Computational imaging (CI) systems are an enabling technology for multifunctional cameras capable of performing a wide variety of imaging tasks. However, given the complexity of CI systems, it is often difficult to characterize their performance. In this research, a novel measurement technique is proposed and tested to evaluate the performance of complex non-shift invariant linear CI systems performing a detection task at the system level. The performance is characterized using detectability indexes such as an average Hotelling's statistic (t2). The proposed measurement technique relies on a previously developed general CI system framework. The detectability predicts the upper-bounded signal-to-noise ratio of a linear algorithm through evaluation of a matched filter. The experimental results are compared with theoretical expected values through the Night Vision Integrated Performance Model (NV-IPM) and Monte Carlo simulations. We demonstrate the experimental results for a variety of target sizes, colors, and brightnesses on different colored flat backgrounds. Our results demonstrate how the detectability indexes can provide valuable insight into the final system performance. Finally, the measurement technique is used to compare the detection performance of two different cameras.