Liquid-crystal adaptive optics based on feedback interferometry for high-resolution retinal imaging

A novel, to our knowledge, adaptive optical imaging system for high-resolution retinal imaging is described. The system is based on a feedback interferometer, in which two-dimensional output fringe intensity from a Mach-Zehnder interferometer with large radial shear is fed back, with the help of a video projector connected with a CCD camera, to an optically addressed phase-only liquid-crystal spatial light modulator. Experiments to verify the system performance have been conducted by use of an artificial eye consisting of a lens, an aberration plate, and a resolution test target. We observed that an image of the test target (mimicking a retina) blurred by the aberration plate (mimicking ocular aberrations) was successfully restored immediately after our adaptive optics system was activated.     

System design considerations to improve isoplanatism for adaptive optics retinal imaging

Adaptive optics (AO) retinal images are limited by anisoplanatism; wavefront shape varies across the field of view such that only a limited area can achieve diffraction-limited image quality at one time. We explored three alternative AO modalities designed to reduce this effect, drawn from work in astronomy. Optical design analysis and computer modeling was undertaken to predict the benefit of each modality for various schematic eyes and various complexities of the imaging system. Off-axis performance was found to be limited by system parameters and not by the eye itself, due to the inherent off-axis characteristics of the eye's gradient index lens. This rendered the alternative AO modalities ineffectual compared with conventional AO but did suggest several methods by which anisoplanatism may be reduced by altering the design of conventional AO systems. Several of these design possibilities were explored with further modeling. The best-performing method involved the replacement of system lenses with gradient index versions inspired by the human eye lens. Mirror-based relay optics also demonstrated good off-axis performance, but their advantage was lost in regions of the system suffering from uncorrected higher-order aberration. Incorporating "off-the-plane" beam deviations ameliorated this loss substantially. In this work we also show, to our knowledge for the first time, that the ideal location of a single AO corrector need not lie in the pupil plane.     

High-resolution adaptive optics scanning laser ophthalmoscope with dual deformable mirrors

Adaptive optics scanning laser ophthalmoscopes have been used to produce noninvasive views of the human retina. However, the range of aberration compensation has been limited by the choice of deformable mirror technology. We demonstrate that the use of dual deformable mirrors can effectively compensate large aberrations in the human eye while maintaining the quality of the retinal imagery. We verified experimentally that the use of dual deformable mirrors improved the dynamic range for correction of the wavefront aberrations compared with the use of the micro-electro-mechanical-system mirror alone and improved the quality of the wavefront correction compared with the use of the bimorph mirror alone. We also demonstrated that the large-stroke bimorph deformable mirror improved the capability for axial sectioning with the confocal imaging system by providing an easier way to move the focus axially through different layers of the retina.     

Deconvolution of adaptive optics retinal images

We quantitatively demonstrate the improvement to adaptively corrected retinal images by using deconvolution to remove the residual wave-front aberrations. Qualitatively, deconvolution improves the contrast of the adaptive optics images. In this work we demonstrate that quantitative information is also increased by investigation of the improvement to cone classification due to the reduction in confusion of adjacent cones because of the extended wings of the point-spread function. The results show that the error in classification between the L and M cones is reduced by a factor of 2, thereby reducing the number of images required by a factor of 4.     

Effect of aberrations and scatter on image resolution assessed by adaptive optics retinal section imaging

The effect of increased high-order wavefront aberrations on image resolution was investigated, and the performance of adaptive optics (AO) for correcting wavefront error in the presence of increased light scatter was assessed in a model eye. An AO section imaging system provided an oblique view of a model retina and incorporated a wavefront sensor and deformable mirror for measurement and compensation of wavefront aberrations. Image resolution was quantified by the width of a Lorentzian curve fitted to a laser line image. Wavefront aberrations were significantly reduced with AO, resulting in improvement of image resolution. In the model eye, image resolution was degraded with increased high-order wavefront aberrations (horizontal coma and spherical) and improved with AO correction of wavefront error in the presence of increased light scatter. The findings of the current study suggest that AO imaging systems can potentially improve image resolution in aging eyes with increased aberrations and scatter.     

