The inexpensive system described provides multiuser local capability and improves the optical designer's access to all major design engineering programs, yet significantly reduces associated costs.

A brief description of the SYNOPSYS program is presented. Examples are given of numerous features and novel applications.

A new look at damped least squares has led to the development of a "smart equation solver" that enables optimization to take place in the least constrained space and to completely prevent singular variables and constraints from destroying the solution. Damping can now be reserved for handling non-linearities - its intended purpose. Reliability has been enhanced and improved speed of convergence is demonstrated in two examples. This lays the foundation for a series of planned future enhancements.

Since the Rochester Conference in 1966 our optical design programs have been significantly extended. Some of this work has already been described (e.g. Worme11³). This paper includes some recent modifications that have been carried out during the development of newer versions. In optimisation programs considerable effort has been devoted to comprehensive boundary condition control and a fully automatic optimisation procedure. Several of our research students have studied problems involved in the optimisation of the geometrical optical transfer function and this has been used for designing lenses for the measurement of bubble-chamber photographs. More recently Finkler has used similar techniques for designing systems with extended depth of focus. Special purpose programs have been written for the design of zoom systems and for semi-interactive use on a terminal to the CDC machines in our computer centre. Work on programs for image evaluation has been concentrated on programs for otf calculation and on programs for ray-tracing through systems without rotational symmetry. During the last year, we have been concerned with the development of programs for desk-top computers, and the first versions of these programs are already used in industry. These programs are described in a separate paper.

Recent advances in desk-top computers have resulted in the production of machines which are capable of carrying out most optical design calculations, perhaps with the exception of the optimization of complex multi-configuration systems. We are using the Hewlett-Packard 9845S, and with a 64K byte memory we can optimise systems with up to 40 surfaces, controlling up to 70 aberrations and varying up to 30 parameters. Image assessment can be carried out using spot diagrams, geometrical mtf and diffraction mtf, each of these calculations being carried out within the 64K memory. In interactive programs it is possible for the program to be able to carry out many short calculations, and it is possible to provide graphical output, whenever this is useful. Advantages of desk-top computers for design are economy, convenience and the speed with which results can be obtained, plus the greater understanding that is possible when the designer is in control of the program, and when hard-copy graphics is available. The only disadvantage is the relatively slow computing speed, but this will probably be overcome when new desk-top computers become available. A smaller program, for the H-P 85 will also be described.

Since the time of the 1975 International Lens Design Conference, we have developed a series of optical design programs for Hewlett-Packard desktop computers. The latest programs in the series, OSLO-25G and OSLO-45G, have most of the capabilities of general-purpose optical design programs, including optimization based on exact ray-trace data. The computational techniques used in the programs are similar to ones used in other programs, but the creative environment experienced by a designer working directly with these small dedicated systems is typically much different from that obtained with shared-computer systems. Some of the differences are due to the psychological factors associated with using a system having zero running cost, while others are due to the design of the program, which emphasizes graphical output and ease of use, as opposed to computational speed.

Advancing computer technology led to the introduction of powerful minicomputer tools for optical design in 1975. Continuing hardware advances have opened up further options for the optical designer while expectations of program performance and scope have risen. Various hardware/software optical design products have appeared and will continue to be developed, giving the optical designer a wide range of choices. The development of an effective system for optical design involves consideration of many goals and tradeoffs relating to both hard-ware and software. These include: scope of program - decentered, multimode, no bilateral symmetry requirement, "large machine" capability; ease of use - the human interface; speed of computation and peripherals - benchmark results; memory size limitations; efficiency of memory use by the program; cost of hardware needed to embody the chosen scope of program; reliability and service; means of software updating; and future growth potential. These tradeoffs will be reviewed in the context of the CODE VTM hardware system.

Historically, the practice of lens design predates the electronic computer. As a result, in the early days of the computer, the lens design application presented a computational workload that strained the available computers. As the computers gained speed and capacity, the computation appetite of the lens design application similarly increased, up to a point. Eventually, the power of the computer evolved far beyond the needs of lens design. The task has changed from obtaining time on the most powerful computer available to selecting the most appropriate computer from a vast list of candidates.

Techniques are discussed which may be used in optical design to speed up the output of micro-computers. Among these are the use of the Aldis Theorem for centered and weakly de-centered surfaces, interpolation formulae for spot diagrams, diffraction based M.T.F. using 'pseudo' spot diagrams, and variational formulae.

