Petzval field curvature

Remarks

A single thin lens with $n = 1.5$ and $f = 100$ mm has $P = 1/150$ per mm, so its Petzval surface has radius $n f = 150$ mm. Two thin lenses with $n_1 f_1 = -n_2 f_2$ satisfy the Petzval condition $P = 0$. If $n_1 \ne n_2$, their total power $1/f_1 + 1/f_2$ is nonzero, so the pair can form a real image on a flat field. With equal indices $n_1 = n_2$, the condition $P = 0$ forces $1/f_1 + 1/f_2 = 0$, and two thin lenses in contact then have no power at all. In the Seidel expansion, field curvature is the term $W_{220} h^2 \rho^2$; astigmatism splits the image into two surfaces, and the Petzval surface is the one obtained when astigmatism is removed.