Signal-to-noise ratio of single-pixel cameras based on photodiodes

Single-pixel cameras have been successfully used in different imaging applications in the last years. One of the key elements affecting the quality of these cameras is the photodetector. Here, we develop a numerical model of a single-pixel camera, which takes into account not only the characteristics of the incident light but also the physical properties of the detector. In particular, our model considers the photocurrent, the dark current, the photocurrent shot noise, the dark-current shot noise, and the Johnson-Nyquist (thermal) noise of the photodiode used as a light detector. The model establishes a clear relationship between the electric signal and the quality of the final image. This allows us to perform a systematic study of the quality of the image obtained with single-pixel cameras in different contexts. In particular, we study the signal-to-noise ratio as a function of the optical power of the incident light, the wavelength, and the photodiode temperature. The results of the model are compared with those obtained experimentally with a single-pixel camera.