The structure of the simulated annealing algorithm is presented and its rationale is discussed. A unifying heuristic is then introduced which serves as a guide in the design of all of the sub-components of the algorithm. Simply put this heuristic principle states that at every cycle in the algorithm the occupation density should be kept as close as possible to the equilibrium distribution. This heuristic has been used as a guide to develop novel step generation and temperature control methods intended to improve the efficiency of the simulated annealing algorithm. The resulting algorithm has been used in attempts to locate good solutions for one of the lens design problems associated with this conference viz. the " monochromatic quartet" and a sample of the results is presented. 1 Global optimization in the context oflens design Whatever the context optimization algorithms relate to problems that take the following form: Given some configuration space with coordinates r (x1 . . x) and a merit function written asffr) find the point r whereftr) takes it lowest value. That is find the global minimum. In many cases there is also a set of auxiliary constraints that must be met so the problem statement becomes: Find the global minimum of the merit function within the region defined by E. (r) 0 j 1 2 . . . p and 0 j 1 2 . . . q.

By examining aspherical surface aberration contributions it is shown that aspheres can be used to simplify zoom lens construction and to improve image quality by allowing the designer to selectively correct aberrations at different zoom positions. 1.

Global Optimization (GO) is an area of applied mathemetics that has been active for many years. A large variety of GO algorithms have been constructed in an effort to find a solution to the general GO problem. Some of these have proved to be successful on certain classes of problems. However no general deterministic algorithm exists that can locate the global optimum for every multidimensional problem. Traditionally in the lens design discipline the search for an optimum solution in the design space has been done by optimization methods. The conventional design methods are in principle local search methods and do not pmvide any global information on the design space. As the available computer power increases GO tools can be used also in optical design. A two phase search algorithm based on global optimization techniques is described. In a first phase using a coarse sampling approach the program finds the favorable regions that correspond to potentially promising configurations. In a second phase conventional optimization routines are used to find the best solutions in eh region. Then an optimum solution is determined according to the application at hand. The pro algorithm is analyzed and compared to more conventional design approaches. A further refmement of the algorithm excludes from the systematic search some unfavorable configuration regions through the use of a simple expert system. Search times are further reduced through parallel-processing methods. We believe this approach to lens design represents new initiative towards the determination of the optimum solution in any lens design problem. 1.

The new decade will bring a wide variety of new developments in optical design. Some of these will be in response to new technologies such as binary optics or the use of optical liquids for secondary color correction. Others will include I hope a new appreciation for how the intelligent use of classical ideas can lead to large improvements in the performance of designs.

Forward looking infrared optics defocus with temperature change due to the materials employed. Methods of elimination this defocus - mechanical, electro-mechanical and optical - are discussed and evaluated.

A new automatic lens design method using singular value decomposition (SVD) is proposed. This method enables the designer to reflect his own intention in optimization via the Rank Down Constant introduced in this paper. This characteristic also makes it possible to accelerate the optimization. An example showing the high performance of this method is demonsirated. Some useful applications of S. V. D. are also proposed. 1 .

Polymeric optical materials provide opportunities to utilize design variables not normally available with glass. Recent developments in molding and tooling technology offer many new implementation opportunities. 1.

Spherical aberration in a flat surfaced radial gradient-index lens (a Wood lens) with a parabolic index profile can be corrected by altering the profile to Include higher order terms. However this results in a large amowfl of third order coma. This paper presents an alternative method of aberration correction similar to that used in the catadiopthc Schmidtsystem. A Wood lens with a parabolic profile is used to provide all or most of the optical power. Coma is corrected by stop shifting and Spherical aberration is corrected by placing a powerless Wood lens corrector plate at the stop. 1.

A review of the methods employed to compute the wavefront shape, the point spread function and the optical transfer function in lens evaluation programs is presented. One of the simplest methods to perform numerical calculations of the diffraction performance of optical systems is to divide the aperture in small squares, as suggested by H. H. Hopkins (1957), and then to consider the wavefront in each of these small squares to be flat and perpendicular to the ray direction in that region. This method however, presents some limitations, since the wavefront has to be flat within a fraction of the wavelength in that small square. This might not be the case if the wavefront is either too aberrated, or the defocusing is too large.

Simultaneous alignment and figure testing have been simulated by computer for components of a Cooke triplet and a two-. Petzval telescope using end-to-end wavefront aberration measurement and computer model reverse optimization. Experimental confirmation is discussed. 2.

Purely diffractive doublets are corrected on-axis at two wavelengths. The doublets are then optimized with respect to their design parameters to achieve wideband imaging on-axis. Completed extensions to this design are also described. 2.

A tutorial introduction to the statistical philosophy of establishing a tolerance budget with a step by step description of the process for a sample case. I .

The sensitivity of infrared optical designs to errors in dispersion is explored through the use of examples. The main cause for a high sensitivity to dispersion tolerances in achromatic designs is explained. Conditions for alerting the optical designer to the need for including dispersion tolerances in the design process as well as to suspect raw refractive-index data for an infrared material are provided. 2. OVERVIEW OF CONCEPTS Dispersion tolerances (dV) rarely limit the performance of optical systems used in the visible spectral band. An optical designer might consider dispersion tolerances on the glasses in a visible-band design when the design has a very high-performance specification and/or when there is very little performance margin for tolerances. In infrared (IR) designs dispersion tolerances are even more rarely considered for the materials. It is also unusual to tolerance the bulk refractive index change (index tolerance dn) for an IR design. The need for dispersion tolerances are analyzed in this paper to highlight for the optical designer the situations and motivations for including dispersion tolerances in the evaluations of optical designs especially in the infrared. Achromatic optical systems in the infrared show a wide range of sensitivity to changes in dispersion. The sensitivity is driven by V-number difference (LV) of the materials used to achieve achromatization and to some extent by aperture diameter and f-number. Therefore the sensitivity to change in dispersion of the materials

The SYNOPSYS - expert-systems program XSYS - is a radical departure from traditional methods of lens design. I describe typical problems that were presented to XSYS and show how the program can find useful sometimes unexpected starting points. 1.

