Optical System Of Eye Research Articles

Modeling the influence of LASIK surgery on optical properties of the human eye

The aim was to model the influence of LASIK surgery on the optical parameters of the human eye and to ascertain which factors besides the central corneal radius of curvature and central thickness play the major role in postsurgical refractive change. Ten patients were included in the study. Pre- and postsurgical measurements included standard refraction, anterior corneal curvature and pachymetry. The optical model used in the analysis was based on the Le Grand and El Hage schematic eye, modified by the measured individual parameters of corneal geometry. A substantial difference between eye refractive error measured after LASIK and estimated from the eye model was observed. In three patients, full correction of the refractive error was achieved. However, analysis of the visual quality in terms of spot diagrams and optical transfer functions of the eye optical system revealed some differences in these measurements. This suggests that other factors besides corneal geometry may play a major role in postsurgical refraction. In this paper we investigated whether the biomechanical properties of the eyeball and changes in intraocular pressure could account for the observed discrepancies.

Luminance Effects on Neural Mechanism at Photopic Level

In order to obtain the influence of the luminance at photopic level on the neural mechanism, a neural contrast sensitivity function (NCSF) measurement system is established. The contrast sensitivity function (CSF) of the visual system and the modulation transfer function (MTF) of the eye's optical system are first measured with correspondent instruments respectively. Then the NCSF is calculated as the ratio of CSF to MTF. Four individual eyes are involved in the cases of green light and white light. With increasing luminance, the tendency of the variation of the CSFs is similar to that of the NCSFs, while the gain is larger than that of the NCSFs, especially in the region of higher spatial frequency. It is the NCSF, rather than CSF, that reflects tie luminance sensitivity in the retina-brain neural system, because the influence of the eye's optical system is excluded.

The improved model of the eye optical system

The improved model of the eye optical system

Microfabricated ommatidia using a laser induced self-writing process for high resolution artificial compound eye optical systems

A microfabricated compound eye, comparable to a natural compound eye shows a spherical arrangement of integrated optical units called artificial ommatidia. Each consists of a self-aligned microlens and waveguide. The increase of waveguide length is imperative to obtain high resolution images through an artificial compound eye for wide field-of - view imaging as well as fast motion detection. This work presents an effective method for increasing the waveguide length of artificial ommatidium using a laser induced self-writing process in a photosensitive polymer resin. The numerical and experimental results show the uniform formation of waveguides and the increment of waveguide length over 850 microm.

Сравнительная оценка аберраций высшего порядка при различных состояниях оптической системы глаза

Сравнительная оценка аберраций высшего порядка при различных состояниях оптической системы глаза

Human eye aberrations: 1. Development of personalised models of the human eye optical system based on measurements

Based on experimental studies of human eye monochromatic aberrations, the eye models are proposed which take into account the individual features of eye aberrations of patients.

Modeling the eye's optical system by ocular wavefront tomography

Ocular wavefront tomography (OWT) is the process of using wavefront aberration maps obtained along multiple lines-of-sight (LoS) to determine the shape and position of the major refracting elements of an eye. One goal of OWT is to create a customized schematic model eye that is anatomically similar and functionally equivalent to the individual eye over a large field of view. Wavefront aberration maps along multiple LoS were used as design goals for configuring a generic, multi-surface model eye with aberrations that match the measurements. The model was constrained by gross anatomical dimensions and optimized to mimic the measured eye. The method was evaluated with two test cases: (1) a physical model eye with a doublet lens measured with a clinical wavefront aberrometer along six LoS between -31 deg and +29 deg eccentricities, and (2) a mathematical model of the myopic eye for which wavefront aberrations were computed by ray tracing. In case 1, the OWT algorithm successfully predicted the structure of the doublet model eye from the experimental on- and off-axis aberration measurements. In case 2, the algorithm started with a symmetric five surface model eye and optimized it to generate the on- and off-axis aberrations of a GRIN myopia model eye. The adjusted model closely mimicked the physical parameters and optical behavior of the expected myopia model eye over a large field of view. The maximum discrepancy between aberrations of the OWT optimized model and measurements was 0.05 microns RMS for test case 1 and 0.2 microns RMS for test case 2. Our implementation of OWT is a valid, feasible, and robust method for constructing an optical model that is anatomically and functionally similar to the eye over a wide field of view.

A Model of the Human Eye

We describe a model of the human eye that incorporates a variable converging lens. The model can be easily constructed by students with low-cost materials. It shows in a comprehensible way the functionality of the eye's optical system. Images of near and far objects can be focused. Also, the defects of near and farsighted eyes can be demonstrated.

