B. Hatfield

Bio: B. Hatfield is an academic researcher. The author has contributed to research in topics: Adaptive optics & Thermal blooming. The author has an hindex of 4, co-authored 23 publications receiving 62 citations.

Perturbative approach to the small-scale physics of the interaction of thermal blooming and turbulence

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.

An exact analytic solution to segmented-mirror adaptive-optics control

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.

Introduction to laser guide star theory versus experiment

Abstract: We discuss the reliance on backscatter by a laser guide star to generate a propagative probe and we show that spatial reciprocity can be accomplished by compensating phase alone. An analytic plane to plane propagation framework is introduced in which the spatial reciprocity of Maxwell's equations Is utilized to demonstrate that the adaptive optics compensation can do no better than the beacon initial conditions (I.e. cannot correct for the beacon too.) It is shown analytically that use of point to point reciprocity reasoning fails. While the laser guide star itself may be compensated to optimize uplink spatial coherence at altitude, the backscattering process is completely incoherent and the backscattering volume constitutes a very bad mirror or diffuse source. While diffraction restores some coherency as described by the van Cittert-Zernike theorem[2,5], the consequences of the incoherency of the beacon, lead to problems for the adaptive optics system which do not affect natural guide stars. The main consequence for the laser guide star system is that the wave sensor of the adaptive optics cannot distinguish between the phase aberrations from the backscattering process and those phase aberrations induced by turbulence. The question of the beacon and propagative path being different is weighed within the context of correlated versus uncorrelated ensemble members of turbulence.

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

Abstract: 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.

Two-Deformable-Mirror Concept for Correcting Scintillation Effects in Laser Beam Projection Through the Turbulent Atmosphere

Abstract: 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 with 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 with a conventional phase-only correction system.

Designing a mirror to form a line-shaped directivity diagram

Abstract: We design a mirror to form a directivity diagram defined as a vector function of one argument. An analytical solution for the problem of generating a line-shaped directivity diagram from a point source is derived. The mirror calculation reduces to solving an ordinary differential equation. A mirror to generate the line-shaped directivity diagram of angular size 120° and uniform intensity is designed.

Wave-optics Investigation of Turbulence Thermal Blooming Interaction: I. Using Steady-state Simulations

Abstract: Part I of this two-part paper uses wave-optics simulations to look at the Monte Carlo averages associated with turbulence and steady-state thermal blooming (SSTB). The goal is to investigate turbulence thermal blooming interaction (TTBI). At wavelengths near 1 μm, TTBI increases the amount of constructive and destructive interference (i.e., scintillation) that results from high-power laser beam propagation through distributed-volume atmospheric aberrations. As a result, we use the spherical-wave Rytov number and the distortion number to gauge the strength of the simulated turbulence and SSTB. These parameters simplify greatly given propagation paths with constant atmospheric conditions. In addition, we use the log-amplitude variance and the branch-point density to quantify the effects of TTBI. These metrics result from a point-source beacon being backpropagated from the target plane to the source plane through the simulated turbulence and SSTB. Overall, the results show that the log-amplitude variance and branch-point density increase significantly due to TTBI. This outcome poses a major problem for beam-control systems that perform phase compensation.

Wave-optics Investigation of Turbulence Thermal Blooming Interaction: II. Using Time-dependent Simulations

Abstract: Part II of this two-part paper uses wave-optics simulations to look at the Monte Carlo averages associated with turbulence and time-dependent thermal blooming (TDTB). The goal is to investigate turbulence thermal blooming interaction (TTBI). At wavelengths near 1 μm, TTBI increases the amount of constructive and destructive interference (i.e., scintillation) that results from high-power laser beam propagation through distributed-volume atmospheric aberrations. As a result, we use the spherical-wave Rytov number, the number of wind-clearing periods, and the distortion number to gauge the strength of the simulated turbulence and TDTB. These parameters simply greatly given propagation paths with constant atmospheric conditions. In addition, we use the log-amplitude variance and the branch-point density to quantify the effects of TTBI. These metrics result from a point-source beacon being backpropagated from the target plane to the source plane through the simulated turbulence and TDTB. Overall, the results show that the log-amplitude variance and branch-point density increase significantly due to TTBI. This outcome poses a major problem for beam-control systems that perform phase compensation.

Cryogenic performance of lightweight SiC and C/SiC mirrors

Abstract: The technology associated with the use of silicon carbide (SiC) for high-performance mirrors has matured significantly over the past 10-20 years. More recently, the material has been considered for cryogenic applications such as space-based infrared telescopes. In light of this, NASA has funded several technology development efforts involving SiC mirrors. As part of these efforts, three lightweight SiC mirrors have been optically tested at cryogenic temperatures within the X-Ray Calibration Facility (XRCF) at Marshall Space Flight Center (MSFC). The three mirrors consisted of a 0.50 m diameter carbon fiber-reinforced SiC, or C/SiC, mirror from IABG in Germany, a 0.51 m diameter SiC mirror from Xinetics, Inc., and a 0.25 m diameter SiC mirror from POCO Graphite, Inc. The surface figure error was measured interferometrically from room temperature (~290 K) to ~30 K for each mirror. The radius-of-curvature (RoC) was also measured over this range for the IABG C/SiC & Xinetics SiC mirrors. This paper will describe the test goals, the test instrumentation, and the test results for these cryogenic tests.