Table 3. Numerical tilt solutions that minimize the field-averaged third order wavefront variance in an afocal reflective telescope formed by two concave spherical mirrors with parameters: $h_0\text{ = 2 mm},HFOV=2^{\circ },f_1=\text{400 mm},m\text{ =-2},$ and ${\varphi }_v\text{ = 0}$. The square root of the wavefront variances was calculated using the small angle approximation and the exact formulae in Table 1, expressed in units of waves.

	$A_{222,x}^d=0.07\lambda$			$A_{222,x}^d=0.28\lambda$
Solution #		1	2		1	2
${\mathit{\alpha }}_1(°)$	0.0	-13.5	13.5	0.0	-55.9	55.9
${\mathit{\alpha }}_2(°)$	0.0	13.5	-13.5	0.0	55.9	-55.9
${\mathit{\beta }}_1(°)$	0.0	19.1	19.1	0.0	76.3	76.3
${\mathit{\beta }}_2(°)$	0.0	9.5	9.5	0.0	38.2	38.2
$\sqrt{{\overline{{\mathit{W}}_{\mathit{v}\mathit{a}\mathit{r}}}}_{\mathit{N}\mathit{R}\mathit{S}}(\text{approx})}$	0.023	0.007	0.007	0.093	0.027	0.027
$\sqrt{{\overline{{\mathit{W}}_{\mathit{v}\mathit{a}\mathit{r}}}}_{\mathit{N}\mathit{R}\mathit{S}}(\text{exact})}$	0.023	0.023	0.023	0.093	2.954	2.954