Volumetric Calibration Refinement using masked back projection and image correlation superposition

This paper deals with a new, reconstruction based, approach of refining a volumetric calibration. The technique is based on a 2D cross-correlation between particle images on the sensor plane with a planar back projection from a tomographic reconstruction in the same sensor plane to determine potential disparities between the initial camera calibration and the measurement. Additive superposition of the correlation maps from different sets or particle images allows reducing the influence of noise and ghost particles such that the systematic errors in the calibration can be corrected. The different sections describe the theory, the principle processing steps and the convergence of the procedure. Furthermore, the concept is proven by simulating the entire process of the measurement chain, with the help of a synthetic comparison. The results show that disparities of over 9 pixels could be corrected to an average of below 0.1 pixels during the refinement steps. Finally, the technique demonstrates it´s potential to measured data, where the numbers of outliers in the raw results are reduced after the volumetric calibration refinement

Projective filtering of a single spatial radiation eigenmode

Lossless filtering of a single coherent (Schmidt) mode from spatially multimode radiation is a problem crucial for optics in general and for quantum optics in particular. It becomes especially important in the case of nonclassical light that is fragile to optical losses. An example is bright squeezed vacuum generated via high-gain parametric down conversion or four-wave mixing. Its highly multiphoton and multimode structure offers a huge increase in the information capacity provided that each mode can be addressed separately. However, the nonclassical signature of bright squeezed vacuum, photon-number correlations, are highly susceptible to losses. Here we demonstrate lossless filtering of a single spatial Schmidt mode by projecting the spatial spectrum of bright squeezed vacuum on the eigenmode of a single-mode fiber. Moreover, we show that the first Schmidt mode can be captured by simply maximizing the fiber-coupled intensity. Importantly, the projection operation does not affect the targeted mode and leaves it usable for further applications.Comment: 10 pages, 9 figure

Three Puzzles on Mathematics, Computation, and Games

In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear programming. The second puzzle is about errors made when votes are counted during elections. The third puzzle is: are quantum computers possible?Comment: ICM 2018 plenary lecture, Rio de Janeiro, 36 pages, 7 Figure