Multichannel detectors like diode arrays and CCDsprovide a signal to noise ratio (SNR) advantage by the ability tomeasure 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 withthese 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 withexposure time, and it adds to other types of noise in themeasurement. Assume the only other source of noise in thesedetectors is shot noise from the signal we aremeasuring.

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

SNR = S/(sqrt[S + (RN)²]).

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

1. What is the signal to noise ratio for a PMT measurementof this luminescence, at a single wavelength, for a 1 secondexposure? For a 100 s exposure?
2. How long will it take to measure 1024 wavelengths usingthe 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 ateach wavelength? Note: the readout noise is different for thesedetectors.
4. Unlike the diode array, the CCD also has pixels in the verticaldirection. This gives an additional SNR advantage for the CCDdetector. Explain why this is?