Alexander V. Goncharov

Wide-field schematic eye models with gradient-index lens

We propose a wide-field schematic eye model, which provides a more realistic description of the optical system of the eye in relation to its anatomical structure. The wide-field model incorporates a gradient-index (GRIN) lens, which enables it to fulfill properties of two well-known schematic eye models, namely, Navarros model for off-axis aberrations and Thiboss chromatic on-axis model (the Indiana eye). These two models are based on extensive experimental data, which makes the derived wide-field eye model also consistent with that data. A mathematical method to construct a GRIN lens with its iso-indicial contours following the optical surfaces of given asphericity is presented. The efficiency of the method is demonstrated with three variants related to different age groups. The role of the GRIN structure in relation to the lens paradox is analyzed. The wide-field model with a GRIN lens can be used as a starting design for the eye inverse problem, i.e., reconstructing the optical structure of the eye from off-axis wavefront measurements. Anatomically more accurate age-dependent optical models of the eye could ultimately help an optical designer to improve wide-field retinal imaging.

Reconstruction of the optical system of the human eye with reverse ray-tracing

We present a practical method for reconstructing the optical system of the human eye from off-axis wavefront measurements. A retinal beacon formed at different locations on the retina allows probing the optical structure of the eye by the outgoing beams that exit the eye through the dilated pupil. A Shack-Hartmann aberrometer measures the amount of wave aberrations in each beam at the exit pupil plane. Wavefront data obtained at different oblique directions is used for tomographic reconstruction by optimizing a generic eye model with reverse ray-tracing. The multi-configuration system is constructed by tracing pre-aberrated beams backwards from each direction through the exit pupil into the optical system of the aberrometer followed by the generic eye model. Matching all wave aberrations measured at each field point is equivalent to minimizing the size of the beacon spots on the retina. The main benefit of having a personalized eye model is the ability to identify the origin of the ocular aberrations and to find the optimal way for their correction.

Laboratory MCAO test-bed for developing wavefront sensing concepts

An experimental optical bench test-bed for developing new wavefront sensing concepts for Multi-Conjugate Adaptive Optics (MCAO) systems is described. The main objective is to resolve imaging problems associated with wavefront sensing of the atmospheric turbulence for future MCAO systems on Extremely Large Telescopes (ELTs). The test-bed incorporates five reference sources, two deformable mirrors (DMs) and atmospheric phase screens to simulate a scaled version of a 10-m adaptive telescope operating at the K band. A recently proposed compact tomographic wavefront sensor is employed for star-oriented DMs control in the MCAO system. The MCAO test-bed is used to verify the feasibility of the wavefront sensing concept utilizing a field lenslet array for multi-pupil imaging on a single detector. First experimental results of MCAO correction with the proposed tomographic wavefront sensor are presented and compared to the theoretical prediction based on the characteristics of the phase screens, actuator density of the DMs and the guide star configuration.

Geometry-invariant gradient refractive index lens: analytical ray tracing.

A new class of gradient refractive index (GRIN) lens is introduced and analyzed. The interior iso-indicial contours mimic the external shape of the lens, which leads to an invariant geometry of the GRIN structure. The lens model employs a conventional surface representation using a coincoid of revolution with a higher-order aspheric term. This model has a unique feature, namely, it allows analytical paraxial ray tracing. The height and the angle of an arbitrary incident ray can be found inside the lens in a closed-form expression, which is used to calculate the main optical characteristics of the lens, including the optical power and third-order monochromatic aberration coefficients. Moreover, due to strong coupling of the external surface shape to the GRIN structure, the proposed GRIN lens is well suited for studying accommodation mechanism in the eye. To show the power of the model, several examples are given emphasizing the usefulness of the analytical solution. The presented geometry-invariant GRIN lens can be used for modeling and reconstructing the crystalline lens of the human eye and other types of eyes featuring a GRIN lens.

