Ellipse fitting for interferometry. Part 3: dynamic method.

We describe a dynamically based method for fitting an ellipse to noisy data, which has for interferometric applications a number of advantages over conventional static methods (originally developed for image processing). Our method relies on the observation that each data point belongs to an ordered time series and thus has a well-defined phase parameter. We demonstrate that for real experimental data it can achieve much greater accuracy than static methods. The precision of the fit is limited only by the statistical reliability of the data, even in extreme cases such as ellipses with a minor axis smaller than the measurement noise.

Ellipse fitting for interferometry. Part 1: static methods.

We compare a number of different methods for fitting an ellipse to a static set of measured data points, specifically considering their suitability for interferometric application. We suggest an improved distance approximation for least-square geometric fitting and alternative normalizations for linear algebraic fitting. Of the methods considered, an algebraic fit using a data-dependent normalization has both the least bias in phase and amplitude estimation and the greatest robustness against uneven distribution of data.

Quantum teleportation of the temporal fluctuations of light.

A scheme for the teleportation of a beam of light including its temporal fluctuations is proposed. Expressions for the teleported degrees of first- and second-order optical coherence are presented. Teleportation of an antibunched photon stream illustrates the proposal.