\right)$                                                                                                                                                                                                                                                                                                                                                                                      

  \[-0.5mm\]                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 

  \[-4.2mm\]       $\hat{{C}}(b,{s}{{\mathcal D}})$                                      $\left( \begin{array}{ccc} {1}/{b} & 0 & 0  \\0  & b & {s}{{\mathcal D}}\\ 0 & 0 & 1 \end{array} \right)$                                                                                                                                                                                                                                                                                                                                                                           

  \[+0.5mm\]                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 

  \[-3.8mm\]       $\hat{{C}}({b_{\cup_{{_{n}}}}},{{{\mathcal D}}_{\cup_{{_{n}}}}})$     $\left( \begin{array}{ccc} {1/b_{\cup_{{_{n}}}}} & 0 & 0  \\ 0  & {b_{\cup_{{_{n}}}}}  & {{{\mathcal D}}_{\cup_{{_{n}}}}} \\ 0 & 0 & 1 \end{array} \right)$                                                                                                                                                                                                                                                                                                                         

  \[-0.5mm\]                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 

  \[-3.8mm\]       $\hat{{K}}({b_{\cup_{{_{n}}}}},{{{\mathcal D}}_{\cup_{{_{n}}}}},l)$   $\left( \begin{array}{ccc} {1/b_{\cup_{{_{n}}}}} & {B_{\cup_{{_{n}}}}} & {G_{\cup_{{_{n}}}}}  \\ 0  & {b_{\cup_{{_{n}}}}}  & {{{\mathcal D}}_{\cup_{{_{n}}}}} \\ 0 & 0 & 1 \end{array} \right)$                                                                                                                                                                                                                                                                                     

  \[-0.5mm\]                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 

  \[-3.8mm\]       $\hat{{F}}(l_{{_{2}}},f,l_{{_{1}}})$                                  $\left( \begin{array}{ccc} 1-\frac{l_{{_{2}}}}{f} & B_{{_{\mathrm {F}}}} & 0  \\ -\frac{1}{f}  & 1-\frac{l_{{_{1}}}}{f} & 0\\ 0 & 0 & 1  \end{array} \right)$                                                                                                                                                                                                                                                                                                                       

  \[-0.5mm\]                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 

  \[-3.8mm\]       $\hat{O}_{{_{\mathrm {D}}}}$                                          $\left(\!\! \begin{array}{ccc} \frac{1}{{b_{\cup_{{_{n}}}}}\!}\!\left(\!1\!-\!\frac{l_{{_{3}}}}{f}\!\right) & 0  &  X {{{\mathcal D}}_{\cup_{{_{n}}}}}  \\                                                                                                                                                                                                                                                                                                                          
                                                                                         -\frac{1}{f{b_{\cup_{{_{n}}}}}}  & {b_{\cup_{{_{n}}}}}\!\!\left(\!1\!-\!\frac{l_{12}}{f}\!\right) & \left(\!1\!-\!\frac{l_{{_{2}}}}{f}\!\right)\!{{{\mathcal D}}_{\cup_{{_{n}}}}} \\                                                                                                                                                                                                                                                                                                
                                                                                         0 & 0 & 1  \end{array}\!\! \right)                                                                                                                                                                                                                                                                                                                                                                                                                                                  
                                                                                          $                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  

  \[-0.5mm\]                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 

  \[-3.8mm\]       $\hat{O}_{{_{\mathrm {R}}}}$                                          $                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   
                                                                                         \left(\!\! \begin{array}{ccc} -\frac{{b_{\cup_{{_{n}}}}}f_{{_{2}}}\!}{f_{{_{1}}}\!}  & 0 &  f_{{_{2}}} {{{\mathcal D}}_{\cup_{{_{n}}}}}  \\ \frac{(\!l_{{_{1}}}\!-\!f_{{_{1}}}\!)\!+\!(\!l_{{_{2}}}\!-\!f_{{_{2}}}\!){b_{\cup_{{_{n}}}}}^2\!}{\!{b_{\cup_{{_{n}}}}}f_{{_{1}}}f_{{_{2}}}\!}  & -\frac{f_{{_{1}}}}{{b_{\cup_{{_{n}}}}}\!f_{{_{2}}}} & \left(\!1\!-\!\frac{l_{{_{2}}}}{f_{{_{2}}}}\!\right)\!{{{\mathcal D}}_{\cup_{{_{n}}}}}\! \\ 0 & 0 & 1 \end{array}\!\! \right)   
                                                                                          $                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
  ---------------- --------------------------------------------------------------------- ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------

CDDW optic as dispersing element {#cddwoptic}
================================

![Dispersing element D$_{{_{\mathrm {{D}}}}}$ (a) of the defocusing system $\hat{O}_{{_{\mathrm {{D}}}}}$ (Fig. 2) and its spectral transmittance function (b). D$_{{_{\mathrm {{D}}}}}$ is an example of an in-line four-crystal CDDW-type 