Advances in optical coherence tomography (OCT) rely on the availability of broadband light that is spatially coherent. We present a technique to characterize coherence properties of broadband light using optical phasespace contours in transverse momentum and position. We demonstrate that these contour plots can be directly measured by a simple heterodyne imaging scheme possessing high dynamic r...

We present our work on phase space rendering. Every radiance sample in space has a location and a direction from which it is received. These degrees of freedom make up a phase space. The rendering problem of generating a discrete image from single radiance values is reduced to reconstruct a continuous radiance function from sparse samples in its phase space. The problem of reconstruction in a s...

Much of the discussion of decoherence has been in terms of a particle moving in one dimension that is placed in an initial superposition state (a Schrödinger ”cat” state) corresponding to two widely separated wave packets. Decoherence refers to the destruction of the interference term in the quantum probability function. Here, we stress that a quantitative measure of decoherence depends not onl...

Existing recurrent net learning algorithms are inadequate. We introduce the conceptual framework of viewing recurrent training as matching vector fields of dynamical systems in phase space. Phasespace reconstruction techniques make the hidden states explicit, reducing temporal learning to a feed-forward problem. In short, we propose viewing iterated prediction [LF88] as the best way of training...

The main result of this paper states that phase retrieval in infinitedimensional Hilbert spaces is never uniformly stable, in sharp contrast to the finite-dimensional setting in which phase retrieval is always stable. This leads us to derive stability results for signals depending on how well they are approximated by finite expansions.

using the riemann-liouville fractional differintegral operator, the lie theory is reformulated. the fractional poisson bracket over the fractional phase space as 3n state vector is defined to be the fractional lie derivative. its properties are outlined and proved. a theorem for the canonicity of the transformation using the exponential operator is proved. the conservation of its generator is p...