Recent advances in zoom systems are discussed and a zoom lens which rivals high performance fixed focal length lenses is described. I .

We describe analysis and compensation of thermal aberration caused in a Nd:YAG laser crystal when it is intensively end-pumped by laser diodes.

A timesaving simplified calculation method by means of the 3rdorder spherical aberration coefficient has been developed to evaluate the root mean square (RMS) wavefront error change of a moisture absorbed aspherical plastic singlet for an optical disk. 1.

Design procedures for simple two- and three-element diffractive telescopes are described. The basic configuration for the two-element design is obtained analytically by solving design equations to set the Seidel aberrations to target values. Computer optimization is used to complete the design of the doublet and triplet telescopes. It is shown that diffraction limited performance can be obtained from these diffractive systems. 1.

A new, coordinate-free version of the exact ray-trace equations for optical systems consisting of conic reflecting, refracting and reference surfaces is presented. These equations are differentiated to obtain closed-form optical sensitivity dyadics. For computation, the sensitivities are evaluated in a single global coordinate frame and combined in linearized ray-trace matrix difference equations that propagate the rays and the sensitivities from element to element. One purpose of this analysis is to create optical models that can be directly integrated with models of the instrument structure and control systems for dynamic simulation.

Hybrid refractive-diffractive elements have the potential to provide chromatic correction with less than half the material content of a conventional doublet. It is shown that the performance of a general hybrid meniscus element can exceed that of the equivalent doublet. Their design and potential advantages are illustrated to good effect in a Petzval objective example. 1.

A novel configuration for a wide angle flat field all reflective unobscured telescope using two figured surfaces which are easily fabricated and aligned is described. DESCRIPTION OF TELESCOPE This paper describes an easily fabricated telescope which forms a high quality image of an extremely wide angle object field on a flat image surface. The telescope uses only reflectors and thus has no chromatic aberrations. An eccentric portion of the rotationally symmetrical field of the telescope is used such that no part of the aperture is obscured. The mirrors are surfsces of revolution described exclusively as flats spheres or conic sections all of which are easily tested and verified in manufacwre using well-known conventional null tests. Each mirror shares a common axis of rotational symmetry facilitating telescope alignment. One mirror is used twice providing the function of a secondary and tertiary mirror while eliminating the need to fabricate and align a separate tertiary mirror. The current design evolved from a form pcpularly known as the WALRUS'' a three mirr rotationally symmetric flat field unobscured design arranged in a " Z" configuration with an aperture stop between the secondary and tertiary mirrors (figure 1). In the WALRUS patent the two concave mirrors are specified as an effipsoid (secondary mirror) and a sphere (tertiary mirror) while the convex (primary) mirror is a sphere. The base curvatures of the three powered mirrors are chosen such

Optical components such as lenses beamsplitters etc. can be fabricated and integrated on single substrates by using photolithographic techniques. This allows to build integrated free-space optical systems for a variety of applications without the need for costly mechanical alignment. I.

The wavefront variance merit function is constructed with aberration orders identified and partitioned. The partitioned merit function topographies of three optical systems are examined. 1. INTRODUCFION The study of the behavior of individual wavefront aberration coefficients with respect to optical system parameters has long been successfully employed to gain insight into the properties of optical systems. However for many optical systems it is more appropriate to examine the wavefront aberrations collectively rather than individually. New insight into the imaging characteristics of optical systems may be obtained by using the individual wavefront aberration coefficients to construct the average wavefront variance function. This can be done in such a way that the merit function may be separated into partitions which are associated with a single aberration order. The partitions are a small number of image quality indicators that may be examined individually. Each indicator ifiustrates the behavior of the optical system at a particular aberration order. 2. FORMULATION OF THE MERIT FUNCTION The wavefront variance merit function is defined by K w2 )ftuld '' (1) where the angle brackets denote averaging over the pupil or field as indicated in the equation and W is the wavefront aberration function as a function of pupil position p. and field position H. For axially symmetric optical systems the aberration coefficients are introduced by writing the wavefront aberration function as a Taylor series expansion in p and

Designers are often asked to optimize the modulation transfer function (MiT) of a particular lens at specific fields and spatial frequencies. Use of a merit function related to mean square spot size or wave aberration to achieve these goals frequently requires considerable designer intervention. We describe an algorithm whereby diffraction MTF is optimized directly. The algorithm is efficient enough (i. e. on the order of five times the run time for classical techniques) to be used as a practical design tool. To illustrate use of the algorithm a previously designed night vision objective lens is reoptimized with the goal of increasing the MTF at a particular spatial frequency thus increasing the modulation margin allowed for tolerancing. Significant improvements in MTF and depth of focus are achieved with minimal designer effort and reasonable computation times. 1 .

