Robert K. Tyson

Principles of Adaptive Optics

History and Background: Introduction. History. Physical Optics: Propagation with Aberrations. Imaging with Aberrations. Representing the Wavefront. Interference. Adaptive Optics Terms. Sources of Aberrations: Atmospheric Turbulence: Descriptions of Atmospheric Turbulence. Refractive Index Structure Constant. Turbulence Effects. Turbulence MTF. Thermal Blooming: Blooming Strength and Critical Power. Turbulence, Jitter, and Thermal Blooming. Non-atmospheric Sources: Optical Misalignments and Jitter. Thermally Induced Distortions of Optics. Manufacturing and Microerrors. Other Sources of Aberrations. Adaptive Optics Compensation: Phase Conjugation. Limitations of Phase Conjugation: Turbulence Spatial Error. Turbulence Temporal Error. Sensor Noise Limitations. Thermal Blooming Compensation. Artificial Guide Stars. Combining the Limitations. Linear Analysis of Random Wavefronts. Linear Analysis of Deterministic Wavefronts: Partial Phase Conjugation. Adaptive Optics Systems: Adaptive Optics Imaging Systems. Beam Propagation Systems: Local Loop Beam Cleanup Systems. Alternative Concepts. Pros and Cons of the Various Approaches. Unconventional Adaptive Optics: Nonlinear Optics. Elastic Photon Scattering, DFWM. Inelastic Photon Scattering. System Engineering. Wavefront Sensing: Directly Measuring Phase: The Non-uniqueness of the Diffraction Pattern. Determining Phase Information from Intensity. Modal and Zonal Sensing. Direct Wavefront Sensing--Modal: Importance of Wavefront Tilt. Measurement of Tilt. Focus Sensing. Modal Sensing of Higher-Order Aberrations. Direct Wavefront Sensing--Zonal: Interferometiric Wavefront Sensing. Hartman Wavefront Sensors. Curvature Sensing. Selecting a Method. Indirect Wavefront Sensing Methods: Multidither Adaptive Optics. Image Sharpening. Wavefront Sampling: Beamsplitters. Hole Gratings. Temporal Duplexing. Reflective Wedges. Diffraction Gratings. Hybrids. Sensitivities of Sampler Concepts. Detectors and Noise. WavefrontCorrection: Modal Tilt Correction. Modal Higher-Order Correction. Segmented Mirrors. Deformable Mirrors: Actuation Techniques. Actuator Influence Functions. Bimorph Corrector Mirrors. Membrane and Micromachine Mirrors. Edge Actuated Mirrors. Large Correcting Optics. Special Correction Devices: Liquid Crystal Phase Modulators. Spatial Light Modulators. Charged-large-array-mirrors. Reconstruction and Controls: Introduction. Single-Channel Linear Control: Fundamental Control Tools. Transfer Functions. Proportional Control. First- and Second-Order Lag. Feedback. Frequency Response of Control Systems. Digital Controls. Multivariate Adaptive Optics Controls: Solution of Linear Equations. Direct Wavefront Reconstruction: Phase from Wavefront Slopes. Modes from Wavefront Slopes. Phase from Wavefront Modes. Modes from Wavefront Modes. Zonal Corrector from Continuous Phase. Modal Corrector from Continuous Phase. Zonal Corrector from Modal Phase. Modal Correctors from Modal Phase. Indirect Reconstructions.Modal Corrector from Wavefront Modes. Zonal Corrector from Wavefront Slopes. Spatiotemporal Considerations. Subject Index.

Vortex beam propagation through atmospheric turbulence and topological charge conservation

The propagation of vortex beams through weak-to-strong atmospheric turbulence is simulated and analyzed. It is demonstrated that the topological charge of such a beam is a robust quantity that could be used as an information carrier in optical communications. The advantages and limitations of such an approach are discussed.

