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## General Signal and Noise considerations

Probably the most important criterion in choosing a detector is the achievement of the required signal to noise ratio in the shortest integration time. The first step is therefore to define what signal to noise ratio is required for the observation to be successful. Having done that, we need to consider how to obtain this signal to noise ratio most efficiently.

The noise level for a typical astronomical observation will consist of three components. The first component is signal independent noise arising from the detector itself, readout noise in the case of a CCD and dark counts in the IPCS. Secondly, we have shot noise in the signal from the object being observed. This follows a Poisson distribution, so its variance is equal to the signal level. Finally, we also have shot noise in any background signal (particularly the sky background). Adding the noise terms in quadrature, the signal to noise ratio (SNR) is given by:

```
E 		= 		Responsive quantum efficiency of the detector
*
= 		 Number of photons per resolution element per second incident on detector
*
from object
*
= 		 Number of photons per resolution element per second incident on detector
*
from background (e.g. sky)
*
t 		= 		 Integration time
*
= 		Detector noise (readout noise, dark current)

```

The signal to noise ratio obtained therefore depends on both the efficiency of the detector and the level of detector noise. The way to choose the optimum detector is therefore to choose the combination of efficiency and detector noise which maximises the signal to noise ratio. The two detector types are complementary in this respect, since the IPCS has the lowest level of detector noise but is also the least efficient, the (thinned) CCDs are the most efficient detector but also have a finite noise level. We now quantify these statements more precisely.

Table gives estimates of the efficiencies of some representative detectors at a number of wavelengths, using data taken from Sections and .

Table: Detector efficiencies

The detector noise of a CCD is dominated by the readout noise. Note however that the number we really need is the readout noise per resolution element, not the readout noise per pixel. The readout noise per resolution element depends on two factors:

• How many CCD pixels are there in a resolution element ? In slit spectroscopy of a point object, the emission typically extends for several pixels along the slit, and we will need to bin these up in order to obtain a spectrum. Similarly, for an experiment to detect a well-resolved emission line, it may be possible to bin up several pixels in the dispersion direction into one resolution element. Note that according to sampling theory, a resolution element must always be at least two pixels in each direction. In order to obtain the effective readout noise per resolution element, the readout noise per pixel must be multiplied by the square root of the number of pixels in a resolution element.

• How many separate CCD exposures are being co-added ? The target object may be so faint that a very long integration time is necessary to obtain the desired signal level. The graphs in Section can be used to estimate the total integration time required for a given telescope and instrument. If the total integration time is greater than about 1 hour, it will be necessary to split the observation into a number of shorter exposures. Each CCD exposure adds in more readout noise, resulting in the effective detector noise being equal to the readout noise per exposure times the square root of the number of exposures.

The detector noise of the IPCS comes from the dark count, which is so small that we can neglect it at all practical light levels.

Next: A comparison between Up: Which detector ? Previous: Which detector ?

Tue Aug 15 16:42:46 BST 1995