Finite Ray Tracing Research Articles

Scaling the Retinal Image of the Wide-Angle Eye Using the Nodal Point

Angles subtended at the second nodal point of the eye (NP2) are approximately the same as input visual angles over a very large angular range, despite the nodal point being a paraxial lens property. Raytracing using an average pseudophakic eye showed that the angular nodal point criterion was only valid up to about 10°, and that the linear relationship was due instead to the cornea and lens initially creating chief ray angles at the exit pupil that are about 0.83 times input values for this particular eye, and then by the retina curving around to meet the rays in a manner that compensates for increasing angle. This linear relationship is then also maintained when retinal intersections are calculated relative to other axial points, with angles rescaled approximately using the equation R/(R + delta), where delta is the axial distance from the center of a spherical retina of radius R. Angles at NP2 approximately match the input angles, but the terminology is misleading because this is not a paraxial property of the eye. Chief rays are used with finite raytracing to determine the actual behavior.

Modified forms of Tscherning ellipses.

Third-order equations are well known for determining sagittal and tangential powers of a thin lens, corresponding to an eye rotating behind a lens to view objects away from the optical axis of the lens. These equations are referenced to the back surface of the lens and do not take into account the peripheral thickness of the lens. They do not give the same results as finite raytracing at small angles in which powers are referenced to the vertex sphere, which is the same distance from the centre-of-rotation for all object angles. Modified forms of the third-order sagittal and tangential image vergence error equations are developed to overcome the discrepancies. These are used to determine Tscherning ellipses for zero oblique astigmatism and zero mean oblique power error. While solutions to oblique astigmatism are not affected by the modifications, there are considerable changes to mean oblique error solutions.

Improved MSMGFSK Models Apply to Gas Radiation Heat Transfer Calculation of Exhaust System of TBCC

The multiscale multigroup full-spectrum k-distribution (MSMGFSK) model was improved to adapt to radiation heat transfer calculations of combustion gas flow field with large temperature and pressure gradient. The improvements in calculation accuracy resulting from new sorting strategy of the spectral absorption coefficients were validated using a series of semi-1D problem in which strong temperature, pressure, and mole fraction inhomogeneities were present. A simpler method to attain compatibility between the MSMGFSK model and the gray-wall radiation emission has been established and validated. Finally, estimates are given for the calculation of wall radiation heat transfer characteristics and thermal emission imaging of the exhaust system of the parallel turbine-based combined cycle (TBCC) engine, using finite volume method (FVM) and ray trace method (RT), respectively.

Liquid Gradient Refractive Index Microlens for Dynamically Adjusting the Beam Focusing

An in-plane liquid gradient index (L-GRIN) microlens is designed for dynamically adjusting the beam focusing. The ethylene glycol solution (core liquid) withde-ionized (DI) water (cladding liquid) is co-injected into the lens chamber to form a gradient refractive index profile. The influences of the diffusion coefficient, mass fraction of ethylene glycol and flow rate of liquids on the refractive index profile of L-GRIN microlens are analyzed, and the finite element method and ray tracing method are used to simulate the convection-diffusion process and beam focusing process, which is helpful for the prediction of focusing effects and manipulation of the device. It is found that not only the focal length but the focal spot of the output beam can be adjusted by the diffusion coefficient, mass fraction and flow rate of liquids. The focal length of the microlens varies from 942 to 11 μm when the mass fraction of the ethylene glycol solution varies from 0.05 to 0.4, and the focal length changes from 127.1 to 8 μm by varying the flow rate of the core liquid from 0.5 × 103 to 5 × 103 pL/s when there is no slip between the core and cladding inlet. The multiple adjustable microlens with a simple planar microfluidic structure can be used in integrated optics and lab-on-chip systems.

Three-Dimensional Analysis of the Autostereoscopic Display with an Array of Lenticulars

Three-dimensional analysis of the optical functionalities of an autostereoscopic display with an array of slanted lenticular lenses was performed. The specification parameters of the lenticular lens for clear separation of the images were first determined using the geometrical optics, and the transmission characteristics of the light ray travelling through a single lenticular were then calculated by finite ray tracing. The properties of light transmission over the entire display panel were then determined by expanding the results obtained for the single lenticular to the entire lenticular lens array. Consequently, each view was confirmed to be located at an inter-ocular distance of 65 mm away from each other. Approximately 5% noise was observed between the views, and the shape of the viewing zone at the optimal viewing distance was tilted towards the direction of the slanted lenticular. Overall, numerical analysis enables a realistic evaluation of the optical functionalities, such as the shape of the viewing zone, of lenticular based autostereoscopic displays.

