Abstract
In preparation of future multiobject spectrographs (MOS) whose one of the major role is to provide an extensive statistical studies of high redshifted galaxies surveyed, the demonstrator CANARY has been designed to tackle technical challenges related to open-loop adaptive optics (AO) control with jointed Natural Guide Star and Laser Guide Star tomography. We have developed a point spread function (PSF) reconstruction algorithm dedicated to multiobject adaptive optics systems using system telemetry to estimate the PSF potentially anywhere in the observed field, a prerequisite to postprocess AO-corrected observations in integral field spectroscopy. We show how to handle off-axis data to estimate the PSF using atmospheric tomography and compare it to a classical approach that uses on-axis residual phase from a truth sensor observing a natural bright source. We have reconstructed over 450 on-sky CANARY PSFs and we get bias/1-s standard-deviation (std) of 1.3/4.8 on the H-band Strehl ratio (SR) with 92.3% of correlation between reconstructed and sky SR. On the full-width at half-maximum, we get, respectively, 2.94 mas, 19.9 mas, and 88.3% for the bias, std, and correlation. The reference method achieves 0.4/3.5/95% on the SR and 2.71 mas/14.9 mas/92.5% on the FWHM for the bias/std/correlation.

Abstract
In tomographic adaptive-optics (AO) systems, errors due to tomographic wavefront reconstruction limit the performance and angular size of the scientific field of view (FoV), where AO correction is effective. We propose a multi time-step tomographic wavefront reconstruction method to reduce the tomographic error by using measurements from both the current and previous time steps simultaneously. We further outline the method to feed the reconstructor with both wind speed and direction of each turbulence layer. An end-to-end numerical simulation, assuming a multi-object AO (MOAO) system on a 30 m aperture telescope, shows that the multi timestep reconstruction increases the Strehl ratio (SR) over a scientific FoV of 10 arc min in diameter by a factor of 1.5-1.8 when compared to the classical tomographic reconstructor, depending on the guide star asterism and with perfect knowledge of wind speeds and directions. We also evaluate the multi time-step reconstruction method and the wind estimation method on the RAVEN demonstrator under laboratory setting conditions. The wind speeds and directions at multiple atmospheric layers are measured successfully in the laboratory experiment by our wind estimation method with errors below 2 ms-1. With these wind estimates, the multi time-step reconstructor increases the SR value by a factor of 1.2-1.5, which is consistent with a prediction from the end-to-end numerical simulation.

Abstract

Abstract
OPTICON currently supports a Joint Research Activity (JRA) dedicated to providing easy to use image reconstruction algorithms for optical/IR interferometric data. This JRA aims to provide state-of-the-art image reconstruction methods with a common interface and comprehensive documentation to the community. These tools will provide the capability to compare the results of using different settings and algorithms in a consistent and unified way. The JRA is also providing tutorials and sample datasets to introduce the principles of image reconstruction and illustrate how to use the software products. We describe the design of the imaging tools, in particular the interface between the graphical user interface and the image reconstruction algorithms, and summarise the current status of their implementation.

Abstract
GRAVITY acquisition camera implements four optical functions to track multiple beams of Very Large Telescope Interferometer (VLTI): a) pupil tracker: a 2 x 2 lenslet images four pupil reference lasers mounted on the spiders of telescope secondary mirror; b) field tracker: images science object; c) pupil imager: reimages telescope pupil; d) aberration tracker: images a Shack-Hartmann. The estimation of beam stabilization parameters from the acquisition camera detector image is carried out, for every 0.7 s, with a dedicated data reduction software. The measured parameters are used in: a) alignment of GRAVITY with the VLTI; b) active pupil and field stabilization; c) defocus correction and engineering purposes. The instrument is now successfully operational on-sky in closed loop. The relevant data reduction and on-sky characterization results are reported.

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.