  Cascaded operations play an important role in traditional electronic
computing systems for the realization of advanced strategies. Here, we
introduce the idea of cascaded operations into all-optical spatial analog
computing. The single function of the firstorder operation is difficult to meet
the requirements of practical applications in image recognition. The
all-optical second-order spatial differentiators are implemented by cascading
two first-order differential operation units, and the image edge detection of
amplitude and phase objects are demonstrated. Our scheme provides a possible
pathway towards the development of compact multifunctional differentiators and
advanced optical analog computing networks.
