Performance of the holographic multivergence target in the subjective measurement of spherical refractive error and amplitude of accommodation of the human eye

We recently suggested the use of a holographic multivergence target to measure the spherical refractive error and the amplitude of accommodation of the human eye [K. V. Avudainayagam and C. S. Avudainayagam, Opt. Lett.28, 123 (2003)]. In this paper we report the performance of the holographic target in measuring real eyes. The holographic technique compared well with subjective refraction and autorefraction in the measurement of spherical refractive error. The performance of the holographic technique in measuring the amplitude of accommodation was similar to that of the minus lens to blur method and that of the push-up method. These results promote holography as a promising technique for testing human vision.     

Three-photon absorption and nonlinear refraction of BaMgF₄ in the ultraviolet region

The nonlinear refraction and nonlinear absorption phenomena are investigated in BaMgF₄ single crystal using the Z-scan technique in the ultraviolet region with a pulsed laser at 400?nm with 1?ps pulse duration. The remarkable nonlinear absorption behavior is identified to be three-photon absorption under the experimental conditions. In addition, both nonlinear refraction and nonlinear absorption have relatively large values and possess small anisotropy along three different crystallographic axes. The large values of nonlinear refractive index are demonstrated through the self-phase modulation effect.     

Metamaterials with gradient negative index of refraction

We propose a new metamaterial with a gradient negative index of refraction, which can focus a collimated beam of light coming from a distant object. A slab of the negative refractive index metamaterial has a focal length that can be tuned by changing the gradient of the negative refractive index. A thin metal film pierced with holes of appropriate size or spacing between them can be used as a metamaterial with the gradient negative index of refraction. We use finite-difference time-domain calculations to show the focusing of a plane electromagnetic wave passing through a system of equidistantly spaced holes in a metal slab with decreasing diameters toward the edges of the slab.     

Optical negative refraction by four-wave mixing in thin metallic nanostructures

The law of refraction first derived by Snellius and later introduced as the Huygens-Fermat principle, states that the incidence and refracted angles of a light wave at the interface of two different materials are related to the ratio of the refractive indices in each medium. Whereas all natural materials have a positive refractive index and therefore exhibit refraction in the positive direction, artificially engineered negative index metamaterials have been shown capable of bending light waves negatively. Such a negative refractive index is the key to achieving a perfect lens that is capable of imaging well below the diffraction limit. However, negative index metamaterials are typically lossy, narrow band, and require complicated fabrication processes. Recently, an alternative approach to obtain negative refraction from a very thin nonlinear film has been proposed and experimentally demonstrated in the microwave region. However, such approaches use phase conjugation, which makes optical implementations difficult. Here, we report a simple but different scheme to demonstrate experimentally nonlinear negative refraction at optical frequencies using four-wave mixing in nanostructured metal films. The refractive index can be designed at will by simply tuning the wavelengths of the interacting waves, which could have potential impact on many important applications, such as superlens imaging.     

The theoretical limit to the accuracy of clinical refraction measurement

A model is proposed for the fluctuations in eye refraction and a physical interpretation of the errors in measuring the clinical refraction in optometry that result from this. A theoretical limit is calculated for the measurement of normal eye refraction, which is about 0.15–0.3 m⁻¹ (diopters). __________ Translated from Izmeritel’naya Tekhnika, No. 3, pp. 51–53, March, 2008.     

Negative refraction in two-dimensional photonic crystals

A two-dimensional, square-lattice photonic crystal model possessing analytical solutions is investigated to ascertain the requirements for negative refraction to occur. The refraction properties are presented for both polarizations assuming in-plane propagation and phase matching conditions across a surface perpendicular to the ΓM-direction of the crystal. It is shown that the most isotropic and highest effective refractive index is obtained near the maximum of the lowest band for a crystal with a high refractive index contrast between its constituent materials.     

Reflection and refraction of an Airy beam at a dielectric interface

Reflection and refraction of a finite-power Airy beam at the interface between two dielectric media are investigated analytically and numerically. The formulation takes into account the paraxial nature of the optical beams to derive convenient field evolution equations in coordinate frames moving along Snell's refraction and reflection axes. Through numerical simulations, the self-accelerating dynamics of the Airy-like refracted and reflected beams are observed. Of special interest are the cases of critical incidence at Brewster and total-internal-reflection (TIR) angles. In the former case, we find that the reflected beam achieves self-healing, despite the severe suppression of a part of its spectrum, while, in the latter case, the beam remains nearly unaffected except for the Goos-H?nchen shift. The self-accelerating quality persists even if the beam is trapped by multiple TIRs inside a dielectric film. The grazing incidence of an Airy beam at the interface between two media with close refractive indices is also investigated, revealing that the interface can act as a filter depending on the beam scale and tilt. We finally consider reverse refraction and perfect imaging of an Airy beam into a left-handed medium.     

