Weiyao Zou

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.

Wavefront-aberration sorting and correction for a dual-deformable-mirror adaptive-optics system

Many next-generation adaptive optics (AO) systems for vision will have two deformable mirrors (DMs) instead of one: a high-stroke, low-resolution mirror (the woofer) and a low-stroke, high-resolution mirror (the tweeter). We developed a zonal wavefront-control algorithm and validated it using simulations. Rather than separating the woofer and tweeter corrections into two independent control processes or using a modal decomposition, the algorithm we proposed uses wavefront slope measurements from a single Shack-Hartmann wavefront sensor to generate control signals for both deformable mirrors within a single zonal control. A Lagrange multiplier is chosen to integrate two DMs into a single-DM wavefront control, and a damped least-squares control is employed to suppress the correlation between the two DMs.

Woofer-tweeter adaptive optics scanning laser ophthalmoscopic imaging based on Lagrange-multiplier damped least-squares algorithm

We implemented a Lagrange-multiplier (LM)-based damped least-squares (DLS) control algorithm in a woofer-tweeter dual deformable-mirror (DM) adaptive optics scanning laser ophthalmoscope (AOSLO). The algorithm uses data from a single Shack-Hartmann wavefront sensor to simultaneously correct large-amplitude low-order aberrations by a woofer DM and small-amplitude higher-order aberrations by a tweeter DM. We measured the in vivo performance of high resolution retinal imaging with the dual DM AOSLO. We compared the simultaneous LM-based DLS dual DM controller with both single DM controller, and a successive dual DM controller. We evaluated performance using both wavefront (RMS) and image quality metrics including brightness and power spectrum. The simultaneous LM-based dual DM AO can consistently provide near diffraction-limited in vivo routine imaging of human retina.

Iterative zonal wave-front estimation algorithm for optical testing with general-shaped pupils.

An iterative zonal wave-front estimation algorithm for slope or gradient-type data in optical testing acquired with regular or irregular pupil shapes is presented. In the mathematical model proposed, the optical surface, or wave-front shape estimation, which may have any pupil shape or size, shares a predefined wave-front estimation matrix that we establish. Owing to the finite pupil of the instrument, the challenge of wave front shape estimation in optical testing lies in large part in how to properly handle boundary conditions. The solution we propose is an efficient iterative process based on Gerchberg-type iterations. The proposed method is validated with data collected from a 15 x 15-grid Shack-Hartmann sensor built at the Nanjing Astronomical Instruments Research Center in China. Results show that the rms deviation error of the estimated wave front from the original wave front is less than lambda/130-lambda/150 after approximately 12 iterations and less than lambda/100 (both for lambda = 632.8 nm) after as few as four iterations. Also, a theoretical analysis of algorithm complexity and error propagation is presented.

Quantifications of error propagation in slope-based wavefront estimations

We discuss error propagation in the slope-based and the difference-based wavefront estimations. The error propagation coefficient can be expressed as a function of the eigenvalues of the wavefront-estimation-related matrices, and we establish such functions for each of the basic geometries with the serial numbering scheme with which a square sampling grid array is sequentially indexed row by row. We first show that for the wavefront estimation with the wavefront piston value determined, the odd-number grid sizes yield better error propagators than the even-number grid sizes for all geometries. We further show that for both slope-based and difference-based wavefront estimations, the Southwell geometry offers the best error propagators with the minimum-norm least-squares solutions. Nolls theoretical result, which was extensively used as a reference in the previous literature for error propagation estimates, corresponds to the Southwell geometry with an odd-number grid size. Typically the Fried geometry is not preferred in slope-based optical testing because it either allows subsize wavefront estimations within the testing domain or yields a two-rank deficient estimations matrix, which usually suffers from high error propagation and the waffle mode problem. The Southwell geometry, with an odd-number grid size if a zero point is assigned for the wavefront, is usually recommended in optical testing because it provides the lowest-error propagation for both slope-based and difference-based wavefront estimations.

High-accuracy wavefront control for retinal imaging with Adaptive-Influence-Matrix Adaptive Optics.

