The multi-monochromatic x-ray imager instrument records arrays of time-gated spectrally resolved images of inertial confinement fusion targets. In the past, the image characteristics and spectral resolution of the instrument were estimated using a paraxial approximation and ignoring the substrate thickness of the pinhole array (PHA). In this work, we remove these two approximations to derive new analytic approximations and test them using a 3D ray tracing model. We show that variations in spatial resolution and transmission through the PHA are realized once the two approximations are removed simultaneously. A combination of the variation in pinhole transmission and solid angle gives rise to an image brightness modulation within the detector area. We also find a limit on the spectral resolution caused by an effective 2D dispersion from the multi-layered mirror and a spectral broadening related to spatial resolution. These findings enable better data processing and synthetic data for testing, and give further knowledge of the instrument's characteristics and limitations.