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stepped_luneburg investigates the scattered light properties of a Luneburg lens approximated as a series of concentric shells with discrete refractive indices. The optical Luneburg lens has promising applications for low-cost, continuous all-sky monitoring to obtain transit light curves of bright, nearby stars. This code implements a stack-based algorithm that tracks all reflected and refracted rays generated at each optical interface of the lens as described by Snell's law. The Luneburg lens model parameters, such as number of lens layers, the power-law that describes the refractive indices, the number of incident rays, and the initial direction of the incident wavefront can be altered to optimize lens performance. The stepped_luneburg module can be imported within the Python environment or used with scripting, and it is accompanied by two other modules, enc_int and int_map, that help the user to determine the resolving power of the lens and the strength of scattered light haloes for the purpose of quality assessment.