We investigate a fundamental limit of atmospheric compensation for adaptive optical systems that use uncooperative beacons or laser guide stars. Laser guide stars are generated by backscattering processes that are naturally incoherent. The limit arises because the wavefront sensing component of the adaptive optics cannot differentiate between the incoherency introduced by atmospheric turbulence from that of the laser guide star generation process. The limit is significant and restrictive. Under absolutely ideal conditions with perfect compensation, the compensated Strehl ratio must be less than 0.3. Realistic conditions will reduce this by more than a factor of 2. OVERVIEWThe plane-to-plane framework [1][2][3][4][5] used in the previous two papers highlights the role played by the initial conditions of the beacon as it begins to propagate back through the atmosphere to the wavefront sensor. The framework shows that complete propagation reciprocity results in the compensated beam reproducing the beacon beam at the opposite plane where the beacon beam starts from. Restated, the adaptive optical system cannot produce a compensated beam with beam quality better than what the beacon starts with. This result ultimately follows from the fact that the wavefront sensor cannot distinguish the aberrations created by the propagative medium, from any aberrations initially present in the beacon beam.Laser guide stars rely on backscattering to generate the beacon beam. While the laser guide star itself may be compensated, thus optimizing the uplink spatial coherence at altitude and minimizing its spread, the backscattering process is completely incoherent. Any remaining spatial coherence of the uplink or outbound laser guide star beam is destroyed upon "reflection" because of the irregular distribution of the scattering centers. The backscattering volume is equivalent to a very bad mirror. Hence, to a good approximation, the backscattered laser guide star beam at a fixed altitude emerging from the bottom of the backscattering layer is initially completely spatially incoherent.The initial conditions of the laser guide star beacon are completely different from that of a natural guide star. One can expect the results from using a laser guide star to be different from using a natural guide star. The backscattering process in the laser guide star generation adds a phase aberration to the laser guide star beam that is not added to the light from astronomical sources and natural guide stars. Since exoatmospheric sources do not suffer the backscatter phase aberrations, only the common phase aberrations induced by turbulence should be compensated for. However, the wavefront sensor of the adaptive optics compensation system cannot distinguish the phase aberrations added to the laser guide star beacon by the backscattering process from the phase aberrations induced by turbulence. We will show that the limit placed on adaptive optics systems using laser guide stars is severe and very significant because of the incoherency of the backscatte...
The symmetry operation associated with propagation reciprocity is complex conjugation and adaptive optics is used to physically carry out this symmetry operation. We use a plane-to-plane framework to describe the fundamental limits placed on implementing propagation reciprocity that arise due to diffraction. Compensation system performance is often analyzed using the ray optics limit (e.g. defining the isoplanatic angle). This limits the applicability of such results by ignoring the diffractive limits on the ability to sense the laser guide star phase and amplitude information. We describe how the diffractive limits of phase-only and full-field compensation arise in terms of this flow of information. The plane-to-plane framework also shows the role of the beacon initial conditions as the end result of complete spatial reciprocity. OVERVIEWOne method to suppress the aberrative effects of atmospheric turbulence is to use propagation reciprocity with respect to the direction of propagation. The symmetry operation associated with propagation reciprocity is complex conjugation and adaptive optics is used to physically carry out this symmetry operation.We are interested in the fundamental limits placed on implementing propagation reciprocity in this way that arise due to diffraction. We are not concerned with hardware specific dependencies. For the most part, we assume that the hardware, e.g. the wavefront sensor and the active optical components such as the deformable mirror, work perfectly and rapidly.In order to investigate these limits, we need a theoretical framework or basis [3,4]. This simple framework is introduced in the following section. Often, point-to-point reciprocity has been used as the guiding principle. The basis for this arises from the fact that the point source propagator or Green's function is symmetric in initial and end points even in the presence of turbulence. However, this application does not account for the boundary conditions. Green's function become uniquely defined by satisfying specific boundary conditions [7]. Indeed, the purpose of adaptive optics for atmospheric compensation is to adjust the boundary conditions. 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. Thus the diffractive limit of phase-only or full-field compensation for a given aperture size is not reached simply by using aberration free hardware with infinite spatial and temporal bandwidths [6,8]. The question is not just whether the beacon p...
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