Branch points are seen in many adaptive optical experiments where the sensed beam has propagated over an extended path, through sufficiently strong turbulence. It has been shown that branch points provide information on how the turbulence responsible for their formation is distributed and moving along the path. Shack-Hartmann wave front sensors have previously been somewhat limited in their ability to fully capture the branch points present within their measurements. A new technique for the detection of branch points based on the second moment statistics of the individual spots in images created with a Shack-Hartmann wave front sensor system is examined. Data collected by Small Mobile Atmospheric Sensing Hartmann (SMASH) units are used to test the method under a range of turbulence conditions. The results of the second moment technique are compared with the standard elementary circulation method.
The Reflective Atmospheric Turbulence Simulator (RATS) in the Air Force Research Laboratory’s Beam Control Laboratory is used to impart realistic distortions to a propagating wavefront for testing in the advancement of adaptive optical technologies. Here RATS is being used to simulate turbulence conditions over which the Small Mobile Atmospheric Sensing Hartmann (SMASH) system has typically operated. An optical clone of the SMASH system installed on the optical bench behind RATS measures the imparted optical disturbance and makes an estimate of the turbulence profile. The results are compared with the profile calculated based on the configuration of the RATS system.
In this paper, we use wave-optics simulations to explore laser propagation system performance. We accomplish this by creating a trade space where we vary turbulence conditions as well as beacon size from a point-source beacon to an extended-source beacon with an object Fresnel number, Nobj, of 20. We explore performance when we employ no compensation, perfect phase compensation, and perfect full-phase compensation. The results of this trade space allow us to arrive at three main conclusions. First, if we have either a point-source beacon or a very small extended-source beacon and turbulence is strong, we get a significant improvement in performance using full-phase compensation compared to least-squares compensation and no compensation. If turbulence is weak, we see similar performance with least-squares and full-phase compensation, however, both are significantly improved over the no compensation case. Second, in strong turbulence conditions, there will be a very large number of turbulence-induced branch points. If left uncompensated, these turbulence-induced branch points will result in a major reduction in performance. Lastly, when the extended-source beacon is large, the associated rough-surface-scattering-induced phase aberrations will corrupt the compensation to the point where the drawbacks of compensating for surface-roughness-induced aberrations significantly outweigh the benefits of compensating for turbulence-induced aberrations. These results (1) inform researchers looking to conduct extended-source-beacon adaptive optics and (2) motivate research to explore methods for speckle mitigation in adaptive-optics systems.
The Reflective Atmospheric Turbulence Simulator (RATS) is an instrument used to simulate the propagation of light through atmospheric turbulence. RATS can simulate up to six layers of atmospheric turbulence using reflective phase wheels with many configurations that can simulate a broad range of atmospheric turbulence conditions. Two ShackHartmann wavefront sensors are integrated with RATS. One of these Shack-Hartmann wavefront sensors has an effective aperture size of 40cm, and the other has an effective aperture size of 6.75cm. We simulated propagation through atmospheric turbulence using RATS and made measurements of turbulence parameters using the two Shack-Hartmann wavefront sensors. In this paper, we compare the measurements of turbulence parameters from both Shack-Hartmann wavefront sensors to each other as well as to the theoretical values for atmosphere turbulence simulated by RATS.
Frodo is a new Differential Image Motion Monitor (DIMM) developed as a companion instrument to the Starfire Atmospheric Monitor (SAM). SAM is a Shack-Hartmann sensor that observes bright stars to provide atmospheric information above the Air Force Research Laboratory’s Starfire Optical Range (SOR). Frodo is designed to extend atmospheric characterization at the SOR into the day, estimating all of the atmospheric parameters that SAM currently provides. The optical train of Frodo has been reproduced on the Multiconjugate Adaptive Optics (MCAO) bench in the Atmospheric Simulation and Adaptive Optics Laboratory Testbed (ASALT) at SOR. The enhanced atmospheric turbulence simulator (ATS) on the MCAO bench generates turbulence conditions with as many as 10 phase screens. The atmospheric parameter estimates from data collected with the ASALT Frodo system are presented alongside the estimates made with the laboratory’s Shack-Hartmann wavefront sensor.
In a previous paper, the authors presented a benchtop demonstrator for a stereo scintillation detection and ranging (SCIDAR) system at the Air Force Research Lab’s Starfire Optical Range. The stereo SCIDAR setup and reconstruction algorithms from this effort accurately characterized the seven-layer atmosphere generated by the atmospheric simulation and adaptive optics laboratory testbed’s (ASALT’s) multi-conjugate adaptive optics (MCAO) bench. This paper details the successful transition of that stereo SCIDAR system to the coudé room of a 1.0m telescope. It shares lessons learned, including additional components and alignment techniques for the on-sky system. Finally, it presents automation efforts of the system to support extended on-sky observations.
