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In typical single-pixel detection multiplexing, an unknown object issequentially illuminated with intensity patterns: the total signal is summedinto a single-pixel detector and is then demultiplexed to retrieve the object.Because of measurement noise, the retrieved object differs from the groundtruth by some error quantified by the signal-to-noise ratio (SNR). Insituations where the noise only arises from the photon counting process, it hasnot been made clear if single-pixel detection multiplexing leads to a betterSNR than simply scanning the object with a focused intensity spot - a modalityknown as raster scanning. This study theoretically assesses the SNR associatedwith certain types of single-pixel detection multiplexing, and compares it withraster scanning. In particular, we show that, under photon noise, when thepositive intensity modulation is based on Hadamard or Cosine patterns,single-pixel detection multiplexing does not systematically improve the SNR ascompared to raster scanning. Instead, it only improves the SNR on object pixelsat least $k$ times brighter than the object mean signal $\bar{x}$, where $k$ isa constant that depends on the modulation scheme.

Signal-to-noise ratio analysis of single-pixel detection multiplexing under photon-noise. Cases of Hadamard and Cosine positive modulation