The history of optical design has been closely associated with the latest techniques for computation because of the heavy requirements for computation in optical design. The microcomputer revolution is one of the latest stages in this process. We describe the application of one of the most common microcomputers, the TRS-80 (Z80), to the optical design problem. Speeds on the order of five ray-surfaces per second and costs of a few microdollars per ray-surface can be readily achieved. Some currently available programs and forthcoming capabilities are described.

A Small Optical Analysis Program, SOAP, has been developed for the Commodore PET computer which is very versatile and easy to use. With this computer and optical program the user will be amazed how easily analysis of complex optical systems can be accomplished. There are three main section 'of the program available the to user; Lens Input and Output (including lens library), Lens Evaluation and Lens Raytrace including Gaussian beam propagation. This program can handle conics which can be deformed asphericallv, rotationally symmetric aspherics, and aspheric toroids and cylinders, all of which can be decentered in both the XZ and YZ planes and tilted in all three planes. The cost of the computer is less than half that of the HP98l5A, vet it is a true computer with the easily understood BASIC language. For the same investment as a HP9815A calculator one could obtain a PET computer, dual disk drive, printer and cassette. This system would constitute a complete business package useful to small businesses. The small business will find the combination of SOAP and the PET a combination that fits the bill.

The nonlinear nature of lens design optimization has been dealt with explicitly in a new program that reaches solutions not possible with damped least squares.

Glatzel's adaptive correction method apparently has been ignored by a large sector of the optical design community. Although based on the same principle as the Hopkins and Spencer method it has definitely better convergence. We incorporated Glatzel's method into our lens design program ten years ago and have consistently obtained satisfactory results, especially working with coefficients of orthogonal expansions of the aberration functions. Our computer program is operated interactively and differs to some extent from Glatzel's. Besides we have found that weights on parameter changes affect convergence significantly and routines for computation of weights were developed.

Circular polynomials orthogonal over an elliptical exit pupil and their use in lens design and tolerancing are described.

An effective procedure for the optimum balancing of aberrations in non-diffraction-limited lenses is an important and unsolved problem in lens design. In order to obtain an understanding of what is involved, an empirical study was conducted for the case of optimizing the modulation transfer function (MTF) in the presence of spherical aberration. The results of this study indicated the reason why direct optimization of the MTF is probably not a very good approach, and also suggested a possible method for accomplishing this balancing based on the Rayleigh quarter-wavelength rule, and using Jacobi orthogonal polynomials, of which the Zernike polynomials are a special case.

Specific needs of a given lens design may significantly affect what is an "optimum" design. A manufacturing process, the intended production quantity, or an unusual customer requirement, for instance, may dictate that the designer use a different merit function than that employed in the optimization program. This paper presents the results of using a new tolerance sensitivity program, ZEST to address the change in merit function. The results include reducing the sensitivity of a lens to manufacturing perturbations, particularly to tilts and decentrations. Other improvements are achieved such as reduced astigmatism and increased axial MTF. A lens designed using a conventional optimization program is evaluated and tuned up by use of the technique.

The design of multi-configuration optical systems leads to the minimization of a merit function whose terms are most conveniently evaluated in groups. The Jacobian or difference matrix associated with these merit functions can be decomposed into blocks corresponding to these groups. The associated constrained least-squares problem can be solved without requiring that more than two or three blocks be in high-speed memory at one time. The algorithm described here is useful for lens-design programs running on mini-computers where high-speed memory is limited but medium-speed storage such as disc is available. An orthogonal factorization of the matrix is obtained so that rank-deficient problems can be handled in a consistent and numerically stable manner. This factorization can be used as an adjunct to a variety of least-squares type algorithms.

Many of the lens design computer programs used today optimize a design by minimizing a list of image errors which have been selected because of their relation to the quality of the image. In many cases, it is preferable to minimize quantities that are direct measures of the image quality of the design. An example of one such quantity is the rms spot size, which is commonly computed by tracing grids of rays through the lens. The method, while very convenient, can be an expensive way to optimize a lens because of the number of rays that must be traced to get reliable spot diagram statistics. We have developed another approach, based on Buchdahl's Optical Aberration Coefficients (OAC's). The OAC's form polynomial models of the imaging behavior of a lens and can therefore be used to compute its performance. We replace the summations in an ordinary spot diagram calculation with integrals over the aperture and thereby obtain the rms spot size. The answers are free from aperture sampling effects, and the optimization is 6:1 faster than a ray-trace based method using 8 rays at three positions in the field. We review the mathematical methods employed and show examples of the accuracy and cost effectiveness of the OAC approach in lens design.

