The Doppler Method for the Detection of Exoplanets - Professor Artie Hatzes

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      The charge transfer efficiency (CTE) is a measure of the fraction of the charge that is lost when moving from pixel to pixel. A poor CTE can affect the shapes of your instrumental profile (see Chapter 6 for a discussion on the instrumental profile). Early CCD devices often had poor CTE, but a modern CCD device has a CTE that is typically about 99.9997%, so for the most part this should not be a concern.

      The amount of charge lost depends on the number of times the packet has been transferred, and this of course depends on the initial location of the charge on the CCD array. The numbers in the corners of the CCD shown in Figure 2.13 show how many photons are actually recorded for 1000 photons striking the CCD. Charge packets near the readout amplifier suffer little loss, but a charge packet in the upper right will suffer a loss of 2.5% because it undergoes the maximum number of transfers: 2048 times along columns followed by another 2048 times along the final row (for a 2048 × 2048 pixel array).

      The CTE may become important as astronomers use ever larger CCD detectors. For example, if you have a 10,000 × 10,000 CCD a charge packet at the left corner would have lost ∼6% of its charge. Although these are relatively low losses, especially for high signal-to-noise data, this can become more important for low light level observations, or if one wants to push the RV precision down to the cm s−1 precision. In Chapter 12, we will discuss further possible sources of error due to CTE.

      An important characteristic of a CCD is its linearity in response to the incident light. The observed count should be linearly proportional to the intensity of the light—expose for twice as long and you should get detect twice as many photons.

      Most modern CCD detectors generally have excellent linearity (Figure 2.18). The linearity of a CCD is trivial to check. Observe a white-light source at different exposure levels and plot the total counts (minus the bias level!) as a function of exposure time. If one sees a deviation from a linear behavior (red dashed line in Figure 2.18), then one should avoid exposure times which produce counts above this level. For Figure 2.18 where we have marked a hypothetical nonlinearity with a red line, this is at approximately 170,000 ADUs.

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      Figure 2.18. The CCD linearity as indicated by the number of detected photons as a function of the exposure time. The red dashed line shown would indicate a strong non-linearity at high count rates.

      CCDs have slight variations in the QE from pixel to pixel. The recorded CCD frame may also have ghost images, reflections, or other artifacts from the spectrograph. If these variations are not properly removed, this will affect the quality of your spectrum and ultimately, your RV precision.

      The process of “flat fielding” consists of taking an observation (spectrum or image) of a white-light source commonly referred to as the “flat lamp.” Divide your observation with your flat-field exposure. Flat-field errors can arise when the variations are not taken out completely. This can be the case because flat lamps are usually inserted in the light path just before the entrance slit of the spectrograph and thus do not follow the same optical path as your observation of the star. For this reason, it is a common practice to take a “dome flat.” The telescope is pointed to a white screen mounted on the interior of the dome, which is then illuminated by the white-light source. The light from the flat field thus follows, more or less, the same optical path through the telescope as the starlight.

      Figure 2.19 shows an example of the flat-fielding process as applied to imaging observations where you can better see the artifacts and their removal. The top-left image is a raw frame taken with the Schmidt Camera of the Tautenburg 2 m telescope. The top-right image shows an observation of the flat lamp, where one can see the structure of the CCD, as well as an image of the telescope pupil caused by reflections. The lower image shows the observed image after dividing by the flat lamp observation. Most of the artifacts and intensity variations have been removed by the division.

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      Figure 2.19. The flat-fielding process for CCD reductions. (Left, top) A raw image taken with a CCD detector. (Right, top) An image taken of a white-light source (flat field) that shows the CCD structure and optical artifacts. (Bottom) The original image after dividing by the flat field.

      The voltage potential well in each pixel can only hold a fixed number of electrons. Above this value, called the “full-well capacity,” the pixels have saturated, and additional electrons then spill over into adjacent pixels along columns in an effect called “blooming” (Figure 2.20). The saturated pixels appear as a hot column with values of the full well (Figure 2.21).

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      Figure 2.20. Blooming in CCD. When the amount of charge exceeds the potential well of the pixel, it starts to spill over into the direction of readout, i.e., columns.

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      Figure 2.21. A CCD image of the Pelican Nebula (north is to the right). The vertical streaks are due to blooming of saturated pixels. Image credit: Thüringer Landessternwarte Tautenburg.

      Modern CCDs have a full-well capacity of ≈100,000–200,000 e−1. The full-well capacity defines the maximum S/N you can achieve in a single exposure. For example, a full well of 100,000 e−1 means you cannot achieve an S/N higher than about 316 in a single exposure.

      Antiblooming CCDs can eliminate the effects of saturation. This is done with additional gates that bleed off the overflow due to saturation. The disadvantage of this is that these “bleed off” gates cover about 30% of the pixel. This results in reduced sensitivity, smaller well depth, and lower resolution, due to the increased size of gaps between pixels.

      Fringing is another problem with CCDs that is caused by the small thickness of the CCD. It occurs because of the interference between the incident light and the light that is internally reflected at the interfaces of the CCD. Figure 2.22 shows a spectrum of a white-light source taken with an echelle spectrograph (see below). Red wavelengths are at the lower part of the figure where one can clearly see the fringe pattern. This pattern is not present in the orders at the top, which are at blue wavelengths.

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      Figure 2.22. Fringing in a CCD. The exposure is of a white-light source taken with an echelle spectrograph. Blue orders (≈5000 Å) are at the top, and red orders (≈7000 Å) are at the bottom. Fringing becomes more pronounced at longer wavelengths.

      CCD fringing is mostly a problem at wavelengths longer than about 6500 Å. For RV measurements made with the iodine technique (Chapter 6), this is generally not a concern because these cover the wavelength range 5000–6000 Å. However, the simultaneous Th–Ar method (Chapter 4) can be extended to longer wavelengths where improper fringe removal may be an issue.

      In principle, the pixel-to-pixel variations of the CCD and the fringe pattern should be removed by the flat-field process, but again, this may not be perfect, and this can introduce RV errors.

      Suppose you have recorded an image with a CCD that had high intensity values (in particular saturated pixels). If you take a subsequent dark exposure, you may find that instead of being completely dark, the frame has a memory, or residual image, of the previous exposure.

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