Generalized ray tracing method for the calculation of the peripheral refraction induced by an ophthalmic lens

This thesis proposes a method to evaluate and quantify in a precise way the peripheral refraction induced by an ophthalmic lens. The motivation for this work stems from the progression of myopia and its possible causes; two of them are particularly key for this PhD: (a) Peripheral refraction of the eye may have an important role in the progression of myopia and (b) ophthalmic lenses are the compensating element more used in children and teenagers. These two elements fully justify the need for a reliable method to quantify the induced peripheral refraction by an ophthalmic lens. This method is based on two pillars: first, it must accurately assess the design of the ophthalmic lens and, second, it should consider what peripheral refractive pattern is acting, that is, without compensating element. The proposed method takes the advantages provided by the ray tracing strategies used in the classic design of ophthalmic lenses but applying them in parallel with amendments to evaluate the peripheral refraction. Thus, the simple scheme used in the classic design of ophthalmic lenses containing a remote sphere and a small aperture at the center of rotation of the eye becomes a scheme where the retina conjugate surface (RCS) and the nodal point of the eye play equivalent roles. In our case, the reference for ray tracing is the nodal point of the eye and the reference for measuring the induced peripheral refraction is the RCS. Ray tracing is based on a finite ray tracing (FRT) from the image space to the object space and on a generalized ray tracing (GRT) from object space to image space. Both have been implemented in a Matlab program and validated to provide a powerful tool for our purpose. GRT allows a quick and accurate assessment of the oblique astigmatism, ie the tangential and sagittal focal lens, in wide field of view considering accurately the lens design. This considers that each ray has a small wavefront associated traveling perpendicular to it. By GRT we are able to know how the wavefront shape changes when is propagated and refracted. Therefore, it is mandatory to have a locally description of the geometry of both the wavefront and the refractive surface at the point where the ray arrives to the refractive surface. This local description is determined by the normal and by the principal curvatures and directions of these surfaces at the point of interest; they can be obtained from a parametric description of the surface and then using Gaussian fundamental forms. This ray tracing procedure has been developed for the general case of any geometry to the surfaces of the ophthalmic lens and has been detailed for the case of an astigmatic lens. For calculating the induced peripheral refraction, a surface is modeled reflecting the peripheral refractive initial values before entering the lens; this is the aforementioned RCS. Two methods have been proposed to model this RCS. One is based on the trends observed in the different studies and uses three-dimensional surfaces power vectors associated with peripheral refraction. The second method uses experimental measurements obtained along four meridians of the retina to interpolate a surface. The expression of these surfaces by power vectors can easily be combined with the results obtained by tracing rays through the lens for the calculation of the induced peripheral refraction. We present in this manuscript some specific examples of how variations on the lens geometry modified the induced peripheral refraction. This opens up the possibility of custom designs ophthalmic lenses to prevent the progression of myopia.

Geometry-invariant GRIN lens: finite ray tracing.

The refractive index distribution of the geometry-invariant gradient refractive index lens (GIGL) model is derived as a function of Cartesian coordinates. The adjustable external geometry of the GIGL model aims to mimic the shape of the human and animal crystalline lens. The refractive index distribution is based on an adjustable power-law profile, which provides additional flexibility of the model. An analytical method for layer-by-layer finite ray tracing through the GIGL model is developed and used to calculate aberrations of the GIGL model. The result of the finite ray tracing aberrations of the GIGL model are compared to those obtained with paraxial ray tracing. The derived analytical expression for the refractive index distribution can be employed in the reconstruction processes of the eye using the conventional ray tracing methods. The layer-by-layer finite ray tracing approach would be an asset in ray tracing through a modified GIGL model, where the refractive index distribution cannot be described analytically. Using the layer-by-layer finite ray-tracing method, the potential of the GIGL model in representing continuous as well as shell-like layered structures is illustrated and the results for both cases are presented and analysed.

Numerical implementation of generalized Coddington equations for ophthalmic lens design

A method for general implementation in any software platform of the generalized Coddington equations is presented, developed, and validated within a Matlab environment. The ophthalmic lens design strategy is presented thoroughly, and the basic concepts of generalized ray tracing are introduced. The methodology for ray tracing is shown to include two inter-related processes. Firstly, finite ray tracing is used to provide the main direction of propagation of the considered ray at the incidence point of interest. Afterwards, generalized ray tracing provides the principal curvatures of the local wavefront at that point, and its orientation after being refracted by the lens. The curvature values of the local wavefront are interpreted as the sagital and tangential powers of the lens at the point of interest. The proposed approach is validated using a double-check of the calculated lens performance in the spherical lens case: while finite ray tracing is validated using a commercial ray tracing software, generalized ray tracing is validated using a software application for ophthalmic lens design based on the classical version of Coddington equations. Equations of the complete tracing process are developed in detail for the case of generic astigmatic ophthalmic lenses as an example. Three-dimensional representation of the sagital and tangential powers of the ophthalmic lens at all directions of gaze then becomes possible, and results are presented for lenses with different geometries.

