In the last years an increasing consideration has been given to the study of Laser Guide Stars (LGS) for the measurement of the disturbance introduced by the atmosphere. Due to the finite distance of the artificial reference source and its vertical extension (the Sodium layer occurs at approximately 90 km, with a vertical thickness of about 10 km), the source itself looks elongated, when observed from the edge of a large aperture. On a 40 m class telescope, for instance, the maximum elongation varies between 4 and 6 arcseconds, depending on the Sodium layer properties and on the launching position. This spot elongation strongly limits the performance of the most common wavefront sensors. A straightforward solution for a Shack-Hartmann wavefront sensor is to increase the laser power, in order to balance the loss of centroiding accuracy due to the elongation. This solution, although appealing in principle, presents drawbacks related, for instance, to the availability of very powerful lasers. We propose in this paper a wavefront sensor concept that provides an optical solution to the perspective elongation problem. It is based on an array of bi-prisms placed in the focal plane of a lenslet array; each bi-prism is aligned to the elongated spot produced by the corresponding lenslet; the spot is split into two beams, that are re-imaged into two micro-images of the sub-aperture itself; the difference in the integrated intensity of these two micro-images is proportional to the local wavefront slope. This method is sensitive only to the slope information in the direction locally orthogonal to the bi-prisms (and to the elongation) and the full information has to be recovered by combining the signals coming from different LGSs launched from different positions at the telescope edge. The pros and cons of this technique, in terms of hardware requirements and photon budget, are discussed in this paper.
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