Analysis of Accommodative Performance of a New Accommodative Intraocular Lens.

PURPOSE: To compare objective and subjective accommodation and visual acuities with a new accommodative intraocular lens (IOL) (Lumina; AkkoLens Clinical BV, Rijswijk, The Netherlands) with a monofocal IOL and young phakic eyes. METHODS: In this prospective, randomized controlled clinical investigation, patients aged 51 to 85 years with symptomatic cataract were enrolled in the study. A total of 25 eyes were implanted with the accommodative IOL and 18 eyes received the monofocal Acrysof SA60AT IOL (Alcon Laboratories, Inc., Fort Worth, TX). Each group included 4 bilateral patients. An additional 20 phakic eyes of young patients aged 19 to 29 years were used to assess the restoration of accommodation. Subjective and objective accommodative amplitudes were evaluated by defocus curves and the WAM-5500 open-field Auto Ref/Keratometer (Grand Seiko, Tokyo, Japan), respectively. RESULTS: The 1-year postoperative examination showed significantly better visual acuities with the accommodative IOL compared to the monofocal IOL, over a defocus range of -0.50 to -5.00 diopters (D) (P < 10-5), and revealed more than 50% of the visual acuities of the young phakic eyes at up to -3.50 D defocus. The depth of focus of the accommodative group exceeded that of the monofocal group by 2.52 ± 0.03 D in a visual acuity range of 0.3 to 0.8 (decimal) (20/63 to 20/25 Snellen). Compared with the monofocal IOL, the accommodative IOL resulted in a similar uncorrected distance visual acuity of 0.99 ± 0.12 (20/20 Snellen) (P > .79) and a significantly better uncorrected near visual acuity of 0.91 ± 0.11 (20/22 Snellen) (P < 2.7 × 10-6). A significant correlation of 0.51 (P < 1.3 × 10-7) was found between the objective and subjective accommodative amplitudes with the accommodative IOL. CONCLUSIONS: Eyes implanted with the accommodative IOL showed similar amounts of objective and subjective accommodation. [J Refract Surg. 2018;34(2):78-83.].

Cramer-Rao bounds in functional form: theory and application to passive optical ranging.

A functional approach to the multivariate statistical model of a generalized incoherent passive optical ranging and imaging system with a CCD sensor is proposed. This approach implies that a large number of discrete, statistically independent, random data (pixel readouts) can be approximated by a continuous random function. Thus, the joint probability density function (PDF) takes a functional form; the statistical averages of the infinite-variate PDF and the Fisher information become functional integrals that can be treated analytically in the Gaussian approximation. The Cramer-Rao bounds on estimator-error variances are obtained for the scalar and functional deterministic parameters of the model. An approximate expression is derived for the PDF of the sum of independent Gaussian and Poisson random variables using the steepest-descent method, and the resulting PDF is shown to be asymptotically Gaussian. As an illustration, we apply the developed approach to a passive optical rangefinder with chiral wavefront coding. Numerical and experimental examples are presented.

Passive ranging and three-dimensional imaging through chiral phase coding.

We present a method for single-image passive ranging and three-dimensional (3D) imaging in incoherent light based on chiral phase coding. A chiral linear phase variation across the aperture of an optical system results in a frequency response with a characteristic pattern of fringes such that the spatial period and inclination of the pattern depend on the focusing error. From this dependency, the absolute focusing error and, hence, the distance to the object can be found. In the experiments a resolution of ~1.4 µm is achieved with a 20 mm aperture lens in a 4 mm interval at a distance of 140 mm from the lens. A resolution of ~0.7 mm is obtained at a distance of ~11 m with the range finder employing two 25.4 mm spherical mirrors spaced apart by ~140 mm. We also demonstrate 3D imaging of weakly textured objects.

Asymptotic behavior of the spatial frequency response of an optical system with defocus and spherical aberration.

Asymptotic expressions are derived for the two-dimensional incoherent optical transfer function (OTF) of an optical system with defocus and spherical aberration. The two-dimensional stationary phase method is used to evaluate the aberrated OTF at large and moderately large defocus and spherical aberration. For small aberrations, the OTF is approximated by a power series in the aberration coefficients. An accurate approximation (in elementary functions) to the OTF is obtained for a defocused optical system with a circular pupil. We experimentally demonstrate the validity of the OTF approximations in sharp-focus image restoration from two defocused images. A digital focusing method is presented.

Sharp-focus image restoration from defocused images.

