  In a single-pixel camera, an unknown object is sequentially illuminated by
intensity patterns. The total reflected or transmitted intensity is summed in a
single-pixel detector from which the object is computationally reconstructed.
In the situation where the measurements are limited by photon-noise, it is
questionable whether a single-pixel camera performs better or worse than simply
scanning the object with a focused intensity spot - a modality known as
\textit{point raster scanning} and employed in many laser scanning systems.
Here, we solve this general question and report that positive intensity
modulation based on Hadamard or Cosine patterns does not necessarily improve
the single-to-noise ratio (SNR) of single-pixel cameras as compared to point
raster scanning, as compared to a raster-scanning. Instead, we show that the
SNR is only improved on object pixels at least k times brighter than the object
mean signal, where k is a constant that depends on the modulation scheme. This
fundamental property is demonstrated theoretically and numerically. It is also
experimentally confirmed in the spatial domain - for widefield fluorescence
imaging - and in the spectral domain - for spontaneous Raman spectral
measurements. Finally, we provide user-oriented guidelines that help decide
when and how multiplexing under photon-noise should be used instead of point
raster scanning.
