Signal-to-noise analysis of task-based imaging systems with defocus

We analyze the signal-to-noise ratio (SNR) of arbitrary imaging systems in the presence of defocus. The modulation transfer function (MTF) and the mean SNR are combined to calculate the spatial-frequency spectrum of the SNR (the spectral SNR). Computational imaging methods are used for extending the depth of field (DOF) of the system. The DOF of a task-specific imaging system is defined as the range of defocus that causes the spectral SNR to drop below a minimum value within a band of spatial frequencies of interest. We introduce the polar-SNR plot as a tool for visualizing the spectral SNR of defocused imaging systems with asymmetric pupil functions. As an example, we perform the analysis of an imaging system used for biometric iris recognition.