Spherical lenses achieve different imaging purposes by changing the spherical radius of the lens, which is difficult to process when the focal length is too short. “Changing the radial refractive index distribution of a cylindrical lens so that light rays with different radius angles converge at a point in the object space to achieve imaging purposes is called a self focusing lens.”. Self focusing lenses have the characteristics of small size, varying focal length with lens length, and varying object image conjugation distances. They are widely used in internal wide mirrors and copier positioners, with very satisfactory results.
Light rays propagate along a straight line in a uniform medium, and when the refractive index of the medium continuously changes, the light rays will bend. If a self focusing lens is made of a radial gradient refractive index material with a relatively high refractive index at the optical axis and a gradual decrease in the radial refractive index along the cross section, the propagation path of meridian light rays in the lens is not a straight line, but a curve.