Real Ray Tracing Research Articles

Hybrid approach for the design of mirror array to produce freeform illumination sources in immersion lithography

Source and mask optimization (SMO) has emerged as a key resolution enhancement technique (RET) for 45nm technology node and below in lithography. The design method of freeform illumination sources predicted by SMO is significant for the scanner development. We present a hybrid approach combining simultaneous and sequential approaches to optimize the tilt angles of the mirrors to produce multi target freeform illumination sources accurately and quickly. The size of spot reflect by plane mirror can be easily controlled by changing different microlens arrays with appropriate focal length, which reduce the complexity of the system and makes it more flexible to produce the specific freeform sources compared to curving the mirrors used in previous work. The relationship between the tilt angles of plane mirrors and the positions of the spots in the pupil is obtained by chief ray tracing. Using the hybrid approach the freeform illumination sources required by SMO can be designed by merely adjusting the tilt angles of mirrors without changing other parameters of optical elements, which is most effective for both lithography tool manufacture and its applications. The real ray tracing results demonstrate that our design method is capable of creating multi freeform illumination sources with high transmittance, and confirm that the effectiveness of the hybrid approach for optimized design and control of mirror array in immersion lithography system.

FPGA Hardware Acceleration for Visualization with Use of the Ray Tracing Algorithm

This paper deals with the issue of hardware acceleration of photorealistic visualization with use of ray tracing technique in real time. First part of the article briefly introduces ray tracing and presents existing hardware architectures that are accelerating computations with aim to bring real time ray tracing; second part of the article introduces the implementation of the designed solution that represents two modules implemented with use of the VHDL language and the FPGA technology. Modules are accelerating the part of ray tracing algorithm that according to the research requires the most system resources. This part consists of computation needed to find the ray-object intersection. The first module computes ray – sphere intersection, and the second computes ray – triangle intersection. Both modules are composed of number of components, which were optimized and parallel computing was applied in highest possible measure.

Seidel aberrations of the Gabor superlens

Equations are presented for the third-order Seidel aberrations of the Gabor superlens (GSL) as a function of microtelescope channel position within the aperture array. To reveal the origin and form of increasing aberration with channel height, Seidel coefficients are derived as a function of the accumulating pitch difference between the lens arrays and the aberrations present in the centered channel. Two- and three-element Gabor lenses are investigated and their aberrations are expressed as a function of first-order design parameters. The derived theory is then compared to a real ray trace simulation to demonstrate the accuracy of third-order aberration theory to predict GSL image quality.

Ray Tracing Methods for Correcting Chromatic Aberrations in Imaging Systems

The correction of chromatic aberrations is typically performed using aberration formulas or by using real ray tracing. While the use of aberration formulas might be effective for some simple optical systems, it has limitations for complex and fast systems. For this reason chromatic aberration correction is usually accomplished with real ray tracing. However, existing optimization tools in lens design software typically mix the correction of monochromatic and chromatic aberrations by construction of an error function that minimizes both aberrations at the same time. This mixing makes the correction of one aberration type dependent on the correction of the other aberration type. We show two methods to separate the chromatic aberrations correction of a lens system. In the first method we use forward and reverse ray tracing and fictitious nondispersive glasses, to cancel the monochromatic aberration content and allow the ray tracing optimization to focus mainly on the color correction. On the second method we provide the algorithm for an error function that separates aberrations. Furthermore, we also demonstrate how these ray tracing methods can be applied to athermalize an optical system. We are unaware that these simple but effective methods have been already discussed in detail by other authors.

