Errors in single pixel laser imaging emerging from spatial size limits in the bucket detector

Abstract In single pixel imaging (SPI) an image is sampled with an orthogonal basis projected by a programmable optical element like a digital micromirror array or a spatial light modulator. The reflected or diffracted light is collected by a lens and measured with a photodiode or bucket detector. In this work we demonstrate that SPI of laser light fields can exhibit cross talk with its phase when the bucket detector is not sufficiently large (i.e. fast photodiodes) and does not integrate the full spectrum of each basis element. In that regime, structured phases can emerge from errors in the optical or light collection system (i.e. misaligned optical elements or aberrations) and can appear in the reconstructed amplitude image. We show this behavior in simulations and experiments where the reconstructed amplitude image will exhibit phase cross-talk if the detector size is smaller than between 50% and 75% of the maximum area spanned by the projected spectrum of the measurement basis. This is important because photodiodes with a fast response time have a small effective area.