High-resolution lidar observations of mesospheric sodium and implications for adaptive optics

Observations of sodium density variability in the upper mesosphere/lower thermosphere, obtained using a high-resolution lidar system, show rapid fluctuations in the sodium centroid altitude. The temporal power spectrum extends above 1 Hz and is well-fit by a power law having a slope that is -1.95±0.12. These fluctuations produce focus errors in adaptive optics systems employing continuous-wave sodium laser guide stars, which can be significant for large-aperture telescopes. For a 30 m aperture diameter, the associated rms wavefront error is approximately 4 nm per meter of altitude change and increases as the square of the aperture diameter. The vertical velocity of the sodium centroid altitude is found to be ~23 ms(-1) on a 1 s time scale. If these high-frequency fluctuations arise primarily from advection of horizontal structure by the mesospheric wind, our data imply that variations in the sodium centroid altitude on the order of tens of meters occur over the horizontal scales spanned by proposed laser guide star asterisms. This leads to substantial differential focus errors (~107 nm over a 1 arc min separation with a 30 m aperture diameter) that may impact the performance of wide-field adaptive optics systems. Short-lasting and narrow sodium density enhancements, more than 1 order of magnitude above the local sodium density, occur due to advection of meteor trails. These have the ability to change the sodium centroid altitude by as much as 1 km in less than 1 s, which could result in temporary disruption of adaptive optics systems.     

天文学自适应光学成像望远镜的模拟

为分析天文学自适应光学(AO)望远镜中AO系统的校正性能,利用Matlab仿真其成像过程。采用正交基为Zernike多项式的自相关法产生符合大气统计特性的大气相位屏,仿真平行光通过大气后的瞬时畸变波前相位;采用快速傅里叶变换仿真哈特曼-夏克波前传感器的成像光斑,根据实际成像与参考平面波成像的质心坐标之差,计算波前传感器子孔径内的平均波前斜率。模拟比较了1.2m望远镜两种AO系统布局的校正性能,结果表明,子孔径为正六边形AO系统的校正性能略优于子孔径为正方形AO系统的校正性能,两种AO系统的SR比(StrechlRatio)分别为0.872和0.859。     

Phase-compensation experiment with a 37-element adaptive optics system

An experimental study on phase compensation for turbulent effects with a 37-element adaptive optics system is performed in both a simulated turbulence cell and in a real atmosphere. The experimental results demonstrate that the compensated Strehl ratio S(0), which is influenced mainly by the deformable-mirror fitting error, has a functional form S(0) = exp[-kappa(d/r(0))(5/3)], where r(0) is Fried's coherence length and d is the average interval of the actuators on the deformable mirror. The fitting parameter kappa is 0.45. Numerical simulations are also performed with the experimental parameters. The numerical results are in agreement with data obtained in the experiment, which shows that the direct-tilt phase-reconstruction method used in our four-dimensional simulation code is reasonable.     

Automated identification of cone photoreceptors in adaptive optics retinal images

In making noninvasive measurements of the human cone mosaic, the task of labeling each individual cone is unavoidable. Manual labeling is a time-consuming process, setting the motivation for the development of an automated method. An automated algorithm for labeling cones in adaptive optics (AO) retinal images is implemented and tested on real data. The optical fiber properties of cones aided the design of the algorithm. Out of 2153 manually labeled cones from six different images, the automated method correctly identified 94.1% of them. The agreement between the automated and the manual labeling methods varied from 92.7% to 96.2% across the six images. Results between the two methods disagreed for 1.2% to 9.1% of the cones. Voronoi analysis of large montages of AO retinal images confirmed the general hexagonal-packing structure of retinal cones as well as the general cone density variability across portions of the retina. The consistency of our measurements demonstrates the reliability and practicality of having an automated solution to this problem.     

Double-deformable-mirror adaptive optics system for phase compensation

Two kinds of algorithm for an adaptive optics (AO) system that uses two deformable mirrors (DMs), one with large stroke and the other with high spatial frequency, to correct different aberrations are described. The algorithms are based on modal method and direction-gradient method, respectively. Numerical simulations for the algorithms have been made. The simulation results indicate that the two DMs in the AO system can correct different aberrations with different characteristics, and the closed-loop performance of a double-DM AO system will be almost the same as that of an AO system that uses a single DM with an ideal stroke.     

