Erhard Glatzel, of Zeiss, keeps talking about "strain" and "relaxation" in optical design. What on earth does this mean?

In the early stages of teaching students the subject of lens design, the author has found it useful to present the concept of image defects in a form which relates the aberration polynomial terms to specific ray intercept data. The normal development of exact ray intercept errors (εx,εy) as a power series in terms of the canonical coordinates (ρ,θ,H,ε) following Buchdahl is in general observed to be theoretically pleasing. Students often find it difficult, however, to quickly grasp the physical interpretation of the numerous aberration coefficients. On the other hand, they seem to readily visualize the concept of real ray intercept deviations from the ideal image point. By expressing the actual ray intercept error at the image plane as additive contributions, it has been found illustrative to show how ray intercept data from a few selected trigonometrically-traced rays can be utilized to compute these contributions including explaining how to identify the oblique spherical and higher-order coma portions of the astigmatic and comatic error contributions. The necessity for including ray-trace data not in either the tangential or sagittal planes [e.g., (ρ,θ,H,ε)=(ρ,45°,H,ε)] to assure that all aberration coefficients are accounted for is also discussed.

The starting point of this work is a general solution of the eikonal equation for a homogeneous, isotropic medium which provides a detailed description of the structure of a train of geometrical wavefronts and also of the associated caustic surface. This description depends ultimately on the k-function, an arbitrary function that arises in the general solution. Suppose a known train of wavefronts, with a known k-function, is incident on a refracting surface, tracing a wavefront involves determining the k-function for the refracted wavefront train. To do this a set of boundary conditions needs to be setup and solved.

One of the basic problems in Optical Design concerns the fact that optimization programs are capable of effectively finding a local minimum, but that this local minimum will usually not be a real global minimum. In order to locate other local minima, it is usually necessary to search, more or less empirically, for alternative solutions. This paper is concerned with this problem, particularly in connection with some simple lens systems, in the expectation that an understanding of simple lenses will assist in dealing with more complex lenses.

Field lenses are familiar to most of us who deal regularly with lens and mirror systems. The extent to which we depend upon field lenses (for proper system function) in a wide variety of applications is not, however, universally recognized. Nor are the details of field lens function always understood by those who rely upon them. Some operating principles and applications of field lenses are discussed.

For many years, Itek's OPUS optical design program has incorporated features that facilitate the design of systems with a single plane of symmetry. These include the use of analytical derivatives, polynomial aberrations, nonsymmetrical surface deformations, and special aberrations for configuration control. Recently, it was decided to extend this capability so that one could design systems without any symmetry at all. This report will describe some of the program changes necessary to accomplish this and some lens systems that we designed by using the new code.

A first order theory has been developed which describes properties of almost general optical systems. It predicts the shape of the image surface and the shape of a square when it is imaged onto a plane which is tangent to the first order image surface at the center of the field. The application of the theory to realistic design problems is discussed.

We have recently completed a parametric analysis of f/2, one through four element lenses, relating monochromatic axial performance (spherical aberration) to refractive indices from 1.5 to 2.0. The literature demonstrates clearly that increasing the number of elements and/or the refractive index causes a reduction of the third-order spherical aberration; in fact the literature shows special cases where the third-order spherical aberration transitions through zero. If we consider an optimum balance for all orders of spherical aberration, we observe a surprising result. One and two element solutions maintain a relatively constant high level of aberration residual for all cases (from 5 - 50 waves peak-to-valley). The three-element solution, however, improves in aberration residual by nearly 6 orders of magnitude from 2 waves peak-to-valley at an index of 1.5 to approximately 0.000005 waves at an index of 2.0. The four-element solution shows a similar, yet not so pronounced, behavior. We will discuss the various solution forms, some of which utilize the aplanatic-concentric principal, and we will show how higher order aberration balancing in the three element case is responsible for the 6 orders of magnitude improvement in performance.

