Atmospheric turbulence imparts phase distortions on propagating optical waves. These distortions couple into amplitude fluctuations at the pupil of a telescope, which, for strong enough phase distortions, produce zeros in the amplitude called branch points. In our earlier work, we presented the case that branch points can be utilized as a source of information on the turbulent atmosphere. Using our bench-top data, we have demonstrated several properties of branch points including motion, density, persistence and separation. We have shown that the pupil plane motion of subsets of branch points scales to the velocities of atmospheric turbulence layers and identifies the number of branch point producing layers. We have identified empirical relationships for density and separation as functions of the strength and altitude for a single layer. All of this work has been done using a bench-top adaptive optics system utilizing a two-layer atmospheric turbulence simulator. In this paper, we use simulations to verify these previous results by showing that all of these branch point properties follow similar behaviors in independently anchored wave optics simulations.
Branch points form from interference within a propagating wave due to phase differences imparted by atmospheric
turbulence. In the companion paper, we demonstrated that the characteristics of density and separation found in
our experimental work are reproducible in an independent wave optical simulation. In this paper, we expand on
this demonstration to include the measurement of the number and velocities of branch point producing turbulence
layers as well as the existence of persistent pairs in pupil plane measurements. Together these two papers verify
our previous experimental results on pupil plane branch point measurements.
Atmospheric turbulence imparts phase distortions on propagating optical waves. These distortions couple into
amplitude
uctuations at the pupil of a telescope, which, for strong enough phase distortions, produce branch
points (zeros in the amplitude). In our earlier work we have presented the case that branch points can be utilized
as a source of information on the turbulent atmosphere. Using our bench-top data, we have demonstrated several
properties of branch points including motion, density, persistence and separation. We have identied empirical
relationships for density and separation as functions of the strength and altitude for a single layer. However, this
work was done using a bench-top adaptive optics system utilizing a two-layer atmospheric turbulence simulator.
In this rst paper, we use independently anchored wave optics simulations to verify these results. This simulation
provides a means to further examine how the turbulence conditions contribute to the branch point distribution.
Additionally, we look at the role of the inner scale in the formation of branch points within the optical simulation.
The companion paper will examine the properties of branch point velocity and persistence.
We propose a sensor that measures the number, strength, altitude and velocity of atmospheric turbulence layers.
Recent research has shown that pupil plane branch points contain four independent and measureable parameters
and that these four parameters can be used to estimate four independent turbulence layer parameters--number,
strength, altitude and velocity--for each atmospheric turbulence layer. Here, we summarized previous results
and then demonstrate how these results allow for construction of a turbulence layer sensor.
Micro-Electro-Machined Systems (MEMS) have been increasingly used as mirrors in place of conventional continuous
face sheet deformable mirrors (DM) in adaptive optics (AO) systems. Here we study the diffraction effects
introduced into the optical path when a segmented MEMS DM is used to correct for the wavefront aberrations.
Diffraction effects are monitored through the intermediate focus plane prior to the wavefront sensor. Low pass
spatial filter is used at that plane in order to investigate how the masking of various diffraction orders affects
the phase. Measured phase and focal image plane data for various turbulence conditions are presented and
analyzed.
In earlier work we have shown that pupil plane branch points carry information about the conditions of the
atmospheric turbulence. Experiments in the Atmospheric Simulation and Adaptive-optic Laboratory Test-bed
(ASALT) at the Air Force Research Laboratory, Directed Energy Directorate's Starfire Optical Range have
shown that branch points can provide the number and velocity of turbulence layers. Here we demonstrate that
these measurements can further be used to estimate the turbulence layers' altitude and strength. This work is
the culmination of research demonstrating that a methodology exists for identification of the number, altitude,
strength, and velocity of atmospheric turbulence layers.
The ASALT lab has been investigating the use of a segmented MEMS
DM in adaptive optics systems. One of the anticipated benefits of a segmented device
is that in monochromatic light the throw is essentially infinite due to the modulo
2π nature of the device. Earlier work demonstrated how this modulo 2π behavior interacts
unexpectedly with a standard proportional integral controller. Here we present
experimental data on this effect to include the testbed on which the data was taken and
the methodology used to measure the effect.