手持式拉曼光谱仪探头系统的杂光抑制新方法

Handheld Raman spectrometer probe system shares the same optical configuration for illumination and light receiving. Thus, stray light caused by multiple reflections of laser, expect for Rayleigh scattering, is a problem to be solved for this kind of probe system. By real ray tracing method, setting up reasonable stray light analysis model and theoretical calculation, we get the total stray light information, together with our actual prototype structural data, such as the size and location of focus, emergent direction, energy in the slit and so on. Then a new approach of stray light suppression for spectrometer probe system that uses black board to block the stray light is proposed. The size and location of the black board are determined according to the analysis of the stray light. The optical simulation analysis results show that the black board suppresses stray light to the level of 10-13 in Raman spectral region. This satisfies the requirements of the handheld Raman spectrometer. With black board method, almost 50% of the laser reflection with incidence angle larger than 2 on the notch filter can be filtered.

Grouping design method with real ray tracing model for extreme ultraviolet lithographic objective

Choosing an adequate initial design for optimization plays an important role in obtaining high-quality extreme ultraviolet (EUV) litho- graphic objectives. A grouping design method with real ray tracing model is developed to acquire initial configurations of high numerical aperture (NA) objective for EUV lithography. In this method, the objective system is first divided into three mirror groups. The initial parameters of each mirror group are then determined by real ray calculation under design constraints. Finally, the three mirror groups are connected directly into a feasible initial system. Due to real ray calculation, the discrepancy of the ray path induced by paraxial approximation and the exhaustive search of variables is avoided in a high-NA objective design. In addition, the incidence angles on reflective mirrors can be controlled in the design of each group, which makes the initial configuration suited to further optimization and compatible multilayer design. An NA 0.33 six-mirror EUV lithographic objective is designed as an example to implement this method. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attri- bution of the original publication, including its DOI. (DOI: 10.1117/1.OE.52.12.125102)

A Low-cost Optimization Design for Minimizing Chromatic Aberration by Doublet Prisms

A low-cost optimal double-prism method is proposed by using the developed MATLAB program to correct chromatic aberration. We present an efficient approach to choose a couple of low-cost glasses to obtain a low aberration double prism. The doublet prisms were made of two lead-free glasses. The relative partial dispersion of the two lead-free glasses is identical and their Abbe numbers are different greatly. The proposed design aims to minimize chromatic aberration, such as in apochromats, for paraxial ray tracing. Finally, an optimization design for real ray tracing can be evaluated by the chromatic aberration curve with a minimal area.

On numerically solving the complex eikonal equation using real ray-tracing methods: A comparison with the exact analytical solution

The exact analytical solution of the complex eikonal equation describing P- and S-waves radiated by a point source situated in a simple type of isotropic viscoelastic medium was ascertained. The velocity-attenuation model is smoothly inhomogeneous with a constant gradient of the square of the complex slowness. The resultant traveltime is complex; its real part describes the wave propagation and its imaginary part describes the attenuation effects. The solution was further used as a reference solution for numerical tests of the accuracy and robustness of two approximate ray-tracing approaches solving the complex eikonal equation: real elastic ray tracing and real viscoelastic ray tracing. Numerical modeling revealed that the real viscoelastic ray tracing method is unequivocally preferable to elastic ray tracing. It is more accurate and works even in situations when the elastic ray tracing fails. Also, the ray fields calculated by the real viscoelastic ray tracing are excellently reproduced even in the case when the elastic ray tracing yields completely distorted results. Compared with complex ray tracing, which is limited to simple types of media, the real viscoelastic ray tracing offers a fast and computationally straightforward procedure for calculating complex traveltimes in complicated 3D inhomogeneous attenuating structures.

Closed-form sag solutions for Cartesian oval surfaces

This paper presents a closed-form solution to the sag of the Cartesian oval and an alternate iterative method for obtaining the sag. The emphasis is in providing a methodology for determining the sag and derivatives of a Cartesian surface for optical design, ray-tracing purposes. We verify our results by comparison of our solutions and by real ray tracing.

Phase plates for generation of variable amounts of primary spherical aberration

We discuss a set of phase plate-pairs for the generation of variable amounts of primary spherical aberration. The surface descriptions of these optical plates are provided, and their aberration-generating properties are verified with real ray-tracing. These plate-pairs are robust in that they allow large tolerances to spacing as well as errors in the relative displacement of the plates. Both primary spherical aberration (r4) and Zernike spherical aberration (6r4- 6r2 + 1) can be generated. The amount of spherical aberration is proportional to the plate-pair displacement and in our example it reaches up to 48 waves (~8 waves Zernike) for a clear aperture of 25 mm.

