An FPGA Architecture for Extracting Real-Time Zernike Coefficients from Measured Phase Gradients

Zernike modes are commonly used in adaptive optics systems to represent optical wavefronts. However, real-time calculation of Zernike modes is time consuming due to two factors: the large factorial components in the radial polynomials used to define them and the large inverse matrix calculation needed for the linear fit. This paper presents an efficient parallel method for calculating Zernike coefficients from phase gradients produced by a Shack-Hartman sensor and its real-time implementation using an FPGA by pre-calculation and storage of subsections of the large inverse matrix. The architecture exploits symmetries within the Zernike modes to achieve a significant reduction in memory requirements and a speed-up of 2.9 when compared to published results utilising a 2D-FFT method for a grid size of 8×8. Analysis of processor element internal word length requirements show that 24-bit precision in precalculated values of the Zernike mode partial derivatives ensures less than 0.5% error per Zernike coefficient and an overall error of <1%. The design has been synthesized on a Xilinx Spartan-6 XC6SLX45 FPGA. The resource utilisation on this device is <3% of slice registers, <15% of slice LUTs, and approximately 48% of available DSP blocks independent of the Shack-Hartmann grid size. Block RAM usage is <16% for Shack-Hartmann grid sizes up to 32×32

Non-topological solitons in brane world models

We examine some general properties of a certain class of scalar filed theory models containing non-topological soliton solutions in the context of brane world models with compact large extra dimensions. If a scalar field is allowed to propagate in extra space, then, beside standard Kaluza-Klein type excitations, a whole new class of very massive soliton-type states can exist. Depending on their abundance, they can be important dark matter candidates or give significant contribution to entropy and energy density in our universe. .Comment: version accepted for publication in Physical Review

Techniques of replica symmetry breaking and the storage problem of the McCulloch-Pitts neuron

In this article the framework for Parisi's spontaneous replica symmetry breaking is reviewed, and subsequently applied to the example of the statistical mechanical description of the storage properties of a McCulloch-Pitts neuron. The technical details are reviewed extensively, with regard to the wide range of systems where the method may be applied. Parisi's partial differential equation and related differential equations are discussed, and a Green function technique introduced for the calculation of replica averages, the key to determining the averages of physical quantities. The ensuing graph rules involve only tree graphs, as appropriate for a mean-field-like model. The lowest order Ward-Takahashi identity is recovered analytically and is shown to lead to the Goldstone modes in continuous replica symmetry breaking phases. The need for a replica symmetry breaking theory in the storage problem of the neuron has arisen due to the thermodynamical instability of formerly given solutions. Variational forms for the neuron's free energy are derived in terms of the order parameter function x(q), for different prior distribution of synapses. Analytically in the high temperature limit and numerically in generic cases various phases are identified, among them one similar to the Parisi phase in the Sherrington-Kirkpatrick model. Extensive quantities like the error per pattern change slightly with respect to the known unstable solutions, but there is a significant difference in the distribution of non-extensive quantities like the synaptic overlaps and the pattern storage stability parameter. A simulation result is also reviewed and compared to the prediction of the theory.Comment: 103 Latex pages (with REVTeX 3.0), including 15 figures (ps, epsi, eepic), accepted for Physics Report

The Fokker-Planck equation for bistable potential in the optimized expansion

The optimized expansion is used to formulate a systematic approximation scheme to the probability distribution of a stochastic system. The first order approximation for the one-dimensional system driven by noise in an anharmonic potential is shown to agree well with the exact solution of the Fokker-Planck equation. Even for a bistable system the whole period of evolution to equilibrium is correctly described at various noise intensities.Comment: 12 pages, LATEX, 3 Postscript figures compressed an

Reconfigurable Complementary Logic Circuits with Ambipolar Organic Transistors

Ambipolar organic electronics offer great potential for simple and low-cost fabrication of complementary logic circuits on large-area and mechanically flexible substrates. Ambipolar transistors are ideal candidates for the simple and low-cost development of complementary logic circuits since they can operate as n-type and p-type transistors. Nevertheless, the experimental demonstration of ambipolar organic complementary circuits is limited to inverters. The control of the transistor polarity is crucial for proper circuit operation. Novel gating techniques enable to control the transistor polarity but result in dramatically reduced performances. Here we show high-performance non-planar ambipolar organic transistors with electrical control of the polarity and orders of magnitude higher performances with respect to state-of-art split-gate ambipolar transistors. Electrically reconfigurable complementary logic gates based on ambipolar organic transistors are experimentally demonstrated, thus opening up new opportunities for ambipolar organic complementary electronics.115Ysciescopu