An all-reflective unobscured flat-field low-distortion telecentric optical design has been developed for non-scanning reduction soft x-ray lithography application. 1. 0

An exact raytrace (Snell''s law refraction) of the discontinuous surfaces of kinoforms (surface relief lenses) can explain their optical performance at different wavelengths without diffraction. A phase-based merit function generated by raytracing can be used to design and optimize systems containing both kinoform and conventional optical surfaces.

The practical use of Generalized Simulated Annealing (GSA) optimization is explored to determine additional benefits beyond the global minima location capability. In particular a means of using the strengths of both GSA and Damped Least Squares (DLS) optimization techniques is examined in order to increase the amount of usable information and to enhance usefulness in a microcomputer environment. 1. BACKGROUND The optimization ofthe performanceofan opticalsystem is most often performed bydamped leastsquares (DLS) techniques. This methodand its variants has proven to beeffective for the reduction ofsystem merit functions overa broad range ofproblem types with quite rapid convergence rates. The effectiveness of DLS optimization will often depend on the quality of the starting point the construction of the merit function and the proximity of the starting point to local minima ofthe merit function. The characteristic of the DLS technique to compute an optimum solution to minimize the merit function based on the instantaneous first and in some cases second partial derivatives gives rise to the technique''s strongest and weakest points. The strongest point is its rapid convergence while the weakest point is the inability to escape local minima in order to locate a superior local minima or the global minima. The strength of rapid convergencewas important when the majority oflens design programs where on a mainframe computers were processing time is costly. The inability to escape local minima weakness was most often overcome

The design for a telescope is presented which calls for small optical components in an all-reflective wide-field-of-view phased-array configuration. Attention is given to the geometric phasing conditions and other phasing requirements for the phased-array design, and analytical expressions are set forth for the paraxial relations and distortion. The design of the subtelescopes is based on a three-mirror design, and particular attention is given to the problem of subtelescope field curvature. It is shown that several configurations provide the required corrections for the field curvature and the stigmatic aberrations. Subtelescope aberrations such as coma can affect optical phasing, which indicates that a tolerance analysis conducted aberration-by-aberration is necessary for developing the all-reflective configuration.

Considering the real pupil curvatures the new exact sine condition in the presence of spherical aberration is derived and its validity is confirmed by ray traces. This new exact sine condition is useful for lens designing and lens evaluation. 1.

A telescope is described that can be used for high-power-laser optical communication links between satellites. An all-refractive design is selected because it is preferred for the application, and the performance specifications are listed for the novel technologies associated with implementation. The telescope is intended to measure 150 x 150 x 350 mm and have a 100/8-mm outside/inside diam ratio and a total FOV ratio of 1.0/12.5 deg exterior/interior. Detailed descriptions are given for telescope components including the collimator, eye piece, scanners, and the pupil imager, and the resulting values for wave-aberration RMS and distortion are discussed. The resulting telescope is found to be about twice as good as the specifications require allowing suitable tolerances for the manufacturing of the telescope.

Some effective usage of the radial GRIN lens in camera zoom systems are presented and lens design examples are shown. Also, effective Abbe number of a cemented GRIN lens is discussed and it is shown that a GRIN lens with uncomon dispersion can be replaced by the cemented GRIN lens with common disparsion.

This paper examines some derivations and applications related to quadric surfaces. The classic lens design conicoids (planes spheres ellipsoids paraboloids and hyperboloids) are special cases of quadric surfaces. Facility with quadric surfaces has applications in optical engineering and analysis aspheric shape specification and reduction of coordinate measuring machine (CMM) data. A numeric example supports all derivations and applications. 1.

A modified differential ray trace method is used to calculate chromatic aberrations. This results in a higher order correction to Conrady''s formula. 1.

This telescope is exactly one power and has an objective, an erecting relay and an eyepiece. As can be seen in the diagram the direction of any object seen at the Entrance Pupil has the exact same direction at the Exit Pupil over the whole of the field of view assuming that the system.is completely corrected for distortion. If this is in fact the case then the direction of any object as seen at the Exit Pupil is constant as the axis of the telescope is rotated. This is the pure definition of a CONSTANT DEVIATION DEVICE.

e describe the various principles used in our optirnizatic'i programs which were developped in a more consequent manner ttlaIl it as done for other known proqramns. The iterative optirnization process in lens design consists ot tio main parts: The use 01: the so called Linear Model and the dynamic adaption to the actual conditions. Corresponding to that the discussion in this paper is built up.

Ray-tracing through Progressive Addition Lenses (PAL) has been performed. PAL is a deep non rotationally symmetric asp1ric lens used for the compensation of presbyopia. PAL and its mathematical model are presented. The special features of the ray-tracing program due to the model of the lens plus eye system are detailed. Typical results are presented showing in particular that computing conditions of contour-plots of power and astigmatism must be very strict and that coma must be taken into account for precise measurements of PAL. 1.

This article addresses the impact of nonlinearity on the problem of designing lenses and the connection of Newton''s method with ordinary differential equations (ODE''s) and describes a method for improving its convergence inspired by the total least squares problem. A possible subtitle for this article might be " Why Haven''t All Possible Lenses Been Designed Already?" I first heard that question asked by Dr. Kingslake when he visited Itek over 15 years ago when we were demonstrating our computer lens design capabilities to him. It''s a question that comes to mind when one contemplates that there are more designers around today than back in precomputer times each of today''s designers can do more computation in a couple of days than a precomputer designer could do in a lifetime and very many different lens forms were already discovered by the time the computer came into use. So one might begin to wonder how many lenses are there? Or more in he spirit of this article how many solutions are there to the nonlinear equation of the lens design problem? In response to this question consider Fig. 1. This is a montage of sixelement lens forms gleaned from several books on the history of the photographic objective about which Dr. Kingslake has written extensively1. The lens forms shown are all from precomputer times and it is evident that there were a large number

T 1st order optical design are classified into different grups, t fonnulas and experiences are transferred into equation and production rules and input to our own design expert system.

