Limits on adaptive optics from laser guide star incoherency

Enguehard, S.; Hatfield, Brian

doi:10.1117/12.619521

Cited by 2 publications

(3 citation statements)

References 3 publications

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“…Diffraction restores some coherency, but still leads to a significant limit on performance. This is detailed in the third paper [2].…”

Section: Overviewmentioning

confidence: 97%

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

Enguehard¹,

Hatfield²,

Whiting³

2005

SPIE Proceedings

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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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“…Diffraction restores some coherency, but still leads to a significant limit on performance. This is detailed in the third paper [2].…”

Section: Overviewmentioning

confidence: 97%

“…Diffraction helps restore some of the coherency, but the limits to achieving reciprocity, even for imaging applications, are significant. The results are detailed in the third paper [2].…”

Section: Role Of Laser Guide Star Initial Conditionsmentioning

confidence: 97%

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

Enguehard¹,

Hatfield²,

Whiting³

2005

SPIE Proceedings

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“…It will also not correctly illuminate turbulence that does need correction. Another consequence [7], especially for imaging applications, is discussed in detail in the next paper [2]. To design a beacon that is a reciprocal pair with a finite sized transmitter/receiver system, strictly speaking, requires knowledge of δn.…”

Section: Diffractive Implications For Choice Of Beaconmentioning

confidence: 99%

The role of diffraction in an extended beacon laser guide star

Enguehard¹,

Hatfield²,

Whiting³

2005

SPIE Proceedings

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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...

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Limits on adaptive optics from laser guide star incoherency

Cited by 2 publications

References 3 publications

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

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

The role of diffraction in an extended beacon laser guide star

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