An electronic device may include a display system with a pixel array and a catadioptric lens. The display system may include a linear polarizer through which image light from the pixel array passes and a first quarter wave plate through which the light passes after passing through the polarizer. The lens may include a partial mirror, a second quarter wave plate, and a reflective polarizer. A third quarter wave plate may be formed between the linear polarizer and the pixel array to mitigate ghost images. Control circuitry may predict potential ghost images based on the geometry of the lens and data from an image frame. Tone mapping circuitry may adjust contrast of the image frame within a region overlapping the predicted ghost image. The control circuitry may adjust luminance of the image frame outside of the region overlapping the predicted ghost image.