Appendix

A formalism is exposed in Wynne (1979), but an easier derivation is possible. We have the following wavelength dependent relationships (according to the notation of Fig. 2):

Basically, the diameter of the Airy disk is:

$$y'(\lambda) = \frac{1.22 \lambda}{2 u'(\lambda)}\cdot$$ (3)

The Lagrange invariant is:

$$y. u = y'(\lambda) . u'(\lambda) .$$ (4)

The Wynne correctors make the exit pupil chromatic and allow the approximation: $u'(\lambda) = a \lambda$. a is a constant determined at $\lambda_0$ where the correctors do not have any effect:

$$a = \frac{u'}{\lambda_0} = u \frac{y}{y'} \frac{1}{\lambda_0} = \frac{u}{\gamma} \frac{1}{\lambda_0}$$ (5)

$\gamma$ is the magnification induced by the achromatic doublets:

$$\gamma = \frac{y'}{y} = \frac{f_2}{f_1}$$ (6)

hence:

$$u'(\lambda) = \frac{u}{\gamma} \frac{\lambda}{\lambda_0}$$ (7)

and:

$$y'(\lambda)=1.22\frac{\lambda_0 \gamma}{2 u} \cdot$$ (8)

The Airy disk diameter no longer depends on wavelength.

  

Figure 6: Final radial chromatism on the detector (f/976) calculated from a numerical simulation, after correction by the Wynne triplets, for 2 different locations in the field (solid line $\theta=0.03\hbox{$^\circ$}$, dashed line $\theta=0.06\hbox{$^\circ$}$)