Design method for ultra-wide field telescopes with manufacturable freeform surfaces

We propose a method to analytically design optical systems achieving a wide field of view (FOV) by freeform surfaces of minimum gradient based on the aberration theory of off-axis optical systems and freeform surfaces. By the method, an F/3 and 200 mm aperture-class optical system with three mirrors was designed that achieves a diffraction limit of 587 nm over a FOV of <i>ϕ</i>4.54 degrees. The maximum gradient of the freeform surfaces on the primary, secondary, and tertiary mirrors are 89, 98, and 94 mdeg, respectively. The maximum gradient of the freeform surfaces is reduced by 46% compared to the optical system designed in the previous study with the same specifications. Our method guarantees the minimum amount of the gradient of the freeform surfaces, which cannot be guaranteed by the conventional design method using optimization by ray-tracing software.