Compact, holographic correction of aberrated telescopes

We demonstrate a compact reflector telescope design that incorporates the holographic correction of a large, low-quality primary spherical mirror by using a laser beacon located at the center of curvature. The simple design makes use of conventional optics and is easily scalable to much larger apertures. Experimental results indicate diffraction-limited performance from a heavily aberrated 0.5-m-diameter spherical mirror.     

Calibration and performance of a pyramid wavefront sensor for the eye

We describe the calibration and performance of a pyramid wavefront sensor designed for use in a retinal imaging camera. The effect of the image modulation and the sensor binning on the measurements are explained in detail and various tests to validate the performance are described. The wavefront sensor was incorporated into an adaptive optics system that used a magnetically actuated deformable mirror, and results on static test optics are shown.     

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 and vision

It has long been recognised that the optical quality of the human eye is far from diffraction limited. This affects our visual acuity and severely limits the resolution at which images of the living retina can be obtained. Adaptive optics is a technique that can correct for the eye's aberrations and provide diffraction limited resolution. The origins of the technique lie in astronomy, but it was successfully adapted to the human eye just over 10 years ago. Since then there have been rapid developments in the field of adaptive optics and vision science. In vivo images of the retina can now be routinely achieved with unprecedented resolution. Sophisticated experiments can be performed to gain a deeper knowledge of the interaction of neural retinal architecture and visual perception. This article presents the theory behind adaptive optics for the human eye and reviews the developments in this field to date.     

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.     

Bayesian 2-D deconvolution: effect of using spatially invariant ultrasound point spread functions

Observed ultrasound images are degraded representations of the true tissue reflectance. The specular reflections at boundaries between regions of different tissue types are blurred, and the diffuse scattering within homogenous regions causes speckle because of the oscillating nature of the transmitted pulse. To reduce both blur and speckle, we have developed algorithms for the restoration of simulated and real ultrasound images based on Markov random field models and Bayesian statistical methods. The algorithm is summarized here. Because the point spread function (psf) is unknown, we investigate the effects of using incorrect frequencies and sizes for the model psf during the restoration process. First, we degrade the images either with a known simulated psf or a measured psf. Then, we use different psf shapes during restoration to study the robustness of the method. We found that small variations in the parameters characterizing the psf, less than ±25% change in frequency, width, or length, still yielded satisfactory results. When altering the psf more than this, the restorations were not acceptable. The restorations were particularly sensitive to large increases in the restoring psf frequency. Thus, 2-D Bayesian restoration using a fixed psf may yield acceptable results as long as the true variant psfs have not varied too much during imaging     

Photoreceptor counting and montaging of en-face retinal images from an adaptive optics fundus camera

A fast and efficient method for quantifying photoreceptor density in images obtained with an en-face flood-illuminated adaptive optics (AO) imaging system is described. To improve accuracy of cone counting, en-face images are analyzed over extended areas. This is achieved with two separate semiautomated algorithms: (1) a montaging algorithm that joins retinal images with overlapping common features without edge effects and (2) a cone density measurement algorithm that counts the individual cones in the montaged image. The accuracy of the cone density measurement algorithm is high, with >97% agreement for a simulated retinal image (of known density, with low contrast) and for AO images from normal eyes when compared with previously reported histological data. Our algorithms do not require spatial regularity in cone packing and are, therefore, useful for counting cones in diseased retinas, as demonstrated for eyes with Stargardt's macular dystrophy and retinitis pigmentosa.     

Adaptive optics in microscopy

The imaging properties of optical microscopes are often compromised by aberrations that reduce image resolution and contrast. Adaptive optics technology has been employed in various systems to correct these aberrations and restore performance. This has required various departures from the traditional adaptive optics schemes that are used in astronomy. This review discusses the sources of aberrations, their effects and their correction with adaptive optics, particularly in confocal and two-photon microscopes. Different methods of wavefront sensing, indirect aberration measurement and aberration correction devices are discussed. Applications of adaptive optics in the related areas of optical data storage, optical tweezers and micro/nanofabrication are also reviewed.     

Discrete-time model of an adaptive optics systems

The standard adaptive optics system can be viewed as a sampled-data feedback system with a continuous-time disturbance (the incident wavefront from the observed object) and discrete-time measurement noise. A common measure of the performance of adaptive optics systems is the time average of the pupil variance of the residual wavefront. This performance can be related to that of a discrete-time system obtained by lifting the incident and residual wavefronts. The corresponding discrete-time model is derived, and the computation of the adaptive optics system residual variance is based on that model. The predicted variance of a single mode of an adaptive optics system is shown to be the same as that obtained via simulation (as expected). The discrete-time prediction is also shown to be superior to a continuous-time approximation of the adaptive optics system.     