Anisometropie und Aniseikonie – ungelöste Probleme der Kataraktchirurgie

Aniseikonia is one of the relevant unsolved problems of modern cataract surgery and may cause severe functional problems such as deteriorated binocular vision, diplopia or headaches. The aim of the present study is to assist the clinician as to how to estimate lateral magnification in a pseudophakic eye and how to reduce or eliminate aniseikonia. Based on the characterisation of a centred optical system in the paraxial space, the optical system eye is modelled with 2 x 2 matrices and the lateral magnification is extracted. This method is applied on the "thin lens model" as well as the "thick lens model" and illustrated in detail with 4 working examples. Additionally, we demonstrate how a predefined lateral magnification (e. g., from the contralateral eye) can be realised during cataract surgery by calculating an appropriate combination of an IOL and a spectacle correction. WORKING EXAMPLES: In example 1 the lateral magnification of the reference eye following cataract surgery is determined. In example 2 we estimate the lateral magnification behaviour that is expected after cataract surgery using the same IOL as in example 1. Example 3 gives an overview of how the magnification varies if the IOL position in the eye, the geometry of the lens or the central thickness is changed. Example 4 shows how to calculate an appropriate combination of an IOL and spectacle correction to realise an eikonic imaging of both eyes. The present study should sensitise ophthalmic surgeons for the still unsolved problem of aniseikonia after cataract surgery and should give them a simple mathematical tool to help determine object-image magnification and show how to reduce or eliminate aniseikonia during cataract surgery.

Modeling of lateral magnification changes due to changes in corneal shape or refraction

Background and Purpose Especially after corneal surgery the lateral magnification of the eye providing the retinal image size of an object is a crucial factor influencing visual acuity and binocularity. The purpose of this study is to describe a paraxial computing scheme calculating lateral magnification changes (ratio of the image sizes before and after surgery) due to variation in corneal shape and spectacle refraction. Calculation strategy From the 4 × 4 refraction and translation matrices the system matrix representing the entire ‘optical system eye’ and the pupil matrix describing the sub-system from the spectacle correction to the aperture stop were defined for the state before and after surgery. As the chief ray is assumed to pass through the centre of the aperture stop, the 2 × 2 matrix of the lateral magnification ratio from preoperative to postoperative is described by the 2 × 2 sub-matrices of the respective pupil matrices. The cardinal meridians can be extracted by calculating the eigenvalues and eigenvectors. Working example Vertex distance 14 mm, measured distance between corneal apex and aperture stop 3.6 mm, keratometry 39 D + 6 D/0° to 47 D + 3 D/30° and refraction 3.5 D − 5 − 5 D/5° to −4.0 D − 3.5 D/25° preoperatively to postoperatively. The matrix of magnification ratio from preop to postop yields (0.8960 −0.0085;0.0074 0.9371) and the eigenvalues decomposition provided a 10.7% minified image at 170.1° and a minified image of 6.1% at 78.7°, which both are clinically relevant. Conclusion We presented a straight-forward computer-based strategy for calculation of retinal image size changes using 4 × 4 matrix notation. With this model the meridional changes in lateral magnification from the preoperative to the postoperative stage or between follow-up stages can be estimated from keratometry, refraction, vertex distance and anterior chamber depth, which might be important for binocularity and vision tests in corneal surgery.

Computerized calculation scheme for retinal image size after implantation of toric intraocular lenses

To describe a paraxial computing scheme for tracing an axial pencil of rays through the 'optical system eye' containing astigmatic surfaces with their axes at random. Two rays (-10 prism diopters from vertical and horizontal) are traced through the uncorrected and corrected eye. In the uncorrected eye one specific ray is selected from the pencil of rays, which passes through the pupil center. In the corrected eye any ray can be traced through the eye. From the slope angle, the intersection of the ray with the refractive surface and the refraction the slope angle of the exiting ray is determined and the ray is traced to the subsequent surface. From both rays traced through the eye an ellipse is fitted to the image to characterize the image distortion of an circular object. Assumptions: target refraction -0.5-1.0D/A = 90 degrees at 14 mm, corneal refraction 42.5 + 3.5D/A = 15 degrees, axial length 23.6 mm, IOL position 4.6 mm, central lens thickness 0.8 mm, refractive index 1.42, front/back surface of the toric IOL 10.0 D/7.14 + 6.47D/A = 101.8 degrees. The vertical incident ray was imaged to (x, y) = (0.0055 mm, -1.6470 mm)/(0.0067 mm, -1.6531 mm) in the uncorrected/corrected eye. The horizontal incident ray was imaged to (x, y) = (1.6266 mm, -0.0055 mm)/(1.6001 mm, -0.0067 mm) in the uncorrected/corrected eye. The ellipse (semi-major/semi-minor meridian) fitted to the conjugate image of a circle sized 1.648 mm/1.625 mm in an orientation 14.2 degrees in the uncorrected and 1.654 mm/1.599 mm in an orientation 7.1 degrees in the corrected eye. This concept may be relevant for the assessment of aniseikonia after implantation of toric intraocular lenses for correction of high corneal astigmatism.

