Fundamental Limits of Long Range Fourier Ptychography: On the Importance of Capturing Data in a Snapshot

Fourier ptychography (FP) is a light-based synthetic aperture imaging technique which has achieved remarkable success in high-resolution microscopy applications, where most targets are optically smooth. To date, however, FP has had far less impact in long-range imaging applications, where most targets are optically rough and so introduce speckle noise. This work attempts to characterize the fundamental limits of long range FP. In particular, we prove that if (a) one sequentially captures measures of a fully diffuse targets and (b) the speckle boils sufficiently that each of these measures are independent, then FP is impossible. We then discuss how to overcome this limitation through snapshot imaging techniques.