Aberration Types for Rays Contained in the
$x\u2013z$
Symmetry Plane 
${D}_{1}=\frac{1}{8}{S}_{Ix}$

${D}_{4}=\frac{1}{2}{S}_{IIx}$

${D}_{8}=\frac{1}{4}(3{S}_{IIIx}+{S}_{IVx})$

${D}_{13}=\frac{1}{2}{S}_{Vx}$

Aberration Types for Rays Contained in the
$y\u2013z$
Symmetry Plane 
${D}_{2}=\frac{1}{8}{S}_{Iy}$

${D}_{7}=\frac{1}{2}{S}_{IIy}$

${D}_{9}=\frac{1}{4}(3{S}_{IIIy}+{S}_{IVy})$

${D}_{14}=\frac{1}{2}{S}_{Vy}$

Additional Primary Aberration Types Associated with Skew Rays 
${D}_{3}=\frac{1}{4}\sum _{j=1}^{k}{A}_{x,j}({h}_{x,j}\mathrm{\Delta}{u}_{y,j}^{2}+{h}_{y,j}^{2}{c}_{y,j}\mathrm{\Delta}{u}_{x,j})$

${D}_{5}=\frac{1}{2}\sum _{j=1}^{k}{A}_{x,j}({h}_{x,j}\mathrm{\Delta}{u}_{y,j}{\overline{u}}_{y,j}+{h}_{y,j}{\overline{h}}_{y,j}{c}_{y,j}\mathrm{\Delta}{u}_{x,j})$

${D}_{6}=\frac{1}{2}\sum _{j=1}^{k}({\overline{A}}_{x,j}{h}_{x,j}\mathrm{\Delta}{u}_{y,j}^{2}+{A}_{x,j}{h}_{y,j}^{2}{c}_{y,j}\mathrm{\Delta}{\overline{u}}_{x,j})$

${D}_{10}=\frac{1}{4}\sum _{j=1}^{k}{A}_{x,j}({h}_{x,j}\mathrm{\Delta}{\overline{u}}_{y,j}^{2}+{\overline{h}}_{y,j}^{2}{c}_{y,j}\mathrm{\Delta}{u}_{x,j})$

${D}_{11}=\frac{1}{4}\sum _{j=1}^{k}{A}_{y,j}({h}_{y,j}\mathrm{\Delta}{\overline{u}}_{x,j}^{2}+{\overline{h}}_{x,j}^{2}{c}_{x,j}\mathrm{\Delta}{u}_{y,j})\frac{1}{4}\sum _{j=1}^{k}({c}_{x,j}{c}_{y,j}^{2}{c}_{x,j}^{2}{c}_{y,j}){\overline{h}}_{x,j}^{2}{h}_{y,j}^{2}\mathrm{\Delta}{n}_{j}$

${D}_{12}=\sum _{j=1}^{k}({\overline{A}}_{x,j}{h}_{x,j}\mathrm{\Delta}{u}_{y,j}{\overline{u}}_{y,j}+{A}_{x,j}{h}_{y,j}{\overline{h}}_{y,j}{c}_{y,j}\mathrm{\Delta}{\overline{u}}_{x,j})$

${D}_{15}=\frac{1}{2}\sum _{j=1}^{k}({\overline{A}}_{x,j}{h}_{x,j}\mathrm{\Delta}{\overline{u}}_{y,j}^{2}+{A}_{x,j}{\overline{h}}_{y,j}^{2}{c}_{y,j}\mathrm{\Delta}{\overline{u}}_{x,j})$

${D}_{16}=\frac{1}{2}\sum _{j=1}^{k}({\overline{A}}_{y,j}{h}_{y,j}\mathrm{\Delta}{\overline{u}}_{x,j}^{2}+{A}_{y,j}{\overline{h}}_{x,j}^{2}{c}_{x,j}\mathrm{\Delta}{\overline{u}}_{y,j})\frac{1}{2}\sum _{j=1}^{k}({c}_{x,j}{c}_{y,j}^{2}{c}_{x,j}^{2}{c}_{y,j}){\overline{h}}_{x,j}^{2}{h}_{y,j}{\overline{h}}_{y,j}\mathrm{\Delta}{n}_{j}$