In order to find the correspondence between actual residual aberrations and Seidel's coefficients, target values are initially set up for the latter, thus simplifying the final optical designing process.

An analytical approach to determining the effects of tilts and decenters on an optical design has been developed. The work has been guided by the desire to provide rapid insight into the cause-and-effect relationship between a component perturbation and the degradation in some measure of image quality. This is done by providing a graphical display of the properties of aberration fields under the influence of tilt and decenter perturbations, and contour plots of the change in the RMS wavefront error or change in RMS spot size over the entire field.

A bursting bundle is a ray trace extension which defines incremental rays spread about a principle ray. The user can define the extent and the geometry of the spread. The burst can originate anywhere within the optical system. This provides the designer a new tool to help model unusual problems. A mathematical development is presented and some examples are discussed.

Two optical ray trace conventions are addressed. The choice of ray-surface intersection has been based on convention rather than examination of the situation. The problem can be handled automatically by specifying an active side to a surface and then associating a direction to the surface normal based on that active side. The two solutions obtained by solving the equation of the line and surface can then be tested by scalar product with the normal. The reflection algorithm is restructured to eliminate the need for a negative index and the concept of rays traveling in negative space.

Software has been developed to calculate the image structure of one-dimensional objects under partially coherent illumination including the effects of aberrations, vignetting, and central obscuration.

A versatile program has been developed for determining the diffracted intensity distribution far from the image center for a wide variety of obscured apertures. The total obscuration is constructed from "building blocks" consisting of triangles, rectangles, bars, and annular rings. Closed formed solutions of the Fraunhofer diffraction integrals for the building blocks are combined by means of Babinet's principle to obtain the point spread function. An example is given demonstrating the influence of fine mechanical structure in the obscuration on the image structure far from the image center.

Consequences of the working project formed in JOERA (JAPAN OPTICAL ENGINEERING RESEARCH ASSOCIATION) from 1976 to 1978 are to be reported. The question, "What is the most reasonable number of mesh divides of entrance pupil to get monochromatic OTF and the most economical sampling method of spectral wavelengths to calculate White Light MTF?" is important in the actual stage of designing to optimize the conflict relationship between numerical accuracy and computing time. We have examined the spectral characteristics of OTF using some typical lenses such as photographic telephoto lens and wide angled retrofocus lens, cleared the structure of the White Light MTF, and found some techniques to get the reasonable numerical results. As a result of trial experiments to get coincidence between measurements and calculat-ions, the standard filter, which should be added to the MTF lens tester and whose spectral transmittance should be installed in the calculation, are proposed.

Interpolation of lateral chromatic aberration and/or Hopkins algorithm of sinc-function are adopted to reduce the numerical error of white light OTF, where lateral chromatic aberration is present.

For a long time lens designers have recognised the desirability of using aspheric optical surfaces for some applications, and recently there have been significant advances in the manufacturing technology for such surfaces. Nevertheless, there is reluctance on the part of manufacturers to install the appropriate equipment unless sufficient advantage can be achieved. The three main methods of aspheric surface manufacture (figuring of spherical surfaces, numerically-controlled machining, and moulding) are briefly reviewed. Design examples of infrared and visible light optical systems are given to show that each of these manufacturing methods can be used to produce lenses incorporating aspheric surfaces that have distinct advantages over the equivalent lens with only spherical surfaces. The manufacturing method must be matched to the system needs and performance requirement.

This paper describes the software that has been developed at Itek for the analysis and tolerancing of solar concentrator optical systems. The software models the conventional as well as the non-imaging components used in high energy solar concentrators. The system model includes an extended solar source, a segmented primary collector, a secondary non-imaging concentrator and a hemispherical receiving surface. Both surface irregularities and alignment of the primary segments are modeled as localized slope perturbations which deviate the surface normal where the geometrical ray intersects the surface. The non-imaging secondary concentrator is input as a single optical surface and a special raytrace code developed such that a ray may have any number of reflections up to a user specified maximum number in transmission through the secondary concentrator. Graphical results are included to illustrate the use of these new codes in analyzing systems with both conventional and non-imaging components. The raytrace procedures developed for the non-imaging secondary concentrator have been used at Itek to analyze grazing incidence x-ray telescope systems. The not obvious connection between codes developed for solar concentrators and their application to x-ray telescopes is explained in this paper.