Image analysis of modified Hamming aperture: application on confocal microscopy and holography

Digital truncated and obstructed Hamming apertures are used in confocal laser scanning microscope (CLSM) to improve the resolution. The resultant point spread function (RPSF) and the coherent transfer function of the defined microscope, using the modified Hamming apertures, are computed. The mammographic images are used in the CLSM to test resolution of the investigated apertures. The image is computed from the modulus square of the convolution product of the RPSF and the complex amplitude of the object. A comparison with the images obtained in case of circular uniform apertures is investigated. Another application on holography allows the recognition of the modulated Hamming apertures.     

Expanding the realm of fiber optic confocal sensing for probing position, displacement, and velocity

We describe a fiber optic confocal sensor (FOCOS) system that uses an optical fiber and a lens to accurately detect the position of an object at, or close to, the image plane of the fiber tip. The fiber characteristics (diameter and numerical aperture) and optics (lens F/# and magnification) define the span and precision of the sensor and may be chosen to fit a desired application of position and displacement sensing. Multiple measurement points (i.e., fiber-tip images) may be achieved by use of multiple wavelengths in the fiber, so that each wavelength images the fiber at a different plane due to the chromatic dispersion of the optics. Further multiplexing may be achieved by adding fibers on the optical axis. A FOCOS with multiplexed fibers and wavelengths may also be used for velocity measurements.     

Compact scanning laser ophthalmoscope with high-speed retinal tracker

The effectiveness of image stabilization with a retinal tracker in a multifunction, compact scanning laser ophthalmoscope (TSLO) was demonstrated in initial human subject tests. The retinal tracking system uses a co confocal reflectometer with a closed-loop optical servo system to lock onto features in the fundus. The system is multifarious and modular to allow configuration for many research a clinical applications. Adult volunteers were tested without mydriasis to optimize the tracking instrumentation and to characterize imaging performance. The retinal tracking system achieves a bandwidth of greater than 1 kHz, which permits tracking at rates that greatly exceed the maximum rate of motion of the human eye. The TSLO system stabilized images to an accuracy of 0.05 deg in all test subjects during ordinary saccades with a velocity up to approximately 500 deg/s. Feature lock was maintained for minutes despite subject eye blinking. Even when nearly 1000 frames were coadded, image blur was minimal. Successful frame coaddition allowed image acquisition with decreased noise in low-light applications. The retinal tracking system significantly enhances the imaging capabilities of the scanning laser ophthalmoscope.     

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.     

Closed-loop stability and performance analysis of least-squares and minimum-variance control algorithms for multiconjugate adaptive optics

Recent progress has been made to compute efficiently the open-loop minimum-variance reconstructor (MVR) for multiconjugate adaptive optics systems by a combination of sparse matrix and iterative techniques. Using spectral analysis, I show that a closed-loop laser guide star multiconjugate adaptive optics control algorithm consisting of MVR cascaded with an integrator control law is unstable. Tosolve this problem, a computationally efficient pseudo-open-loop control (POLC) method was recently proposed. I give a theoretical proof of the stability of this method and demonstrate its superior performance and robustness against misregistration errors compared with conventional least-squares control. This can be accounted for by the fact that POLC incorporates turbulence statistics through its regularization term that can be interpreted as spatial filtering, yielding increased robustness to misregistration. For the Gemini-South 8-m telescope multiconjugate system and for median Cerro Pachon seeing, the performance of POLC in terms of rms wave-front error averaged over a 1-arc min field of view is approximately three times superior to that of a least-squares reconstructor. Performance degradation due to 30% translational misregistration on all three mirrors is approximately a 30% increased rms wave-front error, whereas a least-squares reconstructor is unstable at such a misregistration level.     

Design, assembly, and optical bench testing of a high-numerical-aperture miniature injection-molded objective for fiber-optic confocal reflectance microscopy

The design, analysis, assembly methods, and optical-bench test results for a miniature injection-molded plastic objective lens used in a fiber-optic confocal reflectance microscope are presented. The five-lens plastic objective was tested as a stand-alone optical system before its integration into a confocal microscope for in vivo imaging of cells and tissue. Changing the spacing and rotation of the individual optical elements can compensate for fabrication inaccuracies and improve performance. The system performance of the miniature objective lens is measured by use of an industry-accepted slanted-edge modulation transfer function (MTF) metric. An estimated Strehl ratio of 0.61 and a MTF value of 0.66 at the fiber-optic bundle Nyquist frequency have been obtained. The optical bench testing system is configured to permit interactive optical alignment during testing to optimize performance. These results are part of an effort to demonstrate the manufacturability of low-cost, high-performance biomedical optics for high-resolution in vivo imaging. Disposable endoscopic microscope objectives could help in vivo confocal microscopy technology mature to permit wide-scale clinical screening and detection of early cancers and precancerous lesions.     