Thermal optical path difference analysis of off-axis lens ray trace foot-print

The optical system lens temperature difference will cause optical aberration increase. This study is applying finite element method (FEM) and optical ray tracing; calculate off axis ray thermal optical path difference (OPD). The optical system temperature distribution is calculated from finite element simulation result and weighting temperature to each optical ray path. The simulation result shows off-axis ray major thermal optical aberrations are tilt and piston at this study.

Reformulation of Some Finite Raytracing Equations Through Quadric Surfaces of Revolution

This work exhibits analytical reformulation of four equations of finite raytracing throughquadric surfaces of revolution. This reformulation enhances comprehending the procedure of finiteraytracing firmly besides it shows how to obtain these formulas. The equations reformulated in thiswork clarified that the corresponding ones in [1] were merely typographically incomplete equations.

Fifth-Order Theory of Astigmatism of Thin Spherical Spectacle Lenses

To demonstrate and analyze the fifth-order theory of oblique astigmatism of a thin spherical spectacle lens and make a comparison with the third-order theory and exact ray tracing. Fifth-order equations were derived and used for analysis of oblique astigmatism of a spherical spectacle lens to calculate analytically the shape of the lens with corrected oblique astigmatism for large angles of field of view. These results were compared with those of finite ray tracing and the third-order aberration theory. Formulas for the calculation of oblique astigmatism of a thin spherical spectacle lens were derived. These formulas analytically express oblique astigmatism of the third and fifth order. The theory presented generalizes the third-order description of astigmatism of the spherical spectacle lens and derived equations enable calculation of the shape of the spectacle lens with corrected astigmatism even for a large field of view. The fifth-order solution is compared with the third-order theory and the exact solution found by ray tracing. Differences between the third- and fifth-order theory are <0.05 D for spherical lenses, which is negligible clinically. The presented fifth-order equations, which are a generalization of the third-order formulas for the description of oblique astigmatism, can be used for the analytical expression of the fifth-order astigmatism of the spherical lens. They can simply be applied for the initial design of lenses with corrected astigmatism for large angles of view, something not possible using the third-order theory. We conclude that astigmatism of the fifth order has little effect on the image quality of the spectacle lens, and the third-order theory is satisfactory for practical calculations in optometry.

Simple method to measure the visual axis of the human eye

We propose a simple method to measure the angle "α" that the visual axis (VA) makes with the optical axis of the human eye. In this method, we capture the images of the pupil from three different angles, one along the VA and the other two along angles that are symmetrical with respect to the VA. These views of the pupil are captured simultaneously by a camera in a single photograph using a pair of plane mirrors. Assuming a model eye and with the help of finite ray tracing, we compute the value of α from the measured diameters of the three images of the pupil. Having a simple means to measure the value of α can be useful for optical modeling and analysis of the human eye. Measurement of the VA may also be useful in monitoring progressive myopia.

Lower- and higher-order aberrations predicted by an optomechanical model of arcuate keratotomy for astigmatism

To develop a realistic model of the optomechanical behavior of the cornea after curved relaxing incisions to simulate the induced astigmatic change and predict the optical aberrations produced by the incisions. ICMA Consejo Superior de Investigaciones Científicas and Universidad de Zaragoza, Zaragoza, Spain. A 3-dimensional finite element model of the anterior hemisphere of the ocular surface was used. The corneal tissue was modeled as a quasi-incompressible, anisotropic hyperelastic constitutive behavior strongly dependent on the physiological collagen fibril distribution. Similar behaviors were assigned to the limbus and sclera. With this model, some corneal incisions were computer simulated after the Lindstrom nomogram. The resulting geometry of the biomechanical simulation was analyzed in the optical zone, and finite ray tracing was performed to compute refractive power and higher-order aberrations (HOAs). The finite-element simulation provided new geometry of the corneal surfaces, from which elevation topographies were obtained. The surgically induced astigmatism (SIA) of the simulated incisions according to the Lindstrom nomogram was computed by finite ray tracing. However, paraxial computations would yield slightly different results (undercorrection of astigmatism). In addition, arcuate incisions would induce significant amounts of HOAs. Finite-element models, together with finite ray-tracing computations, yielded realistic simulations of the biomechanical and optical changes induced by relaxing incisions. The model reproduced the SIA indicated by the Lindstrom nomogram for the simulated incisions and predicted a significant increase in optical aberrations induced by arcuate keratotomy.

