Seidel (1821-96)
n_nu refractive index
h_nu incidence height
s_nu intersect width
r_nu curvature
d_nu surface distance
Abbe Invariant:
Q_nu = n_nu (1/r_nu - 1/s_nu) = n'_nu (1/r'_nu - 1/s'_nu)
Delta (1/ns)_nu = 1/(n'_nu * s'_nu) - 1/(n_nu * s_nu)
h_nu/h_1 = (s_2 * s_3 * .. s_nu)/(s'_1 * s'_2 * .. s'_{nu-1})
= Pi_j=2..nu (s_j/s'_{j-1})
theta_nu = Sum_k=2..nu d_k/(n_k * (h_{k-1}/h_1) * (h_k/h_1)) - d_EP
p_nu = 1/((h_nu/h_1)^2 * Q_nu) + theta_nu
Petzval Sum:
P_nu = - (1/r_nu) * (1/n'_nu - 1/n_nu)
Spherical Aberration
I_nu = (h_nu/h_1)^4 Q_nu^2 Delta (1/ns)_nu
Coma
II_nu = p_nu I_nu
Meridional astigmatism
III_nu = 3 p_nu^2 I_nu + P_nu = 3 IIIa_nu + P_nu
Sagittal astigmatism
IV_nu = p_nu^2 I_nu + P_nu = IIIa_nu + P_nu
Distortion
V_nu = p_nu^3 I_nu + p_nu P_nu = p_nu (IIIa_nu + P_nu)
Astigmatic Difference
IIIa_nu = p_nu^2 I_nu = (III_nu - IV_nu)/2
Mean Field Curvature
IVa_nu = 2 p_nu^2 I_nu + P_nu = (III_nu + IV_nu)/2