Impact of decentration of astigmatic intra‐ocular lenses on the residual refraction after cataract surgery*

The purpose of this study is to assess the impact of decentration of astigmatic intra-ocular lenses on the residual refraction after cataract surgery, using a computing scheme with 5 x 5 system matrices. Based on the definition of an optical system in the paraxial Gaussian space containing astigmatic surfaces without restrictions to coaxiality, we derived a method (using 5 x 5 refraction and translation matrices) for calculating the residual refraction and the compensating prism in the spectacle plane after decentred implantation of thin and thick astigmatic intra-ocular lenses. The 'optical system eye' may contain astigmatic refractive surfaces with their axes at random. The capabilities of this computing scheme are demonstrated with two examples. In example 1 we calculate the residual refraction of a decentred 'thin astigmatic lens' for compensation of corneal astigmatism to achieve a spherical target refraction. In example 2 we compute the residual refraction after implantation of a 'thick astigmatic lens', where the spherical and cylindrical power as well as the implantation axis of the lens do not fully match the pre-operative recommendations and the lens is decentred relative to the optical axis. For both examples, we derive the residual prismatic effect in the spectacle plane and the lateral displacement of a ray exiting the spectacle correction when starting coaxially at the retina. We have presented an en bloc matrix-based strategy for the calculation of the residual spherocylindrical refraction at the spectacle plane after implantation of a decentred thin or thick astigmatic intra-ocular lens without restrictions to coaxiality. The resulting system matrix is written as a product of 5 x 5 refraction and translation matrices.

A new method to calculate corneal ablation depth based on optical individual eye model

The corneal shape, axial lengths and the wavefront aberrations of the eye were all considered to calculate the ablation depth based on the individual eye model. The optimization method for the curves surface replaced the direct calculation from only the optical path difference method (OPD). We analyzed the eye's optical system on its exit pupil and offered the optimum corneal anterior surface. And the ablation depth was the difference between the pre- and post-optimization along the optical axis of the eye. In our experiment, the maximum ablation depth decreases by 8.5% and the mean ablation depth decreases by 8.2% compared with the OPD method.

Compensation of aniseikonia with toric intraocular lenses and spherocylindrical spectacles

Magnification disparity between the two eyes (aniseikonia) is one of the major unresolved problems in modern cataract surgery, potentially degrading binocular visual function or causing diplopia. The purpose of this study is to describe a paraxial computing scheme using 4x4 system matrices to simulate a corrected pseudophakic 'optical system eye' with a meridional magnification that matches the magnification of a given contralateral eye. Based on the definition of a centred optical system in the paraxial Gaussian space containing astigmatic surfaces using 4x4 refraction and translation matrices, we derived a methodology for calculating the refractive power and axis of toric intraocular lenses and spherocylindrical spectacle corrections for (i) fully correcting the optical system eye and (ii) realizing an arbitrary meridional magnification by solving a linear equation system. The capabilities of this computing scheme are demonstrated with two examples. In example 1 we calculate a toric lens and a spherocylindrical spectacle correction for compensation of a corneal astigmatism to realize a predefined iso-meridional magnification. In example 2 we first determine the meridional magnification of the contralateral eye, which has been treated with cataract surgery and toric lens implantation, and then we compute the appropriate combination of a fully correcting toric lens and spherocylindrical spectacle refraction, which exactly matches the meridional magnification of the contralateral eye. We presented an en bloc matrix based strategy for the calculation of an optical system eye containing an astigmatic cornea, a toric lens implant and a spherocylindrical spectacle correction, where the toric lens and the spherocylindrical spectacle correction are determined to fully correct the system and to realize an arbitrary meridional magnification i.e. to eliminate aniseikonia.

