Question

Multichannel detectors like diode arrays and CCDs provide a signal to noise ratio (SNR) advantage by the ability to measure many wavelengths simultaneously—a multiplex advantage. Consider the SNR for a photomultiplier tube (PMT), a diode array (DA), and a CCD. Assume the readout noise (RN) associated with these devices is 0 photoelectrons (pe^-) for the PMT, 1000 pe^- for the DA and 10 pe­^‑ for the CCD. The readout noise is a constant number that does not change with exposure time, and it adds to other types of noise in the measurement. Assume the only other source of noise in these detectors is shot noise from the signal we are measuring.

When we consider both shot and readout noise, the SNR for a signal S(pe^‑) is given by,

SNR = S/(sqrt[S + (RN)²]).

Assume we want to measure a luminescence signal using a spectrometer that collects a signal of 10⁵ pe^-/s at the detector at every wavelength (e.g., ignore quantum efficiency differences in the detectors, which by the way are in reality very large).

1. What is the signal to noise ratio for a PMT measurement of this luminescence, at a single wavelength, for a 1 second exposure? For a 100 s exposure?
2. How long will it take to measure 1024 wavelengths using the PMT, to give a SNR of 300 at each wavelength?
3. For a 1024-pixel diode array and a 1024x1024 pixel CCD, what total exposure time would be needed to give a SNR of 300 at each wavelength? Note: the readout noise is different for these detectors.
4. Unlike the diode array, the CCD also has pixels in the vertical direction. This gives an additional SNR advantage for the CCD detector. Explain why this is?

Answer 1