Two methods for identifying branch points from Shack–Hartmann wavefront sensor (SHWFS) measurements were studied: the circulation of phase gradients approach and the beam-spread approach. These approaches were tested using a simple optical-vortex model, with wave-optics simulations, and with experimental data. It was found that these two approaches are synergistic regarding their abilities to detect branch points. Specifically, the beam-spread approach works best when the branch point is located toward the center of the SHWFS’s lenslet pupil, whereas the circulation of phase gradients approach works best when the branch point is located toward the edge of the SHWFS’s lenslet pupil. These behaviors were observed studying the simple optical-vortex model; however, they were further corroborated with the wave-optics and experimental results. The developments presented support researchers studying high scintillation optical-turbulence environments and inform efforts in developing branch-point tolerant reconstruction algorithms.
Estimating the prole of the index of refractive-index structure constant, C2n(z), is of great importance for characterizing the turbulence through which adaptive optical systems operate. Stereo Scintillation Detection and Ranging (SCIDAR) is one of the well developed techniques for making such a prole using light from binary stars. The Air Force Research Laboratory's Starre Optical Range (SOR) is beginning work to add a Stereo SCIDAR capability to the site. This work presents the development and testing of a stereo SCIDAR system in the Atmospheric Simulation and Adaptive Optics Laboratory Testbed (ASALT) at SOR. The stereo SCIDAR system was constructed on the ASALT lab's Multiconjugate Adaptive Optics (MCAO) bench, which features an enhanced atmospheric turbulence simulator (ATS) that can use up to 10 phase screens to test the capabilities of the stereo SCIDAR system in profiling distributed turbulence under a wide range of conditions.
KEYWORDS: Turbulence, Beam path, Air force, Temperature metrology, Atmospheric propagation, Air temperature, Wind measurement, Profiling, Sun, Refractive index
Sonic anemometers are devices that use ultrasound to provide instantaneous wind velocity and sonic temperature measurements. One of these devices, in conjunction with other meteorological equipment, provides characterization of the local atmosphere at a fixed point. Combining multiple sonic anemometers can provide an estimate of the index of refraction structure function, C2n(z), along a beam path. This work details this process for characterization of an optical propagation path for use in the evaluation of the performance of turbulence measurement instruments. Experimental results are presented from a one-kilometer horizontal path.
Knowledge of the atmospheric conditions along an optical path is crucial to many experiments. A technique using differential scintillations was adapted for the Small Mobile Atmospheric Sensing Hartmann (SMASH) system to estimate proles of the refractive-index structure constant, C2n(z), and the wind speed. Estimates of those parameters from data taken along a 1 km horizontal path over level ground at a height of about five feet at Kirtland AFB is presented. Five sonic anemometers, placed along the path, serve as an independent estimate of the turbulence conditions with which to evaluate SMASH's performance.
The advancement of adaptive optics (AO) has a tradition of using benchtop optical simulators to progress control technologies from concept towards fielded systems. This paper presents a reflective atmospheric turbulence simulator (RATS) for the Air Force Research Laboratory's Beam Control Laboratory (BCL) with which the next steps in AO will be tested. The reflective nature of the system allows operation over a broad range of wavelengths. RATS consists of six moveable phase screens etched with Kolmogorov turbulence phase patterns. The configuration of the system can be varied to simulate a wide range of atmospheric turbulence conditions setting the needed parameters of the Fried coherence length, Greenwood frequency, Rytov variance and the isoplanatic angle, to meet a given scenario. Shack-Hartmann measurements of the turbulence generated by RATS are compared to the system design.
In this paper, two methods for identifying branch points from Shack–Hartmann wavefront sensor (SHWFS) measurements were studied; the circulation of phase gradients approach and the beam-spread approach. These approaches were tested using a simple optical-vortex model, wave-optics simulations, and with experimental data. It was found that these two approaches are synergistic regarding their abilities to detect branch points. Specifically, the beam-spread approach works best when the branch point is located towards the center of the SHWFS’s lenslet pupil, while the circulation of phase gradients approach works best when the branch point is located towards the edge of the SHWFS’s lenslet pupil. These behavior were observed studying the simple optical-vortex model; however, they were further corroborated with the wave-optics and experimental results. The developments presented within support researchers looking to study high scintillation optical-turbulence environments as well as will inform efforts looking to develop branch-point tolerant reconstruction algorithms.
