Design and tolerancing of aspherical and gradient-index germanium singlets of equal performance

Two different aspherical singlets, four types of axial gradient-index singlet, and one radial gradient-index singlet achieving the same performance are toleranced for thickness, curvatures, base index, and special coefficient (aspheric or gradient) sensitivities. The results show that the singlet with the most relaxed tolerances has a linear axial gradient which extends through the lens, followed in order by a singlet with a parabolic radial gradient, a singlet with an aspheric surface on the front, and a singlet with a parabolic axial gradient crossing the first surface.