Abstract

A kinoform surface designed to perfectly focus incident plane waves can be expressed¹ by a surface sag s given by where m=0,1,2… is the zone number, g_m=λm/(n₁-n₂) is the offset of the projected vertex plane of the mth zone from the m=0 zone, n₁ is the incident refractive index, n₂ is the refractive index of image space, κ=-(n₁/n₂)² is the conic coefficient, and the curvature in the mth zone is given by where f is the lens focal length. Applying the condition that the path length between adjacent zones differ by one wavelength, the radial height of the zone edges or surface discontinuities is given by The longitudinal surface discontinuity e_m at top of the mth zone is found by equating e_m=s in Eq.(1) at the height y_m+1 given by Eq.(3), Although an approximation to Eq.(4) is given by e_m≈λ/(n₁-n₂), the magnitude of e_m tends to decrease with increasing zone number m. This may be seen by observing the depths of the jumps of the smooth surface in Fig. 1.

© 1992 Optical Society of America