Aleksey Nikolaevich Simonov

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.

Light scanner based on a viscoelastic stretchable grating

We present a new technique for light scanning by use of viscoelastic-based deformable phase diffraction gratings. Mechanical stretching of the grating permits control of its spatial period, and thus the orders of diffraction can be spatially deflected. In the experiments the viscoelastic gratings with triangular and rectangular profiles have been characterized at lambda = 633 nm. It is demonstrated that the reversible elongation can exceed 20% of the initial length. For the triangular profile grating, the diffraction angle of the first order changed from 6.6 degrees to 5.4 degrees while the diffraction efficiency remained almost constant at approximately 17%. Dynamic scanning of a laser beam at frequencies of approximately 1 kHz is demonstrated by use of electromechanically driven viscoelastic gratings.

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.

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.

Adaptive correction of human-eye aberrations in a subjective feedback loop

An adaptive optical system with a subjective feedback loop is used to improve the visual acuity and to determine the aberrations of the human eye. Corrections of as many as 12 low-order aberration modes were made, based on the perceived sharpness of the test object observed through the adaptive optical system. The acuity of vision was improved by adjustment of the weights of the orthogonal modes produced by a deformable mirror. Objective measurements of the correcting aspherical figures, obtained in independent subjective correction cycles for one person, demonstrated good repeatability. Participants in the study with strong ocular aberrations reported moderate to significant improvement of their visual acuity, estimated with the U.S. Air Force 1951 acuity chart.

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.

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.

Low-cost deformable mirrors: technologies and goals

New applications of adaptive optics, especially in the potentially mass markets such as laser optics, imaging and medicine, require development of new components with high quality and low price. These requirements are equally applicable to wavefront sensors, wavefront reconstructors and wavefront correctors. The whole concept of adaptive optics as a science-intensive technology needs to be altered, to facilitate low-cost and service-free deployment and user-unaware exploitation. As an example of a technology, that has a good low-cost potential, we describe the technology of piezoelectric deformable mirrors with actuators based on the transversal piezoelectric effect, as an inexpensive alternative to the deformable mirrors with stacked actuators.

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.