Problem $2.$ Using the same camera specifications given above, design a system using three panchromatic AMC$-$CMV$4000$ CMOS detectors. You should use the part with a cover glass and the standard $5-$micron epi Si wafer $($Mono$-$E$5).$ Use the appropriate nominal operating conditions from the datasheet. Use three dichroic beam splitters to give bands of $400$ nm to $500$ nm $($blue$),500$ nm to $580$ nm $($green$),$ and $580$ nm to $660$ nm $($red$).$ Assume the filters have sharp cut$-$on and cut$-$off edges and $\backslash (90\backslash \%\backslash )$ transmission within the bandpass and block all other wavelengths. $($Each part is $10$ points.$)$

$($a$)$ Roughly sketch the layout of your optical design.