As we know, wave aberration is the difference between the ideal wave and the real wave. One of the important characteristics of ordinary optical system images is the condition of equal optical path distance. If all light from a point A passing through the optical system focuses at A', we can say that point A' is the ideal image of object point A and that the optical path distances of all rays from A to A' are the same. When there is aberration in the optical system, wave aberration is the difference of geometric path distances multiplied by the index. In figure 1 wave front P from point B passing through the optical system forms a new wave surface pp'. Generally we use the intersection point ' of the principal ray and the ideal imaginary surface as the center of the ideal reference spherical surface P"P" so P"P is the wave aberration

Often it is not possible to fix pairs of infrared refractive materials in the γv-v diagram to design achromatic doublets with focal distance thermal change, matching the expansion of the focal plane supporting structure. The problem can be solved with three refractive materials if they form a finite area triangle in the γV-V diagram. We derive formulas for the calculation of the power of the elements that include both the doublet and the triplet solutions.

Aspherical projection lens for large screen television has been designed with a peW idea. The designing process based on this idea is analysed. :L

T types of zoan lens with aspherical surfaces for camcorder has been succssfu11y design1 . The first type has single aspherical glass lens , axx realizes sizeruction of 30% than cxxiventicxal zocxn lens. Ar the secori type consists of light-weight plastic lenses with aspherical surface in order to ru weight of zoan lens.

Neural Networks are part of a revived technology which has received a lot of hype in recent years. As is apt to happen in any hyped technology, jargon and predictions make its assimilation and application difficult. Nevertheless, Neural Networks have found use in a number of areas, working on non-trivial and non-contrived problems. For example, one net has been trained to "read", translating English text into phoneme sequences. Other applications of Neural Networks include data base manipulation and the solving of routing and classification types of optimization problems. It was their use in optimization that got me involved with Neural Networks. As it turned out, "optimization" used in this context was somewhat misleading, because while some network configurations could indeed solve certain kinds of optimization problems, the configuring or "training" of a Neural Network itself is an optimization problem, and most of the literature which talked about Neural Nets and optimization in the same breath did not speak to my goal of using Neural Nets to help solve lens optimization problems. I did eventually apply Neural Network to lens optimization, and I will touch on those results. The application of Neural Nets to the problem of lens selection was much more successful, and those results will dominate this paper.

A static computer-aided method used to align a visible wavelength grazing incidence ring resonator for a free-electron laser (FEL) is presented with a brief description of the hardware, results of numerical simulations, and actual initial data. A computer-aided alignment scheme is particularly useful for this application due to the optical system complexity and the need for precise results. Although the system hardware has not yet been perfected, initial data shows that this technique works and presents a viable solution to this alignment problem. Utilizing information from an interferogram taken at a single axial field point and information about the chief ray of the optical system, it is shown that it is possible to converge to an alignment solution using a constrained damped least squares optimization in a commercially available lens design package.

In this paper we propose a nonlinear model which can be considered as a mathematical programming problem with linear and quadratic constraints to design the optimal tolerance of a lens system. Owing to the negligence of the nonlinear property of a optimized lens system the existing studies on the tolerance design are unable to solve the optimal tolerance design problem. For realizing this purpose i. e. maximizing the tolerance of the lens system we propose a nonlinear model which can be considered as a mathematical programming problem with linear and quadratic constraints to design the optimal tolerance of a lens system. Assuming X (x1 . . . x 2'' EJ and ''F(X) are parameters of a lens system manufacturing error for each parameter and merit function of the image quality respectively. The following statements are supposed adequately. (A1) The probability density of k N(o that is Ek is normal distribution with zero mean and variance a. (A2) The difference of the merit function between the real system and the design system can be approximately expressed by quadratic expression. 4(X+cr)(X) c3a: E1 (1) where V () and H () (A3) The purpose of the optimal tolerance design is to determine the variances (a . . . a) of (E1 . . . E and satisfy the following conditions: (i) D(M) (ii) M(L4) m (2) (iii) E po as great as possible

A new method is proposed to calculate the Strehi Definition for optical systems lacking rotational symmetry. The Strehi Definition(S. D) is one of the commonly used criterion for evaluating the quality of an optical system especially for the microscopic objectives. It is will known that the S. D is defined as follows S. D 7-2 J1J1exp[-27riW(x y)dxdy I 2 (1) Where w(x y) is wave aberrations and (x y) is the coordinate of the pupil plane. For a high quality optical system S. D can be expressed as S. D 1 (2)2[W2(x W(x y) 2j (2) In order to calculate the S. D of the decentral optical system precisely both lateral and longitudinal defocus should be considered simultaneously. The corresponding aberration coefficients are C C01 (along y-direction) and C0 (along x-direction). Owing to the optical systems lacking relational symmetry the asymmetrical aberrations central astigmatism C21 and central coma C should be added in the wave aberration function i. e. the wave aberration for the system lacking symmetry is W(x y) C(x+ y) + C(x + y)2 + C(x + y)3 + C(x + + C02y2+ C22(x2 +y)y + C42(x+?)Y + C62(x+?)3? + Cy4 + C24(x2 + y)y4 + C + y)2y4 + C(x2 + + C41(x2 + y2)2y + C61(x2 + y)3y + Cd + C + y2)y3 +C43(x2+y2)+C01y+C1 x+Cx2+C1 (x2+?)x (3) After tedious but straightforward integral calculation equation

