Tomosynthesis is emerging as a next generation technology in mammography. Combined with photon-counting detectors with the ability for energy discrimination, a novel modality is enabled — spectral tomosynthesis. Further advantages of photon-counting detectors in the context of tomosynthesis include elimination of electronic noise, efficient scatter rejection (in some geometries) and no lag. Fourier-based linear-systems analysis is a well-established method for optimizing image quality in two-dimensional x-ray systems. The method has been successfully adapted to threedimensional imaging, including tomosynthesis, but several areas need further investigation. This study focuses on two such areas: 1) Adaption of the methodology to photon-counting detectors, and 2) violation of the shift-invariance and stationarity assumptions in non-cylindrical geometries. We have developed a Fourier-based framework to study the image quality in a photon-counting tomosynthesis system, assuming locally linear, stationary, and shift-invariant system response. The framework includes a cascaded-systems model to propagate the modulation-transfer function (MTF) and noise-power spectrum (NPS) through the system. The model was validated by measurements of the MTF and NPS. High degrees of non-shift invariance and non-stationarity were observed, in particular for the depth resolution as the angle of incidence relative the reconstruction plane varied throughout the imaging volume. The largest effects on image quality in a given point in space were caused by interpolation from the inherent coordinate system of the x-rays to the coordinate system that was used for reconstruction. This study is part of our efforts to fully characterize the spectral tomosynthesis system, we intend to extend the model further to include the detective-quantum efficiency, observer modelling, and spectral effects.