Inexpensive optical engineering software and PCs have enabled a broad range of engineers and scientists to do the work traditionally done by optical engineers. This paradigm shift has challenged software developers to devise interfaces appropriate for less experienced users. Our contention us that by making complex optical engineering tasks more visual, less qualified users would be more inclined to recognize when something was amiss.
There is a long tradition of analyzing lens designs and establishing their manufacturing tolerances in software. The lens-design codes used for this process are based on sequential, geometric ray tracing techniques and the tolerances are based on geometric image quality as determined by system aberration content. More recently, largely due to the rapid expansion of optical telecom applications, there has been increased interest in the non-sequential propagation of complex optical fields, rather than geometric rays, through optical systems. Starting with sources of varying degrees of coherence or from the output from fibers or waveguides, fields can be non-sequentially propagated through optical systems, and the amplitude and phase of these fields can be examined at any position in space. This has enabled an enormous increase in the ability to analyze and tolerance coherent optical systems used in two main categories of optical systems: (1) measurement systems and (2) systems used to propagate coherent optical signals. This paper addresses the methodology involved in modeling, analyzing, and tolerancing coherent systems and highlights the main differences between the methods used with coherent systems and traditional lens designs. Coherent systems models include components that require modeling diffraction and interference effects. They typically extend the path length of the model, beginning at the source and continuing through to a detailed description of the detector or a coupling into an output waveguide. They may even include a measurement algorithm within the system model. Additionally, unlike the traditional lens-design models, the performance parameters used in establishing the manufacturing tolerances of these coherent systems, are not necessarily based on the image quality of the system. Instead, tolerancing of coherent systems is usually more directly related to the functionality of that system. To further demonstrate the methodology of modeling, analyzing, and tolerancing coherent systems in software, two examples of coherent system models, an interferometer and a telecom component, are presented. Some of the tolerancing results from these systems are presented.
Thermal and structural output from general purpose finite element and finite difference programs is not in a form useful for optical analysis software. Temperatures, displacements and stresses at arbitrarily located FE nodes can not be input directly into optical software. This paper discusses the post-processing steps required to present the FE data in a useable format. Specific issues include optical surface deformations, thermo-optic effects, adaptive optics, optimization, and dynamic response. Finite element computed optical surface deformations are fit to several polynomial types including Zernikes, aspheric, and XY polynomials. Higher frequency deformations are interpolated to a user-defined uniform grid size using linear, quadratic, or cubic finite element shape functions to create interferogram files. Three-dimensional shape function interpolation is used to create OPD maps due to thermo-optic effects (dn/dT), which are subsequently fit to polynomials and/or interferogram files. Similar techniques are also used for stress birefringence effects. Adaptive optics uses influence functions to minimize surface error before or after pointing and focus correction. A dynamic analysis interface allows optical surface perturbations (rigid-body motions, elastic surface deformations) to be calculated for transient, harmonic and random response.
A method to compute polarization changes and wavefront error due to mechanical stress in transmissive optical elements is presented. In general, stress produces an anisotropic and inhomogeneous optical medium where the magnitude and direction of the indices of refraction vary at every point. Jones calculus is used to incrementally evaluate the effects of stress for a grid of rays traced through a three-dimensional finite element stress field. For each ray, a system Jones matrix is computed representing the effective retarder properties of the stress path. The magnitude of birefringence, orientation, and ellipticity may then be derived for a grid of rays over the optical aperture. In addition, the stress-induced index changes generate wavefront error. Thus wavefront maps may be computed across the optical aperture. This method to compute the optical errors due to mechanical stress has been implemented in the optomechanical analysis software package SigFit. Birefringence and orientation data as computed by SigFit for arbitrary three-dimensional stress states may be output as CODE V stress birefringence interferogram files to evaluate the effects of stress on optical performance.
Opto-mechanical engineers are taking advantage of the birefringence exhibited in uniaxial crystals to control light in a wide range of applications. Software tools are required which can handle light propagation through such crystals; but these tools must also offer an intuitive interface to the user. Rigorous physics calculations are required at the optical component level to deal with beam doubling and flux propagation. However, these components are immediately combined into sub-assemblies where opto-mechanical packaging concerns arise. An intuitive, CAD-like interface coupled with accurate ray propagation algorithms has been implemented in TracePro, a commercial optical analysis program. In this tool components, sub-assemblies, and assemblies can be readily positioned and oriented. The performance of the optical systems is evaluated via raytracing. In essence, the software presents a virtual laboratory or optical bench. The birefringence ray tracing capability in a three dimensional, computer aided design (CAD) environment will be described. This analysis provides the design engineer the capability to model a variety of optical components used in telecom applications such as polarization independent isolators, circulators, beam displacers and interleavers. Several examples illustrating the application of this analysis will be presented.
Conventionally an optical system is defined by a static description. In this case the raytracing is a deterministic process. But if one allows specific statistical variations of the parameters of the optical system or the parameters of the ray, the options of the raytracing can be extended considerably. Thus, new features for the simulation of optical systems arise. The principles and applications of Monte Carlo methods are shown and discussed. Several examples are presented.
The act of performing a sequential trigonometric ray trace through an optical system is as simple as applying Snell's Laws of refraction and reflection, along with some form of the grating equation, to the geometric description of the lenses and mirrors which can comprise that system. The orderly incorporation of these physical laws into an algorithm, which at the same time incorporates all possible geometries which may occur in this optical system, will be the result of this paper. The ray/surface equations and other useful numerical techniques will be spelled out in detail so that this paper can be used as a starting point for their own ray tracing program when commercial optical design codes are either not available or inappropriate.