The use of electronic computers in optical design and analysis is well established. In fact, optical calculations were among the first applications of the first computers that were built in the 40's, and Donald Feder, starting in 1951 [1], proved that the use of these machines went far beyond removing the tediousness of laborious calculations and offered new dimensions in understanding the actual design process [2]. By today's standards, of course, the equipment which had such a remarkable impact at its time, was primitive and slow. A modern inexpensive programmable calculator easily outperforms the any computers in both speed and memory capacity, not to mention accuracy and reliability. This also implies, that today, even computers at the low end of the cost and performance scale can be turned into remarkably powerful tools for optical design and analysis. This has been demonstrated for the class of programmable calculators [3] but applies, of course, even more convincingly to the present generation of low-cost personal computers, which are typically based on 16- or 32-bit processors, and where prices start well below $ 1000.-. Any degree of higher performance is available at steadily increased prices, so that there appears to be a fit for each requirement.

Superachromatic designs of lens systems utilizing two optical materials are described. Design examples comprising an infrared doublet a hybrid refractive-diffractive lens catadioptric systems and Gauss objectives are presented. The performance evaluations of these designs are also shown. 1.

The baseline multiaperture echelle spectrometer for the Atmospheric IR Sounder (AIRS) is described in terms of design and applications. The functional requirements for the optical design are set forth including the 1-K measurement goal, the 3.4-15.4 spectral bandpass, and the full global coverage twice daily. The multiaperture spectrometer is compared to the cross-dispersed spectrometer, and the multiaperture model is found to permit specific adjustments to the signal-to-noise ratio. The optical design of the spectrometer is described in terms of the focal-plane constraints, the multiaperture pupil-imaging relay, the spectrometer collimator, and the grating format and efficiency. The multiaperture design is found to have a good spectral-response function, and a 1.2 percent signal change is noted for a 95-percent unpolarized scene. The AIRS instrument is illustrated in its deployment configuration and is concluded to be capable of fulfilling the performance requirements.

A problem can arise when a set of optics must be aligned but intrinsic surface errors dominate alignment wavefront errors. Aligning diamond-turned optics interferometrically at visible wavelengths is one such example. Diamond-turned optics can exhibit a high-spatialfrequency surface ripple from the machining process, which, in many cases, can render an interferogram unintelligible to the point that even serious alignment errors cannot be detected. In an alignment demonstration conducted last year this problem was encountered head on and two techniques were applied to extract meaningful wavefront data. The first relied on spatial filtering of the return wavefront to smooth out the effects of high-slope surface errors. This approach showed potential in that it is a simple method that can be easily applied. The second approach used a new software algorithm, available as part of the Zygo Mark lV phase measuring interferometer, where regions of fringe discontinuities are discarded and the resultant piece-wise phase map is reconstructed as a continuous wavefront. Using this latter approach, we were able to precisely align a three-mirror telescope comprised of diamondturned mirrors and used in a double-pass configuration. The approaches to be described are applicable to the alignment of infrared and visible sensors and metrology of single surfaces.

The concentric lenses symmetrical about the stop constitute the first order Double-Gauss. Third order aberrations lens parameters relationship and optimization results are discussed. 1 .

Optics for head-up displays (HUDs) with two combiners are reviewed with respect to aberration correction and the optimization of the azimuth field. The impetus for utilizing two combiners is discussed by comparison with conventional HUD designs, and the requirements for aberration correction are listed. The use of a CRT that incorporates the P-53 phosphor is shown to increase the azimuth instantaneous FOV (IFOV), and HUDs with dual combiners enhance the elevation IFOV. A dual-combiner HUD is shown to require a P-1 phosphor CRT, improved color correction, a reduced Petzval sum, and aberration control that is extended over more of the pupil as compared to single-combiner HUDs. The P-53 phosphor can be used to filter spectral sidebands and thereby permit the use of a lens that is not capable of good chromatic correction as well as enhance the azimuth IFOV without changing the module depth.

The design process for an all-reflective zoom telescope is presented. Special consideration is given to the development of the starting configuration and the subsequent optimization process. The non-traditional optimization route utilized as a result of the unusual pupil characteristics of such an all-reflective zoom system is examined. Results of the design are presented.

For the past year or so, we have been exploring a technique for finding potential solutions of what might be called the generalized imaging problem. The underlying hypothesis is that any basic imaging problem can be solved, if at all, by using not more than two generic lenses. A generic lens can comprise a number of elements to affect aberration control, distribute power, etc. Application of this technique yields a plot of regions where potential solution may exist (conversely, regions where solution do not exist). Typically, the abscissa and ordinate are the powers of the two lenses. Once a "power pair" is chosen for evaluation, the spatial positions of the lenses are readily calculated. This technique will be discussed in detail in an upcoming paper. After some success was realized in employing the method to fixed geometries, we investigated its application to finding possible regions of solutions for problems involving zoom lenses. Although the same technique is employed to find potential solutions, presentation of the information for use by the designer is significantly more involved than when dealing with the fixed geometry case. Various parametric constraints can be imposed to appropriately limit solution space. Further discussion of this subject will be contained in the aforementioned paper.

