Active laser frequency stabilization using neutral praseodymium (Pr)

We present a new possibility for the active frequency stabilization of a laser using transitions in neutral praseodymium. Because of its five outer electrons, this element shows a high density of energy levels leading to an extremely line-rich excitation spectrum with more than 25000 known spectral lines ranging from the UV to the infrared. We demonstrate the active frequency stabilization of a diode laser on several praseodymium lines between 1105 and 1123 nm. The excitation signals were recorded in a hollow cathode lamp and observed via laser-induced fluorescence. These signals are strong enough to lock the diode laser onto most of the lines by using standard laser locking techniques. In this way, the frequency drifts of the unlocked laser of more than 30 MHz/h were eliminated and the laser frequency stabilized to within 1.4(1) MHz for averaging times >0.2 s. Frequency quadrupling the stabilized diode laser can produce frequency-stable UV-light in the range from 276 to 281 nm. In particular, using a strong hyperfine component of the praseodymium excitation line E = 16 502.616_7/2 cm^-1 -> E' = 25 442.742_9/2 cm^-1 at lambda = 1118.5397(4) nm makes it possible - after frequency quadruplication - to produce laser radiation at lambda/4 = 279.6349(1) nm, which can be used to excite the D2 line in Mg^+.Comment: 10 pages, 14 figure

Linear Paul trap design for an optical clock with Coulomb crystals

We report on the design of a segmented linear Paul trap for optical clock applications using trapped ion Coulomb crystals. For an optical clock with an improved short-term stability and a fractional frequency uncertainty of 10^-18, we propose 115In+ ions sympathetically cooled by 172Yb+. We discuss the systematic frequency shifts of such a frequency standard. In particular, we elaborate on high precision calculations of the electric radiofrequency field of the ion trap using the finite element method. These calculations are used to find a scalable design with minimized excess micromotion of the ions at a level at which the corresponding second- order Doppler shift contributes less than 10^-18 to the relative uncertainty of the frequency standard

Absolute frequency measurement of the In+^{+} clock transition with a mode-locked laser

The absolute frequency of the In$^{+}$ $5s^{2 1}S_{0}$ - $5s5p^{3}P_{0}$ clock transition at 237 nm was measured with an accuracy of 1.8 parts in $10^{13}$. Using a phase-coherent frequency chain, we compared the $^{1}S_{0}$ - $^{3}P_{0}$ transition with a methane-stabilized He-Ne laser at 3.39 $\mu$m which was calibrated against an atomic cesium fountain clock. A frequency gap of 37 THz at the fourth harmonic of the He-Ne standard was bridged by a frequency comb generated by a mode-locked femtosecond laser. The frequency of the In$^{+}$ clock transition was found to be $1 267 402 452 899.92 (0.23)$ kHz, the accuracy being limited by the uncertainty of the He-Ne laser reference. This represents an improvement in accuracy of more than 2 orders of magnitude on previous measurements of the line and now stands as the most accurate measurement of an optical transition in a single ion.Comment: 3 pages, 2 figures. accepted for publication in Opt. Let

Scenes, saliency maps and scanpaths

The aim of this chapter is to review some of the key research investigating how people look at pictures. In particular, my goal is to provide theoretical background for those that are new to the field, while also explaining some of the relevant methods and analyses. I begin by introducing eye movements in the context of natural scene perception. As in other complex tasks, eye movements provide a measure of attention and information processing over time, and they tell us about how the foveated visual system determines what to prioritise. I then describe some of the many measures which have been derived to summarize where people look in complex images. These include global measures, analyses based on regions of interest and comparisons based on heat maps. A particularly popular approach for trying to explain fixation locations is the saliency map approach, and the first half of the chapter is mostly devoted to this topic. A large number of papers and models are built on this approach, but it is also worth spending time on this topic because the methods involved have been used across a wide range of applications. The saliency map approach is based on the fact that the visual system has topographic maps of visual features, that contrast within these features seems to be represented and prioritized, and that a central representation can be used to control attention and eye movements. This approach, and the underlying principles, has led to an increase in the number of researchers using complex natural scenes as stimuli. It is therefore important that those new to the field are familiar with saliency maps, their usage, and their pitfalls. I describe the original implementation of this approach (Itti & Koch, 2000), which uses spatial filtering at different levels of coarseness and combines them in an attempt to identify the regions which stand out from their background. Evaluating this model requires comparing fixation locations to model predictions. Several different experimental and comparison methods have been used, but most recent research shows that bottom-up guidance is rather limited in terms of predicting real eye movements. The second part of the chapter is largely concerned with measuring eye movement scanpaths. Scanpaths are the sequential patterns of fixations and saccades made when looking at something for a period of time. They show regularities which may reflect top-down attention, and some have attempted to link these to memory and an individual’s mental model of what they are looking at. While not all researchers will be testing hypotheses about scanpaths, an understanding of the underlying methods and theory will be of benefit to all. I describe the theories behind analyzing eye movements in this way, and various methods which have been used to represent and compare them. These methods allow one to quantify the similarity between two viewing patterns, and this similarity is linked to both the image and the observer. The last part of the chapter describes some applications of eye movements in image viewing. The methods discussed can be applied to complex images, and therefore these experiments can tell us about perception in art and marketing, as well as about machine vision

Mesh dependence in PDE-constrained optimisation: an application in tidal turbine array layouts

This book provides an introduction to PDE-constrained optimisation using finite elements and the adjoint approach. The practical impact of the mathematical insights presented here are demonstrated using the realistic scenario of the optimal placement of marine power turbines, thereby illustrating the real-world relevance of best-practice Hilbert space aware approaches to PDE-constrained optimisation problems. Many optimisation problems that arise in a real-world context are constrained by partial differential equations (PDEs). That is, the system whose configuration is to be optimised follows physical laws given by PDEs. This book describes general Hilbert space formulations of optimisation algorithms, thereby facilitating optimisations whose controls are functions of space. It demonstrates the importance of methods that respect the Hilbert space structure of the problem by analysing the mathematical drawbacks of failing to do so. The approaches considered are illustrated using the optimisation problem arising in tidal array layouts mentioned above. This book will be useful to readers from engineering, computer science, mathematics and physics backgrounds interested in PDE-constrained optimisation and their real-world applications