The role of diffraction in an extended beacon laser guide star

Abstract

The limits to the ability of adaptive optics to achieve spatial propagation reciprocity are determined by diffraction. The beacon is a prominent component in defining the diffractive limit, so diffraction plays a role in the optimal choice of beacon parameters. We show with an explicit example that a point-source beacon is not the optimal choice, and that a point-source beacon cannot be used to measure the diffractive limit of phase-only compensation. At the single scattering level, diffraction dictates the use of an extended coherent beacon. We also show with an explicit example that optical vortices are not branch points, thus a well-defined phase reconstruction from an initially coherent beacon propagated through strong or extensive turbulence will not be hindered by the presence of optical vortices. OVERVIEWRay-optics has been extensively in the analysis of adaptive optics and in atmospheric propagation. The limits to the ability of adaptive optics to achieve spatial propagation reciprocity, however, are based on diffraction. This was demonstrated in the previous paper[1] where the plane-to-plane framework showed that phase compensation can achieve complete reciprocity in the ray-optics limit. The emphasis on ray-optics has led to the misuse of point-to-point reciprocity. One example of this, the use of a point source beacon to attempt to infer the diffractive limit of phase compensation, is discussed in detail below.The emphasis on ray-optics has also led to the confusion of what constitutes an ensemble member of optical turbulence in quantities involving ensemble averages. From the ray-optics viewpoint, and by extension the point-to-point basis, the turbulence along a single ray constitutes an ensemble member (see, for example, the definition and derivation of the isoplanatic angle). This clearly cannot be the case: short exposure stellar images are not smooth. The plane-to-plane framework dictates that an ensemble member is the distribution of optical turbulence that resides between to planes at an instant [5]. This is consistent with the morphology of short and long exposures.The scaled coherence length of the ensemble averaged mutual coherence function, r 0 , is a quantity that characterizes the entire ensemble distribution (and therefore averages) and not individual ensemble members. Therefore, r 0 should not change unless the entire distribution is changing. It makes no sense to build "r 0 telescopes" to measure the rapid fluctuations. Rapid fluctuations are a result of the ensemble members changing, not the ensemble distribution. A rapidly changing distribution makes no dynamical sense. Any technique used to infer C 2 n should also not fluctuate for the same reason. Rapid changes in the measurement of C 2 n indicate a limitation in the technique, not an actual measurement. In the following two sections we show explicitly that, due to diffraction, a point-source beacon is not universal for directed energy applications, and that a point-source beacon cannot be used to infer the diffractive limit of phas...

The diffractive limits of atmospheric compensation and laser guide star return initial conditions

“…The question is not just whether the beacon phase and amplitude are measured and applied perfectly, but also a question whether the beacon beam is the appropriate one to measure. This is discussed below and in the following paper [1].…”

“…Use of point-to-point reciprocity has led to the misconception that a point source (at the aimpoint) is the universal ideal beacon for directed energy applications. An example of the breakdown of the point-to-point framework in the context of a point source beacon is given in the following paper [1].…”

“…Use of point-to-point reciprocity has led to the misconception that a point source (at the aimpoint) is the universal ideal beacon for directed energy applications. An example of the breakdown of the point-to-point framework in the context of a point source beacon is given in the following paper [1].There are diffractive limits in the ordinary sense to both phase-only and full-field compensation that arise from the fact that the adaptive optics (wavefront sensor, active optics and beam director or telescope) have finite apertures [6]. However, atmospheric compensation involves a flow of information which is affected by diffraction.…”