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

zone. This is remedied by thinning the p-Si layer from 625μm to about 15μm. This is a nonstandard process that decreases the yield of CCD chips and thus increases the costs. Devices are often destroyed during the thinning process. However, the increase in QE, often by a factor of 2–3, is well worth the risk.

      One disadvantage of thin devices is that the CCD is now more transparent to near-infrared photons, making the red response of the CCD poorer. The gain in the blue, however, more than offsets the loss at redder wavelengths. Virtually all modern CCDs in use at astronomical observatories are thin, front-side-illuminated devices.

      Modern CCDs can be optimized for better performance in either the red or blue wavelength regions. Figure 2.15 shows the QE curves for red- and blue-optimized CCDs from MIT Lincoln Labs. The red-optimized CCD reaches a QE of nearly 100% in the wavelength range 7000–8000 Å. However, the response below 4000 Å is quite low at approximately 20%. The blue-optimized CCD now has a much improved QE of approximately 90%, but with only a slight loss at red wavelengths. The performance of all CCD detectors dies off at approximately 10,000 Å, due to the fact that photons no longer have sufficient energy to dislodge electrons from the silicon atoms.

      Figure 2.15. The quantum efficiency versus wavelength for an MIT/LL CCD. Such curves are typical for modern CCD detectors. (Data courtesy of ESO.)

2.3.3 Bias Level

      The bias level of a CCD is an electronic offset that is artificially applied to the data at the time the CCD is read out. Its purpose is to ensure that the analog-to-digital converter (ADC) always receives a positive signal. This bias level must be removed from the data values if these are to reflect the true number of counts (photons) recorded by each pixel.

      All astronomical CCD detectors have a so-called overscan region of the chip that is masked so that it receives no light during an exposure (Figure 2.13). The overscan region can be easily found by taking an exposure of a lamp source and plotting along a row or column to see where the intensity sharply drops (seen as a step function). Typical bias levels are a few hundred to about a thousand ADUs.

      The first step of any CCD reduction process is to remove the bias level. The bias frame is simply an observation with the CCD shutter closed (dark frame) with a zero exposure time. The bias levels can be removed using several methods:

       Measure the count level in the overscan region and subtract this value from each frame. The disadvantage of this method is that it will not remove any structure in the bias level if some are present across the CCD.

       Take a series of several (>10) frames and compute a “master bias,” consisting of a frame having the average (or better yet, the median) value for each pixel. This master bias is then subtracted from each science frame. The disadvantage is that this will introduce some noise into the data frames.

       Take a single bias frame, or the median of several, and fit a surface to it using a low-order, two-dimensional polynomial. Subtracting this fit will not introduce noise into your data frame. This can be done on the master bias and is the preferred method.

      Most CCDs in use today are relatively stable so that one can take the bias frames at the beginning or end of the night. The bias level is the first indication of problems with the CCD, so it is a good idea to monitor the stability of the CCD by checking it regularly. This is easily done by looking at the counts in the overscan region. The author once had the experience where the bias level was seen to change throughout the night, but this only became evident during the reduction process after the observing run. Fortunately, the overscan region provided a “real time” measurement of the bias level. We will see in Chapter 12 that a significant change in the bias level will be an early indication that something is amiss in your detector.

2.3.4 Gain

      For photon statistics, the uncertainty in the detected photons, N_p, is σ=Np. The S/N is simply S/N=Np/σ=NpNp=Np. So, for astronomical observations, the important quantity is the number of detected photons. However, CCD pixel values are ADUs, which are related to the actual number of photons through the gain factor (G), Np=GNp. When using a CCD for the first time, it is wise to check the gain factor and not merely rely on documentation or information in the headers of the observations as these may be outdated. The CCD gain can be easily measured using either of two methods.

      Method 1

      For photon statistics, σ2=Np=GNp. A series of exposures of a white-light source at increasing intensity levels (exposure times) is made, the bias level from each frame is subtracted, and the standard deviation on a region of the detector is calculated. The slope of the σ2 versus the intensity (ADU) level (after subtracting the bias level) yields the gain (Figure 2.16).

      Figure 2.16. The standard deviation of ADU values from a CCD as a function of the intensity (ADU) level. The slope indicates a CCD gain of 0.56 electrons per ADU.

      Method 2

      The gain can also be calculated from just a couple of flat and dark frames:

       Two frames are taken, f1 and f2, at reasonably high intensity levels (∼10,000) as well as two bias frames, b1 and b2 (zero exposure times).

       Difference frames are produced from the bias and flats: b12=b1−b2 and f12=f1−f2. The use of differences removes any underlying structure that may be present.

       One then calculates the mean values of the bias frames, mb1 and mb2, the flat frames, mf1 and mf2, as well as the standard deviations of the difference frames, σf12 and σb12.

       The gain is given byG=mf1+mf2−mb1−mb2σf122−σb122.(2.21)

2.3.5 Readout Noise and Dark Current

      The readout noise results from the conversion of the electrons in each pixel to a voltage on the on-chip amplifier. The readout is the ultimate noise limit of a CCD. Figure 2.17 shows the S/N that is achieved as a function of the detected photons and readout noise. With no readout noise, this follows photon statistics, with S/N merely the square root of the number of detected photons. However, with nonzero readout noise, this deviates from the ideal expression for low signal levels. For a rather high readout noise of 10 e⁻¹, the performance of the CCD is seriously affected and one can never achieve an S/N below about 3.

      Figure 2.17. The signal-to-noise ratio (S/N) as a function of the number of detected photons for different levels of readout noise (0, 1, 3, and 10 e⁻¹). The black line is for the ideal case of photon noise (no readout noise).

      When CCDs first came into regular use by astronomers in the 1980–1990s, CCDs with readout noise of 10 e⁻¹ were common. Modern CCDs now have a readout noise of typically 2–3 e⁻¹. Most precision RV measurements are taken at S/N > 10, so the readout noise is never an issue influencing the uncertainty in the RV measurement.

      The readout noise of a CCD can easily be measured by taking these steps:

       Take a large number (≈10) of bias frames.

       Create a master bias by taking the median of the bias frames.

       Subtract the master bias from each bias frame.

       Take the standard deviation of these images and multiply by the gain because you want the readout noise in electrons and not ADUs. This value is your readout noise.

2.3.6