We address the issue of creating stereo imagery on a screen that, when viewed by naked human eyes, will be indistinguishable from the original scene as viewed through a visual accessory. In doing so we investigate effects that appear because real optical systems are not ideal. Namely, we consider optical systems that are not free from geometric aberrations. We present an analysis and confirming computational experiments of the simulations of stereoscopic optical accessories in the presence of aberrations. We describe an accessory in the framework of the Seidel-Schwarzschild theory. That means that we represent its deviation from an ideal (Gaussian) device by means of five constants. Correspondingly, we are able to simulate five fundamental types of monochromatic geometric aberrations: spherical aberration, coma, astigmatism, curvature-of-field, and distortion (barrel and pincushion). We derive and illustrate how these aberrations in stereoscopic optical systems, can lead to anomalous perception of depth, e.g., the misperception of planar surfaces as curved, or even twisted as well as to circumstances under which stereoscopic perception is destroyed. The analysis and numerical simulations also allow us to simulate the related but not identical effects that occur when lenses with aberrations are used in stereoscopic cameras.