The proposed procedure works on the basis of a merit function of the 4th degree and is used for the optimization of the Seidel image errors of a system composed of thin lenses by means of lens bendings. Between the thin lenses air spaces may exist. All solutions which lie within the permissible intervals of bending are taken into consideration when the sums and the corresponding surface contributions of the Seidel image errors are situated below a limit that may be selected at will. The search for a relative minimum is successful too if a relative maximum lies on the path to the relative minimum. The procedure is especially suitable when in a given system thin lenses are preferred for reasons of weight material price transmission or broadband colour correction. 1. Procedure Lens bending means equal curvature change at each surface of a lens. The advantage of bending lenses of thickness zero is that the angles and heights of all paraxial rays the focal length the axial color the lateral color and the Petzvalsum of the lens system remain constant. The sums of the Seidel image errors are constant linear or square functions of the lens bendings. The merit function is the sum of the squared Seidel sums. In the general case of in independent lens bendings the merit function is a function of 4th degree of in independent variables. These

For a given homogeneous optical syswn, potential axial gradient configurations are identified.. A sysrematic approach is propose.cl for localing the most useful axial gradient configuration that reduces the homogeneous syswn's Seidel aberrations. The design of a linear axial gradient Coote aiplet using the proposed method is discussed.

Focusing of illumination bundles by lens systems for a wide variety of sources such as optical fibers and light emitting diodes is analyzed with modified Gaussian beam equations and spot diagrams. 1. 0

Waveguide grating couplers have important applications to optical data storage. Focusing grating couplers eliminate the need for focusing optics and can be used in both read and write modes. It is convenient to fabricate the gratings at short visible wavelengths although they are used at laser diode radiation wavelengths in the near infrared to visible range. This paper discusses a design technique for introducing compensating aberrations during fabrication which account for the wavelength change. A sample design is presented and the tolerance limits on the alignment parameters are derived. 2. 0

Theoretical and practical aspects are examined that relate to the development of multiple-array telescope systems that offer aspheric correction with the fewest components. The paper compares two designs and investigates the effects of different relative apertures for the primary mirror and different system lengths on the symmetry and order of aberrations generated by the eccentric aspheric. The first approach involves the use of Mersenne collecting telescopes, and the second configuration is based on four-mirror telescopes. It is shown that the use of special surfaces for decentered aspheric correction is limited and that pupil matching is important in the shared-symmetry array systems. Three- and five-mirror designs are analyzed and found to be diffraction-limited for a field of up to 60 arcmin, and reference is made to the complex calculations for determining the decentered asphericity.

Due to an apparent conflict between transparency and dispersion the near ultra violet transmission of achromatic lenses is strongly dependant on glass choice. The design of achromats for this waveband is described and the choice of optical glass is reviewed in detail. Designs are given. 1.

Advantages and shortcomings of the use of HOE for imaging systems are demonstrated by examples: high aperture 1:1 and 5:1 imaging systems for the wavelength 193 nm to be used for lithography and an innovative achromatic holographic doublet. 1.

1 . The results of an industry-wide survey on the cost impact of different tolerance levels will be presented. This is in effect a couprehensive update of the now lOyear old John Plununer table (SPIE Vol. 181 P. 92) plus additional new material relating to the overall subject The survey forms were sent to nearly 100 optics manufacturers in the U. S. and Canada. The survey results indicate the relative cost impact of requiring increasingly tighter tolerances from relatively loose tolerances (such as the impact of going from inches in diameter to 0. 00008 in diameter). The parameters to be included are: . dn . sn . centerthickness thickness ratio fringes of power Iirregulazity surface finish number of elements on a block Knoop hardness edge thickness (wedge) coating specifications radius 1dianterratio In addition a series of interesting and revealing questions were posed to manufacturers such as " what are your three BIGGEST gripes with lens designers among others. The results of this survey will be summarized. 2. Lens designers are often faced with many cost driving tradeoffs and decisions. A discussion of some of these tradeoffs in a clear and easy to understand fashion will also be presented. Topics to be included are: small air spaces -cennted versus air spaced doublets glass selection tradeoffs relative to availability and other properties

By combining achromatic and super achromatic lens groups we may achieve improved tertiary spectrum residuals in apochromatic systems. The application of this technique is reported. 1.

We show that when designers and fabricators understand each other''s art there are ways to combine their techniques to achieve the best results with the minimum difficulty. We share some problems that we have encountered and sometimes caused ourselves in hopes of helping the reader avoid the same pitfalls. 1 .

BinarY optical elements are investigated and evaluated in a Schmidt camera system. Design considerations including approach optimization efficiency scatter fabrication and cost are addressed. Additional applications for binary optics are also d 2.

The higher speeds and lower costs of current workstations make feasible Monte-Carlo performance simulations of manufacturing processes for complex optical systems. 1.

Originally conceived at a time whenlens design was carried out on Marchand calculators SYNOPSYS was one ofthe earliest and is now one of the largest design programs. SYNOPSYS was for many years the personal design tool ofits author. Since it was then the only tool available itwas necessary to develop a comprehensive set of capabilities requiring much innovation and experimentation.

The OSLO series of optical design programs are intended to be "open" programs that can be easily adapted to a large variety of optical design tasks. Some techniques and tradeoffs used during the development of the programs will be described.