A simple method of correcting exactly the third order aberrations of a tilted plate beam-splitter in converging light is presented. Various well corrected design examples are given.

This year 140 years have elapsed since the first photographic objective was designed, more than 90 years have passed since the first anastigmatic lenses were created and about 20 years ago computer-aided lens design was started. The double Gauss lens will be used as an example to outline the problems, procedures and results obtained in designing optical systems. In retrospect a search will be made for the first introduction and development of the double Gauss lens in order to draw further conclusions from the historical facts as to the ideas that have led to the present state of the art. Contemporary systems of the double Gauss lens will be demonstrated with regard to the available construction parameters and the numerous fields of application. While discussing several variants emphasis will be placed on the choice of glass types for high speed lenses, the relationship between refractive index and image quality and the comparison between performance and costs. Recent explorations led to double Gauss lenses with special properties. New objectives with stabilized performance, ultra high speed lenses and lenses with reduced secondary spectrum will be presented.

Classification of photographic lens types has been undertaken in several ways of which the historical approach and the approach by Kingslake are the most important ones. A new classification is proposed which is based on the method of the Petzvalsum (P) correction. It is shown that the correction of P is the pivotal problem in photographic lens design and that all lenstypes can be considered as a consequence thereof. Most aberrations originate in the process of correcting P and their reduction can best be undertaken as an effort to improve the method of P correction. Fifth order field curvature is often characteristic of the method of P correction and is for most lenses the performance-limiting aberration. This classification is useful in understanding a lensform, as a guide to improve the aberration correction, and as a method to find new lensforms.

A procedure for the design of basic Double Gauss lenses has been developed that uses fifth-order interpolating aberrations in the framework of a damped-least-squares program. It proceeds from a rough model directly to a solution.

A simple method is described for quickly and easily designing high-performance optical systems. It involves little iteration, if any, and requires neither a computer nor extensive hand calculations. The systematic application of this design method allows one to construct configurations where the function of every surface is clearly understood. As a result, new design configurations tend to suggest themselves to the designer. This insight, which is an integral part of the design method to be described, also makes it clear how to compound designs so as to extend the f/# and/or field of view over which high performance is obtained. Although the design method only uses well-known principles of aberration control, it combines them and systematically applies them in a particular way that has not gained the wide use it merits. Several design examples illustrate how this design method is applied. They include a telephoto lens, an inverse telephoto lens, a fisheye type lens and a catadioptric system.

Zoom lenses generally contain moveable lens groups. The behavior of one moveable lens, two moveable lenses, and two moveable lenses together with one fixed lens is discussed in terms of the Delano and Aperture diagrams. This is followed by a discussion of the important features of the two diagrams with respect to zoom lenses: stop shift, partial vignetting, sensitivity to cam mechanism, aberrational behavior of thin lenses, additional aberrations of aspheres. Then the most widely used zoom lenses in photography and cinematography, the standard mechanically compensated zoom lenses, are presented. The four principal types are explained in terms of the diagrams and are discussed with respect to vignetting, aberrational behavior and sensitivity to cam mechanism. Further on simple zoom lenses which contain only a two-lens zoom kernel and a relay lens are considered. Two main types exist, each of which can be divided into three different subgroups. It is true that the Delano diagram offers an impressive and quick overall view of the features of a zoom lens. But designing a new zoom lens from scratch requires a little more than merely looking at beautiful diagrams. What can and must be done is demonstrated by the following design example of a simple zoom lens.

A wide variety of designs are described, using only two optical surfaces, that can perform useful functions with good aberration correction. Several use no aspherics.

A ray trace program, ACCOS V, was used to create optical path difference arrays for axicon-type cylindrical laser components. The arrays were used as data for an interferogram reduction program called MCI, which calculates coefficients for a set of orthogonal functions containing the aberrations encountered in aligning and using reflaxicons and waxicons. It is shown that a linear reflaxicon is free of spherical aberration for all conjugates and that it is a flat-field anastigmat. Contour plots with respect to several pertinent planes are shown for decentrations and tilts of the resonator components. Completeness of the orthogonal functions with respect to misalignment aberrations is demonstrated. Solutions to several difficulties encountered in ray tracing such systems with ACCOS V are described.