Evaluation of the meridional longitudinal spherical aberration from corneal topography measurements

This paper shows how corneal topographic data can be used to determine the value of the longitudinal spherical aberration. We have obtained the corneal profiles and the values of the longitudinal spherical aberration for the rays propagating within the steepest and flattest meridional planes, by using a real raytracing algorithm. These corneal profiles have been also fitted to conicoids and the asphericity parameter has been calculated. We have found that the longitudinal spherical aberration follows a parabolic dependence for a circular region of 5 mm in diameter. This parabolic dependence has been fitted with a polynomial function. The data provided by commercial topographic systems can be used to obtain the longitudinal spherical aberration along the selected meridians.

Real Ray Tracing Simulation Versus Clinical Outcomes of Corneal Excimer Laser Surface Ablations

To investigate the recently reported discrepancy between theoretical expectations and clinical outcomes of corneal ablations after excimer laser corneal refractive surgery. Thirty-four eyes of 25 patients who had laser epithelial keratomileusis (LASEK) for myopia (mean -6.26±2.52 diopters [D], full correction diameter 6.71±0.25 mm) without astigmatism correction were assessed. Based on preoperative topographies, corneal ablation was simulated using the Munnerlyn formula--one with homogeneous beam fluence and another with variable beam fluence (including reflection loss and non-normal laser beam incidence). Corneal shape was analyzed pre- and postoperatively. Corneal wavefront aberration was calculated with real ray tracing and reported according to the Optical Society of America standard. Corneal asphericity for a 6.0-mm diameter showed that preoperative measured corneas (-0.21±0.11) and postoperative simulated corneas (homogeneous beam fluence -0.32±0.19, variable beam fluence -0.41±0.22) were prolate, whereas postoperative measured corneas (0.40±0.57) were oblate. Corneal wavefront aberration (higher order aberrations 3rd to 6th/spherical aberration Z[4,0] in microns) for a 6.0-mm diameter, compared to the preoperative state (0.34±0.19/0.15±0.09), did not increase in postoperative simulation (homogeneous beam fluence 0.29±0.15/0.05±0.08, variable beam fluence 0.34±0.14/0.16±0.08), but in contrast increased for postoperative measurements (0.64±0.17/0.49±0.15). The increase in oblateness, higher order aberrations, and spherical aberration of real patients' postoperative corneas was not seen in simulations using a Munnerlyn ablation profile. The fluence loss of the laser was one important factor, but did not explain all increasing aberrations observed clinically. We hypothesize that corneal wound healing and biomechanics play a role.

Design of unobscured reflective zoom system with three mirrors

A method for the design of an unobscured reflective zoom system with three mirrors is described. This method applies the vector aberration theory, which helps designers analyze third-order aberrations for optical systems with decentered and tilted surfaces. As the vector aberration theory presents the variation of third-order aberrations in asymmetric systems through analytic expressions, real ray tracing is unnec-essary. Hence, the design with vector aberration theory is faster, and the analytic expressions are more comprehensive and intuitive. To demonstrate the practicability of the method, a design example is given, which shows that the presented method can guide designers achieve a good unobscured reflective zoom system with three mirrors.