A method of polarization ray tracing for calculating the instrumental polarization function of an optical system using the Jones calculus is presented. Polarization ray tracing supplements the equations of ray tracing to include amplitude, phase, polarization and retardance effects of thin films, polarization elements and polarizing materials. Results of a polarization ray trace analysis of a Cassegrain telescope are presented.

Continuous development of lenses for photographic applications has led to the design of a variety of high performance objective lenses. Several fixed focal length lens designs are concentrated upon in the paper with particular attention being paid to the utilization of special glass types and how they influence the overall performance of the final lens design. The paper also illustrates how severe requirements imposed at the design stage have resulted in substantial improvements in overall performance compared to previous lens designs. Important features including low f/number, low T/number, low residual secondary colour and constant colour balance are described for different focal length lenses.

Two-dimensional diffraction calculations for image forming systems and laser systems require a computer which is fast and has a reasonably large amount of memory. We have written a program, IMAGE, for the IBM-PC to perform diffraction calculations. It represents the complex electric field with a 128 by 128 array. IMAGE is written in C with an FFT routine written in assembly language. It produces numerical and graphical output for user described optical systems. Input parameters include F# or pupil diameter, wavelength, aberration coefficients and Gaussian amplitude scale factor. Output includes geometric spot diagram, encircled energy, point spread function, wavefront contours, MTF, and PTF.

Only a few meetings qualify as landmark meetings in the recent history of optical design. Each of these meetings demonstrated the significant issues of the day. The Rochester meeting of 1966 marked an early high point in the development of automated lens-design programs and set the tone for several years in which the principal topics of discussion centered around computers rather than lenses.

A major research project at OSD involves investigating the potentials of artificial intelligence (AI) when applied to the problem of computer-aided lens design. Two primary approaches have been taken to date: natural-language interfacing and the use of expert systems. The first allows the user to communicate with an intelligent processor routine to alter or inquire about nearly any lens or system parameter. Many different sentence syntaxes are parsed by the program, which determines what the sentence means and then acts accordingly. The second, and potentially more powerful application, provides a means for the software to "learn" about optics by studying a set of lenses designed by experts, and formulating its own rules for going about the design process. In essence, the results of the program are not predetermined by the programmer, and the results get better as the program learns more. Finding starting points and escaping from local minima are two typical applications.

Most of the problems solved by designers and engineers on a daily basis are small but important details, instead of extremely complex tasks. Optical design tends to be no exception. The tools for day to day problem solving need to be easy to learn and use. In today's environment of computer availability, many engineers have an occasional need for optical design and evaluation, but do not spend all of their time designing optics. These people need a tool which is powerful enough to solve or evaluate their problems but that is simple and easy to understand, remember, and use. This is the user that the TRACE V program set addresses. The programs allow the evaluation of most of the types of optical systems that may be encountered. These include those with aspherics, tilts, decentrations, toroids, etc. The images of points are displayed on the screen and the lens configuration can be drawn and examined. Simplicity is maintained in the merit function used for optimization. It is based on: the RMS size of the image of an on-axis and off-axis image, the curvature of the focal plane on which the images lie, the distortion shown by those images, and violations of boundary conditions. The images can be heterochromatic combinations of three colors, one central and two half power wavelengths. The programs have evolved from practical application over 25 years of use on a variety of computers and are now best suited for the personal computer. There are more appropriate and powerful tools for the career lens designer, but this is a practical and easy to use tool for the occasional optical design engineer.

A two-element axial gradient-index binocular objective has been designed and fabricated. A prototype system has been assembled and tested.

As the complexity and variety of laser systems has expanded over the years the capabilities and sophistication of analytical tools has increased as well. In this paper, the General Laser Analysis and Design (GLAD) code is described. This code is very versatile and has been used to analyze laser fusion, isotope separation, high energy laser, free-electron laser, excimer/Raman and other nonlinear optical systems. GLADV is user friendly and is fully documented with theory, command description, and numerous examples of operation.