Using a versatile command line interface one ASAP module (RABET) can simulate virtually any optical effect in any imaginable 3D geometry. Another module (GALOP) is a less powerful but easier-to-use layout and optimization code with an entirely graphical interface. Issues driving the development of their features and capabilities are discussed. 1. 0

This paper is part of a session that is aimed at briefly describing some of today''s optical design software packages with emphasis on the program''s philosophy and technology. CODE V is the ongoing result of a development process that began in the 1960''s it is now the result of many people''s efforts. This paper summarizes the roots of the program some of its history dominant philosophies and technologies that have contributed to its usefulness and some that drive its continued development. ROOTS OF CODE V Conceived in the early 60''s This was at a time when there was skepticism that " automatic design" could design lenses equal or better than " hand" methods. The concepts underlying CODE V and its predecessors were based on ten years of experience and exposure to the problems of a group of lens designers in a design-for-manufacture environment. The basic challenge was to show that lens design could be done better easier and faster by high quality computer-assisted design tools. The earliest development was for our own use as an engineering services organization -an in-house tool for custom design. As a tool it had to make us efficient in providing lens design and engineering services as a self-sustaining business. PHILOSOPHY OF OVTIM!ZATION IN CODE V Error function formation Based on experience as a designer we felt very strongly that there should be a clear separation of

The optics industry has not followed the lead of the machining and electronics industries in applying advances in computer aided engineering (CAE), computer assisted manufacturing (CAM), automation or quality management techniques. Automation based on computer integrated manufacturing (CIM) and flexible machining systems (FMS) has been widely implemented in these industries. Optics continues to rely on standalone equipment that preserves the highly skilled, labor intensive optical fabrication systems developed in the 1940's. This paper describes development initiatives at the Center for Optics Manufacturing that will create computer integrated manufacturing technology and support processes for the optical industry.

The need to achieve control of specific aberrations and to investigate the aberrational properties of lens systems has led to the development of an interactive design tool based on multi-dimensional quadratic extrapolation. A quadratic approximation to the non-linearly varying aberrations allows the step length of this differential correction technique to be extended and the underlying relationships between goups of constructional parameters and aberrations are revealed. Examples are given.

This paper considers a novel approach to color correction by a compound lens group with an adjacent single thin aplanat, which introduces chromatic magnification.

Small fast lenslet arrays have been fabricated in GaP and lnP substrates. These semiconductors have high refractive indices (n3) and are transparent at A. 0. 55 p. m and 0. 93 jim respectively. Diffractioniimited performance has been obtained from small-diameter (''60-130 pin) f/1 refractive lenslet arrays fabricated by the mass transport process. These lenslets are ideal for use with diode laser sources and can be readily included in monolithic integration schemes. An example of each of these applications is presented. Binary diffractive lenslets fabricated in lnP are also described. The need for small fast high quality lenslets has become apparent over the last few years with the development of diode laser sources and in particular diode laser arrays. Since diode lasers typically have a beam divergence of several tens of degrees collimating the output beams generally leads to greatly improved far-field patterns. The preferred substrate for lenslet fabrication has been fused silica on which both diffractive1 and refractive2 lenslets have been investigated with good results. However the small index of refraction of quartz (n . 5) can present problems with high aspect ratio features such as the outer rings of Fresnel zone plates. In this paper we describe the fabrication and performance of f/I microlenses fabricated on semiconductors where n" 3. Binary Fresnel lenslets were fabricated in lnP by wet etching while InP and GaP were used to fabricate refractive lenslets

Illuminance at a detector is calculated by means of raytracing. A method of synthesis already known from related fields - is demonstrated: the Edge Ray Principle. 1. 1 Concepts of photometry 1. ANALYSIS We have to recall the basic physical concepts of photometry namely luminance light intensity light flux and illuminance [21 The definition of a Lambertian Source is given here again due to its fundamental importance: we call a radiating surface a Lambertian Source its luminance is independent of surface coordinates and viewing angle. An equivalent formulation is: the source obeys ''Lamberts cosine law of intensity'' for any surface element dA and any angle B dl L * cos B * dA (1) L luminance dA surface element at source I intensity B angle between surface normal and viewing direction The Lambertian Source has several interesting attributes for instance that we cannot judge its position or shape by just looking at it. A more precise formulation of this phenomenon can be stated as following: 1. 2 Pseudo luminance of the hole Let D be some area on a detector H be a hole in an opaque screen (both not necessarily small) and Si and S2 be lambertian radiating surfaces (alternatively existing) then the following theorem holds: SPIE Vol. 1354 International Lens Design Conference (1990) / 617 y D (p y H (p Fig. i

This paper describes a method by which designs for high power lenses and lenses constrained to very short spaces can be evaluated or started. First the fundamentally highest power refractive lens is presented. Then the paraxial properties of this lens are fully described followed by a brief third order analysis. 1.

This study of the triplet shows that there may be at least 1 1 local minima even for this simple case. Reasons for the existence of these minima are discussed and ways in which poor local mimima can be avoided are considered. 1.

A technique for optimizing the real part of the opticai transfer function (OTF) is described with an example illustrating the results to be obtained. 1.

Techniques for representing multi-configuration lenses in computer software are described with particular reference to the design of athermalized lenses. 1.

The availability and quality of the existing data on popular materials are reviewed. The needs and the possibilities for meeting these needs are then discussed. I .

Inthgued by the multiplicity of solutions of a triplet lens David Shafer devised a problem to seek out the best solution for a four lens design. To simplify things all elements were made of BK7 glass so that the lens would work only at a single wavelength. This is a report on the response of members of the lens design community to this intriguing problem. After a profile of the participants the form of the best solutions will be discussed. The prescriptions for the lenses with evaluated spot sizes below 3 im are given. 1.

