We have developed an optical design program for the Hewlett-Packard 9815 desktop computer and used it in teaching an optical design laboratory course. The program carries out most of the standard calculations used in optical design programs, but is limited to optimization of third-order aberrations. This paper describes our experience in teaching this course, and gives some of the optical design examples considered.

Paraxial solves are used to maintain some first-order property of an optical system (such as image position or paraxial ray angle) at a predetermined value by adjusting the curvature or thickness for a specified surface. Solves simplify the specification of an optical system and remove side constraints from the merit function for image quality. The application of paraxial solves is referenced to the program style of ACCOS V. The various types of paraxial solves allowed by ACCOS V are discussed first. Several new solves are intro-duced. One of these is a yy solve that permits optical systems to be specified by a yy diagram. Another new solve sets the curvature of a surface to maintain a specified value of paraxial ray height at the following surface. Examples of application of these solves are given. Familiarity with ACCOS V is assumed.

Several commercially available optical design and analysis programs have been written with the express intention of being as versatile as possible. The program writers' concern for versatility has not been without just cause--optical systems are becoming more sophisticated every day. Off-axis elements, steep aspherics, tilted and decentered components, and holographic lenses, for example, are rapidly becoming de rigueur for the modern optical system. The need to simulate these requirements on standard design programs has become a must. ACCOS V is a prime example of an optical design program with the ability to design and analyze "wierd" systems. In addition to the computer program, a certain amount of ingenuity is required on the part of the designer. This paper discusses some tricks useful for simulating "wierd" systems on ACCOS V plus tricks that are probably suitable for most other design programs as well.

Techniques for the Fraunhofer diffraction evaluation of general optical systems have been developed and incorporated in the computer program ACCOS V. No restrictions are made with respect to symmetry, allowing any combination of tilted, decentered or deformed elements, arbitrary off-axis field points, and unusual aperture shapes. Systems with non-uniform illuminance over the image space wavefront (in the presence of pupil aberrations or apodization, for example) are correctly treated. Significant features of the methods used and applications to selected optical systems are discussed.

This paper describes a method of multiconfiguration or zoom optimization of optical systems using a conventional optical design program, even though the program was not explicitly designed to provide such a capability. This is accomplished by using the three indices of refraction that are accepted by the program (which are usually used to identify different spectral wavelengths) to identify different multiconfiguration or zoom modes. When using the indices for this mode identification purpose, it is not possible to control chromatic aberrations. There are, however, a number of design applications where a multiconfiguration or zoom optimization is required, but the control of chromatic aberrations is not. These ap-plications include all-reflective systems, laser systems or other narrow spectral bandwidth systems, and certain IR systems. Two procedures for utilizing the indices of refraction to represent multiconfiguration or zoom modes are the transparent mode method and the variable path method. Illustrative examples using both procedures are presented.

An optical design and analysis program structured for operation on a mini-computer has been developed at NRC (National Research Council of Canada). It has been designed to be used interactively giving the user both flexibility and ease of operation. The computer on which it runs at present is a Digital PDP11 with a memory of around 28K, and this represents a great saving in computer costs when compared to those of a large computer upon which most lens design work is carried out. This program has capabilities for optimizing a lens system, for pupil exploration, for fitting the computed wavefront aberration to a polynomial and for evaluating the diffraction optical transfer function. Although only 10 finite rays are traced in the optimization routine, the aberrations computed, together with the Seidel aberrations obtained from the paraxial ray trace, provide the user with adequate control of the aberrations over both aperture and field. A Double Gauss and a Maksutov-Cassegrain system are used as practical examples to illustrate this.

The author, a new user of lens design computer programs, makes an intercomparison of several commercially available programs in order to provide an unbiased overview of each system's performance. The programs used are ACCOS V of Scientific Calculations, Inc., CODE V of Optical Research Associates, and COOL-GENII and Grey of Genesee Computer Center, Inc. Two fairly standard lenses were designed on each computer program as a means of investigating each program's operating characteristics. First, a Cooke triplet design was developed from a first-order thin lens solution. Second, a double Gauss was redesigned from a lens patent to satisfy new first-order specifications. The evaluation of the computer systems considered in this paper is based primarily on how well each program aids the designer in his task. That is, the emphasis here is on the details of setting up the design problem, optimizing lens performance, and analyzing and interpreting design results. Some topics that are discussed include lens description input; library storage and editing; merit function development and optimization control; design analysis features and tolerancing; and usability and clarity of user manuals, program instruction procedures, and computer data printouts and graphics.

The use of an optimization program on a large computer for the design of lenses is a very recent phenomenon. Prior to about 1930 all lenses were designed by logarithms, and from 1930 to about 1960 they were designed by hand with the aid of a mechanical desk calculator and a book of sine tables. It is the purpose of this paper to indicate the kind of procedure that used to be followed when lenses were designed in this way. A numerical example is included to illustrate the process.

During lens optimization we monitor the sensitivity of lens surfaces and lens groups to errors in tilt and decentration. These sensitivities can he included as items to be bounded to specified limits during optimization. Often manyfold reduction of sensitivity of critical surfaces can he achieved with little or no degradation of nominal computed image quality.