Isoplanatism in a multiconjugate adaptive optics system

Turbulence correction in a large field of view by use of an adaptive optics imaging system with several deformable mirrors (DM's) conjugated to various heights is considered. The residual phase variance is computed for an optimized linear algorithm in which a correction of each turbulent layer is achieved by applying a combination of suitably smoothed and scaled input phase screens to all DM's. Finite turbulence outer scale and finite spatial resolution of the DM's are taken into account. A general expression for the isoplanatic angle thetaM of a system with M mirrors is derived in the limiting case of infinitely large apertures and Kolmogorov turbulence. Like Fried's isoplanatic angle theta0,thetaM is a function only of the turbulence vertical profile, is scalable with wavelength, and is independent of the telescope diameter. Use of angle thetaM permits the gain in the field of view due to the increased number of DM's to be quantified and their optimal conjugate heights to be found. Calculations with real turbulence profiles show that with three DM's a gain of 7-10x is possible, giving the typical and best isoplanatic field-of-view radii of 16 and 30 arcseconds, respectively, at lambda = 0.5 microm. It is shown that in the actual systems the isoplanatic field will be somewhat larger than thetaM owing to the combined effects of finite aperture diameter, finite outer scale, and optimized wave-front spatial filtering. However, this additional gain is not dramatic; it is less than 1.5x for large-aperture telescopes.     

Adaptive optics scanning laser ophthalmoscope with integrated wide-field retinal imaging and tracking

We have developed a new, unified implementation of the adaptive optics scanning laser ophthalmoscope (AOSLO) incorporating a wide-field line-scanning ophthalmoscope (LSO) and a closed-loop optical retinal tracker. AOSLO raster scans are deflected by the integrated tracking mirrors so that direct AOSLO stabilization is automatic during tracking. The wide-field imager and large-spherical-mirror optical interface design, as well as a large-stroke deformable mirror (DM), enable the AOSLO image field to be corrected at any retinal coordinates of interest in a field of >25 deg. AO performance was assessed by imaging individuals with a range of refractive errors. In most subjects, image contrast was measurable at spatial frequencies close to the diffraction limit. Closed-loop optical (hardware) tracking performance was assessed by comparing sequential image series with and without stabilization. Though usually better than 10 μm rms, or 0.03 deg, tracking does not yet stabilize to single cone precision but significantly improves average image quality and increases the number of frames that can be successfully aligned by software-based post-processing methods. The new optical interface allows the high-resolution imaging field to be placed anywhere within the wide field without requiring the subject to re-fixate, enabling easier retinal navigation and faster, more efficient AOSLO montage capture and stitching.     

Image-quality metrics for characterizing adaptive optics system performance

Adaptive optics system (AOS) performance is a function of the system design, seeing conditions, and light level of the wave-front beacon. It is desirable to optimize the controllable parameters in an AOS to maximize some measure of performance. For this optimization to be useful, it is necessary that a set of image-quality metrics be developed that vary monotonically with the AOS performance under a wide variety of imaging environments. Accordingly, as conditions change, one can be confident that the computed metrics dictate appropriate system settings that will optimize performance. Three such candidate metrics are presented. The first is the Strehl ratio; the second is a novel metric that modifies the Strehl ratio by integration of the modulus of the average system optical transfer function to a noise-effective cutoff frequency at which some specified image spectrum signal-to-noise ratio level is attained; and the third is simply the cutoff frequency just mentioned. It is shown that all three metrics are correlated with the rms error (RMSE) between the measured image and the associated diffraction-limited image. Of these, the Strehl ratio and the modified Strehl ratio exhibit consistently high correlations with the RMSE across a broad range of conditions and system settings. Furthermore, under conditions that yield a constant average system optical transfer function, the modified Strehl ratio can still be used to delineate image quality, whereas the Strehl ratio cannot.     

Hysteresis correction in the curvature adaptive optics system

An enhancing Coleman-Hodgdon model is introduced to describe the hysteresis curves of the bimorph deformable mirror (DM). Hysteresis curves are measured from a bimorph DM and then experiment is set up for the correction of hysteresis. Finally, step response and transfer functions of a curvature adaptive optics (AO) system are compared in three cases: with DM hysteresis, without hysteresis, and with hysteresis but corrected. Simulation results show that the bandwidth of a curvature AO system is improved significantly under different loop gains after hysteresis of the DM is corrected.     

Microelectromechanical system programmable aberration generator for adaptive optics

Adaptive optics systems and control algorithms can be tested in the laboratory with controlled disturbances. We have a micromachined deformable mirror that we use as a programmable aberration generator. We present a method of programming the actuator amplitudes so that the wave front reflecting from the surface will simulate atmospheric turbulence. We present experimental results that show that we can simulate the Kolmogorov spatial spectrum within the constraints of the useful region of the deformable mirror.     

