Signal to noise ratio of layer-oriented measurements for multiconjugate adaptive optics

Multiconjugate adaptive optics (MCAO) employing several deformable mirrors conjugated to different altitudes has been proposed in order to extend the size of the corrected field of view. A three dimensional measurement of the turbulent volume is needed in order to collect the information to control the deformable mirrors. Given a set of guide stars in the field of view, this can be done either using star-oriented or layer-oriented techniques. In the star-oriented measurement each wavefront sensor is coupled to a guide star while in layer-oriented techniques, wavefront sensors are coupled to different layers in the atmosphere and each of them collect light from the whole set of guide stars. This type of measurement is more exactly called optical layer-oriented (OPTLO) as the co-addition of light is done optically. The same information can also be obtained by combining, in a numerical way, star-oriented measurements. This hybrid approach is called numerical layer-oriented (NUMLO). In order to compare their performance, we present an analytical study of the signal to noise ratio (SNR) in the optical and numerical layer-oriented measurements. Optical layer oriented measurements are shown to be more efficient in the regime of faint flux and a large number of guide stars, while low detector noise allows numerical layer-oriented schemes to be more efficient in terms of SNR.