Matrix‐based calculation scheme for toric intraocular lenses*

While a number of intraocular lens power prediction formulas are well established for determination of spherical lenses, no common strategy is published for the computation of toric intraocular lenses. The purpose of this study is to describe a paraxial computing scheme using 4 x 4 system matrices to describe the 'optical system eye' containing astigmatic refractive surfaces with their axes at random. Based on the definition of a centred optical system in the paraxial Gaussian space containing astigmatic surfaces using 4 x 4 refraction and translation matrices, we derived a methodology for calculating the refractive power of thin and thick toric intraocular lenses by solving a linear equation system. In a second step, we derived a methodology for prediction of the residual spectacle refraction after implantation of any toric lens implant with any orientation. The capabilities of this computing scheme are demonstrated with three examples. In example 1 we calculate a 'thin toric lens' for compensation of a corneal astigmatism to achieve a spherical target refraction. In example 2 we compute a 'thick toric lens', which has to compensate for an oblique corneal astigmatism and rotate the spectacle cylinder to the 'against the rule' position to enhance near vision. In example 3 we predict the residual refraction at the corneal plane after implantation of a thick toric lens, when the cylinder of the lens implant is compensating the corneal cylinder in part and the axis of implantation is not fully aligned with the axis of the corneal astigmatism. We present an en bloc matrix-based strategy for the calculation of thick or thin toric intraocular lenses, with the flexibility of crossing an unlimited number of cylinders with restrictions to paraxial optics. The resulting system matrix S is written as a product of 4 x 4 refraction and translation matrices. Residual refraction at the corneal (contact lens) or spectacle plane can be derived by inverting the order of matrices for calculation of the system matrix.

Computerized calculation scheme for toric intraocular lenses.

While a number of intraocular lens (IOL) power prediction formulae are well established for determination of spherical lenses, no common strategy has been published for the computation of toric IOLs. The purpose of this study is to describe a paraxial computing scheme for tracing an axial pencil of rays through the 'optical system eye' containing astigmatic refractive surfaces with their axes at random. The capabilities of this computing scheme are demonstrated with clinical examples. Based on a schematic model eye with spherocylindric surfaces, we use two alternative notations for description of vergences or prescriptions: (1) standard notation (refraction in both cardinal meridians and axis), and (2) component notation (spherical equivalent and cylindric component in 0 degrees and 45 degrees. Refractive surfaces are added to the vergence in component notation, whereas the transformation of the vergence through media is performed in the standard notation for both cardinal meridians. For calculation of the toric lens implant, a pencil of rays is traced through the spectacle and the cornea to the estimated lens position as well as backwards from the retina to the estimated lens position. For calculation of residual spectacle refraction, a pencil of rays is traced backwards from the retina through the toric lens implant and the cornea to the spectacle plane. In example 1 we calculate a 'thin toric lens' for compensation of a corneal astigmatism to achieve a spherical target refraction. In example 2 we compute a 'thick toric lens', which has to compensate for an oblique corneal astigmatism and rotate the spectacle cylinder to the against the rule position to enhance near vision. In example 3 we estimate the residual refraction at the corneal plane after implantation of a thick toric lens, when the cylinder of the lens implant is compensating the corneal cylinder in part and the axis of implantation is not fully aligned with the axis of the corneal astigmatism. This novel mathematical concept for computation of toric IOLs or prediction of the refractive outcome with a toric implant in place is a straightforward, computer-based approach, which may substitute for more or less empirical methods of determining toric IOL implants.

Function of the pupil in vision and information capacity of retinal image

AbstractThe light–pupil reflex system has been the object of study in physiological engineering, as a typical example of involuntary biological systems. As regards the variable that actually controls the pupil, however, there has been little discussion of its role in vision. This study notes that the pupil is closely related to the spatial frequency response of the eye's optical system, and discusses the relation between the quality of the retinal image and the pupil size, as determined by the external image and the characteristics of the eye's optical system. By defining the information capacity of the retinal image as the evaluation measure, the quality of the retinal image is represented quantitatively. The relation between the pupil size and the information capacity of the retinal image is examined for various conditions. It is shown that the human pupil is controlled so that the quality of the retinal image is optimized, in the sense of the information capacity of the retinal image for each luminance level, when the external image is a natural image. On the other hand, when the external image is not a natural image, or when the characteristic of the eye's optical system or the relation between the visual cell arrangement and the pupillary diameter differs from the actual situation, it is not necessarily true that the pupil optimizes the quality of the retinal image. The above results suggest that the function of the pupil in vision is optimization of the quality of the retinal image. It is also suggested that the adjustment function of the pupillary diameter is acquired under the constraints of the external image and the hardware of the eye. © 2003 Wiley Periodicals, Inc. Syst Comp Jpn, 34(9): 48–57, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.10344

Computerized calculation scheme for bitoric eikonic intraocular lenses.

