Red box: Fulcher group in an optimized design in which all lenses have the same material. Blue box: the shapes of the same four lenses resulting from the present thin-lens model using $z_k=1/8$ and the marginal ray angles α and β before and after the four-lens group, extracted from the optimized design. In the drawing, the lens thicknesses, which are assumed to be zero in the calculations, are kept the same as in the red box.