We present an iterative technique for improving adaptive optics (AO) wavefront correction for retinal imaging, called the Adaptive-Influence-Matrix (AIM) method. This method is based on the fact that the deflection-to-voltage relation of common deformable mirrors used in AO are nonlinear, and the fact that in general the wavefront errors of the eye can be considered to be composed of a static, non-zero wavefront error (such as the defocus and astigmatism), and a time-varying wavefront error. The aberrated wavefront is first corrected with a generic influence matrix, providing a mirror compensation figure for the static wavefront error. Then a new influence matrix that is more accurate for the specific static wavefront error is calibrated based on the mirror compensation figure. Experimental results show that with the AIM method the AO wavefront correction accuracy can be improved significantly in comparison to the generic AO correction. The AIM method is most useful in AO modalities where there are large static contributions to the wavefront aberrations.

Experimental system of segmented-mirror active optics

In this system, the segmented-mirror consists of three submirrors. They are hexagonal with 250 mm diagonal. The shape of each submirror is spherical with 3000 mm radius and the departure of each radius from the mean radius is less than 0.025 mm. A special S-H test device is used for co- focus measurement. It includes nine sub-apertures in three groups and each group is for a submirror. There are six displacement actuators in this system. The based unites of it are flexure hinges. The actuator is driven by a stepping motor with ten subdivisions. Six capacity displacement sensors are used in this experiment system. It is made in Tianjin University. A computer is used for data collecting, calculating and controlling. A special method for co-focus is developed in our work. By using this method the error of co-focus, i.e. the tilt error of submirror, is less than rms 0.035 arcseconds. The methods of calibration and maintaining for co-phase are also introduced in this paper. After once calibration, the diffraction limit image can be observed in about 220 mm aperture at (lambda) 650 nm, and it can be maintained about 20 minutes.

Testing of Lagrange multiplier damped least-squares control algorithm for woofer-tweeter adaptive optics

A Lagrange multiplier-based damped least-squares control algorithm for woofer-tweeter (W-T) dual deformable-mirror (DM) adaptive optics (AO) is tested with a breadboard system. We show that the algorithm can complementarily command the two DMs to correct wavefront aberrations within a single optimization process: the woofer DM correcting the high-stroke, low-order aberrations, and the tweeter DM correcting the low-stroke, high-order aberrations. The optimal damping factor for a DM is found to be the median of the eigenvalue spectrum of the influence matrix of that DM. Wavefront control accuracy is maximized with the optimized control parameters. For the breadboard system, the residual wavefront error can be controlled to the precision of 0.03 μm in root mean square. The W-T dual-DM AO has applications in both ophthalmology and astronomy.

Experiment system of thin-mirror active optics

In this system, the experiment mirror has 500 mm aperture and 6 mm thickness. There are 58 actuators and three fixed points in it. A Shack-Hartmann test apparatus is used for the measurement of wavefront aberration. In this apparatus an ingenious equivalent of lenslet array is used. All image points formed by it appear very clear theoretical diffraction pattern. And a CCD from a TV camera is used. Like European Southern Observatory, we use quasi-Zernike polynomial to fit the wavefront aberration for correcting. But in our work correction is to the whole wavefront aberration (except lateral focus and longitudinal focus). In our work, another important character is that the damp least square method is used for determining the forces. The correction results are the root mean square of wavefront aberration about 0.02 - 0.04 micrometers . A circle including measuring and correcting the wavefront aberration takes about 3.3 minutes. A more precise algorithm proposed by us is used for calculating the wavefront aberration for checking.

Dual electro-optical modulator polarimeter based on adaptive optics scanning laser ophthalmoscope

We constructed a high speed and high-resolution Stokes vector retinal imaging polarimeter with dual electro-optical modulators based on adaptive optics scanning laser ophthalmoscope. By varying the voltages on the EO crystals line by line, we were able to measure over 500,000 Stokes vectors per second. We used this system in three human subjects demonstrating the capability of the system to be employed in vivo. The high speed effectively decreases the adverse impact of eye motion induced errors in polarization calculations, improving the contrast of retinal structures based on their polarization properties.