It is shown that by using a simple convention for surface orientation the valid intersection is given by the traditional ray-tracing formulae under all conditions. I.

The motivation for this work was the need for an unusual optical system satisfying unusual design requirements. In conventional parlance it was to be a telescope attachment the features of which resemble those of an eyepiece and a camera assessory. It was to operate over a wide range of infrared wave lengths split into three disjoint wave length domains each acted upon by a different optical subsystem forming images on three distinctly different detector arrays. These three subsystems were to operate simultaneously. In addition. the overa I 1 system was to have two distinct modes of operation. By switching a minimal number of optical elements the power of the overall system was to be changed by a factor of four.

A physical optics code provides the optical designer a means to develop many types of systems which can not be treated properly by geometrical optics. Physical optics must consider a much broader range of effects and components and computational times are longer but the sophistication of physical optics software is now comparable to that of geometrical optics programs and allow the optical designer to work on systems that go beyond " classical" geometrical optics. 1.

General optimization has been added to a physical optics code allowing semi-automatic design similar to geometrical design codes but including more varied capabilities. 1.

The International Lens Design Conference (ILDC) has traditionally included one or more lens design problems for members of the design community to consider. 1''2''3 This year there are two: the Monochromatic QUartet and the NonLens. The problems are intended to be enjoyable and instructive for participants conference attendees and even for readers of these Proceedings! The NonLens was suggested by Professor Adriaan Waither of Worcester Polytechnic Institote. It is an unusual lens that requires the participants to determine the design form and optimization method that best satisfies the requirements. Furthermore it is of theoretical interest explained by Waither later in this paper. Eighteen individuals submitted twenty solutions. They are all included here along with several simple solutions that were generated for comparison. 1. The problem: A NonLens The following statement of the NonLens problem was distributed with the ILDC Call for Papers: 2. Background of the NonLens Prof. Walther sent a history of his interest in NonLenses which follows (slightly paraphrased) " As a graduate swdent in Deift I worked as a research assistant for A. C. S. van Heel. He was the man who. . . had revived the art of lens design in Holland. He played an important role in the creation of Oldelft company and had trained their original design staff. He was also a superb teher one of the old gentlemen of science. During and after the

The design of two broadband hybrid diffrve-refrve optical systems a landscape type lens and a Schmidt telescope was investigated. The systems were achromatized using the large negative dispersion characteristic of kinoforms. In the scalar wave regime these strucwres can approach 100 efficiency for one object point and wavelength but efficiency inevitably decreases when these parameters change. We evaluated polychromatic image quality taking diffraction efficiency into account by constructing properly weighted geometric point spread functions from several diffracted orders and calculating modulation transfer functions. The MTFs of the hybrid achmmats were improved at high spatial frequencies but reduced at low frequencies because inefficiency caused diffrtion into non-design ders. 2.

A few unusual concentric optical configurations that are evolved from Dyson and Offner systems are presented for possible adaptation as spectrographs. CONTENT Two sufficient conditions for good unit-magnification imaging are that the optical system be concentric and retroreflecting. These conditions are satisfied by both the Dyson and the Of fner2 systems. Many years ago I speculated3 and later verified4 that the Dyson system might make a good concavegrating spectrograph. The verification required modifying the paraxial design to satisfy telecentricity. That modification considered in terms of an invariance to rocking led to recognition of the aforementioned two conditions. Furthermore the modification can be fulfilled over the entire field by including a Schmidt corrector. Thusly the Dyson and Offner systems are shown in figure 1. The Of fner version now clearly appears as a Schmidt retroreflecting telescope whose image and pupil planes have been interchanged. The rationale behind exploring these concepts is to increase the information handling capabilities of spectrographs. Fiber optic communication networks offer one application where the diffraction-limited stiginatic quality of the Dyson system could be quite useful for wavelength-division multiplexing and demultiplexing. One spectrograph would have adequate field to serve a large network. Another application would be to gain throughput for codedaperture spectroscopy5 or mock interferometry5 at low-light-levels and in the ultraviolet. However the thoroughness of the spectrographic verification for the Dyson system still leaves something to be desired. Does

Optical systems are extensively utilized by industry government and military organizations. The conceptual design engineering design fabrication and testing of these systems presently requires significant time typically on the order of 3-5 years. The Knowledge-Based Environment for Optical System Design (KB-OSD) Program has as its principal objectives the development of a methodology and tool(s) that will make a notable reduction in the development time of optical system projects reduce technical risk and overall cost. KB-OSD can be considered as a computer-based optical design associate for system engineers and design engineers. By utilizing artificial intelligence technology coupled with extensive design/evaluation computer application programs and knowledge bases the KB-OSD will provide the user with assistance and guidance to accomplish such activities as (i) develop system level and hardware level requirements from mission requirements (ii) formulate conceptual designs (iii) construct a statement of work for an RFP (iv) develop engineering level designs (v) evaluate an existing design and (vi) explore the sensitivity of a system to changing scenarios. The KB-OSD comprises a variety of computer platforms including a Stardent Titan supercomputer numerous design programs (lens design coating design thermal materials structural atmospherics etc. ) data bases and heuristic knowledge bases. An important element of the KB-OSD Program is the inclusion of the knowledge of individual experts in various areas of optics and optical system engineering. This knowledge is obtained by KB-OSD knowledge engineers performing