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Purpose: Design and optimization of medical imaging systems benefit from accurate theoretical modeling that identifies the physical factors governing image quality, particularly in the early stages of system development. This work extends Fourier metrics of imaging performance and detectability index (d′) to tomosynthesis and cone-beam CT (CBCT) and investigates the extent to which d′ is a valid descriptor of task-based imaging performance as assessed by human observers. Methods: The detectability index for tasks presented in 2D slices (dslice′) was derived from 3D cascaded systems analysis of tomosynthesis and CBCT. Anatomical background noise measured in a physical phantom presenting power-law spectral density was incorporated in the 'generalized' noise-equivalent quanta. Theoretical calculations of dslice′ were performed as a function of total angular extent (θtot) of source-detector orbit ranging 10°-360° under two acquisition schemes: (i) Constant angular separation between projections (constant-Δθ), giving variable number of projections (Nproj) and dose vs θtot and (ii) constant number of projections (constant-Nproj), giving constant dose (but variable angular sampling) with θtot. Five simple observer models were investigated: Prewhitening (PW), prewhitening with eye filter and internal noise (PWEi), nonprewhitening (NPW), nonprewhitening with eye filter (NPWE), and nonprewhitening with eye filter and internal noise (NPWEi). Human observer performance was measured in 9AFC tests for five simple imaging tasks presented within uniform and power-law clutter backgrounds. Measurements (from 9AFC tests) and theoretical calculations (from cascaded systems analysis of dslice′) were compared in terms of area under the ROC curve (Az) Results: Reasonable correspondence between theoretical calculations and human observer performance was achieved for all imaging tasks over the broad range of experimental conditions and acquisition schemes. The PW and PWEi observer models tended to overestimate detectability, while the various NPW models predicted observer performance fairly well, with NPWEi giving the best overall agreement. Detectability was shown to increase with θtot due to the reduction of out-of-plane clutter, reaching a plateau after a particular θtot that depended on the imaging task. Depending on the acquisition scheme, however (i.e., constant-Nproj or Δθ), detectability was seen in some cases to decline at higher θtot due to tradeoffs among quantum noise, background clutter, and view sampling. Conclusions: Generalized detectability index derived from a 3D cascaded systems model shows reasonable correspondence with human observer performance over a fairly broad range of imaging tasks and conditions, although discrepancies were observed in cases relating to orbits intermediate to 180° and 360°. The basic correspondence of theoretical and measured performance supports the application of such a theoretical framework for system design and optimization of tomosynthesis and CBCT. [ABSTRACT FROM AUTHOR]