What Is LensLab?
Introduction
Welcome to LensLab.
LensLab brings optics to Mathematica. Both simple and complex optical systems can be defined and analyzed with the LensLab package. In addition to LensLab's built-in library of lenses, mirrors, prisms, and gratings, new components can be created and existing ones modified with "generic building blocks", LensLab's component-structuring language.
LensLab sets a new landmark for user-designed component and diagnostic capabilities. Written in the Mathematica programming language, the open-code architecture of LensLab enables users to make additions and programming changes on any level that is comfortable for them. Because LensLab uses Mathematica, it works with most computer platforms.
A Design Tool
Scientists and engineers who are developing equipment and experimental setups involving optics will find LensLab a useful tool for determining component specifications and system layouts. LensLab enables evaluation and optimization of alternative system designs before capital expenditures on equipment are made. The high-quality graphics generated by LensLab can be used directly in blueprints, grant proposals, and research reports.
An Educational Tool
LensLab is also useful for educational purposes, providing a foundation for Mathematica-based courseware in optics. LensLab enables computer-based laboratory experiments, in some cases replacing physical experiments and circumventing exposure to hazardous laser emissions and use of fragile or expensive laboratory equipment. By using LensLab, students can conduct experiments in optics with greater flexibility, precision, and in less time than is required using physical hardware. In other cases, LensLab can be used to supplement the laboratory experience to help students gain greater insights into physical experiments.
LensLab's Components
LensLab is a language extension of Mathematica for ray tracing and rendering of optical systems. By using LensLab, you can define lenses, mirrors, prisms, cavities, ring cavities, fresnel mirrors and lenses, lens doublets and triplets, pin holes, gratings, pipes, liquid-air interfaces, slits, optical fibers, lasers, amplifiers, beam splitters, screens, baffles, and paraxial components. Some paraxial components include thin lenses, thick lenses, ABCD matrix components, and paraxial-modeled graded index components. Regardless of their form, all components can have rectangular, circular, elliptical, or arbitrary polygonal edges.
In addition to using LensLab's standard library of on-axis and off-axis spherical, cylindrical, and parabolic curved components, you can easily create new components having curved surfaces of your own design.
LensLab makes it easy for you to add new types of refractive materials to LensLab's existing catalog of commonly used glasses, crystals, liquids, and gases. With LensLab's built-in functions for creating new refractive index function models, you can use wavelength-dependent index measurement tables to generate new refractive material definitions. Once defined, these new materials can be used immediately in components.
LensLab's Component-Structuring Language
You can create hybrid optical components using "generic building blocks", LensLab's component-structuring language. In this way the standard lenses and mirrors can have holes inserted in them or gratings placed on top of them. You can easily define new components from scratch with generic building blocks, just as LensLab does for its built-in component definitions. Because of LensLab's open code, you can check how LensLab defines its stock components as a first step to designing your own custom components.
Features in LensLab
LensLab supports:
User-directed and nonsequential ray tracing
Off-axis surface curvatures
Arbitrary user-defined surfaces
High-level component-structuring language
User-defined refractive materials
User-defined intensity amplification models
Components with off-axis rectangular, elliptical, and polygonal holes
Full three-dimensional placement and evaluation of optics
Ray tracing for both imaging and nonimaging applications
Complete quantitative information about all optical surfaces
Two-dimensional and three-dimensional rendering of the same system
Wide range of component-rendering options including solid or wire-framed surfaces
Magnified presentations of selected system subgroupings
"Spot" diagrams of any optical surface
Optical systems can be defined in modular segments that can be assigned distinct variable names, independently moved in three-dimensional space, and chained together for modeling a total system.
LensLab has built-in functions for measuring focal lengths of real and virtual imaging systems. By adding your own Mathematica routines, LensLab can be used for creating phase plots and determining modulation transfer functions of optical systems.
It is not possible for LensLab to include built-in solutions for every project. Instead, coupled with the existing capabilities of Mathematica, LensLab is more like a well-stocked workshop ready for any project. If a component or analysis function doesn't exist in the LensLab package, you have the necessary tools to build it!