The design of wide-angle reflective optical systems has been to a large degree a pursuit of symmetry. Major systems developed in the 1970s can be broken down as modular design combinations of three classical systems--Schmidt, Schwarzschild, and Baker. These configurations are based on the following four constructional principles: 1) aperture stop and correction at the center of curvature of a spherical mirror, 2) confocality of two parabolic mirrors working at infinite conjugates, 3) concentric mirrors, 4) polar strip field coverage. Five notable wide-angle reflective systems developed in '70s are: 1) Two-Axis Baker, 2) Hughes WALRUS, 3) Honeywell Wide-Angle Conical Scanner, 4) Perkin-Elmer Ring Telescope, 5) Corrected Schwarzschild.

An optical sub-system design for a solar concentrator having applications to high temperatures thermal photovoltaic concepts has been developed. The baseline system consists of a spherically segmented primary mirror optically coupled to a compound parabolic concentrator and a hemispherical receiver. Secondary concentrators having conical, parabolic and hyperbolic cross sections are considered Parametrically. Performance trade-offs relative to, concentration ratio, system configuration and manufacturing sensitivities have been rigor-ously evaluated using geometric ray tracing techniques. The advantages of using a two stage concentrator over a single collecting aperture are discussed. Performance of typical systems are reviewed and cover transmission, flux distribution, and tolerance sensitivities.

The camera viewfinder would consist of a two-element objective lens, a field stop, a tilted concave mirror, an aperture stop, a second tilted concave mirror, and a two-element eyepiece. This forms a Z shaped configuration with the mirrors at the corners of the Z. The two mirrors, with the aperture stop midway between them, form a 1:1 telescopic erecting relay system. Two types of mirrors are studied: spherical and parabolic. The main problems encountered in the spherical mirror system are axial astigmatism and field tilt, both caused by the tilted mirrors. By using confocal, coaxial, decentered parabolic mirrors, with the aperture stop at the common focal point, the axial astigmatism can be eliminated; however, the field tilt problem is aggravated. By rotating the axis of the second parabolic mirror about the common focal point, the field tilt can be minimized, and the astigmatism in all beams eliminated. This last configuration is, however, plagued by distortion and coma. We conclude that none of these systems is satisfactory for image quality.

The full aperture meniscus corrector catadioptric lens is a compact, fast flat-field configuration which should find application in wide field, long focal length systems which place a premium on high acutance image quality; i.e., aerial photography. Additionally, since the lens power is mainly in the primary mirror, the meniscus corrector catadioptric lens is capable of covering a much wider spectral bandwidth than can be achieved with a refractor of comparable aperture and focal length. The basic configuration consists of a primary mirror, a weak meniscus corrector lens and a single positive lens close to the image plane, to flatten the field. The under-corrected spherical aberration of the primary mirror is essentially balanced out by the over-corrected spherical aberration contributed by the weak meniscus lens. When design requirements dictate a smaller f-number, the single corrector lens generally evolves into a multiple lens configuration used in either the single pass or double pass mode. Axial color correction is achieved by either the achromatic single glass meniscus lens, or the two glass meniscus doublet. Characteristically, the higher order spherical aberration is corrected by the meniscus lens thickness as the f-number is decreased. However, for large scale systems the corrector thickness may become prohibitive. For the large scale designs the utilization of an aspheric figure on one of the corrector surfaces will produce a significantly thinner lens element. Similarly, the benefits of aspheric surfaces can be realized in the field flattening lenses. For a wide field of view, covering a square/circular field format, the obstruction is quite large; in fact, complete occultation is common in these instances. Consequently, the wide field versions will have to be used in the slit field mode with the resultant bar obstruction. However, this poses no serious problems in aerial photographic applications since the utilization of these designs would be either in the "push broom" or the scanning mode which would require auxiliary mirrors.

Giving the imaging bundle of rays two substantial bulges makes it possible to design 10x reduction lenses with large aperture and field size for microlithography without using high index glasses with poor transmission.