Population study of the variation in monochromatic aberrations of the normal human eye over the central visual field

We present data analysis for ocular aberrations of 60 normal eyes measured with a Hartmann-Shack (HS) wavefront sensor (WFS). Aberration measurements were made on-axis and at 5 degree field angles in the nasal, inferior, temporal and superior semi-meridians. Particular attention is given to aberration distributions and possible strategies for aberration correction are discussed. A versatile HS WFS was designed and constructed with features of simultaneous pupil centre determination, off-axis capability, real-time data displays, and efficient lenslet sampling orientation. The subject alignment is achieved by the use of a parallel channel that is recombined with the sensing channel to simultaneously image the eye and the HS spots onto a single CCD. The pupil centre is determined using this image of the eye (iris edge), rather than the HS spots. The optical design includes a square lenslet array positioned with its diagonals aligned with the most typical principal astigmatic meridians of the eye. This favourable orientation helps to enlarge the dynamic range of the WFS. The telecentric re-imaging of the HS spots increases the robustness of the system to defocus in the event of CCD misalignment.

Lens axicons in oblique illumination

Lens axicons, i.e., lenses or lens systems designed to work like axicons, can be a simple and inexpensive way of generating the characteristic axicon focal line. In the design of most lens axicons, only on-axis properties have been considered. We present the design of a lens axicon with improved off-axis characteristics. It is constructed from a singlet lens but with a double-pass feature that allows for a line of uniform width and a stop positioned to minimize aberrations. We perform off-axis analysis and experiments for this system and for another lens axicon, one designed for its on-axis characteristics. We conclude that the off-axis performance of the double-pass axicon is better than both that of an ordinary cone axicon and that of the other lens axicon.

Chromatic effects of the atmosphere on astronomical adaptive optics

The atmosphere introduces chromatic errors that may limit the performance of adaptive optics (AO) systems on large telescopes. Various aspects of this problem have been considered in the literature over the past two decades. It is necessary to revisit this problem in order to examine the effect on currently planned systems, including very high-order AO on current 8-10 m class telescopes and on future 30-42 m extremely large telescopes. We review the literature on chromatic effects and combine an analysis of all effects in one place. We examine implications for AO and point out some effects that should be taken into account in the design of future systems. In particular we show that attention should be paid to chromatic pupil shifts, which may arise in components such as atmospheric dispersion compensators.

Atmospheric dispersion compensation for extremely large telescopes

Achieving diffraction limited imaging with future ground-based optical telescopes will require adaptive optics for correction of atmospheric turbulence and also efficient techniques for atmospheric dispersion compensation. We study the benefit of using a linear atmospheric dispersion corrector (ADC) coupled with a deformable mirror on a 42-m Extremely Large Telescope (ELT) operating in the VIRJ spectral bands. The ADC design consists of two identical thin wedges made of F5 glass. The amount of dispersion introduced by the ADC is adjusted by translating one of the wedges along the optical axis so that it always cancels atmospheric dispersion as it varies with telescope elevation. We show that the ADC working in conjunction with a deformable mirror provides diffraction-limited image quality over a 1-arcmin field.

Compact multireference wavefront sensor design

We present a compact optical design for a multireference Shack-Hartmann-based wavefront sensor (WFS) for multiconjugate adaptive optical systems. The key component of this WFS design is a field lenslet array that separates the exit pupil images in the sensing plane for all reference sources. An analytical method for WFS optical design is presented, and the optimal strategy for selecting optical components from a discrete set is outlined. The feasibility of the WFS design has been demonstrated for a prototype WFS system in a laboratory setup with five reference sources and two deformable mirrors representing a wavefront-distorting medium.

Inverse optical design of the human eye using likelihood methods and wavefront sensing

We are developing a method for estimating patient-specific ocular parameters, including surface curvatures, conic constants, tilts, decentrations, thicknesses, refractive indices, and index gradients. The data consist of the raw detector outputs from one or more Shack-Hartmann wavefront sensors, and the parameters in the eye model are estimated by maximizing the likelihood. A Gaussian noise model is used to emulate electronic noise, so maximum likelihood reduces to nonlinear least-squares fitting between the data and the output of our optical design program. The Fisher information matrix for the Gaussian model was explored to compute bounds on the variance of the estimates for different system configurations. In this preliminary study, an accurate estimate of a chosen subset of ocular parameters was obtained using a custom search algorithm and a nearby starting point to avoid local minima in the complex likelihood surface.