Splines are commonly used to describe smooth freeform surfaces in Computer Aided Design (CAD) and computer graphic rendering programs. Various spline surface implementations are also available in optical design programs including lens design software. These surface forms may be used to describe general aspheric surfaces, surfaces thermally perturbed and interpolated surfaces from data sets. Splines are often used to fit a surface to a set of data points either on the surface or acting as control points. Spline functions are piecewise cubic polynomials defined over several discrete intervals. Continuity conditions are assigned at the intersections as the function crosses intervals defining a smooth transition. Bi-Cubic splines provide C2 continuity, meaning that the first and second derivatives are equal at the crossover point. C2 continuity is useful outcome of this interpolation for optical surface representation. This analysis will provide a review of the various types of spline interpolation methods used and consider additional forms that may be useful. A summary of the data inputs necessary for two and three-dimensional splines will be included. An assessment will be made for the fitting accuracy of the various types of splines to optical surfaces. And a survey of applications of spline surfaces in optical systems analysis will be presented.
Methods for computing bin-by-bin error estimates of 2-D illumination and chromaticity distributions generated from Monte-Carlo raytracing data will be introduced, as well as algorithms for choosing the optimal number of bins based on the desired accuracy. Methods of improving the accuracy of such distributions will also be discussed, along with methods for smoothing these results for display purposes.
The Shack-Hartmann wavefront sensor is a powerful tool for optical analysis. A vital step in the data analysis chain involves reconstructing the wavefront incident upon the lenslet array from hundreds or thousands of slope measurements. We discuss here the basics of reconstruction and the differences in reconstruction for the case of Hartmann and Shack-Hartmann sensors. Hartmann sensors take point samples of the wavefront but Shack-Hartmann sensors measure the average slope over small regions. This results in subtle differences in the reconstruction.
In general the center of mass technique is a fast and robust way to approximate the location of a focal spot. This paper discusses in detail the relationship between the focal spot location and the center of mass. We start with a mathematical analysis and conclude with a few practical ideas to improve the accuracy of the center of mass technique.
The circle polynomials of Zernike play a prominent role in optical analysis. While decompositions of wavefronts into Zernike polynomial series can yield valuable insight, computing with the polynomials themselves is quite inefficient. Here we outline how rational polynomials like those of Zernike, Legendre, Chebyshev and Laguerre can be handled as affine combinations of a Taylor monomial set. We demonstrate how calculations can be performed much more rapidly in the Taylor basis and how to use integer transformations to recover the exact amplitudes in the desired basis. We also explore C++ optimizations for storing the Zernike amplitudes and transforming between Zernike polynomials and Taylor monomials.
Synchrotron Radiation Workshop (SRW) - a physical optics computer code optimized for the simulation of emission and propagation of coherent and partially-coherent synchrotron radiation is presented. The code consists of two parts, which can be used independently. One part is dedicated to the computation of electric field, intensity, spectral-angular characteristics of radiation emitted by relativistic electrons in undulators, wigglers, short magnets, etc. The other part of the code implements physical optics methods for wavefront propagation. The propagation in free space is made according to the Huygens-Fresnel principle, by means of a prime-factor 2D FFT. Normal-incident optical elements are described by a complex transmission function. Fast algorithm for the propagation of electro-magnetic field through simple waveguides is implemented. The propagation of partially-coherent radiation is done by summing up contributions to the final intensity from different sources (e.g. from distinct emitting electrons), taking into account the sources' properties and applying, when possible, the convolution theorem with respect to intensity. SRW code can be used for physical optics simulations, design and optimization of refractive and diffractive optical elements for various spectral ranges, from far infrared to hard X-rays.
The Beam Propagation Method (BPM) is the most widely used tool for the investigation of complex photonic structures. Since the original BPM was introduced, many improvements and extensions have been proposed. We have developed a computer program based on the Finite Difference BPM for modeling propagation in optical waveguides. This method has been successfully applied for several 3D problems such as propagation on Bragg Fiber. The main drawback of this method is its complexity and long computation time using a personal computer. In this paper, a simple efficient numerical solution method, we called double 2D-BPM, is proposed. This technique is based on the decomposition of the 3D field propagation equation onto two 2D equations related to transverse plans. Propagation along the x and y axes is computed separately in two steps. Using a similar technique, a finite difference approximation for each propagation step involves the solution of two equations and the complete problem splits into two independent 2D problems. We performed propagation tests in elementary 3D problems but also on Bragg fiber. The numerical results of 3D-BPM and double 2D-BPM have been compared. The propagation step along the propagation axis has been experimentally determined. Parameters that affect the accuracy and the stability of this method were discussed. Losses induced by propagation on Bragg fiber were also considered. We have established that the global effect of the double 2D-BPM is equivalent to 3D-BPM technique. Comparison with exact results obtained from analytical expressions also shows excellent agreement.
We developed algorithms and full-vector mode solver as a tool for new optical components design that allows simulation of components with anisotropic optical characteristics. Algorithms are developed without assumption of weak guidance, which allows applications of the method and software in simulation of components with strong optical anisotropy. Method and software were tested by comparison with semi-analytical solutions for isotropic and anisotropic fibers. We observed reasonably good agreement (up to five non-zero digits in the effective indices) between calculated and analytical data for several low order modes. In this paper we present results of calculations for single polarization D-shaped and cylindrical fibers with anisotropic coating.
Presented is a macro running in CODE V® that automatically calculates the return loss from all surfaces in a lens system using either a Gaussian beam approach or a ray-based Gaussian apodization method. Results are compared between the two methods and with output from a diffraction-based beam propagator for a couple of simple cases. A method for optimizing return loss and coupling efficiency simultaneously based upon a simplex optimizer is presented.