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.     

Adaptive optics with four laser guide stars: correction of the cone effect in large telescopes

We study the performance of an adaptive optics (AO) system with four laser guide stars (LGSs) and a natural guide star (NGS). The residual cone effect with four LGSs is obtained by a numerical simulation. This method allows the adaptive optics system to be extended toward the visible part of the spectrum without tomographic reconstruction of three-dimensional atmospheric perturbations, resolving the cone effect in the visible. Diffraction-limited images are obtained with 17-arc ms precision in median atmospheric conditions at wavelengths longer than 600 nm. The gain achievable with such a system operated on an existing AO system is studied. For comparison, performance in terms of achievable Strehl ratio is also computed for a reasonable system composed of a 40 x 40 Shack-Hartmann wave-front sensor optimized for the I band. Typical errors of a NGS wave front are computed by use of analytical formulas. With the NGS errors and the cone effect, the Strehl ratio can reach 0.45 at 1.25 microm under good-seeing conditions with the Nasmyth Adaptive Optics System (NAOS; a 14 x 14 subpupil wave-front sensor) at the Very Large Telescope and 0.8 with a 40 x 40 Shack-Hartmann wave-front sensor.     

Beaconless stochastic parallel gradient descent laser beam control: numerical experiments

We apply a target-in-the-loop strategy to the case of adaptive optics beam control in the presence of strong atmospheric turbulence for air-to-ground directed energy laser applications. Using numerical simulations we show that in the absence of a cooperative beacon to probe the atmosphere it is possible to extract information suitable for effective beam control from images of the speckled and strongly turbulence degraded intensity distribution of the laser energy at the target. We use a closed-loop, single-deformable-mirror adaptive optics system driven by a target-in-the-loop stochastic parallel gradient descent optimization algorithm minimizing a mean-radius performance metric defined on the image of the laser beam intensity distribution formed at the receiver. We show that a relatively low order 25-channel zonal adaptive optical beam control system controlled in this way is capable of achieving a high degree of turbulence compensation with respect to energy concentration if the tilt can be corrected separately.     

Target-in-the-loop beam control: basic considerations for analysis and wave-front sensing

Target-in-the-loop (TIL) wave propagation geometry represents perhaps the most challenging case for adaptive optics applications that are related to maximization of irradiance power density on extended remotely located surfaces in the presence of dynamically changing refractive-index inhomogeneities in the propagation medium. We introduce a TIL propagation model that uses a combination of the parabolic equation describing coherent outgoing-wave propagation, and the equation describing evolution of the mutual correlation function (MCF) for the backscattered wave (return wave). The resulting evolution equation for the MCF is further simplified by use of the smooth-refractive-index approximation. This approximation permits derivation of the transport equation for the return-wave brightness function, analyzed here by the method of characteristics (brightness function trajectories). The equations for the brightness function trajectories (ray equations) can be efficiently integrated numerically. We also consider wave-front sensors that perform sensing of speckle-averaged characteristics of the wave-front phase (TIL sensors). Analysis of the wave-front phase reconstructed from Shack-Hartmann TIL sensor measurements shows that an extended target introduces a phase modulation (target-induced phase) that cannot be easily separated from the atmospheric-turbulence-related phase aberrations. We also show that wave-front sensing results depend on the extended target shape, surface roughness, and outgoing-beam intensity distribution on the target surface. For targets with smooth surfaces and nonflat shapes, the target-induced phase can contain aberrations. The presence of target-induced aberrations in the conjugated phase may result in a deterioration of adaptive system performance.     

Pulsed-interleaved excitation FRET measurements on single duplex DNA molecules inside C-shaped nanoapertures

Single-molecule fluorescence resonant energy transfer (FRET) is a widely accepted method for determining the spatial separation between molecules. In combination with pulsed interleaved excitation (PIE), additional information about the stoichiometry of molecular interactions is obtained. PIE-FRET, however, as implemented with standard confocal optics, requires the dilution of the sample to biologically low concentrations. Here, we show that PIE-FRET measurements inside nanometer-sized apertures yield meaningful biochemical data at 1000 x higher concentrations.