Optical slicing of human retinal tissue in vivo with the adaptive optics scanning laser ophthalmoscope

We present imaging results in human retinal tissue in vivo that allowed us to determine the axial resolution of the adaptive optics scanning laser ophthalmoscope (AOSLO). The instrument is briefly described, and the imaging results from human subjects are compared with (a) the estimated axial resolution values for a diffraction-limited, double-pass instrument and (b) the measured one for a calibrated diffuse retinal model. The comparison showed that the measured axial resolution, as obtained from optical sectioning of human retinas in vivo, can be as low as 71 microm for a 50 microm confocal pinhole after focusing a 3.5 mm beam with a 100 mm focal-length lens. The axial resolution values typically fall between the predictions from numerical models for diffuse and specular reflectors. This suggests that the reflection from the retinal blood vessel combines diffuse and specular components. This conclusion is supported by the almost universal interpretation that the image of a cylindrical blood vessel exhibits a bright reflection along its apex that is considered specular. The enhanced axial resolution achieved through use of adaptive optics leads to an improvement in the volume resolution of almost 2 orders of magnitude when compared with a conventional scanning laser ophthalmoscope and almost a factor of 3 better than commercially available optical coherence tomographic instruments.     

Adaptive optics retinal imaging reveals S-cone dystrophy in tritan color-vision deficiency

Tritan color-vision deficiency is an autosomal dominant disorder associated with mutations in the short-wavelength-sensitive- (S-) cone-pigment gene. An unexplained feature of the disorder is that individuals with the same mutation manifest different degrees of deficiency. To date, it has not been possible to examine whether any loss of S-cone function is accompanied by physical disruption in the cone mosaic. Two related tritan subjects with the same novel mutation in their S-cone-opsin gene, but different degrees of deficiency, were examined. Adaptive optics was used to obtain high-resolution retinal images, which revealed distinctly different S-cone mosaics consistent with their discrepant phenotypes. In addition, a significant disruption in the regularity of the overall cone mosaic was observed in the subject completely lacking S-cone function. These results taken together with other recent findings from molecular genetics indicate that, with rare exceptions, tritan deficiency is progressive in nature.     

Field dependent amplitude calibration of adaptive optics supported solar speckle imaging

Adaptive optics supported solar speckle imaging requires the calibration of the source's Fourier amplitudes with the transfer function of atmosphere and optics. We present analytical models for the relevant transfer functions of an adaptive optics systems. The models include the effect of an arbitrary correction as well as anisoplanatism. The proposed models have been compared with observational data using measurements of alpha-Orionis and of the solar surface delivering both a direct and indirect method (using the spectral ratio technique) for validation. We find that measurements and model agree to a satisfactory degree.     

Distributed modal command for a two-deformable-mirror adaptive optics system

The design of future single-altitude conjugated adaptive optics (AO) systems may include at least two deformable mirrors (DMs) instead of one as in the current AO system. Each DM will have to correct for a specific spatial frequency range. A method is presented to derive a DM modal basis based on the influence functions of the DM. The modal bases are derived such that they are orthogonal to a given set of modes that restrict the DM correction to a spatial frequency domain. The modal bases have been tested on the woofer-tweeter test bench at the University of Victoria. It has been shown that the rms amplitude of the woofer DM and tweeter DM stroke can be reduced by factors of 3 and 9, respectively, when making the transition from a zonal-driven closed loop to a modal-driven closed loop with the same performance in both cases.     

Time-sharing wave-front-sensing adaptive optics

Based on the concept of common-path/common-mode adaptive optics, the time-sharing wave-front-sensing adaptive optics system contains only one Hartmann-Shack (H-S) wave-front sensor, which detects two aberrations in the beam path alternately. After data fusion of the two aberrations, the actuator voltage of the deformable mirror (DM) is obtained. How the disturbances of the slope data and the response matrix influence the DM's actuator voltage in the data fusion methods is discussed, and the effective upper limits are given. Feasible data fusion methods are tested, and experiments verify that the performance of the system is good. The time-sharing technique is limited in sampling rate and is suitable only for corrections of slowly changing phases, because the H-S wave-front sensor's sampling frequency must be adequate for the alternate detection of two aberrations.