In some designs, an eye-mounted display includes multiple femtoprojectors contained inside a contact lens. Femtoprojectors that project to peripheral regions of the retina can have lower resolution. In some designs, these peripheral femtoprojector optical system includes an optically transparent core with two ends. The image source is located at one end, and a lens element is located at the other end. The end with the image source is the same size or larger than the end with the lens element. The core may be a cylinder or a frustum, for example. The sidewall structure extending between the two ends is designed to reduce stray rays from the image source. For example, the sidewall structure may absorb stray rays or may redirect rays so that they do not exit the core or so that they do not enter the pupil of the eye.