Scanning a focus through scattering media without using the optical memory effect

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, to the best of our knowledge, for focusing and scanning the focus at any arbitrary position behind the medium by measuring only a subset of the TM, 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 TM. Our experimental results agree well with our theoretical model. We expect that this method will find applications in imaging through scattering media, especially when the optical memory effect range is small.