Advances in computer technology have dramatically increased raytrace speeds in optical engineering software. Increases in raytrace speed have, in turn, led to new methods for evaluating optical system performance. Designers traditionally evaluate imaging system performance with spot diagrams, MTF plots, ray aberration plots, and distortion plots. These tools are invaluable for two reasons: (1) they provide the information experienced designers need to make design decisions, and (2) they require only a coarse sampling of rays. However, these tools are an indirect representation of imaging system performance. The designer must `wait and see' how the lens performs in situ. With today's computers and optical engineering software, it is now possible to evaluate imaging system performance visually as well as numerically--prior to lens fabrication. This paper will discuss the benefits of visual characterization for various practical optical systems. Distortion, diffraction, imagery with 3D objects, and other optical phenomenon will be evaluated.
Software has been developed to propagate uniform or non- uniform beams through an optical system using diffraction techniques. The optical system can be divided into regions where geometrical ray tracing is appropriate and regions where diffraction propagation is necessary. This combines the accuracy of diffraction propagation with the speed of geometrical ray tracing to obtain accurate diffraction analyses at any surface in the system in the fastest manner. This software has been incorporated into the CODE VTM optical design program.
The Global Explorer (GE) algorithm proposed by Isshiki is implemented in the GOLD program developed by Beijing Institute of Technology. Global optimization with GE consists of many local optimization runs with or without the escape function using the damped-least-squares method. In order to improve the efficiency of the local optimization, two search schemes are incorporated into the program. The first one searches for the best damping factor which effectively determines the optimum direction of the solution vector in the multi-dimensional variable space, and the second search is conducted along that direction to find the optimum length of the solution vector. Experiments are also made to determine the optimum default values for the parameters of the escape function.
Global optimization of optical system designs is difficult because of the complex solution space and extreme non- linearity of system performance with respect to design parameters. Genetic algorithms (GA's) have been used to effectively solve complex non-linear optimizations in other fields of science. GA's model each design parameter as part of a genetic code for an imaginary creature, and the system performance is interpreted to be the fitness for survival of this creature. The GA's goal is to improve the system performance by selective breeding of simulated creatures to yield simulated offspring with desirable traits. An algorithm for doing this along with results will be presented.
Caused by several personal wishes for special features in an optical design program, which were not found in commercial software, and caused by the need of an easy documentation and handling of standard optical components from the catalog a new low cost optical analysis software was created. Meanwhile this analysis software grew up to a very useful optical design program. The intention for the development, the state today, and some special features of the software will be discussed.
Some years ago Lawrence and Moore developed the basic principles of integrating geometrical and physical optics by incorporating conventional ray-based methods into the diffraction-based program GLAD. This paper discusses more specifically the difficulties in ray-based methods and hybrid methods in which physical optics is encapsulated within a ray-based program. Phase singularities are common in physical optics analysis and are shown to pose severe difficulties for ray-based methods. Time-averaged, through- focus behavior of a clipped excimer beam is taken as an illustration of a problem which can not be solved by ray- based methods but is readily solved with the lensgroup operator method of Lawrence and Moore. Beam reshaping is taken as a second example where diffractive effects should be considered.
The development of original devices requires the calculation of the propagation in guiding structures with complex geometry, in particular, when optical circuits are stacked on several levels. New software tools adapted to our devices, in particular, multi level circuits were developed, on the basis of directed programming objects (Java), user- friendly, evolutionary, and executable on the Internet network.