Customized aspheric intraocular lenses calculated with real ray tracing

To calculate the exact geometry of custom intraocular lenses (IOLs) for pseudophakic eyes and theoretically predict the residual wavefront error by real ray tracing based on Snell's law. Centre for Ophthalmology, University Hospital, Tübingen, Germany. Individual computer models were constructed based on measurements, including corneal topography and axial length. The geometry of custom spherical, aspheric, toric, and toric aspheric IOLs was calculated in an optimization process with real ray tracing to provide the minimum root mean square wavefront error. The geometric optical properties in terms of residual wavefront error was simulated and approximated by Zernike polynomials. Data from 45 pseudophakic eyes were used to construct the models. Defocus was almost completely corrected by the spherical IOL and astigmatism, by the toric IOL. The aspheric IOL strongly reduced spherical aberration but only slightly reduced total higher-order aberrations (HOAs); both theoretical predictions corresponded to clinical investigations of wavefront measurements in pseudophakic eyes with a spherical or aspheric IOL. Real ray tracing calculated the exact geometry of custom IOLs to provide the minimum wavefront error, going beyond simple diopter information. Results show spherical aberration can be significantly reduced with aspheric IOLs. However, the limited possible reduction of total HOAs, even perfectly positioned custom aspheric IOLs, may be a reason for the unclear results in studies assessing the potential benefit to visual performance of currently used aspheric IOLs.

The Individual Virtual Eye: a Computer Model for Advanced Intraocular Lens Calculation

Purpose To describe the individual virtual eye, a computer model of a human eye with respect to its optical properties. It is based on measurements of an individual person and one of its major application is calculating intraocular lenses (IOLs) for cataract surgery. Methods The model is constructed from an eye's geometry, including axial length and topographic measurements of the anterior corneal surface. All optical components of a pseudophakic eye are modeled with computer scientific methods. A spline-based interpolation method efficiently includes data from corneal topographic measurements. The geometrical optical properties, such as the wavefront aberration, are simulated with real ray-tracing using Snell's law. Optical components can be calculated using computer scientific optimization procedures. The geometry of customized aspheric IOLs was calculated for 32 eyes and the resulting wavefront aberration was investigated. Results The more complex the calculated IOL is, the lower the residual wavefront error is. Spherical IOLs are only able to correct for the defocus, while toric IOLs also eliminate astigmatism. Spherical aberration is additionally reduced by aspheric and toric aspheric IOLs. The efficient implementation of time-critical numerical ray-tracing and optimization procedures allows for short calculation times, which may lead to a practicable method integrated in some device. Conclusions The individual virtual eye allows for simulations and calculations regarding geometrical optics for individual persons. This leads to clinical applications like IOL calculation, with the potential to overcome the limitations of those current calculation methods that are based on paraxial optics, exemplary shown by calculating customized aspheric IOLs.

Calculating Intraocular Lens Geometry by Real Ray Tracing

An implementation of real ray tracing based on Snell's law is tested by predicting the refraction of pseudophakic eyes and calculating the geometry of intraocular lenses (IOLs). The refraction of 30 pseudophakic eyes was predicted with the measured corneal topography, axial length, and the known IOL geometry and compared to the manifest refraction. Intraocular lens calculation was performed for 30 normal eyes and 12 eyes that had previous refractive surgery for myopia correction and compared to state-of-the-art IOL calculation formulae. Mean difference between predicted and manifest refraction for a 2.5-mm pupil were sphere 0.11 +/- 0.43 diopters (D), cylinder -0.18 +/- 0.52 D, and axis 5.13 degrees +/- 30.19 degrees. Pearson's correlation coefficient was sphere r = 0.92, P < .01; cylinder r = 0.79, P < .01; and axis r = 0.91, P < .01. Intraocular lens calculation for the normal group showed that the mean absolute error regarding refractive outcome is largest for SRK II (0.49 D); all other formulae including ray tracing result in similar values ranging from 0.36 to 0.40 D. Intraocular lens calculation for the refractive group showed that depending on pupil size (3.5 to 2.5 mm), ray tracing delivers values 0.95 to 1.90 D higher compared to the average of Holladay 1, SRK/T, Haigis, and Hoffer Q formulae. It has been shown that ray tracing can compete with state-of-the-art IOL calculation formulae for normal eyes. For eyes with previous refractive surgery, IOL powers obtained by ray tracing are significantly higher than those from the other formulae. Thus, a hyperopic shift may be avoided using ray tracing even without clinical history.