Programs written to assist in the design and evaluation of microelectronic lenses are briefly described. Over the past 15 years, several families of lenses were designed using these programs. Basically, the higher order aberrations are mapped for a series of similar designs with corrected Seidel aberrations. The OTF program is used to guide the final stages of design. Two lens structures are described that a fully automatic program could not produce. The last section deals with the practical aspects of making lens elements, mechanical assembly, and testing completed objectives.

New technology in the field of integrated circuits has created a demand for photolithographic projection lenses capable of producing submicron line structures. Tropel has introduced a series of UV Micro Tropar objectives for this specific application.These lenses achieve their superior performance by utilizing the 365nm line and increasing the numerical aperture to 0.40. Optical design considerations in the development of these lenses included appropriate materials selection, field vs. aperture tradeoffs, telecentricity constraints, and partial coherence effects due to underfill of the lens pupil. Manufacturing problems are accentuated by the extremely tight tolerances on all of the construction parameters of the lens system. Special interferometric test equipment, used to provide precise measurements of each lens element, has proven to be indispensable in the fabrication of these objectives. Mounting of these elements on a common optical axis is an absolute necessity if the ultimate resolution of the design is to be achieved. Testing of these lenses is also a challenge due to the high spatial frequencies involved and limitations on visual examination of the image. Methods of circumventing these difficulties will be discussed. Typical MTF test results and performance data will be presented.

Large modern computer programs were used to teach lens design. The effectiveness of large centralized computing facilities were compared with small desk calculators. The large programs were found to be powerful but extremely unfriendly. The input and output procedures were designed by computer people and aimed to meet the needs of a wide variety of users. Close supervision is required to reduce the volume of useless computing. To provide guide lines, a set of fundamental lens types are provided. The series of lenses are, a single lens, telescope objectives, curved field Petzval lens, telephoto, flat field triplets, four element derivative of the triplet and the double Gauss. It is suggested computers be designed to require a written review of the problem, with previous results, and reasons for additional computing.

A lens design problem has been configured for comparison on several different lens design programs and by several different users. The problem sets up a starting point lens of double Gauss form of speed F/2 covering a 30 degree field and then, using only the computer program, the designer must reoptimize the lens for different speeds and fields. As expected, different computer programs resulted in different final lens designs, but different users also got different results using the same program. The conclusions indicate the skill of the designer and amount of effort expended contribute more to the final design than which program is used.

The subject of gradient-index optics dates from the 1850s. However, only in the last 10 years has it been possible to design lenses, manufacture materials, measure the properties, and fabricate lens elements. The current status of gradient-index optics is reviewed.

The color correction of a gradient index lens was investigated bythe Gradient Index Design Group at the University of Rochester. The object of the analysis was to meet the specifications of an f/3 binocular objective with a 7° field of view consisting of four homogeneous elements. A series of radial gradient singlets, each with a different base glass, was designed to meet these criteria. A study was made of the effects of varying the dispersion of the gradient on the imaging quality of the lens. It was then possible to compute the dispersion that was needed to achromatize the singlet. This calculation was compared with the dispersions in lenses produced by the ion exchange technique and these results will be reported. An extensive tolerance analysis was performed for the various designs. Each coefficient of the index distribution, the surface curvatures, and the thickness were toleranced. Also the tilt and decentration of the gradient within the singlet were toleranced. Methods of tolerancing the dispersion of the gradient were examined and tolerances in terms of relevant parameters were found.

While the optimization software employed in optical design has indirect knowledge of the nature of the medium, characterizing the material only in terms of refractive indices and dispersion coefficients, optimized real life optical systems should be quite different in glass and polymer materials. To achieve an optimum system in polymer optical materials, the computer optimization must be guided by one who understands the differences in physical and chemical properties of the materials and the implications of a totally different set of fabrication techniques. While some of these considerations fall outside the realm which is of interest to the lens designer, it may be worthwhile to examine some of those considerations which bear directly upon the raytrace optimization procedures and techniques.

Athermalization, the elimination of thermal focus shift in systems which contain plastic elements, is achieved by use of ficticious refractive indices and correction of an artifical secondary color.

The limited availability of thermally compensated triplet solutions are studied and a paraxial mathematical expression for directly controlling thermal shifts are derived. Application of this expression is used to achieved families of thermally controlled triplet solutions. The solutions, depending upon aberration requirements, become finished designs or optimum starting points for surface aspherization and/or the addition of elements.