Real world beam propagation and diffraction problems can rarely be solved by the analytical expressions commonly found in optics and lasers textbooks. These equations are typically valid only for paraxial geometries, for specific boundary conditions (e.g., infinite apertures), or for special assumptions (e.g., at focus). Numerical techniques must be used to solve the equations for the general case. LOTS, a public domain numerical beam propagation software package developed for this purpose, is a widely used and proven tool. The graphical presentation of results combined with a well designed command language make LOTS particularly user-friendly, and the recent implementation of LOTS on the IBM PC/XT family of desktop computers will make this capability available to a much larger group of users. This paper surveys several applications demonstrating the need for such a capability.

To better understand the exploitation of bit mapped/interactive graphics in lens design, a research computer program for first order optical design based on the Delano y-y diagram has been developed which runs on the Macintosh personal computer.

A technique is described for accurately modeling a class of two-mirror aplanatic systems on the commercial ACCOSV program. The differential equations that define the mirror profiles are solved numerically. For each surface, an approximate representation in terms of vertex radii, aspheric coefficients, and axial separation is then obtained by matching a polynomial exactly to the surface at discrete points. The residual difference between the polynomial and the true surface is then computed at several points. These differences are input as spline function values. The superposition of polynomial and spline function gives a close approximation to the true surface. This process is embodied in a computer program that performs the required computations and writes a lens input file for ACCOSV.

A preliminary optical design is proposed to convert the existing Multiple Mirror Telescope (MT) on Mount Hopkins to the maximum diameter, filled-aperture optical/infrared telescope that can be accommodated by the existing telescope mounting and building without substantial modification. The design utilizes a 256-inch diameter f/1.00 primary mirror which is chosen to be parabolic in order to provide adequate field of view at the required f/45.0 infrared Cassegrain focus. A 40-arcmin-diameter flat field of view is provided at an f/4.5 optical Cassegrain focus such that the resulting image scale gives a sampling factor of 3.5 (27 μ) pixels per (2/3 arcsec) spatial information element. The three-element refracting field corrector contains material for an atmospheric dispersion compensator (ADC) and it is fully color-corrected such that the entire passband from 0.33 μ to 1.60 μ can be imaged simultaneously. An f/9.0 Cassegrain focal expander-corrector with (ADC) is provided which uses the f/4.5 secondary mirror and enables the new telescope optics to be coupled to existing ancillary MMT instrumentation without substantial modification to the latter. A two-element all-spherical null-lens design is presented which provides a diffraction limited optical null-test arrangement for the unprecedentedly large f/1.00 parabolic primary mirror.

A new relayed three-mirror anastigmat (TMA) optical form is presented in this paper. Although several variants of the form, are shown, the most interesting is one that utilizes spherical secondary and tertiary mirrors in conjunction with a point testable ellipsoid primary. The designs are especially suited to high aspect ratio line fields of view (FOV). Exceptionally good correction of aberrations and a number of other desirable features principally related to pupil imagery are exhibited for FOVs from 1 X 7 degrees, 1 X 10 degrees, 1 X 12 degrees up to a 30 degree line. The highly practical nature of the form for many applications is established through theory and example.

A procedure is presented for the design of primary and secondary baffles (light shields) for telescopes with tiltable secondary mirrors (typically for use in the infrared). The procedure is applied to the Space Infrared Telescope Facility (SIRTF) for which results are presented.

We developed a computer program that uses Newton's method to calculate the shape of a secondary mirror which corrects the spherical aberration of a spherical primary mirror. For each user selected ray, the program calculates the distance from the ideal surface to a user defined conic surface. A set of distances can be used as spline deformations in ACCOS V*, accelerating the optimization of the two mirror system by more than an order of magnitude.

Aberrations of the off-axis mirrors are derived and plotted as a function of local mirror coordinates. The sagittal surface is calculated up to the fifth order for evaluation of misalignment induced aberrations.

A two-lens system provides a simple and versatile means to relay a laser beam. The pair of lenses can provide true volume imaging, reproducing both amplitude and phase of the input beam. By using cylindrical lenses it is possible to change the aspect ratio of the beam. By adjusting the cylindrical curvatures, it is possible to minimize reflections by tilting the lenses at the Brewster angle.

