  Wavefront shaping makes it possible to form a focus through opaque scattering
materials. In some cases, this focus may be scanned over a small distance using
the optical memory effect. However, in many cases of interest, the optical
memory effect has a limited range or is even too small to be measured. In such
cases, one often resorts to measuring the full transmission matrix (TM) of the
sample to completely control the light transmission. However, this process is
time-consuming and may not always be possible. We introduce a new method for
focusing and scanning the focus at any arbitrary position behind the medium by
measuring only a subset of the transmission matrix, called Sparse Field
Focusing (SFF). With SFF, the scan range is not limited to the memory effect
and there is no need to measure the full transmission matrix. Our experimental
results agree well with our theoretical model. We expect this method will find
applications in imaging through scattering media, especially when the optical
memory effect range is small.
