Transfer of autocollimator calibration for use with scanning gantry profilometers for accurate determination of surface slope and curvature of state of the art x ray mirrors

X ray optics, desired for beamlines at free electron laser and diffraction limited storage ring x ray light sources, must have almost perfect surfaces, capable of delivering light to experiments without significant degradation of brightness and coherence. To accurately characterize such optics at an optical metrology lab, two basic types of surface slope profilometers are used the long trace profilers LTPs and nanometer optical measuring NOM like angular deflectometers, based on electronic autocollimator AC ELCOMAT 3000. The inherent systematic errors of the instrument s optical sensors set the principle limit to their measuring performance. Where autocollimator of a NOM like profiler may be calibrated at a unique dedicated facility, this is for a particular configuration of distance, aperture size, and angular range that does not always match the exact use in a scanning measurement with the profiler. Here we discuss the developed methodology, experimental set up, and numerical methods of transferring the calibration of one reference AC to the scanning AC of the Optical Surface Measuring System OSMS , recently brought to operation at the ALS Xray Optics Laboratory. We show that precision calibration of the OSMS performed in three steps, allows us to provide high confidence and accuracy low spatial frequency metrology and not print into measurements the inherent systematic error of tool in use. With the examples of the OSMS measurements with a state of the art x ray aspherical mirror, available from one of the most advanced vendors of X ray optics, we demonstrate the high efficacy of the developed calibration procedure. The results of our work are important for obtaining high reliability data, needed for sophisticated numerical simulations of beamline performance and optimization of beamline usage of the optics. This work was supported by the U. S. Department of Energy under contract number DE AC02 05CH1123

Using small-angle scattering and contrast matching to understand molecular packing in low molecular weight gels

It is difficult to determine exactly the molecular packing in the aggregates in low molecular weight gels. Attempts to understand the packing have been made using X-ray diffraction, but there are complications with drying and questions as to whether the crystal structures represent the packing in the gel phase. Here, we exploit contrast matching in small-angle neutron scattering experiments. By preparing selectively deuterated analogs of the same molecule, the scattering from that section of the molecule decreases compared with the hydrogenated molecule. We examine packing in the pre-gelled solutions at high pH and in the gels at low pH. The data from the final gels show a lack of specific order in the aggregates that form the gel matrix. The packing in these systems is not well ordered in the gel state and so implies that it is likely that current models and cartoons are not correct

Ultra precise characterization of LCLS hard X ray focusing mirrors by high resolution slope measuring deflectometry

We present recent results on the inspection of a first diffractionlimited hard X ray Kirkpatrick Baez KB mirror pair for the Coherent Xray Imaging CXI instrument at the Linac Coherent Light Source LCLS . The full KB system mirrors and holders was under inspection by use of high resolution slope measuring deflectometry. The tests confirmed that KB mirrors of 350mm aperture length characterized by an outstanding residual figure error of lt;1 nm rms has been realized. This corresponds to the residual figure slope error of about 0.05 amp; 956;rad rms, unprecedented on such long elliptical mirrors. Additional measurements show the clamping of the mirrors to be a critical step for the final shape preserving installation of such outstanding optic

Coherent oscillations in a Cooper-pair box

This paper is devoted to an analysis of the experiment by Nakamura {\it et al.} (Nature {\bf 398}, 786 (1999)) on the quantum state control in Josephson junctions devices. By considering the relevant processes involved in the detection of the charge state of the box and a realistic description of the gate pulse we are able to analyze some aspects of the experiment (like the amplitude of the measurement current) in a quantitative way

Quantum algorithms for Josephson networks

We analyze possible implementations of quantum algorithms in a system of (macroscopic) Josephson charge qubits. System layout and parameters to realize the Deutsch algorithm with up to three qubits are provided. Special attention is paid to the necessity of entangled states in the various implementations. Further, we demonstrate explicitely that the gates to implement the Bernstein-Vazirani algorithm can be realized by using a system of uncoupled qubits

Hole burning in a nanomechanical resonator coupled to a Cooper pair box

We propose a scheme to create holes in the statistical distribution of excitations of a nanomechanical resonator. It employs a controllable coupling between this system and a Cooper pair box. The success probability and the fidelity are calculated and compared with those obtained in the atom-field system via distinct schemes. As an application we show how to use the hole-burning scheme to prepare (low excited) Fock states.Comment: 7 pages, 10 figure

The Wright ω Function

This paper defines the Wright ω function, and presents some of its properties. As well as being of intrinsic mathematical interest, the function has a specific interest in the context of symbolic computation and automatic reasoning with nonstandard functions. In particular, although Wright ω is a cognate of the Lambert W function, it presents a di#erent model for handling the branches and multiple values that make the properties of W difficult to work with. By choosing a form for the function that has fewer discontinuities (and numerical difficulties), we make reasoning about expressions containing such functions easier. A final point of interest is that some of the techniques used to establish the mathematical properties can themselves potentially be automated, as was discussed in a paper presented at AISC Madrid [3]