Techniques of optical design have been applied to integrated optical systems. A novel class of waveguide lenses is presented, called CHARLES (Corrected Homogeneous Acircular Refractive LEns System). CHARLES consists of a small number of single lenses bounded by non circular arcs and non-uniformly spaced: it is capable of diffraction-limited performance over relatively large field angles, i.e. up to 10° from the axis for f/number about 3.

An 8 element refractive lens of 324.4 mm EFL and f/4.5 was designed for the spectral band 520nm to 590nm. The FOV of the lens was +- 5 degrees. The computed MTF of this lens system was better than 0.7 for spatial frequencies up to 60 1p/mm, as against the diffraction limited MTF of 0.81. A similar lens was designed for the spectral band 770nm to 860nm. These two lenses will be configured alongwith a panchromatic catadioptric lens of 900 mm EFL for high resolution spacecraft remote sensing applications. The design details of these lenses were presented in this paper.

Modern objective lenses for cinematography, television or photography, and particularly zoom lenses, are composed of several groups of lenses which are axially displaced during zooming and/or focusing. The number of these groups has increased recently as well as the complexity of their relative movements and functions. In this paper, we give a short history of zooming and focusing techniques ; we discuss the inconvenience of traditional solutions. We then introduce the concept of bidimensional law. We propose a systematic classification of possible lens-types according to the 4 possible types of group. We finally present a few types of lenses in the form of truth tables and parametered diagrams explaining which groups move and how during focusing and/or zooming.

Payload space limitiations, high optical fidelity and the desirability of fast slew rates imply that certain broadband active pointing systems should be lightweight, compact and high performance with small moments of inertia. This paper describes a 12 inch diameter, F/5 reflective hybrid with two fields of view in the visible SWIR, and one field of view in the LWIR region. By incorporating two classic optical designs, these stringent requirements are met at a level as to assure reasonably attainable weight, size and performance estimates.

As a core of the Canon still video system, we have developed an electronic still video (SV) Tamera, RC-701, which records image information on a standard 2 inch video floppy disk. The RC-701 is composed of a 2/3 inch CCD, a viewfinder, signal processing circuitry, a disk drive unit and system control circuitry which controls the functions of all units. This report represents the analyses for designing the optimum viewfinder optical system of the RC-701, by solving various restricting factors caused from the structure of the SV camera, and introduces optical components used in the RC-701.

A near diffraction limited catadioptric lens of EFL=324.4 mm and f/3.6 was designed for the spectral range 546 to 852 nm. This is a 5 element lens with a field of view of ±2.5°. The obscuration ratio is 0.5 and relative illumination at the edge of the field is 81.4%. The distortion is less than 0.16%. This lens can be used for high resolution imaging applications using CCDs. The design details were presented in this paper.

Scientific Calculations, founded in 1963, is a supplier of software-based design automation products, i.e., we write, market, and support computer programs. Our first series of products was and is for the design and analysis of optical systems. Our current offering is ACCOS V, an acronym for Automatic Correction of Centered Optical Systems version V. The restriction to centered optical systems was removed long ago. Through the sixties, the predecessors of ACCOS V were batch oriented codes. Work was begun on ACCOS V in 1970 with the goal of developing a general purpose interactive code. Work continues today.

My name is Jonathan Vanderwall and I am by profession an electronics engineer at the Army's Harry Diamond Laboratories in Adelphi, Maryland, although I have worked in electrooptics for the past 15 years. About five years ago, Clive Sinclair put out the first really cheap computer, and I have had a Sinclair computer of the latest type on my desk ever since. Then, three years ago, Don Small published his program, "Small Optical Design and Analysis," (SODA-I) and gave the listing away to interested parties. I discarded the optics program that I had been working on, and began to translate SODA-I for my Timex-Sinclair 2068. Later, I recruited a colleague, Walter Hattery, who also likes the idea of inexpensive computation for scientific purposes, and we have been doing the final debugging and testing for about the last year, not, I rush to add, on taxpayers' time.

