Zernike spherical mode
= Zernike spherical mode
{c}
{title2=$Z_4^0=6\rho^4-6\rho^2+1$}
The unnormalized rotationally symmetric mode is $Z_4^0(\rho)=6\rho^4-6\rho^2+1$. It describes balanced primary <spherical aberration>. The lower-degree terms make it orthogonal to constant piston and quadratic defocus under the disk area measure: direct integration gives $\int_0^1 Z_4^0\rho\,d\rho=0$ and $\int_0^1 Z_4^0(2\rho^2-1)\rho\,d\rho=0$.