A procedure is described which calculates the variation of MTF with respect to the constructional parameters of a lens system including the effects of diffraction, spectral band, obscuration, and vignetting. The calculation is much faster than the common procedure of changing a parameter and re-evaluating, and is applicable to systems in any state of correction. Compensating parameters such as defocus and image plane tilt are included in the procedure to account for adjustments made during assembly of the lens. The basic approach is an expansion of the OTF integral into a power series up to second order in the parameter. Each of the terms in the expansion is an integral over the convolved aperture. The integration is carried out by tracing a grid of rays through the system and using the H. H. Hopkins algorithm. The system is evaluated only once; differential ray tracing being used to obtain the wavefront derivatives, and hence the MTF variation, for each parameter. The relationship between MTF and any parameter is quadratic for small variations of the parameter, but not necessarily symmetric with respect to positive and negative incremental changes in the parameter. The changes in MTF for both positive and negative perturbations of all the constructional parameters are combined in a statistical manner to arrive at a probable degradation for the manufactured and assembled system. In addition to MTF, the resulting change in distortion for each field is calculated based on the parameter changes and adjustments.

A common procedure in modern lens tolerancing is to use Monte Carlo, or direct random simulation models of manufacturing errors to determine the probability of achieving certain performance levels. The results of such calculations are usually the probability of achieving specific performance levels as a minimum, and provide an excellent overview of the impact of a set of manufacturing tolerances. Unfortunately, the use of such methods generally requires a high speed computer, and the results are not easily modified for tolerance changes without performing additional simulations. As an alternative approach to direct simulation, a second moment statistical method is described that provides a simple algebraic computational scheme to estimate the same probabilities. The methods allow direct computation on a desk calculator once parameter sensitivities are known and are also useful in substantially reducing the amount of time required when using a high speed computer. Applications to linearly related phenomena (such as focal length, distortion, back focal distance, etc.) as well as non-linear phenomena (e.g., RMS wavefront error, MTF at some frequency, etc.) are discussed. Commonly used techniques such as finding the root of the sum of the squares of perturbations (RSS) are reviewed and shown to be a subset of this more accurate and general approach. Some discussion of accuracy compared to direct simulation is included.

Computer programs for automatic optimization of optical designs provide numerous opportunities for production cost reduction. Some of these opportunities have been exploited heavily. For example, many manually designed systems have been replaced with less complex systems of comparable performance, designed with the aid of such computer programs. Cost sensitive parameters such as blocking factors, diameter to thickness ratios, and sharp diameters are readily controlled within automatic optimization procedures. Additional opportunities for savings are available. Convertible and multi-channel systems are commonly comprised of individually well-corrected modules. Several computer programs now have the ability to optimize the various configurations of such multi-configuration systems simultaneously, leading to a potential reduction in complexity for such systems. Options to control and reduce sensitivity to manufacturing errors as part of the optimization process are used infrequently, despite the fact that these options have produced dramatic solutions to several disastrous manufacturing problems. In more routine designs the worst sensitivity may be reduced on the order of one half, leading to worthwhile manufacturing economies. Illustrative examples are presented.

Large numbers of rays must be traced to obtain an accurate assessment of the sensitivity of a lens to certain manufacturing perturbations, such as optical surface irregularity and aspheric departures. To properly assess image quality changes, the perturbed lens must be re-focussed. This paper deals with the development and testing of an algorithm to automatically determine the focus of aberrated images with a computer.

1. Design techniques for all-reflecting optics from first-order layout through final design based on large optical design programs with interactive plotting are discussed. The design process is demonstrated for three different optical designs, each having a unique set of FOV, packaging, and resolution requirements.

Aspects of the design of complex photographic lenses for low cost, high production are considered. Extensive use is made of through-focus MTF for the assessment of image quality and for the establishment of tolerances and this concept is described in detail. The problem of desensitizing and tolerancing lenses is discussed and illustrated in terms of the design of a high quality, ultra wide-angle lens covering a field of 102° at f/3.5. The evolution of this design is shown and some interesting problems involved in the aberration correction are described. Brief mention is made of some manufacturing considerations and the extent to which these affect the optical design.

Efficient design and evaluation of infrared cryogenic sensors that must operate in changing thermal and mechanical environments require using automatized data transfer among thermal, structural and optical computer programs. The thermal and mechanical environments during which the sensors must operate to specifications include Sinusoidal and Random Vibration, Steady State Acceleration, Shock Spectrum, thermal soaks and gradients. The design of infrared cryogenic sensors to system requirements involves trade-offs among structural, thermal, and optical requirements. These trade-offs are performed using our Thermal/Structural/Optical (T/S/O) integrated design analysis process. This T/S/O process permits us to perform iterative cost effective systems evaluations of alternate designs by efficient data transfer among thermal, structural and optical programs. Examples are presented showing how Honeywell Electro-Optics Center (EOC) has used the T/S/0 process to design sensors that are subjected to varying thermal and mechanical loads.

Techniques in designing corrector lenses for color television tubes are described with recent improvements to cope with the use of tubular light sources.

