Multifunctional cameras capable of performing a wide variety of nearly simultaneous imaging tasks are expected to play a major role in the near future. Computational imaging (CI) systems will serve as one of the main enabling technologies for multifunctional cameras, especially due to the abundance of low-cost, high-speed computational processing available today. An important aspect of these systems is to be able to quantify their performance with respect to specific imaging tasks. However, the non-traditional design of CI systems, both available and proposed, presents a considerable challenge to modeling, comparing, specifying, and measuring their performance. To solve this problem, this paper presents a standardized detection signal-to-noise ratio, referred to as a detectivity metric, along with a general CI system framework. This metric has the flexibility to handle various types of CI systems and specific targets while minimizing the complexity and assumptions needed. The detectivity metric is designed to assess the performance of a CI system searching for a specific known target or signal of interest. An analytical version of the detectivity metric is also presented for a compressive sensing CI system. Special considerations for standardization are also discussed.