Photon counting performance

In order to operate the electron multiplying CCDs as photon counting devices the gain must be sufficiently high that the output signal produced by one photon can usually be distinguished from the readout noise of the CCD. If the readout noise has an RMS $\sigma_{read}$, and we choose to treat all signals greater than $5\sigma_{read}$ as a detected photo-electron, the fraction $f$ of electrons which are correctly discriminated from the noise will be given by a summation over Equation 4.25:

$$f = \left ( \exp \left ( \frac{1}{g-\frac{1}{2}}\right ) - 1 \right ) \sum_{i=5\sigma}^{\infty} \exp \left ( \frac{-i}{g - \frac{1}{2}} \right )$$ (4.28)

$$= \exp{ \left ( \frac{1-5\sigma}{g-\frac{1}{2}} \right )}$$ (4.29)

where $5\sigma \ge 1e^{-}$ and $g \gg 1$.

Under suitable operating conditions individual photo-electrons can be detected efficiently above the noise - for example with a readout noise of $\sigma=50e^{-}$ and a gain of $g=5000$ the fraction of photo-electrons detected would be $f=0.95$. The effective quantum efficiency of the device would be equal to the quantum efficiency for photo-electron generation in the sensor array multiplied by this factor. If the readout noise was Gaussian distributed, the number of photon events attributable to the readout noise would be $3\times 10^{-7}$ per pixel read out - lower than the sky background count rate in most astronomical applications.

As with other photon counting systems, the performance of these devices is limited at high light levels by coincidence losses. The electron multiplying CCDs do not suffer from many of the problems which plague conventional photon-counting systems, such as a loss of sensitivity after detection of a photon in the vicinity of the photon event (except within the pixel and frame concerned). Basden et al. (2003) have shown that at light levels where photon counting becomes limited by coincidence losses, the signal-to-noise for optical flux measurements can be improved by applying a thresholding scheme to the output of the CCD.