Bit-error rate for free-space adaptive optics laser communications

An analysis of adaptive optics compensation for atmospheric-turbulence-induced scintillation is presented with the figure of merit being the laser communications bit-error rate. The formulation covers weak, moderate, and strong turbulence; on-off keying; and amplitude-shift keying, over horizontal propagation paths or on a ground-to-space uplink or downlink. The theory shows that under some circumstances the bit-error rate can be improved by a few orders of magnitude with the addition of adaptive optics to compensate for the scintillation. Low-order compensation (less than 40 Zernike modes) appears to be feasible as well as beneficial for reducing the bit-error rate and increasing the throughput of the communication link.

Adaptive optics engineering handbook

System design and optimization guide state system considerations wavefront sensors deformable mirror wavefront correctors innovative wavefront estimators for zonal adaptive optics systems micromachined membrane deformable mirrors surfacemicromachined deformable mirrors liquid crystal adaptive optics wavefront sensing and compensation for the human eye wide field-of-view wavefront sensing.

Adaptive optics and ground-to-space laser communications.

The relationships between laser communication system parameters and adaptive optics system parameters are addressed. Improvement in optical signal propagation between space-based receivers and ground-based transmitters is possible with adaptive optics systems that compensate for a few degrees of freedom. Beginning with the relationship between optical signal fade and surge and the atmospheric log-amplitude variance and coupling to expressions that combine adaptive optics systems performance with the reduction in log-amplitude variance, system level examinations of the effects of adaptive optics can be done. Examples are given that show the advantageous reduction in signal fade and surge when adaptive optics are built into the optical system.

Generation of an optical vortex with a segmented deformable mirror

We present a method for the creation of optical vortices by using a deformable mirror. Optical vortices of integer and fractional charge were successfully generated at a wavelength of 633 nm and observed in the far field (2000 mm). The obtained intensity patterns proved to be in agreement with the theoretical predictions on integer and fractional charge optical vortices. Interference patterns between the created optical vortex carrying beams and a reference plane wave were also produced to verify and confirm the existence of the phase singularities.

Indirect measurement of a laser communications bit-error-rate reduction with low-order adaptive optics.

In experimental measurements of the bit-error rate for a laser communication system, we show improved performance with the implementation of low-order (tip/tilt) adaptive optics in a free-space link. With simulated atmospheric tilt injected by a conventional piezoelectric tilt mirror, an adaptive optics system with a Xinetics tilt mirror was used in a closed loop. The laboratory experiment replicated a monostatic propagation with a cooperative wave front beacon at the receiver. Owing to constraints in the speed of the processing hardware, the data is scaled to represent an actual propagation of a few kilometers under moderate scintillation conditions. We compare the experimental data and indirect measurement of the bit-error rate before correction and after correction, with a theoretical prediction.

Using the deformable mirror as a spatial filter: application to circular beams

Adaptive optics correction of a wave front by a deformable mirror that acts as a lossless spatial filter is studied. The decomposition of the wave front into Zernike polynomials provides a means for deriving the rms error of a corrected wave front in analytic form. The spatial filter is given in a functional form related to deformable mirror characteristics. A step filter approximation is derived and the conditions where the approximation holds are examined. An example is provided to demonstrate the utility of the spatial filtering concept for adaptive optics systems analysis.

Measurement of the bit-error rate of an adaptive optics, free-space laser communications system, part 1: tip-tilt configuration, diagnostics, and closed-loop results

We describe an experiment where we made a direct measurement of the bit-error rate of a low-order adaptive optics laser communications system. The adaptive optics system consisted of a two-axis tip-tilt corrector. In the paper we describe the driver system for the tilt aberration generator, the tilt sensor, the control system for the corrector mirror, and the diagnostic electronics for measuring and recording the bit-error rate. Finally, we present results of a closed-loop experiment where we report bit-error rate improvement up to a factor of 42.

Measurement of the bit-error rate of an adaptive optics, free-space laser communications system, part 2: multichannel configuration, aberration characterization, and closed-loop results

We describe an experiment where we made a direct measurement of the bit-error rate of a high-order adaptive optics laser communications system. We describe a quantitative characterization of a repeatable atmospheric turbulence aberration generator and both static and dynamic characterizations of a 19-channel adaptive optics system. We show a reduction of the bit-error rate by a factor of 41.5 under specific laboratory conditions.