We present a new simple optical design for a cat's eye retroreflector. We describe the design of the new optical configuration and its use in tilt-immune interferometry where it enables the tracking of the displacement of a plane target mirror with minimum sensitivity to its tilt about axes orthogonal to the interferometer's optical axis. In this application the new cat's eye does not behave as a perfect retroreflector and we refer to it as a "pseudo"-cat's eye (PCE). The device allows, for the first time, tilt-immune interferometric displacement measurements in cases where the nominal distance to the target mirror is significantly larger than the length of the cat's eye. We describe the general optical characteristics of the PCE and compare its performance in our application with that of a conventional cat's eye optical configuration using ABCD matrices and Zemax analyses. We further suggest a simple modification to the design that would enable the PCE to behave as a perfect cat's eye, and this design may provide an advantageous solution for other applications.