Work carried out at PPE over the last ten years has resulted in the development of four head-mounted passive night vision goggles of unity magnification. Considered in relation to each other, these systems illustrate the technical progression from the oriainal sight, a twin image intensifier tube device that employed conventional optics, through a series of three single tube goggles of decreasing complexity, weight and cost. The MkI and MkII single tube devices, of beamsplitter/relay lens and collimator/multireflector design respectively, required precise manufacture: the later of the two designs, however,was both simpler in construction and more advanced in technical specification than the earlier. The concept of the MkIII single tube goggle was influenced by the lower relative cost of current intensifier tubes and resulted in a lens design that can be fabricated in its entirety in optical plastics. Compared with the original two tube goggle, the final system has a similar technical specification but is much cheaper and less than half the weight. The paper describes the optical design philosophy behind each goggle and the evolution of each subsequent stage.

An 0.8 meter Cassegrain, reflecting relay and matching optics comprise a system which incorporates a Nike Hercules pedestal for an infrared tracking system. Optical design criteria and performance will be discussed.

Optical materials for the 8 - 13 micron waveband are discussed and a range of high performance infrared telescopes incorporating chalcogenide glass is described.

This paper describes a computer program, for evaluating the tolerance range to be assigned to each parameter of an optical system, when the perform ance specifications are given. The results obtained are not statistical, that is if all parameters are within their computed ranges, it is certain, not probable, that the optical system perform ance is with in specifications. The process is iterative. A very small alteration is assigned to each parameter, and the resulting wave front alteration is evaluated. During the first scanning and for each parameter, the program chooses the directions of alteration causing the greater worsening effect on the wavefront. These directions are kept fixed during all the subsequent scannings. After each scanning, the performances of the modified optical system are checked to be within specifications. If so, a new scanning process starts. The iterative search ends when either suitable boundary conditions are reached, or the system performances exceed the specifications. In both cases, one of the two tolerance limits for each involved parameter is obtained. The other limit is computed by returning the program to the starting system, and repeating the procedure with all the directions of the parameter variations reversed. The validity of the method is based on the assumption that each alteration is so small, that, within the same scanning, it does not appreciably change the effect on the wavefront of the subsequent parameter variations.

A series of Seya-Namioka monochromators using concave aberration corrected holographic gratings have been designed to cover the spectrum from 180-900 nm. This broad wavelength range (4.5 octaves) severely tests the aberration correction ability of this monochromator All holographic Seya-Namioka monochromators displayed severe loss of resolution at one or both ends of the spectrum. Over this wavelength range, when compared at equal f/4, the Littrow and Czerny-Turner monochromators outperform the holographic Seya-Namioka mono-chromator for resolution specifications less than 0.6 nm.

Most lens designers nowadays spend a great deal of their lives working with standard types of lens such as the double Gauss (which, of course, was not invented by Gauss) and the Cooke Triplet (which was not designed by Cooke). So I thought it might be of interest on this occasion if I were to consider some of the more unusual types of lens which are often extremely interesting from an optical standpoint.

Three areas of optical component specifications are discussed in detail: (1) purely optical, (2) opto-mechanical, and (3) beauty or scattering specifications. Emphasis is placed on the level of tolerancing as it affects the function of the final optical system. Numerous graphs and tables are used to interpret the functional meaning of the specifications.

When the lens designer asks of the manufacturer, "Why didn't you make my lens right?" the stock answer is often another question: "Why didn't you design something I could make?" Now we all know that this is not what we would call making progress. There are a number of lens design factors - we call them rules of thumb - that, from experience, the lens designer imposes on himself, because he knows that violating them produces thunder and lightning from the shop, and thunder and lightning are not what we are trying to produce. This paper deals with some of these constraints and the trade-offs faced by the lens designer in dealing with them.

The seven steps in the fabrication of a lens are discussed and examples are included to indicate the complexity of some of the steps. The types of tooling required are described as well as the accuracy to which some of the steps can be performed. Emphasis is on the practical aspects of manufacture.

Optical fabrication nightmares come in a variety of forms. They are generally caused by "toos": too thin, too thick, too large, too small, too many, too few, etc. In practice I believe many optical fabrication problems could be eliminated - or at least minimized -if there were more communication between the designer and the process engineer, up front. However, since the purpose of this paper is to describe difficult items to fabricate and possible solutions for their fabrication, I will get off my soap-box and proceed to my assigned task.

