This article describes the optical design of a wide-angle lens suitable for long-wave infrared (LWIR) earth sensor whose operating wavelength range is 10 to 16 microns

and full angle of view is up to 135 degrees

having an uncooled staring focal plane array. The optical system only consists of three germanium lenses with a "negative-positive-positive" reversed telephoto telecentric structure in the image space. This type of wide-angle lens can balance the correctness of off-axis aberrations against the evenness of illumination at its image plane very well. The designed lens has the advantages of simplicity

compactness and long back working distance. Its imaging quality is nearly diffraction limited

so that its modulated transfer function (MTF) value is higher than 0.6 at the 20 lines/mm spatial frequency in the image plane

and the relative error of the linearity between its image height and field angle is lower than 15%. Its manufacture and alignment tolerance are also analyzed with the CODE V optical design software.