5. Sag Equation

Written by Scott Sparrold

"Sag" is a distant measurement of how far the optical surface is from a flat plane. It is a function of aperture, ρ,  or the vertical distance from the optical axis.

The approximate sag is calculated by:

ρ = aperture distance
R = Optical surface radius of curvature

This is an approximation and is valid for R>>ρ. The exact equation for reference is

An asphere takes the spherical equation and add even ordered polynominal terms (ρ^2n)

I have not included a ρ^2 term, because it repeats or competes with the radius of curvature, R, and conic, K.

K = conic constant
CN = aspheric coefficient

This aspheric equation lends no intuitive understanding of manufacturability. See Greg Forbes work to see recent advancements in optical engineering!