Metrology measurements for alignment of extreme ultraviolet lithography (EUVL) projection cameras can be optimized using the concept of misalignment modes. Using a metric called distance between subspaces, metrology measurements can be adjusted to increase sensitivity to a chosen camera- performance measure. For example, we have found that collecting exit-pupil wavefront measurements at locations outside the EUVL projection-camera's ring field of view can increase the sensitivity of such metrology measurements to chief-ray distortion. This paper describes the development of the University of Arizona Lithography Package (UALP), a software package that supports the types of computation, e.g., sensitivity-matrix calculation, and the types of analysis, e.g., singular value decomposition, that are required by the optimization of metrology measurements using misalignment modes. The description begins with a discussion of the ideas behind each step of the development process of UALP, including its use of ZEMAX. Along with the discussion of these steps, we describe the progression of our interface to ZEMAX. We describe the transition from the original ZEMAX extension model to the model using the Win32 library, and also our final version written using the Microsoft Foundation Class Library. We also introduce a diagnostic tool that was created to help a programmer interact with ZEMAX.
A surface impedance boundary condition (SIBC) is presented for the finite difference time domain (FDTD) simulation of surface emitting lasers with Bragg stacks. This method eliminates the need for directly implementing the actual Bragg stack structure in the FDTD code and enables 3D FDTD modeling of surface emitting lasers such as vertical cavity surface emitting lasers (VCSELs). The SIBC is derived from the equivalent surface impedance properties at the interface between the cavity and Bragg stack. The 3D finite-difference formulations of the SIBC are given in this paper. Simulations of VCSELs are performed with both the SIBC and the actual Bragg stack structure. The excellent agreement obtained between these two simulations shows the validity of the SIBC developed in this work.
Interpolation routines based on polynomials, splines, linear triangulation, and distance weighting techniques are tested. Two data sets containing irregularly distributed point values with two independent variables (wavelength and angle of incidence) are used as input data. The accuracy of interpolated values at unvisited points and processing time are used as criteria to determine the merits of the various interpolation algorithms. Effectiveness of distance weighting methods was found to be largely dependent on the number of neighbors used. For both gradually and abruptly changing data, the most accurate models used squared inverse distance weighting. Linear triangulation was found to be the fastest method.
A new method for calculating the irradiance of the broad area illuminated by the extended incoherent light source through an optical system is proposed. In this method, PSF with a frequency window function is attempted to be used to save time in the calculation of the irradiance distributions of the illuminated area. The efficiency of this method is remarkable for practical optical design work, especially for illumination optical systems. The interpolation formula of PSF can be obtained by an inverse Fourier transformation of the geometric optical transfer function, which is band- limited in a certain range of spatial frequency. The boundary of the range sets the cuff-off frequency. The frequency window function with the shape automatically controlled is used for adequately limiting or suppressing the high frequency components. A simulation of a point image and an example of an application for a practical illumination analysis by this method are reported.
Various simulations of volume-based sources are explored, beginning with an overview of optical design software, the industry that utilizes it, and a procedural outline for source simulation. These simulations are explained from the simplest to most complex methodologies to date. Two basic approximations of the volume-emitter, (1) a tubular surface distribution and (2) a cylindrical volume distribution, that cannot model the asymmetry of the original emitting-volume are considered. Simulation methodologies that rely on mathematical tools are investigated. Using a CCD image of the emission and the inverse Abel transform, a 2D irradiance distribution is transformed into a 3D emitting volume. An algorithm developed to handle asymmetric volume-emitters is discussed, and the results of the simulated arc are compared to its original CCD image. In addition, the geometry of the arc source is modeled into a CAD (Computer Aided Design) program, and optical properties are assigned to its components in the optical/illumination design program. Using the most detailed emitter simulation, an assessment of the source geometry's influence on system output is made. The need for a detailed volume-emitter simulation is demonstrated through system output comparison between those utilizing the most complicated simulation and those using basic surface and volume approximations of the actual emitting-volume.
We have developed is a modeling package that allows a system engineer to perform an end-to-end electro-optical simulation to determine system performance. Called EO Model, it is built upon TraceProTM, an Opto-Mechanical design and analysis tool developed by Lambda Research Corporation.
Faster, better, and cheaper computers make it seem as if any optical calculation can be performed. However, in most cases brute force stray light calculations are still impossible. This paper discusses why this is so, and why it is unlikely to change in the near future. Standard software techniques for solving this problem are then presented, along with a discussion of how old techniques are used to take advantage of the new features that are available in the latest generation of optical analysis software.