RAY-CODE includes two methods of optimization: Glatzel's adaptive correction and Spencer's damped least squares with Lagrange multipliers. In Glatzel's method hard targets may be applied to selected coefficients of polynomial expansions of the aberration functions as well as to a number of opto-mechanical constraints. In Spencer's method a merit function is formed with weighted sample values of the aberration function. In addition, the same coefficients and constraints may be either assigned soft targets and weights and included into the merit function, or assigned hard targets and treated with Lagrange undetermined multipliers. Sample values of the aberration function may be obtained by interpolation with the polynomial expansion or by straightforward tracing of sets of user-defined rays. The program can be used for designing and optimizing conventional, multiple-configuration, anamorphic, afocal and other systems, and to evaluate them with all the standard methods.

The general features of the Super-Oslo optical design program are described, including its integration with an interpreted programming language that can be used to extend its capabilities.

The philosophy and history of the TRACE V lens design and evaluation programs have been described in another paper(l) at this same conference. We will describe some of the technical features here and give a simple examples of the use of the program.

GAL-2 is a comprehensive lens design program which serves as a tool for lens designers and engineers to evaluate and optimize optical systems. The combination of versatile optical calculations, friendly features, and fast computation on the DEC VAX/VMS, makes GAL-2 an extraordinary, powerful, easy to learn lens design program. This paper will briefly present some of the features of the program in terms of lens design requirements.

A brief synopsis of the SYNOPSYS lens design program is presented.

GENII is a versatile, interactive optical design optimization and analysis program. It can be run on a variety of computers from two thousand dollar desktop PC's to multi-million dollar supercomputers. Its capabilities, even on a PC, are comparable to those of programs available only on minicomputers or mainframes. COOL/GENII, an optional combination with David Grey's COP (described in a separate paper), provides further enhanced optimization capabilities. Consideration of the following program areas will be used to describe the capabilities of GENII: Optical system characteristics simulated Analyses available Merit function (defect function) used in optimization Optimization procedures User interface

Certain features of the PC version of the lens design program Fovly are discussed in relation to artificial intelligence.

In view of the time available for this talk, I will discuss mainly some of the most imporatant features of our program for the Apple Macintosh, because I believe that it illustrates some of the features that are needed in Optical Design software, if it is to be as user-friendly as some of the best general-purpose software. Other recent papers, particularly reference 2, describe other programs in more detail.

IMAGE is an optical modeling program written in C for IBM PC computers. The program is intended to provide the optical engineer with accurate answers to geometrical optics questions and to problems requiring consideration of scalar diffraction theory. Although there are several very good programs for optical design and evaluation already available, they are intended for lens designers and not for system designers and general optical engineers. Additionally, these large programs require fabrication data in order to calculate spot diagrams, wavefront maps, and point spread functions. In our own work, we often have had the need to answer rather simple questions such as: What is the point spread function of a Gaussian beam clipped at the 1/e2 radius if the beam has 0.5 waves of spherical aberration? IMAGE enables easy computation of answers to such questions.

Damped Least Squares (DLS) optimization techniques have been used in lens design programs for many years. Although capable of significant improvement in a wide range of applications DLS techniques often converge to local merit function minima. Generalized Simulated Annealing (GSA) algorithms have been suggested as an alternative to DLS in order to arrive at a global merit function minima, and to reduce the dependance on operator expertise. In this paper we describe an effort to use the preliminary results of the DLS process to provide a starting point in a semi automatic manner for the GSA algorithm.

The technical features of the CODE V program for computer-aided optical design and analysis are described. Examples of typical applications are presented which illustrate various special features of the program. The recently introduced interferogram interface is presented in more detail as an example of CODE V's technical depth and approach to new technological requirements.

The wide spectral regions over which some infrared lens systems are required to function makes the lens material selection very critical. A particular design had a 1 to 5 micrometer spectral band. There are many combinations of materials in this hand, and a systematic way of narrowing the selection process was sought. A reference was found which addressed this problem, but which needed to be updated and expanded.