We present a noniterative algorithm for sharp-focus image restoration from multiple defocused images having known relative defocus values between the image planes but unknown absolute defocus values with respect to the in-focus plane. Starting from an arbitrary value of defocus relative to the in-focus plane and using the optical transfer function, the algorithm evaluates the absolute defocus and retrieves the in-focus image of an incoherently illuminated planar object. Experiments with a circular-aperture imaging system confirm the efficiency and robustness of the algorithm. A reconstruction time of approximately 100 ms is attained with two defocused 512x512 pixel images (captured by a 10 bit camera) on a 2.16 GHz laptop.

Optical system invariant to second-order aberrations.

An approximate analytical expression is derived for the two-dimensional incoherent optical transfer function (OTF) of an imaging system invariant to second-order aberrations. The system broadband behavior resulting from a third-order phase mask in its pupil plane is analyzed by using the two-dimensional stationary phase method. This approach does not require mathematical separability of the pupil function and can be applied to any pupil shape. The OTF is found to be a well-defined and smooth function at all nonzero spatial frequencies when the phase mask function includes third-order mixed terms in the pupil coordinates.

Liquid-crystal intraocular adaptive lens with wireless control.

We present a prototype of an adaptive intraocular lens based on a modal liquid-crystal spatial phase modulator with wireless control. The modal corrector consists of a nematic liquid-crystal layer sandwiched between two glass substrates with transparent low- and high-ohmic electrodes, respectively. Adaptive correction of ocular aberrations is achieved by changing the amplitude and the frequency of the applied control voltage. The convex-shaped glass substrates provide the required initial focusing power of the lens. A loop antenna mounded on the rim of the lens delivers an amplitude-modulated radio-frequency control signal to the integrated rectifier circuit that drives the liquid-crystal modal corrector. In vitro measurements of a 5-mm clear aperture prototype with an initial focusing power of +12.5 diopter, remotely driven by a radio-frequency control unit at ~6 MHz, were carried out using a Shack-Hartmann wavefront sensor. The lens based on a 40-mum thick liquid-crystal layer allows for an adjustable defocus of 4 waves, i. e. an accommodation of ~2.51 dioptres at a wavelength of 534 nm, and correction of spherical aberration coefficient ranging from -0.8 to 0.67 waves. Frequency-switching technique was employed to increase the response speed and eliminate transient overshoots in aberration coefficients. The full-scale settling time of the adaptive modal corrector was measured to be ~4 s.

Stretchable diffraction gratings for spectrometry.

We have investigated the possibility of using transparent stretchable diffraction gratings for spectrometric applications. The gratings were fabricated by replication of a triangular-groove master into a transparent viscoelastic. The sample length, and hence the spatial period, can be reversibly changed by mechanical stretching. When used in a monochromator with two slits, the stretchable grating permits scanning the spectral components over the output slit, converting the monochromator into a scanning spectrometer. The spectral resolution of such a spectrometer was found to be limited mainly by the wave-front aberrations due to the grating deformation. A model relating the deformation-induced aberrations in different diffraction orders is presented. In the experiments, a 12-mm long viscoelastic grating with a spatial frequency of 600 line pairs/mm provided a full-width at half-maximum resolution of up to ~1.2 nm in the 580-680 nm spectral range when slowly stretched by a micrometer screw and ~3 nm when repeatedly stretched by a voice coil at 15 Hz. Comparison of aberrations in transmitted and diffracted beams measured by a Shack- Hartmann wave-front sensor showed that astigmatisms caused by stretch-dependent wedge deformation are the main factors limiting the resolution of the viscoelastic-grating-based spectrometer.

Cubic optical elements for an accommodative intraocular lens.

We present a new accommodative intraocular lens based on a two-element varifocal Alvarez lens. The intraocular lens consists of (1) an anterior element combining a spherical lens for refractive power with a cubic surface for the varifocal effect, and (2) a posterior element with a cubic surface only. The focal length of the IOL lens changes when the superimposed refractive elements shift in opposite directions in a plane perpendicular to the optical axis. The ciliary muscle will drive the accommodation by a natural process of contraction and relaxation. Results of ray-tracing simulations of the model eye with the two-element intraocular lens are presented for on-axis and off-axis vision. The configuration of the lens is optimized to reduce refractive errors as well as effects of misalignment. A prototype with a clear aperture of ~5.7 mm is manufactured and evaluated in air with a Shack-Hartmann wave-front sensor. It provides an accommodation range of ~4 dioptres in the eye at a ~0.75-mm lateral displacement of the optical elements. The experimentally measured on-axis optical performance of the IOL lens agrees with the theoretically predicted performance.