The use of a laser guidestar (LGS) for the purpose of a beacon in an adaptive-optics (AO) system is prone to
perspective elongation effects on the spots of a Shack-Hartmann wavefront sensor. The elongated spots can
vary in size over the subapertures and affect the gradient sensitivity of the sensor. The Air Force Research
Laboratory (AFRL) has developed a LGS model that outputs gradient gains which represent the effects of an
extended beacon on the spots for a Shack-Hartmann wavefront sensor. This paper investigates the application
of these gains in an experimental setup in order to both analyze the effects of the variation in those gains due to
spot size elongation and to measure the impact on the performance of an AO system.
This paper is the 3rd in a series of papers discussing characterization of a Micro-Electrical-Mechanical-System (MEMS)
deformable mirror in adaptive optics. Here we present a comparison between a conventional adaptive optics system
using a Xinetics continuous face sheet deformable mirror with that of segmented MEMS deformable mirror. We
intentionally designed the optical layout to mimic that of a conventional adaptive optics system. We present this initial
optical layout for the MEMS adaptive optics system and discuss problems incurred with implementing such a layout;
also presented is an enhanced optical layout that partially addresses these problems. Closed loop Strehl highlighting the
two systems will be shown for each case as well. Finally the performances of both conventional adaptive optics and the
MEMS adaptive optics system is presented for a range of adaptive optics parameters pertinent to astronomical adaptive
optics leading to a discussion of the possible implication of introducing a MEMS adaptive optics system into the science
community.
Recent research has shown that branch points, as they appear in astronomical applications, have a rich collective
behavior, showing, in particular, that branch point pairs have a well-defined, non-stoichastic velocity, and that
once a branch point pairs location is measured, it can be tracked in open-loop adaptive optics operation. The
research presented here uses this new information as a priori knowledge in closed-loop AO. Specifically, an
algorithm was developed that measures branch point location and velocity at time tk and then uses this to
estimate the phase contribution at time tk+n, giving it an effective memory of where branch points appear and
allowing it to determine more accurately between real branch points and noise. The output of the new algorithm
is used as a second input to the DM control law. Results of initial closed-loop AO tests will be presented.
The conventional adaptive-optics (AO) system configuration consisting of a Shack-Hartmann wavefront sensor
using the Fried geometry is prone to an unsensed waffle mode because of an inability to have discrete point
reconstruction of the phase at the actuator positions. Techniques that involve filtering and/or projecting out the
waffle mode in the reconstructor have been shown to be effective at not allowing the unwanted mode to occur,
but come at the cost of also omitting relevant high frequency content from the measured phase. This paper
analyzes a technique of sensing the waffle mode in the deformable mirror commands and applying a spatial filter
to those commands in order to mitigate for the waffle mode. Directly spatially filtering the deformable mirror
commands gives the benefit of maintaining the reconstruction of high frequency phase of interest while having
the ability to alleviate for the waffle pattern when it arises.
The Atmospheric Turbulence Simulator used in testing in the Atmospheric Simulation and Adaptive-optic Laboratory
Test-bed at Air Force Research Laboratory, Directed Energy Directorate's Starfire Optical Range is
configured based on three characteristics; Fried's parameter, r0, the Rytov number, σ2χ
, and the Greenwood
Frequency, fG. All three may be estimated from open loop data as a means of verifying the simulated turbulence
conditions for a given test configuration. However, unlike r0 and fG, the Rytov number isn't directly calculated.
Instead the scintillation index is estimated from intensity measurements. At low Rytov values, (< 0.3 - 0.4),
this measurement can approximate the Rytov number, however beyond a Rytov of 0.4 this parameter becomes
saturated. Branch Points begin to appear after the Rytov value exceeds 0.1. In this work the behavior of the
branch point density is examined to determine its viability as another parameter for calibration our turbulence
simulator.
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