Compensated atmospheric optics

Self Cite

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...

Section: Overviewmentioning

confidence: 99%

Limits on adaptive optics from laser guide star incoherency

Enguehard¹,

Hatfield²

2005

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“…In the previous papers [1,3] we introduced a plane-to-plane framework [4][5] upon which to analyze the ability of a an adaptive optics system to achieve propagation reciprocity. Point-to-point reciprocity has often been used instead but this can lead to and has lead to many false conclusions.…”

Section: Plane-to-plane Reciprocitymentioning

confidence: 99%

The role of diffraction in an extended beacon laser guide star

Enguehard¹,

Hatfield²,

Whiting³

2005

Self Cite

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 highest frequency frnax which is present in an array which has been operated on by the FFT is 0.5x1. We require that fmax > p' , leading to the condition that Lx < O.5PO• In one dimension the angular spectrum transfer function H(f) is given by (12) where z is the propagation distance, and f is a spatial frequency. The instantaneous frequency of H(f) with respect to f is given by dH(f) 2Azf (13) for the case of weak forward scattering.…”

Section: Simulation Descriptionmentioning

confidence: 99%

“…Note that in writing Eq. (3) we have assumed that the amplitude of B(xf ) is small enough so that there are no nonlinear effects such as blooming [5,12] The amplitude of the field illuminating DM2 is established by applying a phase deformation to DM1 , and projecting the resulting field into the Fraunhofer diffraction region using the Fourier transforming mirror [13]. The field falling on DM1 is assumed to be a well-collimated laser beam of amplitude A.…”

Section: Theorymentioning

confidence: 99%

<title>Two deformable mirror concept for correcting scintillation effects in laser beam projection</title>

Roggemann

Lee

1998

A two deformable mirror concept for correcting scintillation effects in laser beam projection through the turbulent atmosphere is presented. This system uses a deformable mirror and a Fourier transforming mirror to adjust the amplitude of the wave front in the telescope pupil, similar to kinoforms used in laser beam shaping. A second deformable mirror is used to correct the phase of the wave front before it leaves the aperture. The phase applied to the deformable mirror used for controlling the beam amplitude is obtained using a technique based on the Fienup phase retrieval algorithm. Simulations of propagation through a single turbulent layer sufficiently distant from the beacon observation and laser beam transmission aperture to cause scintillation shows that, for an ideal deformable mirror system, this field conjugation approach improves the on-axis field amplitude by a factor of approximately 1.4 to 1.5 compared to a conventional phase-only correction system.