On-axis diffraction-limited design of bi-parabolic singlet lenses

A lens limited by diffraction and having two parabolic surfaces is presented. The knowledge of the following parameters: object distance, relative refractive index, lens thickness, and image distance, enables to analytically calculate the parabolic front and back surfaces. The conditions to obtain diffraction-limited images for these lenses and its maximal diameter are described. These bi-parabolic lenses can be easily manufactured at reduced costs and can be used for several commercial and industrial applications. The method to obtain such surfaces and a simple example validated by using Oslo are described here.