In this paper we explain why a non-linear curvature wavefront sensor (nlCWFS) is more sensitive than conventional wavefront sensors such as the Shack Hartmann wavefront sensor (SHWFS) and the conventional curvature wavefront sensor (cCWFS) for sensing mV < 14 natural guide stars. The non-linear approach builds on the successful curvature wavefront sensing concept but uses a non-linear Gerchberg-Saxton (GS) phase diversity algorithm to reconstruct the wavefront. The nonlinear reconstruction algorithm is an advantage for sensitivity but a challenge for fast computation. The current speed is a factor of 10 to 100 times slower than needed for high performance groundbased AO. We present a two step strategy to increase the speed of the algorithm. In the last paper3 we presented laboratory results obtained with a monochromatic source, here we extend our experiment to incorporate a broadband source. The sensitivity of the nlCWFS depends on the ability to extract wavefront phase from diffraction limited speckles therefore it is essential that the speckles do not suffer from chromatic aberration when used with a polychromatic source. We discuss the design for the chromatic re-imaging optics, which through chromatic compensation, allow us to obtain diffraction limited speckles in Fresnel propagated planes on either side of the pupil plane.