Phasing optical phased arrays using an exact solution for adaptive optics
09 Mar 2002-Vol. 3, pp 3-3
TL;DR: In this paper, the phase reconstruction from wavefront slopes is optimized for a 2D optical phased array (OPA) in a two-dimensional mode where the phase profile varies in both transverse directions.
Abstract: The pixelized nature of optical phased arrays (OPAs) or spatial light modulators such as liquid crystal devices (LCDs) or micro electromechanical devices (MEMs) allows us to treat these devices as segmented active optical elements. The individual OPA elements, for example, the LCD pixels, only control phase i.e. the piston degree of freedom parallel to the optical axis and not the tip and tilt or phase gradients. We assume in this paper that the OPAs operate in a 2-dimensional mode where the phase profile varies in both transverse directions. Wavefront sensor components of an adaptive optical system generally provide wavefront slope measurements (tip and tilt) and not piston. Thus, wavefront sensor measurements cannot be directly applied to OPAs. Since the wavefront slope measurements do not form a curl-free vector field, the phase reconstruction from the wavefront slopes must be optimized. The optimized phase reconstruction can be directly applied to the OPA device and therefore represents a control solution. We have found an exact analytic solution for the optimal phase reconstruction given a set of discrete gradient measurements.
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TL;DR: In this paper, a pedagogical review of several new methods and solutions to calculate the performance and limits of phase-only compensating adaptive optics systems is presented, and the performance of phase only adaptive optics is evaluated.
13 citations
TL;DR: In this article, the authors analytically solve the linearized equations of thermal blooming for uplink propagation of an infinite beam in uniform atmosphere and wind as a perturbation series in blooming.
Abstract: In the past the combined effects of thermal blooming and atmospheric turbulence in the wave-optics regime were considered analytically intractable and were treated heuristically or left to 1wave-optics codes. We demonstrate that, at least for uniform atmosphere and wind, the linearized problem for small-scale blooming is tractable and leads to considerable physical insight. We analytically solve the linearized equations of thermal blooming for uplink propagation of an infinite beam in uniform atmosphere and wind as a perturbation series in blooming for the case of compensated and uncompensated propagation. A Feynman diagram representation of the series is presented. Most importantly, the propagators are used to compute the mutual coherence function and the Strehl ratio also as a perturbation series in blooming. The dependence of the results on the actuator Fresnel number of the adaptive optics is discussed along with the relative roles of the phase-compensation instability and stimulated thermal Rayleigh scattering. A brief comparison is made with nonlinear numerical simulations in order to show that the nonlinearities may be neglected for realistic levels of atmospheric turbulence.
11 citations
"Phasing optical phased arrays using..." refers background in this paper
...For example, AMPERES modules incorporate exact results for to the interaction of thermal blooming and turbulence[ 6 ] and functional scaling[7] for accurate results for large diameter beams....
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TL;DR: In this paper, the authors proposed a solution for the segmented-mirror configuration that minimizes the sum of the squares of the differences in height of adjacent segment midpoints.
Abstract: An innovative method of phase compensation employs a segmented primary mirror in place of a conventional deformable mirror. Segmentation of the primary mirror offers an inexpensive method to produce large, active telescopes or beam directors. The success of this approach for adaptive optics hinges on the ability to control the segments. The segmented mirror will adopt the requisite conjugate beacon phase front to the level of precision of the wave-front-sensor measurements if it is made to behave like a continuous deformable membrane. We show that this is equivalent to applying the measured wave-front slopes directly to the segments and then matching adjacent edge midpoints. This discrete linear system of equations for the segment pistons is singular, and no general solution exists. We have succeeded in analytically solving for the segmented-mirror configuration that minimizes the sum of the squares of the differences in height of adjacent segment midpoints. This solution results from the identification of constraints on the surface. The constraints have a natural geometric interpretation as continuity loops. The knowledge of this constructive solution eliminates the need to do iterations or the need to develop iterative control algorithms. This solution functional can be found in advance for any particular mirror design and relates segment-midpoint height differences to the measured input tilt field in a fully deterministic and unique way.
11 citations
"Phasing optical phased arrays using..." refers background in this paper
...AMP Research has discovered an exact solution to the segmented membrane problem[ 8 ]....
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TL;DR: In this article, the authors developed analytical functional scaling of absorption profiles to develop a fast and accurate systems model for the whole-beam Strehl ratio, which is based on the exact analytic theory for the structure functions in nonuniform atmospheres.
Abstract: Compensated Strehl-ratio predictions for a finite-sized beam in the presence of thermal blooming and atmospheric turbulence can be obtained from infinite-beam results by use of a propagation reconstruction theory and the exact analytic solution to the thermal blooming problem. From this exact solution of the linear theory for the structure functions in nonuniform atmospheres, we have developed analytical functional scaling of absorption profiles. We have used this analytic scaling to develop a fast and accurate systems model for the whole-beam Strehl ratio. The results from this systems model, taking only seconds on a microcomputer, agree with the exact analytic theory and with nonlinear four-dimensional wave-optics simulations.
3 citations
"Phasing optical phased arrays using..." refers background in this paper
...For example, AMPERES modules incorporate exact results for to the interaction of thermal blooming and turbulence[6] and functional scaling[ 7 ] for accurate results for large diameter beams....
[...]
...In fact, the functional scaling provides results that are better resolved than the Cray results for large diameter beams[ 7 ]....
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