Nested shell optical model of the lens of the human eye

A nested shell model of the human lens is developed based on the known anatomical construction of the lens, on the known way in which the lens grows throughout its life, on the measured characteristics of the lens surfaces as a function of the age of the lens, on the measured changes in the shape of the lens during accommodation, and on measured material characteristics of the lens materials, such as density and index of refraction throughout. The observed changes in central surface curvature and thickness force the shell thicknesses to vary in a predictable way and in turn force the shell surface asphericity to take certain values. Thus, in addition to giving the shape of each shell, the model predicts the change expected in the asphericity of the lens surfaces as the lens ages and adds cortical cell layers. Two examples are given, one for a 25-year-old lens and one for a 40-year-old lens, to show how the cortical layers change their shapes throughout the cortex and over time as the lens ages. The performance of the model of this paper is compared to that of two other nested shell models, one where the layers have constant thickness and one where the lens posterior is fixed within the eye over time, to show the superior performance of this model with respect to maintaining a constant refractive error for the eye as the lens ages and grows.     

Negative refraction in the visible range in water-infiltrated opal photonic crystals

A negative refraction effect has been found in opal photonic crystals in the visible range. We have calculated the dispersion branches of a photonic crystal and determined the position of its photonic band gap. The frequency range has been identified where the refractive index of the opal is negative. An experimental arrangement is proposed for focusing a light beam by passing it through a plane-parallel opal photonic crystal and experimental evidence is presented in favor of negative refraction in the visible range.     

Measuring the refractive state of an eye based on the intensity of the retinal reflex

When examining the fundus of the eye with an ophthalmoscope, the intensity of the retinal reflex depends on the refractive state of the eye. In this study, application of this phenomenon for measuring the refractive state of the eye is demonstrated. First, a calibration curve relating the intensity of the retinal reflex and the refractive state was obtained using a model eye. Next, the intensity of the retinal reflex was measured while subjects were viewing a checker-board pattern, the distance of which was varied within the range from 0.17 to 1 m. Further, the relation between the refractive state and the optical power of the stimulus could be determined based on the measured light intensity and the calibration curve. Generally, the measured refractive state increased with the optical power of the stimulus. However, blinking and fluctuations in accommodation had undesired effects on the results.     

Single-shot measurement of nonlinear absorption and nonlinear refraction

A single-shot method for measurement of nonlinear optical absorption and refraction is described and analyzed. A spatial intensity variation of an elliptical Gaussian beam in conjugation with an array detector is the key element of this method. The advantages of this single-shot technique were demonstrated by measuring the two-photon absorption and free-carrier absorption in GaAs as well as the nonlinear refractive index of CS2 using a modified optical Kerr setup.     

Aging of the human lens: changes in lens shape upon accommodation and with accommodative loss.

Accommodation in the human eye occurs through controlled changes in crystalline lens shape, thickness, and refractive surface placement relative to the cornea. The changes in lens curvatures, whether surface or internal, have been characterized as a function of accommodation and subject age by use of quantitative analysis of Scheimpflug slit-lamp photographic images. Radii of curvature of the major lens refractive surfaces--the external and nuclear boundaries--decrease linearly with increasing accommodation in all eyes that are capable of accommodation. The rates at which they change with accommodation are age dependent, decreasing steadily toward zero with increased age. For the curves visible in each lens half, arising from boundaries between adjacent zones of discontinuity, radius of curvature and location are linearly related over the entire accommodative range for a given lens and over the age range for the population. The slope of this relationship changes with both accommodation and age, decreasing linearly in both cases. The relationship between these geometric changes and the loss of accommodative amplitude is discussed.     

Effect of partially coherent light on the subjective measurement of ocular astigmatism

Abstract

In this paper, we study the effect of meridional accommodation response of the eye, in the measurement of ocular astigmatism, using different targets (single slit, multiple slit and interference fringes) under different illumination conditions (white light, quasimonochromatic light and partially coherent light) in a subjective optometer. We have found that, under natural illumination conditions (incoherent white light), the accommodation of a subject viewing different orientations of a target varies in a manner that compensates for his or her ocular astigmatism. The compensation effect is minimum when interference fringes are used as targets. We also form interference images of different orientations, directly on the retina of the eye, using the meridional refraction properties of the eye and an optical field that has coherence only along specific meridians. Use of interference images formed directly on the retina yields values of cylinder that compares well with objective measurements obtained using an autorefractor.     

Bayesian assessment of uncertainty in aerosol size distributions and index of refraction retrieved from multiwavelength lidar measurements

We investigate the assessment of uncertainty in the inference of aerosol size distributions from backscatter and extinction measurements that can be obtained from a modern elastic/Raman lidar system with a Nd:YAG laser transmitter. To calculate the uncertainty, an analytic formula for the correlated probability density function (PDF) describing the error for an optical coefficient ratio is derived based on a normally distributed fractional error in the optical coefficients. Assuming a monomodal lognormal particle size distribution of spherical, homogeneous particles with a known index of refraction, we compare the assessment of uncertainty using a more conventional forward Monte Carlo method with that obtained from a Bayesian posterior PDF assuming a uniform prior PDF and show that substantial differences between the two methods exist. In addition, we use the posterior PDF formalism, which was extended to include an unknown refractive index, to find credible sets for a variety of optical measurement scenarios. We find the uncertainty is greatly reduced with the addition of suitable extinction measurements in contrast to the inclusion of extra backscatter coefficients, which we show to have a minimal effect and strengthens similar observations based on numerical regularization methods.     