Despite full correction of the corneal astigmatism with toric intraocular lenses, the retinal image is distorted and the lateral image-object magnification is different in different meridians. The purpose of this study is to describe an iteration strategy for tracing an axial pencil of rays through the 'optical system eye' containing astigmatic refractive surfaces with their axes at random to calculate a thick bitoric lens implant which eliminates image distortion. The capabilities of this computing scheme are demonstrated with two clinical examples. We present a mathematically straightforward computer-based strategy for the calculation of thick bitoric eikonic lens implants. The iteration algorithm is initialized with a spherical front and a toric back surface and stepwise decreases the image distortion by adding cylinder lenses to the front lens surface corrected by the toric lens back surface. Total magnification can be modulated by varying the front-to-back surface power of the thick lens.

Interpretation of corneal topography after penetrating keratoplasty with wave-front parameters--comparison between non-mechanical trepanation with excimer laser and motor trepanation

Besides irregular astigmatism characterized by the asymmetric components of the corneal surface, the aberration of the cornea from an ideal sphere degrades the optical performance of the "optical system eye". Best-corrected visual acuity may be markedly decreased with an increasing aperture diameter. The purpose of this study was to evaluate the time course of the symmetrical part of the aberration from an ideal sphere and to correlate it with functional results after penetrating keratoplasty (PK). Fifty patients each (20 primary dystrophies, 30 keratoconus) underwent nonmechanical trephination (NMT) (excimer laser MEL60, Aesculap-Meditec, Heroldsberg, Germany) or mechanical motor trephination (MT) in penetrating keratoplasty. All procedures (7.5 mm in dystrophies, 8.0 mm in keratoconus, 8 orientation teeth in NMT, double-running 10-0 nylon suture) were performed by one surgeon (GOHN). At a postoperative gate of 6 weeks, 6 months, before partial suture removal and after complete suture removal, corneal topography analysis (TMS-1, Tomey, Tennenlohe, Germany) was performed. After a Gram-Schmidt-orthogonalization, corneal topography height data of 25 noncentric rings in 256 hemimeridians were decomposed into Zernike components of radial order n = 16 in the sense of minimizing the root mean square error. The symmetrical part of the deviation from an ideal spherical surface was calculated from the Zernike components Z4(0), Z6(0), ..., Z16(0). From the Zernike components, the longitudinal focus distribution and its standard deviation (SDF) was determined. SDF was correlated with the surface asymmetry index (SAI), the surface regularity index (SRI), the potential visual acuity (PVA) of the TMS-1 and the spectacle-corrected visual acuity. In the time course after PK, SDF decreased from the 6 weeks follow-up examination to the end of the follow-up from 1.27 mm to 0.77 mm in NMT (p = 0.01) and from 1.29 mm to 1.20 mm following MT (p = 0.24) within the central corneal region of 3 mm in diameter. The SAI did not depend on SDF, whereas the SRI correlated significantly inversely with the SDF within the 3 mm zone immediately before (p = 0.01 and p = 0.02) and after suture removal (p = 0.01 each) after NMT. After MT, only a mild inverse correlation was observed before (p = 0.05) and after suture removal (p = 0.04). In the time course after the 6 months follow-up the SDF within the 3 mm central area correlated inversely with the best-corrected visual acuity, more with NMT than with MT (p = 0.005 and p = 0.04 after suture removal). Best-corrected visual acuity was approximately 2 decimal lines better following NMT. Zernike decomposition of corneal topography height data allows a separation and quantification of aberration of corneal graft surface from an ideal sphere. Although corneal surfaces with a high degree of local irregularities can be decomposed due to the orthogonality condition. Following NMT, SDF was markedly lower after suture removal.

Double-pass measurements of the retinal-image quality with unequal entrance and exit pupil sizes and the reversibility of the eye's optical system.

We have used a modified double-pass apparatus with unequal entrance and exit pupil sizes to measure the optical transfer function in the human eye and have applied the technique to three different problems. First, we confirm that in the eye the double-pass spread function is the cross correlation of the input spread function with the output spread function [J. Opt. Soc. Am. A 12, 195 (1995)]. Consequently, when entrance and exit pupil sizes are equal, phase information is lost from the double-pass images. Second, we show that in double-pass measurements the eye behaves like a reversible optical system. That is, when entrance and exit pupils are equal, the double-pass image results from two passes through an optical system having a transfer function that is the same in both directions. To test for reversibility in the living eye we have used a double-pass apparatus with different exit and entrance pupil sizes (one of them small enough to consider the eye diffraction limited), so that the ingoing and the outgoing transfer functions are different. The measured image quality was unchanged when the pupils were interchanged, i.e., when the first-pass entrance pupil size becomes the second-pass exit pupil size, and vice versa. Third, the technique provides a means for inferring the complete optical transfer function of the eye, including the phase transfer function, and the shape of the point-spread function.