The tilted shearing interferometer (tSI) wavefront sensor (WFS) is being developed to expand characterization capabilities for optical propagation experiments at the Air Force Research Laboratory's Environmental Laser Test Facility (ELTF). The instrument utilizes the phase retrieval technique of a digital holographic WFS with laterally sheared beams rather than a local oscillator reference. This WFS provides gradients similar to a Shack-Hartmann WFS, allowing it to benefit from all of the processing developed for the Small Mobile Atmospheric Sensing Hartmann (SMASH). At the same time, the interferometric nature of the wave front sensor provides access to additional information, i.e. branch cuts. Initial development of the tilted shearing interferometer in the Air Force Research Laboratory's Beam Control Lab (BCL) is presented.
An implementation of differential scintillations to characterize the C2n(z) profile along a nearly horizontal propagation path measured by a Shack-Hartmann wavefront sensor is developed and demonstrated. Measurements from a Small Mobile Atmospheric Sensing Hartmann (SMASH) instrument using an LED source to characterize 500 m, 1 km and 2 km paths at the Environmental Laser Test Facility (ELTF) are presented.
The inner scale plays a critical role in beam scintillation and branch point evolution in optical propagation through atmospheric turbulence. Understanding this parameter, in-situ, during experiments is therefore of great interest. We compare different methods of estimating the inner scale using AFRL’s Small Mobile Atmospheric Sensing Hartmann (SMASH). The investigations are conducted with data collected at Kirtland, AFB in New Mexico along multiple paths varying from weak to strong irradiance fluctuation conditions.
The performance of closed-loop tilt-control and adaptive-optics systems suffers when conditions change. Examples of changing conditions are angular extent of the object, signal-to-noise ratio, and characteristics of the disturbance. A simple learning algorithm motivated by neural network theory is developed to change the closed-loop gain in real-time to adapt quickly to changing conditions. This technique finds the correct loop gain within seconds with no operator intervention, which saves several minutes for each observation. Simulation and experimental results show improvement for both tilt-control and adaptive-optics systems.
An experiment, specifically undertaken in order to measure terrestrial turbulence-induced photonic orbital angular momentum, was conducted at the RACHL site at the Starfire Optical Range. We present an overview of the experiment, to include methodology and calibration.
We develop a metric that measures the isotropy of atmospheric turbulence. We then apply that metric to data from the RACHL experiment as a test of the Kolmogarity of the turbulence encountered in that experiment.
At the Starfire Optical Range in 2011, the first measurements of photonic orbital angular momentum in starlight were made. Although that survey conclusively demonstrated that POAM exists in starlight, the survey was limited. We have subsequently obtained access to the SAM data archive with its seven years of data. Here the SAM data is analyzed to include the two metrics, branch point density, ρ , and the conversion efficiency η, that were used in the analysis of the 2011 observations.
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.
Previous theoretical work, to first order, demonstrated that branch points are markers for photons carrying orbital angular momentum (OAM), but gave to indication of the flux associated with a given branch point distribution. In a parallel effort, the OAM flux as a ratio of the total flux is calculated, but that work relies on knowing the non-zero elements in the slope discrepancy Hilbert space. Here, we calculate the “size” of the slope discrepancy Hilbert space for our previously published data.
The Air Force Research Laboratory (AFRL) is developing and extending a model of the boundary layer that takes, as input,
common atmospheric measurements and ground condition parameters, and predicts key parameters of optical turbulence
such as strength and inner scale. In order to anchor the model, a field campaign is also being conducted. The campaign will
include co-located meteorological instruments and an open loop Hartmann wavefront sensor. Here, a portion of the
boundary layer model is discussed: that relevant for the daytime surface layer. A sensitivity analysis of input parameters is
presented.
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.
In our first work in this research thread, we demonstrated that turbulence-created optical vortices are created
innitesimally close together in pairs of opposite helicity--call these creation pairs. In that rst work, we postu-
lated that creation pairs separate as they propagate, and that they carry both the velocity of, and distance to,
the turbulence layer that created them. Subsequent experimental papers have demonstrated this to be true. Our
purpose here is to ll two gaps in our original theoretical results and demonstrate both how, in a mathematical
treatment, turbulence-created optical vortices can have the velocity of the turbulence layer that created them,
and also, present calculation of their separation velocity.
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.
High contrast imaging, also known as extreme adaptive optics, has been a topic of research in the astronomic
community as an approach to image dim objects near bright objects, such as extra-solar planets. There are
a variety of techniques ranging from coronagraphs, shaped pupils, pupil apodization, and the use of multiple
deformable mirrors that have been employed to improve the contrast between the two objects. We integrated
shaped pupils into our adaptive optics system. Here we will present experimental results exploring the viability
of using our testbed to perform dim object detection using shaped pupils in the presence of turbulence.
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.
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 ASALT lab has been investigating the use of a segmented MEMS DM in adaptive optics systems. Here, we
investigate the fitting error for a segmented deformable mirror with flat subaperture segments. This investigation
is done in the regime where the hidden phase is significant. Data from both simulation and theory are presented
giving initial estimates of the magnitude of the error.