Trade-offs in miniature quadrupole designs

Pressing needs for miniature mass spectrometers became apparent during the last decade in process monitoring and control, space exploration, and environmental screening. Besides the small footprint, common requirements include low cost, low power consumption, field portability, reliability, autonomy, and ease-of-use. Design concepts and construction technologies of miniaturized quadrupole sensors were guided by cost reduction requirements without sacrifice of performance. The first miniature and complete quadrupole mass spectrometer system was introduced as the Micropole sensor. The concept featured a novel technique to assemble and operate multiple miniature quadrupoles in parallel. The short analyzer length offers a significant advantage by enabling direct mass filtering at pressures up in the 10 −2 torr range. High voltages at higher frequencies (10–20 MHz) are required for acceptable mass resolving powers. Additional trade-offs were uncovered in miniature sensors leading to designs optimized for each class of applications. Real time ray tracing of ions injected and filtered in the quadrupole field is used early in the design stage to predict the performance and reliability of the device.

Diffraction of pulses in the vicinity of simple caustics and caustic cusps

The objective of this paper is an extension of the Geometrical Theory of Diffraction (GTD) taking account of caustics. A closed list of those cuspoid caustics which are stable in the absence of symmetry constraints in a space of at most 5 dimensions is given along with integral expressions for the associated pulse shapes. Ludwig's formulae for harmonic fields are rederived by a new method. Universally valid time-domain expressions are associated with each caustic type. For the simple caustic and caustic cusp time-domain expressions are obtained in closed form. Finally, algorithms for the computation of time-domain expressions for a given wave field based on real and complex ray tracing are discussed.

Analysis of a photovoltaic static concentrator prototype

The aim of this work is the theoretical analysis and measurement of a truncated compound parabolic concentrator prototype with bifacial cells, filled with dielectric, made at the E.U. de Ingeniería Técnica Industrial de Jaén (Granada University). The prototype filled with a transparent mineral oil of refraction index n = 1.47, has a final meridian acceptance angle of ± 21° and it is truncated at 65% with a total height of 10 cm. The concentrator contains only one bifacial cell of 2 cm × 0.87 cm for minimizing the effects of its finite length. The rest of the collector area is simulated by a black plate. The mirror surface is made by deposition of evaporated aluminium. The theoretical analysis is based on a ray-tracing made with a computer. In this way we obtain some figures of merit which characterize this concentrator [A. Luque, Solar Cells , 3 , 355 (1981)]. This calculation takes into account the concentrator losses (the reflection of mirror and cell, and oil absorption). The experimental analysis is based on a real ray-tracing on the prototype made by means of a laser. We measured the short circuit current of the cell for different incidence angles of the laser beam. There is a very close relationship between the theoretical and experimental results of the ray-tracing. So, we have proved the validity of the theoretical analysis. Also we have developed a method for performing experimental measurement closely related with the theoretical analysis of static and quasi-static concentrators. Finally, we conclude that the results of this analysis encourage us to think of the truncated CPCs as adequate solutions for static and quasi-static photovoltaic concentrators.

Ray-trace analysis and data reduction methods for the Ritchey-Common test

The relationships between figure errors on an optical flat and wave-front aberrations when the flat is tested in the Ritchey-Common configuration are examined by the real ray-tracing lens analysis program polycon. A new data reduction method for the test is demonstrated. The test is simulated, and rays are traced using polycon. Unit magnitude Zernike term surface errors are added, one by one, to the flat under simulated test, and the effect on the wave front is derived by real ray tracing. This results in a table of influence functions for the particular test geometry. The simulation is repeated for one or more different field angles or azimuthal rotations of the flat to obtain other sets of influence functions. By using these influence functions it is possible to deduce what surface errors on the flat are responsible for any arbitrary test wave-front errors measured up to the order of the influence functions derived. The effectiveness of this method is compared with other existing methods by computer simulations.