Astronomy Principles and Practice Fourth Edition.pdf

Charge coupled devices 303
target frames. Occasionally, a cosmic ray passes through the chip to produce a glitch in the image.
According to the type of study, it is sometimes possible to clean the data of the defect.
It may be noted that the final outputs of the signal levels are expressed in ‘analogue-to-digital’
units or ADUs. In assessing the noise levels of any observational exercise, it is important to know
the relationship between the number of electrons (related to incident photons) and the ADU number
and this can be done by simple calibration experiments. The gradation of intensities or ‘grey levels’
depends on the number of bits used in the digitization process within the chip. For professional CCDs,
the number of bits used is normally 2 16 so providing a dynamic range of 2 16 or 65 536 grey levels.
With such a discrimination in the recording of intensity, the potential photometric accuracy is 1 part in
2 16 per pixel or 1 part in 65 536 or ±0·0015%. Some of the CCDs used by amateurs may provide only
a2 8 bit conversion, so providing a lower potential photometric accuracy of 1 part in 256 or ±0·39%.
Approximate values for the number of photoelectrons corresponding to each ADU can be obtained
from the manufacturer’s specification of the pixel full-well capacity and the number of bits used in the
analogue-to-digital conversion. If, for example, the full-well capacity ∼5 × 10 5 e − and the chip uses
2 16 bits, each ADU corresponds to
5 × 10 5
2 16 ≈ 8 electrons.
With this figure, the accuracy of any single pixel measurement based on the ADU value and
photon-counting statistics can be easily assessed. Quite generally, brightness assessments involve
the combination of signals from several pixels, so improving the overall signal-to-noise ratio of any
measurement.
One of the considerable advantages of the two-dimensional detector is its ability to allow for the
night-sky background component, whether it be a direct image of a star field or a record of the spectrum
of a source. Those pixels not forming the target area of the main measurements may be taken to provide
a reference for the general illumination of the light from the night sky (for example, scattering from
distant urban lighting, atmospheric airglow spectral lines or the integrated extra galactic background).
Using an extrapolation from the pixels surrounding the target areas, the contribution of the night-sky
background may be subtracted.
Suppose that over an exposure a star provides N ∗ photons spread over p pixels and the background
sky signal provides N sky photons to the same pixels, the signal-to-noise ratio of the stellar brightness
measurement is given by
N ∗
S/N = √ .
N∗ + N sky
For bright stars, the contribution of N sky to the S/N calculation can usually be neglected.
For the exploration of very faint stars, in addition to the noise from the sky background subtraction
process, noise associated with dark-signal subtraction and readout noise need to be included in S/N
determinations. For an exposure time of t with a background signal of N d s −1 per pixel and with a
readout noise of ±σ per pixel, the S/N ratio obtained from p pixels may be determined from
S/N =
N ∗
√N ∗ + N sky + pN d t + pσ 2 . (18.4)
Unlike the photographic plate with its random scatter of small detectors with positions which
are different for each used plate, the CCD has a regular structure of pixels and, providing that the
registration can be maintained, the rows and columns of the matrix can be used to provide a scale
for repeated positional measurements. This has advantages in such areas as the measurement of the
separation of visual binary stars or in radial velocity measurements (see section 15.8.2).
The main advantages of the CCD are the high quantum efficiency of the photo-detection and the
linearity between the output signals and the illumination of the pixels. The device also only requires