Henryk T. Kasprzak

Interferometric measurements of dynamic changes of tear film

Tear film stability plays an important role in the quality of vision. We present an interferometric method for assessing the stability of precorneal tear film in real time. A lateral shearing technique is applied as a noninvasive and sensitive method for investigating tear film stability and the smoothness of the tear film surface by quantitative evaluation of the interference fringe pattern. The evaporation of tears and the appearance of tear film break-up between blinks cause changes in the fringe geometry. For quantitative assessment of the fringe smoothness and consequently of the tear film structure, the fast Fourier transform (FFT) is applied. Four parameters are used to quantitatively estimate dynamic changes in the tear film stability of the cornea 20 s after the eye blink. Examples of examined interferograms recorded in patients with healthy eyes, patients suffering from dry-eye syndrome, and patients wearing contact lenses are given. Significant differences between the stability of the tear film in the healthy eye and that in the dry eye and the eye with a contact lens are observed. The favorable influence of artificial tears applied in patients with dry-eye syndrome or contact lenses is also discussed.

Analysis of Shearing Interferograms of Tear Film Using Fast Fourier Transforms

A new method for evaluating tear film stability on the human eye is reported. The tear film distribution on the cornea is measured by the lateral shearing interference technique. The eye is kept open during approximately a 2-min recording, when blinking has to be prevented. Continuous recording and viewing of interferograms allows the changes in disturbances of the interference fringes to be registered during elapsed time. The changes in fringes are caused by the evaporation of tears from the ocular surface and appearance of the breakups. For precise and repetitive assessment of the tear film breakup time, a fast fourier transform (FFT) is applied to consecutive interferograms. Larger fringe disturbances result in wider Fourier spectra. The tear breakup time can be evaluated noninvasively by comparing the value of the second momentum of Fourier spectra calculated from the consecutive interferograms.

Schematic eye with a gradient-index lens and aspheric surfaces

A new schematic eye with aspheric surfaces and a radially varying refractive-index distribution lens is proposed. Image quality and spherical aberration are determined by use of ray tracing, and the results are presented as spot diagrams and compared with five existing model eyes. The proposed model provides the best image quality and lowest spherical aberration.

New approximation for the whole profile of the human crystalline lens

This paper presents a new approximation for the whole profile of the human crystalline lens by the use of only one analytical function for both unaccommodated lens and the lens on accommodation. Approximation of the anterior and posterior lens profile is composed of hyperbolic cosine functions and is given in polar coordinates. Each of the hyperbolic cosines is modulated by the function of hyperbolic tangent type. The curvature of the hyperbolic cosine in polar coordinates is discussed and some results concerning the stability of its central radius of curvature are shown. Fitting of the hyperbolic cosine type curve to various results of the lens curvature measurements is presented. Examples of profiles of the lens under accommodation are given. It is shown that this approximation can be used for the description of iso‐indical profiles inside the lens.

Modelling the elastic properties of the anterior eye and their contribution to maintenance of image quality: the role of the limbus

PurposeThe elastic moduli of the cornea, sclera, and limbus for different corneal eccentricities (e) and varying levels of intraocular pressure (IOP) were modelled in order to determine how the rheological properties, especially those of the limbus, need to alter to maintain optical image quality when the eye is subjected to small variations in IOP.MethodsFinite element analysis (FEA) was used to construct eyeball models with four different corneal eccentricities (e=0, 0.33, 0.5, 0.65). Three values for Youngs modulus of the cornea were tested in all models (0.2 megapascal (MPa), 1.2 and 10 MPa). For each corneal modulus, scleral moduli of 3, 4, 5, 7, and 10 times that of the corneal modulus were selected. The limbal modulus was varied to optimise image quality of the eye model subjected to IOP variations of ±0.8 mmHg for three different levels of IOP (8, 16, and 32 mmHg).ResultsThe elastic modulus of the limbal ring increases with an increase in corneal modulus and rises to a peak when the ratio of scleral to corneal moduli is between 5 and 7 depending on corneal eccentricity. Different levels of IOP produce only slight differences in the relative moduli required to maintain optical image quality.ConclusionsThe significance of a peak in the value of Youngs modulus of the limbus is not clear but suggests that there may be an optimal limbal modulus that must be balanced with the moduli of cornea and sclera for preservation of image quality.

