Simultaneous Water Vapor and Dry Air Optical Path Length Measurements and Compensation with the Large Binocular Telescope Interferometer

The Large Binocular Telescope Interferometer uses a near-infrared camera to measure the optical path length variations between the two AO-corrected apertures and provide high-angular resolution observations for all its science channels (1.5-13 $\mu$m). There is however a wavelength dependent component to the atmospheric turbulence, which can introduce optical path length errors when observing at a wavelength different from that of the fringe sensing camera. Water vapor in particular is highly dispersive and its effect must be taken into account for high-precision infrared interferometric observations as described previously for VLTI/MIDI or the Keck Interferometer Nuller. In this paper, we describe the new sensing approach that has been developed at the LBT to measure and monitor the optical path length fluctuations due to dry air and water vapor separately. After reviewing the current performance of the system for dry air seeing compensation, we present simultaneous H-, K-, and N-band observations that illustrate the feasibility of our feedforward approach to stabilize the path length fluctuations seen by the LBTI nuller.Comment: SPIE conference proceeding

Finding the Minimum-Weight k-Path

Given a weighted $n$-vertex graph $G$ with integer edge-weights taken from a range $[-M,M]$, we show that the minimum-weight simple path visiting $k$ vertices can be found in time \tilde{O}(2^k \poly(k) M n^\omega) = O^*(2^k M). If the weights are reals in $[1,M]$, we provide a $(1+\varepsilon)$-approximation which has a running time of \tilde{O}(2^k \poly(k) n^\omega(\log\log M + 1/\varepsilon)). For the more general problem of $k$-tree, in which we wish to find a minimum-weight copy of a $k$-node tree $T$ in a given weighted graph $G$, under the same restrictions on edge weights respectively, we give an exact solution of running time \tilde{O}(2^k \poly(k) M n^3) and a $(1+\varepsilon)$-approximate solution of running time \tilde{O}(2^k \poly(k) n^3(\log\log M + 1/\varepsilon)). All of the above algorithms are randomized with a polynomially-small error probability.Comment: To appear at WADS 201

Effects of Glide Path on the Centering Ability and Preparation Time of Two Reciprocating Instruments

Introduction: The aim of this in vitro study was to evaluate the effects of establishing glide path on the centering ability and preparation time of two single-file reciprocating systems in mesial root canals of mandibular molars. Methods and Materials: Sixty extracted mandibular molars with curvatures of 25-39 degrees and separate foramina for the mesiobuccal and mesiolingual canals, were divided into four groups (n=15); WaveOne+glide path; WaveOne; Reciproc+glide path and Reciproc. Non-patent canals were excluded and only one canal in each tooth was instrumented. A manual glide path was established in first and third groups with #10, 15 and 20 hand K-files. Preparation was performed with reciprocating in-and-out motion, with a 3-4 mm amplitude and slight apical pressure. Initial and final radiographs were taken to analyze the amount of dentin removed in the instrumented canals. The radiographs were superimposed with an image editing software and examined to assess discrepancies at 3-, 6- and 9-mm distances from the apex. The Kruskal-Wallis test was used for statistical analysis. The level of significance was set at 0.05. Results: Preparation in groups without glide paths was swifter than the other groups (P=0.001). However, no difference was observed regarding centering ability. Conclusion: Establishing a glide path increased the total instrumentation time for preparing curved canals with WaveOne and Reciproc instruments. Glide path had no influence on the centering ability of these systems.Keywords: Centering Ability; Glide Path; Reciproc; Root Canal Preparation; Single-File Instrumentation; WaveOn