OARDAS (Off-Axis Rejection Design Analysis Software) is a Raytheon in-house code designed to aid in stray light analysis. The code development started in 1982, and by 1986 the program was fully operational. Since that time, the work has continued--not with the goal of creating a marketable product, but with a focus on creating a powerful, user- friendly, highly graphical tool that makes stray light analysis as easy and efficient as possible. The goal has been to optimize the analysis process, with a clear emphasis on designing an interface between computer and user that allows each to do what he does best. The code evolution has resulted in a number of analysis features that are unique to the industry. This paper looks at a variety of stray light analysis problems that the analyst is typically faced with and shows how they are approached using OARDAS.
In many optical systems, the polarization state of light is of critical importance and must be considered during their design. In other systems, the polarization state is used and manipulated as an integral part of the design. Three methods exist for modeling the polarization state of light: the Mueller calculus; the Jones calculus; and the polarization ray tracing calculus. The relative advances of these methods for simulating the polarization behavior of real devices using Monte Carlo ray tracing software is discussed, including simulation of the polarization properties of scattered light.
Monte Carlo ray tracing programs are now being used to solve many optical analysis problems in which the entire optomechanical system must be considered. In many analyses, it is desired to consider the effects of diffraction by mechanical edges. Smoothly melding the effects of diffraction, a wave phenomenon, into a ray-tracing program is a significant technical challenge. This paper discusses the suitability of several methods of calculating diffraction for use in ray tracing programs. A method based on the Heisenberg Uncertainty Principle was chosen for use in TracePro, a commercial Monte Carlo ray tracing program, and is discussed in detail.
The computer model for partial coherent image based on vector theory of diffraction is presented. In this model the complex amplitude of light field is represented as superposition of basic vector plane waves. The optical system is considered as the amplitude-phase filter of a plane waves spectrum. The partial coherent illumination is described with the well-known approach--the source integration method. The presented model allows to carry out simulation of partial coherent image of amplitude-phase object with taking into account aberration and polarization effects in high NA optical systems.
Principles and mathematics for computer aided high precision optical system alignment and tolerancing are discussed as applied to photolithography projection lenses. All aberrations of an optical system including distortion are described by using global polychromatic Zernike polynomial expansion of the wave front aberration, so to optimize the lens quality one has to minimize each coefficient of the expansion. The procedure of aberrations measurement which is based on Hartmann test is discussed and the processing technique which easily offers to define the overfield coma, spherical aberration, distortion and astigmatism is proposed. Least squares method is used to calculate from measured data the aberration coefficients for a real system. After optimum selection of adjustable parameters axial symmetry and decentered aberrations are being compensated separately of each other.
The traditional ways to compute the displacements of zoom lens movable components are generalized and subjected to criticism. The new simple, easy realized, universal method is considered. This method is applied to designing various complicated zoom optical systems.
The simple, easy formalized, universal method for the first order lens layout is considered. It allows automatically to set up and to solve manifold paraxial equations. All the possible solutions can be found. The method is applied to designing various complicated optical systems including zoom lenses.
Optimization of the Cooke triplet with various evolution strategies an the damped least squares is presented. All algorithms are described and their advantages and shortcomings are presented. After detailed presentation of the evolution strategies their adaptation to the optimization of optical systems are discussed. Analysis of the Cooke triplet optimizations is given and optimum optimized optical system is chosen.
An data interface is proposed that will port Bidirectional Scattering Distribution Function (BSDF) data, spectral reflectance, transmittance, and absorptance data from SORIC's software database for PC-based computers, SOLEXICTM, to: commercial optical design and analysis software (i.e. ASAP, TraceProTM, OptiCADTM, OSLO, ZEMAX, ZELUMTM and others); and from both scatterometers employing the ASTM standard format of BSDF data (e.g. CASI Scatterometer) and scatterometers using non standard formats.