Third-Order Aberrations of Inhomogeneous Lenses

Various organizations in the United States and abroad are experimenting with techniques for manufacturing glass with a continuously varying refractive index. Use of such glasses in lens design would provide valuable additional degrees of freedom for the control of aberrations. This paper presents formulas by means of which the third-order (monochromatic) aberration coefficients of a symmetric system may be computed when the lenses are manufactured from glasses with continuously varying refractive indices. Each coefficient is expressed as a sum of contributions by each surface separating two distinct media and a sum of integrals over each inhomogeneous medium. The surface contribution consists of the usual contribution based on the assumption that the media are homogeneous, and an additional term that takes into account the variation of the index along the surface.