In response to increased interest in the details of the glassmaker's characterization of the homogeneity of his ware, an outline is presented which defines the nature, cause, effects, techniques of detection, and measurement of the various forms of inhomoaeneities found in optical glass.

Modern computers and optimisation programs have made the design of unconventional optical systems such as those containing aspheric surfaces relatively straightforward. For thermal infrared systems, where materials are expensive and transmission important, there is an understandable feeling amongst designers that aspherics should be employed, provided that their use results in a reduction in the number of lens elements required for a given system. Much can be achieved with spheric optics however; indeed it is arguable that the use of only spherical optics represents a greater design challenge. Therefore, considering their relative difficulty of manufacture and testing, the choice of aspheric rather than spheric surfaces requires some justification. This paper gives a summary of the results of a short investigation into optimised spheric and aspheric optical systems of comparable performance for use in the 8 to 13 micron bandwidth. Applications covered are:- pyrovidicon objectives of high aperture (N.A. = 0.78); catadioptric objectives; and afocal telescopes.

Some aspects of the optical design of high-speed wide-angle lenses are discussed. Particular attention is paid to the problems of designing for the use of common parts as a means of significant cost reduction of manufacturing in commercial quantities. 24mm f/2.0 and 28mm f/2.0 Vivitar wide-angle lenses covering the 35mm format are used in the discussion as examples.

The design of infrared optical systems, particularly scanning type FLIR systems, imposes requirements on the optical design not normally seen in the design of visual/photographic type systems. This, in turn, means that modifications need to be made to the computer programs used to be able to design these systems. This paper describes some of the modifications required in future optical design programs.

The optical design of a holographic visor helmet-mounted display built by Hughes Aircraft Company is described. In order to design the system, a technique for ray tracing holographic optical elements constructed with aberrated wavefronts has been incorporated into a comprehensive computer program. The design illustrates the use of aberrated wavefronts for constructing a highly off-axis holographic element on a helmet visor such that its aberrations are of a form that may be readily corrected with a relay lens containing cylindrical surfaces and with a tilted prism assembly. High diffraction efficiency across a wide field of view (FOV) with a volume hologram is obtained by placing the two coherent hologram construction sources close to the desired pupil locations. The chief rays are then reconstructed in a geometry similar to that used for hologram construction. Good correction of the monochromatic aberrations and high efficiency is achieved over a 30° FOV with a speed of F/2. 3

An unusual type of surface that has been found to be very useful in the design of certain kinds of unobscured telescopes is described. This surface has an aspheric deformation which is the superposition of two separate conventional aspherics with axes that are shifted relative to one another. For example, a parabolic departure from a sphere might be super-imposed on top of a conventional parabola but with the axis of the superimposed deformation displaced laterally from the axis of the base parabola. Another example might be an aspheric deformation added to a sphere but with the axis of the deformation not going through the center of curvature of the base sphere. Such surfaces allow the designer to optimize unobscured telescope configuration types that otherwise are very difficult to handle. In particular, the use of these surfaces allows the designer to avoid coming to grips with a full Zernike set of aspheric terms, which are very expensive to use in optimization and usually contain a lot of excess variables that are not really needed. The two-axis aspherics only have terms relevant to the design tasks for which they are best suited, and make the design task simpler and more efficient. The way in which these surfaces are set up in the Perkin-Elmer design program is described and several design examples which feature these surfaces are given.

This paper describes a method of incorporating a command language in a computer program by which the user can easily specify operations to be performed on a matrix of complex numbers. Through a series of simple commands, the user can calculate both near-and far-field diffraction integrals, polychromatic spread functions, optical transfer functions, line spread functions as well as radial and knife-edge energy distributions; he can convolve spread functions with detectors or apertures of various shanes. Any or all intermediate calculations can be stored for further processing. Both actual plots and printer plots in two or three dimensions can be produced.

The LASL CO₂ laser fusion systems present some unique problems preventing successful utilization of conventional techniques. A few of them are: 1) use of tight spatial filters renders techniques based on ray tracing ineffective; 2) the spatial filters remove only certain aberrations and the saturable gain and loss media alter intensity distributions in a nonlinear fashion; 3) high and low Fresnel numbers are encountered at different parts of the system; 4) the use of state-of-the-art novel components like dia-mond point turned optical elements and 16-inch NaCl windows which degrade the nominally diffraction-limited performance; 5) the pulse being nominally nanosecond does not help. Hence, a custom tailored combination of programs' and a different approach (utilizing detailed examination of the Zernike polynomial set by which each component is characterized) appears necessary. An example using the LASL Two Beam CO₂ Laser Fusion System is presented.

An optical probe is described that utilizes refraction and then reflection from an ellipsoid to obtain a field of view of 45 to 101") degrees around the circumfrence. The image (nearly linear with respect to input angle) is a 23.3 mm wide annulus.

Unique optical design problems occur in the specification of high energy laser systems. The design of each optical component must ensure that no damage will occur in the laser system due to light transmitted, reflected or absorbed by that component. In order to fully assess the possibilities of laser induced damage in the laser system, we use a number of paraxial calculations, real ray traces, and diffraction based calculations. Once problems are identified, solutions must be found to eliminate or minimize damage problems.