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.
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.
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.
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.
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.
It has long been known that branch points cause degradation in adaptive optic performance. Here, we begin
a study on the aggregate nature of branch points, specifically beginning the process to relate branch points
measured in the pupil to the upstream turbulence that created them. As such, we study not only the wave
as measured in the telescope's pupil, but also the wave in the intervening region between the turbulence layer
and the pupil with this paper's focus on the intervening region. We show that for optical waves propagating in
atmospheric turbulence upstream of the pupil, branch points are created infinitesimally close together in pairs
of opposite polarity. Branch points are shown to be enduring features of the propagating wave and their branch
cuts are shown to evolve smoothly in time. It is postulated that atmospherically created branch point pairs
separate as they propagate, and that they carry both the velocity of, and distance to, the turbulence layer that
created them. Subsequent papers will demonstrate this to be true.
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 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.
This is the first of two papers discussing aspects of placing the deformable mirror in a location
not conjugate to the pupil plane of the telescope.
The Starfire Optical Range, Air Force Research Laboratory's Directed Energy Directorate
is in the process of developing a high efficiency AO system for its 3.5m optical telescope. The
objective is to achieve maximum diffraction limited performance, i.e., largest pupil diameter
possible, and maximum optical throughput. The later can be achieved by placing the deformable
mirror outside the pupil. However placing the DM in a location not conjugate to the pupil results
in a degradation in optical performance. This paper discusses experimental measurements of
the degradation.
In this paper we discuss the DM-not-in-pupil experimental testbed, the difficulties associated
with creating this type of testbed, and how these difficulties were overcome. We also present
results from the successful lab demonstration of closed loop performance with the DM placed out
of pupil. We experimentally measured the degradation in Strehl and implemented a mitigation
technique. Our experimental results indicate the mean degradation in Strehl as a result of placing
the DM out of pupil to be between 7% and 9 %. This result is comparable with wave optics
simulation and theoretical results which will be discussed in a companion paper, "Adaptive
optics with DM not in pupil - Part 2: Mitigation of Degradation".
Multi-Conjugate Adaptive-Optical (MCAO) systems have been proposed as a means of compensating both
intensity and phase aberrations in a beam propagating through strong-scintillation environments. Progress made
on implementing a MCAO system at the Starfire Optical Range (SOR), Air Force Research Laboratory, Kirtland
AFB, is discussed. In previous work, it was shown that the First-stage Intensity Redistribution Experiment
(FIRE) controlled and compensated wavefront intensity for static cases. As a secondary step toward controlling
a two deformable mirror (DM) system, the FIRE experimental layout is used to examine another aspect of an
MCAO system faster control of wavefront intensity. The FIRE experimental layout employs two wavefront
sensors (WFS) and a single DM. One WFS is placed conjugate to the DM while the second WFS is located at a
distance which produces a desired Fresnel number for the propagation between theWFSs. A modified Gerchberg-
Saxton (GS) algorithm that propagates between image planes is employed for determining DM commands. The
forward and back propagation portion of each GS iteration are computed in software. Using the GS solution, a
control loop is closed on a WFS reconstructor in order to maintain beam shape in moving optical turbulence.
The forward propagation phase pattern produced by the GS algorithm is tailored, via constraints, so that beam
propagation along the path between the two WFSs produces a desired intensity profile and minimizes phase
aberrations at the second WFS. In the next phase of MCAO development, a second DM will be added conjugate
to the second WFS in order to correct the remaining phase aberrations.
A few years ago the Air Force Research Laboratory developed a Self-Referencing Interferometer (SRI) wavefront
sensor (WFS) that is able to accurately detect the magnitude and phase of propagating electromagnetic waves in
a strong scintillation environment. This proved to be very useful in applications of adaptive optics when detecting
light or transmitting laser beams through moderate to high turbulence. The SRI operates by interfering a beacon
beam, which has been aberrated by atmospheric turbulence, with a reference beam having a known phase and
detecting the intensity of the interference pattern. The phase of the beacon is then determined from those
interference patterns. At least three different phases of a reference beam are needed to accurately determine
the phase on the beacon beam, but four are preferable. These phases shift the reference beam by 0, π/2, π,
and 3π/2. In this paper we examine the effects of phase shift errors. Our method can be extrapolated to any
WFS utilizing the Carré algorithm with π/2 phase steps. These results show that the SRI is amazingly tolerable
to phase shifting errors, specifically that an adaptive optic loop still closes even with a phase error 'epsilon' of
nearly ±π/2. Even more unexpected, it is possible to increase Strehl over the nominally aligned system by as
much as 11% in closed loop operation when phase errors are purposefully induced.
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