  The nonlinear curvature wavefront sensor (nlCWFS) uses multiple (typically
four) out-of-focus images to reconstruct the phase and amplitude of a
propagating light beam. Because these images are located between the pupil and
focal planes, they contain tip/tilt information. Rather than using a separate
sensor to measure image locations, it would be beneficial to extract tip/tilt
information directly and routinely as part of the reconstruction process. In
the presence of atmospheric turbulence, recovering precise centroid offsets for
each out-of-focus image becomes a dynamic process as image structure is altered
by changing aberrations. We examine several tip/tilt extraction methods and
compare their precision and accuracy using numerical simulations. We find that
the nlCWFS outer measurement planes confer more accurate and reliable tip/tilt
information than the inner measurement planes, due to their larger geometric
lever arm. However, in practice, finite field of view (detector region of
interest) effects bias tip/tilt retrieval when using the outer planes due to
diffraction. Using knowledge of the $z$-distance to each plane, we find that
applying a best-fit linear model to multiple image centroid locations can offer
fast and accurate tip/tilt mode retrieval. For the most demanding applications,
a non-linear tip/tilt extraction method that self-consistently uses the speckle
field may need to be developed.