About This Manual
The Scope of This Manual
This manual provides a comprehensive view of LensLab's functions and capabilities. However, it is not the purpose of this manual to teach about the general Mathematica system. There are many helpful books written for that purpose.
In most uses of LensLab, you will need to know a small part of LensLab's functions. This manual is organized to make it easy for you to learn the specific information you need for a particular calculation. In many cases, for example, you may be able to set up your calculation simply by adapting some appropriate examples from this manual. You should understand, however, that the examples in this manual are chosen primarily for their simplicity rather than to correspond to realistic optical modeling situations.
LensLab is a system built on a fairly small set of very powerful principles. This manual describes these principles, but by no means spells out all of their implications. In particular, while the manual describes the elements that go into modeling optical systems, it does not give detailed examples of optical system design.
The Parts of This Manual
This manual contains ten chapters and an appendix. The four initial chapters provide essential information about using the LensLab system. Chapter 1 introduces you to LensLab's basic features. By learning the functions presented in the first chapter, you will have a foothold for using LensLab. The second chapter shows you how LensLab does ray tracing. Understanding the ray-tracing process is essential for effective use of LensLab. In addition to explaining LensLab's ray-tracing process, Chapter 2 introduces you to the built-in functions for generating rays. Next, Chapter 3 gives you a tour of LensLab's built-in component functions. Then, Chapter 4 shows you how to use the different built-in Move functions to position components and rays in both two-dimensional and three-dimensional space.
Chapters 5 - 7 contain advanced information about the LensLab system. Chapter 5 introduces features of LensLab important to the advanced user. In Chapter 6, you learn how to perform some advanced experiments using LensLab. Then, Chapter 7 gives you a single example that demonstrates the basic design and layout techniques employed by the author for modeling more complex optical systems in LensLab.
The three final chapters in the manual provide reference information about particular elements of the system. Chapter 8 serves as a reference about the various parameters of the Ray object. Next, Chapter 9 serves as a reference about the Component object. Finally, the Appendix shows you a summary of LensLab's built-in object and function names, followed by a complete reference guide of definitions for LensLab's built-in objects and functions.
How to Read This Manual
If at all possible, you should read this manual in conjunction with using the actual LensLab package. When you see examples in this manual, you should try them out on your computer. For your convenience, this manual is provided in both printed and on-line notebook formats.
The first eight chapters in this manual are intended to be pedagogical, and can meaningfully be read in a sequential fashion. The last two chapters and appendix, however, are intended solely for reference purposes. Once you are familiar with LensLab, you will probably find the list of functions in the Appendix the best place to look up the details you need.
Copyright Statement
LensLab is a trademark of Optica Software.
Mathematica ® is a registered trademark of Wolfram Research, Inc. All other product names mentioned are trademarks of their producers. Mathematica is not associated with Mathematica Policy Research, Inc. or MathTech, Inc.
Copyright ©1995-2005 by Optica Software, Urbana, Illinois, Champaign, Illinois.
All rights reserved. No part of this document may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior written permission of the author, Optica Software.
Optica Software is the holder of the copyright to the LensLab package software and documentation ("Product") described in this document, including without limitation such aspects of the Product as its code, structure, sequence, organization, "look and feel", programming language and compilation of command names. Use of the Product, unless pursuant to the terms of a license granted by Optica Software. or as otherwise authorized by law, is an infringement of the copyright.
Optica Software makes no representations, express or implied, with respect to this Product, including without limitations, any implied warranties of merchantability or fitness for a particular purpose, all of which are expressly disclaimed. Users should be aware that included in the terms and conditions under which Optica Software is willing to license the Product is a provision that the author, Optica Software and distribution licensees, distributors and dealers shall in no event be liable for any indirect, incidental or consequential damages, and that liability for direct damages shall be limited to the amount of the purchase price paid for the Product.
In addition to the foregoing, users should recognize that all complex software systems and their documentation contain errors and omissions. Optica Software shall not be responsible under any circumstances for providing information on or corrections to errors and omissions discovered at any time in this document or the package software it describes, whether or not they are aware of the errors or omissions. Optica Software does not recommend the use of the software described in this document for applications in which errors or omissions could threaten life, injury or significant loss.
Created by Mathematica (November 3, 2005)