Design and analysis of polygonal mirror-based scan engines for improved spatial frequency modulation imaging.

Spatial frequency modulation imaging (SPIFI) is a structured illumination single pixel imaging technique that is most often achieved via a rotating modulation disk. This implementation produces line images with exposure times on the order of tens of milliseconds. Here, we present a new architecture for SPIFI using a polygonal scan mirror with the following advances: (1) reducing SPIFI line image exposure times by 2 orders of magnitude, (2) facet-to-facet measurement and correction for polygonal scan design, and (3) a new anamorphic magnification scheme that improves resolution for long working distance optics.

Single-shot spatial frequency modulation for imaging.

Spatial frequency modulation for imaging (SPIFI) has traditionally employed a time-varying spatial modulation of the excitation beam. Here, for the first time to our knowledge, we introduce single-shot SPIFI, where the spatial frequency modulation is imposed across the entire spatial bandwidth of the optical system simultaneously enabling single-shot operation.

Relations between Coherence and Path Information.

We find two relations between coherence and path information in a multipath interferometer. The first builds on earlier results for the two-path interferometer, which used minimum-error state discrimination between detector states to provide the path information. For visibility, which was used in the two-path case, we substitute a recently defined l_{1} measure of quantum coherence. The second is an entropic relation in which the path information is characterized by the mutual information between the detector states and the outcome of the measurement performed on them, and the coherence measure is one based on relative entropy.

Finding structural anomalies in star graphs using quantum walks.

We develop a general theory for a quantum-walk search on a star graph. A star graph has N edges each of which is attached to a central vertex. A graph G is attached to one of these edges, and we would like to find out to which edge it is attached. This is done by means of a quantum walk, a quantum version of a random walk. This walk contains O(sqrt[N]) steps, which represents a speedup over a classical search, which would require O(N) steps. The overall graph, star plus G, is divided into two parts, and we find that for a quantum speedup to occur, the eigenvalues associated with these two parts in the N→∞ limit must be the same. Our theory tells us how the initial state of the walk should be chosen, and how many steps the walk must make in order to find G.