The exposure lens is a useful tool for fast and convenient chirpiness detection. An exposure lens is proposed by adopting square-root space mapping within the framework of transformation optics, thereby exposing a portion of the optical axis within the body of a conventional graded index lens at the lens surface, while compressing the input facet. This compression enables the proposed lens to detect higher chirpiness than conventional lenses. The results of numerical simulations verify the enhanced chirpiness detection. The family of exposure lenses provides a complete kit for investigating a wide chirpiness range, which has potential for optics signal processing.