Atmospheric refraction effects on optical-infrared sensor performance in a littoral-maritime environment

During a number of transmission experiments over littoral waters, quantitative measurements of atmospheric refraction phenomena were carried out to determine the range performance of optical-IR sensors. Examples of distortion and intensity gain generated by spatial variations of the atmospheric refractive index are shown. A high-precision ray-tracing model has been developed for better understanding of the phenomena and to satisfy the requirements for accuracy of the meteorological data used in refraction models. The output of the model includes the propagation function, the intensity gain, and details of the ray curvature and of the optical phase behavior along the path between the target and the observer. Examples of measured transmission data and their interpretation are presented.     

A highly-sensitive label-free biosensor based on two dimensional photonic crystals with negative refraction

In this work, we present a novel high-sensitive optical label-free biosensor based on a two-dimensional photonic crystal (2D PC). The suggested structure is composed of a negative refraction structure in a hexagonal lattice PC, along with a positive refraction structure which is arranged in a square lattice PC. The frequency shift of the transmission peak is measured respect to the changes of refractive indices of the studied materials (the blood plasma, water, dry air and normal air). The studied materials are filled into a W1 line-defect waveguide which is located in the PC structure with positive refraction (the microfluidic nanochannel). Our numerical simulations, which are based on finite-difference time-domain (FDTD) method, show that in the proposed structure, a sensitivity about 1100 nm/RIU and a transmission efficiency more than 75% can be achieved. With this design, to the best of our knowledge, the obtained sensitivity and the transmission efficiency are one of the highest values in the reported PC label-free biosensors.     

Accommodative lag versus different stimuli

The purpose of this study was to investigate change in accommodative lag with different stimuli such as font size, background colour, luminance contrast, fixation disparity and lens-induced accommodation in emmetropes. Accommodative responses of 86 eyes of 43 emmetropic patients were measured using the MEM retinoscopy technique while they were viewing different stimuli. The mean accommodative lag increased upon increasing font size, statistically significant (p?<?0.05). The mean lag of accommodation for green as the background colour was higher when compared to the red and blue background colours, statistically significant (p?<?0.05). There exists no statistical difference between the accommodative lag measured with stimuli of different contrast. The mean accommodative response was more than the accommodative demand, in the case of stereoscopic targets when used as stimuli, statistically significant (p?<?0.05). The mean accommodative lag for stimuli with normal polarity was lower than those presented with reverse polarity, statistically significant (p?<?0.05). The lag of accommodative response for free-space accommodative stimulus is significantly higher than the lag of accommodative response for minus lens (p?<?0.05). Study suggests that when viewing a larger font, black letter on green background, 2-dimensional object and free-space stimuli, the eye tends to be comparatively in a more relaxed state.     

A modified algebraic reconstruction technique taking refraction into account with an application in terahertz tomography

Terahertz (THz) tomography is a rather novel technique for non-destructive testing that is particularly suited for the testing of plastics and ceramics. Previous publications showed a large variety of conventional algorithms adapted from computed tomography or ultrasound tomography which were directly applied to THz tomography. Conventional algorithms neglect the specific nature of THz radiation, i.e. refraction at interfaces, reflection losses and the beam profile (Gaussian beam), which results in poor reconstructions. The aim is the efficient reconstruction of the complex refractive index, since it indicates inhomogeneities in the material. A hybrid algorithm has been developed based on the algebraic reconstruction technique (ART). ART is adapted by including refraction (Snell’s law) and reflection losses (Fresnel equations). Our method uses a priori information about the interface and layer geometry of the sample. This results in the ‘Modified ART for THz tomography’, which reconstructs simultaneously the complex refractive index from transmission coefficient and travel time measurements.     

Direct index of refraction measurements at extreme-ultraviolet and soft-x-ray wavelengths

Coherent radiation from undulator beamlines has been used to directly measure the real and imaginary parts of the index of refraction of several materials at both extreme-ultraviolet and soft-x-ray wavelengths. Using the XOR interferometer, we measure the refractive indices of silicon and ruthenium, essential materials for extreme-ultraviolet lithography. Both materials are tested at wavelength (13.4 nm) and across silicon's L2 (99.8 eV) and L3 (99.2 eV) absorption edges. We further extend this direct phase measurement method into the soft-x-ray region, where measurements of chromium and vanadium are performed around their L3 absorption edges at 574.1 and 512.1 eV, respectively. These are the first direct measurements, to our knowledge, of the real part of the index of refraction made in the soft-x-ray region.