Spectral characteristics of longitudinal corneal apex velocities and their relation to the cardiopulmonary system

PurposeTo study the naturally occurring kinetic characteristics of corneal surface.MethodsThe right eyes of three subjects (young, early presbyope, and presbyope) were examined. Cardiac signal and longitudinal corneal apex movements were simultaneously measured with electrocardiography (ECG) and a high-speed videokeratoscope, respectively. Time, frequency, and combined time–frequency representations of the acquired signals were derived to establish their temporal and spectral contents. Coherence analysis was used to assess the correlation between the corneal apex velocities and the cardiopulmonary system.ResultsIn all measurements, longitudinal corneal apex velocity signals showed close correlation with the corresponding ECG signals. The signatures of the pulse frequency, which was inferred from the ECG spectra and their variations in time, were clearly visible in the spectral content of corneal apex velocities. For the young subject, the correlation was the strongest and all of the spectral content of the pulse signal including the harmonics was propagating to the corneal apex velocities. For the other two subjects, there was a clear propagation of the pulse signal itself but not of all pulse harmonics.ConclusionsLongitudinal movements of the corneal apex are closely related to the cardiopulmonary system. The differences in propagation of pulse harmonics to the corneal apex velocities for different subjects suggest that the frequency characteristics of apex velocity could be related to pulsative variations in the intraocular pressure and biomechanical properties of the eye. These findings could potentially be used in noninvasive assessment of the hemodynamic status of the eye with high-speed videokeratoscopy.

Model of the optical system of the human eye during accommodation

A model of the human eye with a gradient index crystalline lens is presented. The crystalline lens shape at different accommodation levels is described by a single function which is a combination of hyperbolic cosine functions and hyperbolic tangent functions. Using the experimental data published in the literature a model of the variations of the external lens shape was created. Formulae for the lens shape parameters and gradient index distribution for different accommodation levels are given.

A new analytical approximation of corneal topography

Abstract It is shown that a rotationally symmetric surface, which is the border between two optical media, can focus a parallel light beam to a point only when the profile of the surface is an ellipse or a hyperbola with eccentricity equal to the ratio of refractive indices of both media. In fact, as is well known, the conic sections do not describe the corneal profile well, so a new analytical approximation for the corneal contour is given. This simple approximation in the case of a rotationally symmetric surface is based on the hyperbolic cosine function with two parameters, the radius of curvature at the apex of the cornea and a parameter describing the stability of the central curvature. The hyperbolic cosine function can also be used to approximate a 3-D non-rotational surface in the case of a cornea with axial astigmatism. The 3-D contour map of deviation of the hyperbolic cosine approximation from a reference sphere is compared with an interferogram of a cornea in vivo, recorded in a Twyman-Green i...

Dynamics in longitudinal eye movements and corneal shape.

The magnitude and character of longitudinal movements of the eye were studied in the context of high speed videokeratoscopy. It was of interest to determine whether these dynamic changes in the eye movements can affect the corneal shape and its estimation. A high speed videokeratoscope with a sampling frequency of 50 Hz was used for measuring the corneal apex movements as well as for measuring variations in the best‐fit sphere radius and central radius of curvature. The magnitude of the measured longitudinal apex movements could reach over 200 μm showing a slow trend. The estimated local changes of the apex movements that could be associated with the cardiopulmonary system were about 40–50 μm. The temporal variations in the equivalent estimated central radius of curvature ranged between 10 and 15 μm. Spectral analysis of the longitudinal eye movements revealed strong signatures of the pulse and respiration signals as well as the assumed blink control signal. No clear association between the longitudinal apex movements and the corneal curvature was found. However, very slow significant changes in the corneal shape were observed. The central radius of curvature of the cornea revealed slow changes of up to 120 μm. Understanding the nature of such changes will be of benefit in ophthalmic applications requiring highly accurate measurements of corneal shape, such as contact lens design and refractive surgery.

Linear birefringence measurements of the in vitro human cornea.

This paper presents results of an in vitro investigation of the optical anisotropy of the human cornea. Computer controlled imaging polarimetry and the Jones formalism were used to investigate the distribution of the birefringence and the azimuth angle across the surface of 12 corneas taken from the corneal bank. Each map of the birefringence and the azimuth angle has no rotational symmetry and is different for each cornea. The minimal value of the birefringence always appears in the corneal centre and varies from 9 to 43° for different corneas. Birefringence of the cornea increases monotonically more than one order in the direction of the corneal periphery. Close to the centre of the cornea the azimuth angle is almost constant and varies significantly away from the optical part of the cornea.