Abstract
The electromagnetic theory presents a unifying explanation of electric and magnetic phenomena underlying our technological society. It is a fundamental physical theory taught in engineering schools at university level. In this theory the electromagnetic field is a vector field permeating space. An important aspect relating to students difficulties and misconceptions is the difficulty in visualizing vector fields. With the goal of enhancing student understanding and studying student engagement we have developed high quality 3D visualizations of electromagnetic situations. These make use of accurate computation of the field lines, together with realistic rendering using the open source software Blender. We present examples of electrostatic situations with both an assessment of the student understanding and an evaluation of the students' perceptions of the importance of the visualizations. Complex interplay between visualization specific issues and the abstract notion of the field is identified in the students' conceptions. It is found that the visualizations are not used as substitutes of other learning resources. They are perceived as allowing a quick access to content and prompting motivation. The adequacy of the visualization to the subject content as well as the capacity to use it as self-assessment is valued by the students.

Abstract
The GRAVITY acquisition camera has four 9x9 Shack-Hartmann sensors operating in the near-infrared. It measures the slow variations of a quasi-distorted wavefront of four telescope beams simultaneously, by imaging the Galactic Center field. The Shack-Hartmann lenslet images of the Galactic Center are generated. Since the lenslet array images are filled with the crowded Galactic Center stellar field, an extended object, the local shifts of the distorted wavefront have to be estimated with a correlation algorithm. In this paper we report on the accuracy of six existing centroid algorithms for the Galactic Center stellar field. We show the VLTI tunnel atmospheric turbulence phases are reconstructed back with a precision of 100 nm at 2 s integration.

Abstract
The acquisition camera for the GRAVITY/VLTI instrument implements four functions: a) field imager: science field imaging, tip-tilt; b) pupil tracker: telescope pupil lateral and longitudinal positions; c) pupil imager: telescope pupil imaging and d) aberration sensor: The VLTI beam higher order aberrations measurement. We present the dedicated algorithms that simulate the GRAVITY acquisition camera detector measurements considering the realistic imaging conditions, complemented by the pipeline used to extract the data. The data reduction procedure was tested with real aberrations at the VLTI lab and reconstructed back accurately. The acquisition camera software undertakes the measurements simultaneously for all four AT/UTs in 1 s. The measured parameters are updated in the instrument online database. The data reduction software uses the ESO Common Library for Image Processing (CLIP), integrated in to the ESO VLT software environment.

Abstract
The so-called "phase delay tracking" attempts to estimate the effects of the turbulence on the phase of the interferograms in order to numerically cophase the measured complex visibilities and to coherently integrate them. This is implemented by the "coherent fringe analysis" of MIDI instrument1 but has only been used for high SNR data. In this paper, we investigate whether the sensitivity of this technique can be pushed to its theoretical limits and thus applied to fainter sources. In the general framework of the maximum likelihood and exploiting the chromatic behavior of the turbulence effects, we propose a global optimization strategy to compute various estimators of the differential pistons between two data frames. The most efficient estimators appear to be the ones based on the phasors, even though they do not yet reach the theoretical limits.

Abstract
Two simulated astronomical objects (a star cluster, and a young stellar object) were mock observed with the VLTI for different array configurations and instruments, and their images reconstructed and compared. The aim of the work is to infer when/if phase referencing with less telescopes is a better choice over closure phases with more telescopes. Three scenarios were put under scrutiny: Phase Referencing (PhR) with 2 telescopes vs Closure Phase (CPh) with 3 telescopes, PhR with 3 telescopes vs CPh with 4 telescopes, and PhR with 4 telescopes vs CPh with 6 telescopes. The number of nights is kept fixed for a given PhR vs CPh configuration. The UV-coverage was improved for the PhR case, by uniformly paving the (u, v) plane while keeping fixed the total number of sampled spatial frequencies. For the majority of the configurations, the results point to comparable performances of phase referencing and closure phases, when the UV-space is judiciously chosen.

Abstract
Wave front sensing for solar telescopes is commonly implemented with the Shack-Hartmann sensors. Correlation algorithms are usually used to estimate the extended scene Shack-Hartmann sub-aperture image shifts or slopes. The image shift is computed by correlating a reference sub-aperture image with the target distorted sub aperture image. The pixel position where the maximum correlation is located gives the image shift in integer pixel coordinates. Sub-pixel precision image shifts are computed by applying a peak-finding algorithm to the correlation peak Poyneer (2003); Ladahl (2010). However, the peak-finding algorithm results are usually biased towards the integer pixels, these errors are called as systematic bias errors Sjodahl (1994). These errors are caused due to the low pixel sampling of the images. The amplitude of these errors depends on the type of correlation algorithm and the type of peak-finding algorithm being used. To study the systematic errors in detail, solar sub-aperture synthetic images are constructed by using a Swedish Solar Telescope solar granulation image 1. The performance of cross-correlation algorithm in combination with different peak-finding algorithms is investigated. The studied peak-finding algorithms are: parabola Poyneer (2003); quadratic polynomial Difdahl (2010); threshold center of gravity Bailey (2003); Gaussian Nobach & Honkanen (2005) and Pyramid Bailey (2003). The systematic error study reveals that that the pyramid fit is the most robust to pixel locking effects. The RMS error analysis study reveals that the threshold centre of gravity behaves better in low SNR, although the systematic errors in the measurement are large. It is found that no algorithm is best for both the systematic and the RMS error reduction. To overcome the above problem, a new solution is proposed. In this solution, the image sampling is increased prior to the actual correlation matching. The method is realized in two steps to improve its computational efficiency. In the first step, the cross correlation is implemented at the original image spatial resolution grid (1 pixel). In the second step, the cross-correlation is performed using a sub-pixel level grid by limiting the field of search to 4 x 4 pixels centered at the first step delivered initial position. The generation of these sub-pixel grid based region of interest images is achieved with the bi-cubic interpolation. The correlation matching with sub-pixel grid technique was previously reported in electronic speckle photography Sjodahl (1994). This technique is applied here for the solar wavefront sensing. A large dynamic range and a better accuracy in the measurements are achieved with the combination of the original pixel grid based correlation matching in a large field of view and a sub-pixel interpolated image grid based correlation matching within a small field of view. The results revealed that the proposed method outperforms all the different peak finding algorithms studied in the first approach. It reduces both the systematic error and the RMS error by a factor of 5 (i.e., 75% systematic error reduction), when 5 times improved image sampling was used. This measurement is achieved at the expense of twice the computational cost. With the 5 times improved image sampling, the wave front accuracy is increased by a factor of 5. The proposed solution is strongly recommended for wave front sensing in the solar telescopes, particularly, for measuring large dynamic image shifts involved open loop adaptive optics. Also, by choosing an appropriate increment of image sampling in trade-off between the computational speed limitation and the aimed sub-pixel image shift accuracy, it can be employed in closed loop adaptive optics. The study is extended to three other class of sub-aperture images (a point source; a laser guide star; a Galactic Center extended scene). The results are planned to submit for the Optical Express journal.