These remarks are directed to professional lens designers, optical systems engineers and fabricators. You are the thoroughly capable experts who configure and construct optical systems that image superbly over vast areas. Many of the systems contain optical coatings that perform some of the functions shown in Figure 1. They serve to enhance the radiant reflectance of a surface, to reduce the Fresnel losses to low values, to alter the state of polarization of the flux, to divide beams into various channels, or to isolate some part of the electromagnetic spectrum. Figure 2 depicts a procedure that is sometimes used to select coatings. Here they are not specified until after the optical system design is frozen. In essence, coatings are allocated the same level of importance as the shade of paint on the exterior of the instrument. Not infrequently disaster lurks in this approach because the coatings are unattainable or they impact the optical system in some unexpected manner. The strategy shown in Figure 3 is safer. Here, the coating selection is integrated into the optical design. If the coatings are difficult (and, hence, costly) to produce, then compromises are investigated that lessen the overall cost of the system.

Compact telephoto zoom lenses with continuous close focusing have been designed for 35mm photography. These lenses are less complex optically and mechanically than previous design types.

With recent lenses, the focusing range has become increasingly wider, and so we have developed various methods to minimize aberration changes by focusing. As the result, the 500 mm F/8 catadioptric lens, the 300mm F/5.6 telephoto lens, the 90mm F/2.5 portrait/macro lens, the 70-210mm F/3.5-4 tele zoom lens, the 35-80mm F/2.8-3.5 standard zoom lens, etc. have been developed, which enable the camera man to execute conventionally difficult camera work.

The results of investigations about ghost images caused by internal reflections in photographic objectives will be described as follows. (1) Ghost images in photographic objectives are classified according to their generation processes. (2) The analysis method of ghost images based on computer simulation is briefly explained. (3) The comparisons between real ghost images recorded on a photographic film and the results of computer simulation are examined. (4) Relations between objective types and the generation processes of ghost images are discussed about some typical objective types. (5) The methods to reduce ghost images are investigated. Finally, some ideas to reduce ghost images in the designing stage for photographic objectives referring to the above results are proposed.

Image characteristics of 35mm still camera lenses have been measured at the Laboratory of Modern Photography Magazine for more than fifteen years. In an attempt to speed up measurements and quantitative evaluations, a single image frequency was selected for those measurements on a photoelectric contrast-transfer optical bench. Comparisons were made of MTF curves obtained for a group of lenses, and comparisons were also made of subjectively judged photographic color transparencies and enlarged prints of black-and-white negatives taken with these lenses. When the MTFs and the relative rankings were correlated, it was found that an image frequency of 30 lines (or cycles) per millimeter yields good comparative judgements and good discrimination among the lenses tested. Similar correlations were tried for MTF values at 15 and 45 lines per mm. It was observed that better correlation is obtained when picture rankings and measured contrast at 30 lines per mm are used. When combined with resolving power obtained from measurements of fine-grained black-and-white negative film, a consistent and repeatable relative evaluation is achieved.

The use of a comprehensive data sheet to tabulate optical design data, specify tolerances and summarize system assembly, alignment and test requirements is explained.

Airborne map displays have been in use for over 30 years. Over this period they have evolved from directly viewed paper maps to extreme optical systems projecting a combined image of a film based map and a Cathode-Ray-Tube (CRT). In the Horizontal Indicator used in the F13 Hornet, a magnified image of the map is formed on a screen. The screen image and the CRT display are then combined and reimaged within a restrictive space envelope using a high aperture (F/0.8), wide field (75°) inverse telephoto transfer lens. At this second image plane a field lens produces a real exit pupil at the pilot's head position. This system arrangement maximises the image brightness yet minimises the effect of high ambient illumination washing out the display. Greater resolution was required for a vehicle based Map/CRT display. This prevented the adoption of any optical system using intermediate screen images. A conventional system employing a double Gauss relay lens and binocular Erfle eyepieces was adopted.

Characteristics of wide angle (fish-eye) optical systems having fields of view greater than 100 degrees are discussed. Design problems such as pupil aberration and glass selection are discussed. A table of lens characteristics for lenses of 140 to 190 degree fields is presented comparing image heights, lens diameters, focal length, etc. It is demonstrated that such lenses generally obey an image height relationship of y = .015F0 (0 is in degrees)