The Kepler Space Telescope is currently the only telescope that is dedicated to soley hunting exoplanets, and scientists still have to rely heavily on telescopes which were simply not made with this task in mind. As a result, modifications are constantly being made to how these telescopes are being used and how to process and interpret their data.

It is a common misconception that data gathered from telescopes is clean and organized, and that once a telescope is pointed at a given target star, it is a relatively straightforward process to determine whether this star has planets, and what the properties of those planets are. This section will give some insight as to what goes on 'behind the scenes' of planet hunting.

Case Study: Spitzer's Systematic Errors

The Spitzer Telescope is one the most effective telescopes for hunting exoplanets besides Kepler. However, its original purpose was to detect infrared radiation and study (for example) distant galaxies and the early Universe. These purposes are quite far from the purpose of hunting exoplanets. This case study will detail some of the systematic errors particular to Spitzer, and how astronomers overcome these errors.

Interpixel Variation

The Spitzer InfraRed Array Camera (IRAC) is one of three on-board focal plane instruments. It has four channels composed of two short wavelength InSb detector arrays and two longer wavelength Si:As detectors. Each of these channels is affected by small variations in interpixel gain or sensitivity. That is, when staring at a flat, featureless field, small variations in the detector pixels will produce an image which is not flat at all. Some of this error is introduced through random noise, but some is also produced by systematic errors in the detectors themselves. The image below demonstrates this error when the Spitzer IRAC is pointed at a flat (featureless) target.

http://irsa.ipac.caltech.edu/data/SPITZER/docs/irac/iracinstrumenthandbook/58/

In the above image, the top two outputs are for channels one and two, while the bottom outputs are for channels three and four. Although the outputs and the errors vary among detectors, we can point out some key features. First, notice the dark spot on channels two and four, about half way up on the left side. This error is due to contamination on the shared mirror used by these detectors. Second, notice the long thin 'checkerboard' pattern seen prominently at the top of channel 3. This error is a result of unwanted diffuse stray light affecting the detectors. Channels 1, 2 and 3 are also affected by stray light, though the errors are not as easily seen.

The result of this error is that it can be very hard to detect small, faint objects in such a noisy background. To correct this error, IRAC operators use these 'error' images as shown above (known as 'skyflats') to generate a pixel-to-pixel gain map, known as a 'flatfield'. The flatfield is generated by adjusting the gain of each individual pixel in the detectors to account for the error generated in the above image, so that the resulting image is as flat and featureless as the target. Once this is done, small, faint objects can be detected with much greater accuracy than before.

Intrapixel Phase Effect

http://arxiv.org/abs/1005.4037

The previous description of interpixel variation is apparent when viewing the array of pixels on a given detector as a group. However, each pixel may itself suffer from another serious error known as the intrapixel phase effect. Since each individual pixel is a surface, sensitivity variations across the surface of the pixel can add noise to the output. It is generally assumed that pixel sensitivity is greatest at the center, and trails off towards the edges. Fortunately, this error can be modelled and corrected. Here, the left image shows the intrapixel phase effect occurring during an exoplanet transit, while the right image shows the cleaned version with the error removed.

Periodic Drift

http://authors.library.caltech.edu/24032/1/MORapj06.pdf

Another type of error in Spitzer becomes apparent only during long term exposures, for example during photometric monitoring. In this case, it can be seen in the image (right) that the detector sensitivity seems to oscillate periodically every 3000 seconds. Though the source of this periodic drift has not been confirmed, most agree that it is due to the periodic cycling of onboard heaters, since pixel sensitivity is affected by temperature, and these heaters also cycle every 3000 seconds matching the error.

http://arxiv.org/abs/1005.4037

Intrapixel Ramping (Charge Buildup)

Intrapixel ramping is observed with individual pixels on a detector, and is characterized by an increase in sensitivity with time. The effect is that the measured signal will appear to 'ramp' and eventually stabilize, even the though the target brightness is roughly constant. This ramp is apparent in the top image to right. In the bottom image, a portion of the top image has been expanded in time to show that there was in fact a transit in the top image that is almost impossible to detect due to the ramp.

The error can be modelled as a charge buildup on the pixels as photons continue to strike the detector. The charge buildup increases quickly at first, and then stabilizes. The error can then be removed from the data using this charge buildup model; or, the detector can simply be 'preheated' by pointing at an object of similar brightness until the ramp has stabilized. It should be mentioned that a negative ramping error can also be observed, which doesn't fit well with the charge buildup model. The ramping is a result of very complex physics going on in the detectors, and it is possible that the true cause of the error may never be known. However, although the ultimate cause of the error remains a mystery, the error can still be removed using an appropriate ramp model.

The image below shows errors in channels 1-4 for a given observation. Channel 1 shows the intrapixed phase effect, channel 2 has no significant error, while channels 3 and 4 illustrate negative and positive ramping errors, respectively.

http://arxiv.org/abs/1005.4037

Atmospheric Interference

The most significant errors for ground based telescopes are due to variations in the Earth's atmosphere. Light from a target in space approaches the top of our atmosphere as a flat wavefront. As the waves interact with the different layers of our atmosphere, they may refract through volumes of different gasses with different temperatures and motions. This variation in the wavefront when it reaches our groundbased detectors causes distoritions which negatively affect the image quality. This variability in the atmosphere is often referred to as 'seeing', and can be measured, for example, by the Danjon Scale shown below. Although most ground-based telescopes do have methods of correcting these systematic errors, the process is difficult and this is ultimately the reason for placing telescopes in space (along with lower light pollution, and some other secondary benefits).

http://lot.astro.utoronto.ca/whyao_new.html
http://certificate.ulo.ucl.ac.uk/diffraction_effects.html