The effect of videokeratoscope faceplate design on radius of curvature maps

A computer model using finite ray tracing methods was developed to simulate a videokeratoscope analysing an average cornea. Different faceplate designs were tested using five points on the faceplate subtending angles at the corneal vertex between 15 degrees and 75 degrees in 15 degrees intervals. Image quality was assessed by adding the geometrical blurs of the five image points. Differences (error) between true sagittal radius of curvature, and sagittal radius of curvature calculated by the van Saarloos algorithm, were calculated for selected surfaces at the same corneal points. Differences equal to or bigger than 0.02 mm were regarded as clinically significant. The faceplate surface that provided the sharpest image for an average cornea was a cylinder with the base 120 mm away from the corneal vertex and a diameter of 26 mm. Changing the faceplate design results in clinically significant differences for an average cornea. Image quality is not proportional to corneal surface reconstruction accuracy.

조명각 변조 방식의 3차원 입체영상 표시장치설계 및 공차분석

In order to realize a 3-D stereoscopic display module with alternating illumination angles, several conditions required for a lenticular lens sheet were established, and then both the lens specification and the module structure were designed. Also the performance of the stereoscopic module and its tolerance characteristics were evaluated by simulating the intensity distribution on the observation plane with a finite-ray tracing technique. From the evaluation, it was known that an intersection area between two adjacent lenses should not be filled and that the lateral mismatch between a planar liquid crystal shutter and a lens sheet should be minimized.

Analysis, search, and classification for reflective ring-field projection systems.

Extreme ultraviolet (EUV) lithography uses reflective ring-field projection systems. Geometrical obstruction limits the possible system configurations to small domains of the parameter space. We present an analysis, a search method, and a classification of these unobstructed domains. The exhaustive search method based on paraxial analysis provides an effective means for determining all possible design forms and for finding useful starting configurations for optimization. The approach is validated through comparison with finite ray tracing.

Field restriction and vignetting in contact lenses with opaque peripheries

Background: Some previous researchers have shown empirically that visual fields can be restricted by contact lenses with opaque and semi‐opaque peripheral zones. However, there has been no formal statement of the optical theory behind such restriction.Methods: Calculations are made of fields of view with opaque periphery contact lenses, based on paraxial theory and meridional finite ray tracing in the Gullstrand‐Emsley schematic eye.Results: This analysis shows that paraxial theory is adequate for predicting ‘half fields of full illumination’ for ocular pupil diameters smaller than six millimetres, although paraxial estimates of ‘half total field’ can substantially underestimate those obtained by finite ray tracing for a wide range of ocular pupil sizes. Therefore finite ray tracing may be a more appropriate method of calculating half total field. ‘Total field’ will be smaller with smaller ocular pupils and smaller contact lens apertures. A clinical method is suggested for assessing total field with such contact lenses in situ. The analysis applied to opaque periphery contact lenses is extended to the semi‐opaque periphery contact lenses used for cosmetic alteration of eye appearance.Conclusion: Semi‐opaque periphery contact lenses will decrease retinal illuminance most at regions outside those tested by previous empirical static perimetry studies.

Accurate calculation of Narcissus signatures by using finite ray tracing

In scanning IR systems with cooled quantum detectors, the Narcissus signature usually has a limiting effect on the perceived image quality, and so it is important that it be assessed accurately before manufacture. We describe a new finite ray-tracing method in which each ray represents an equal amount of flux falling on the detector. Such methods require many rays; therefore a full error treatment is given that allows designers to estimate the necessary number of rays to obtain the required accuracy and also to calculate the standard deviation of the error in the final computed result.

The Use of Simple Relationships between Wavefront Aberration and Wavelength to Approximate the Polychromatic Optical Transfer Functions of 8 to 12 µm Thermal Imaging Lenses

Abstract Two methods are described which can be used to predict polychromatic optical transfer functions (OTFs) of thermal imaging lenses to good accuracy from only one finite ray trace. These methods offer some saving in calculation time and could be used to predict polychromatic OTFs from monochromatic test data provided suitable paraxial data and spectral details are available.

Ray failures in finite ray tracing

Le rayon peut manquer la surface geometrique definie par l'equation de surface, il peut subir une reflexion interne totale a la limite milieu dense-milieu moins dense, et la hauteur du rayon a la surface, peut depasser la demi-ouverture indiquee pour cette surface, le rayon peut rencontrer la meme surface apres refraction