The pseudo-eikonal is obtained by inserting in the sum of component eikonals of an optical system the linear approximations of the coordinates of the intermediate spaces as functions of the coordinates of the object and image space. The pseudo-eikonal can be expressed in the component data more easily then the exact system eikonal. Nevertheless it can be used in the same way as the exact eikonal for the optimization of optical systems. The use of eikonals in the optimization of optical systems was described by Simons in his doctoral dissertation (Delft, Technical University, 1969). An additional advantage of the pseudo-eikonal is that it allows simultaneous correction of third and higher order aberrations. We evaluated the pseudo-eikonal after each step of an existing optimization program. The optimum of a merit function that involves a comparison of the pseudo-eikonal with an ideal eikonal is different from the optimum found by using the spot diameter as a merit function. This difference correlates with the degree of "strain" inherent in the design considered; a measure for the degree of strain is the difference between the pseudo-eikonal and the exact eikonal.
Differential ray tracing is performed here in the general case. For that it is very suitable to use a set of orthogonal vectors; that holds especially when non-rotationally symmetric systems are considered too. The use of orthogonal vectors allows to eliminate the components in direction of the optical axis easily. So, distinct formulae are derived which are more simple than those in earlier publications. It is especially advantageous to split up differential ray tracing into three steps. The resulting formulae are as simple as possible and therefore easy to program and to apply. The following applications are of main interest: a) Evaluation of imaging performance; b) Analysis of tolerance sets for design data; c) Exact determination of the derivatives of aberrations relative to the design data; the important application is given in optimization techniques. Furthermore the differential ray tracing formulae allow to derive imaging properties of optical systems. In this way relations between aperture and field variations may be deduced.
Applications of differential ray tracing are shown. Special attention is focussed on aspheric surfaces. Differential ray tracing formulae are an efficient tool to calculate the changes of imaging errors in an easy, fast, and accurate way. These changes are caused by the following parameters: - initial ray data variation in the object space - design data variation of the optical system. By varying the initial ray data in the object space additional information about the in-fluence of aperture and field angle is given. Aberrations of higher order which must be taken into account in aspheric systems can be seen as well. Speed and accuracy of differential ray tracing prefer this method to calculate the solu-tion matrix which is needed for optimation. Here the system data of the optical system are varied. Actually finite differences are still used nowadays. By variations of the design data information is obtained about the tolerance sensitivity of the system. Special atten-tion is directed to the aspheric coefficients. Here especially spherical surfaces are considered, too, because they may become aspheric by manufacturing errors.
Zoom lens design is complicated. The application of rapid and disciplined procedures in nested iterative loops, with the designer interactively included is the best chance we have to be creative in this situation. This feature of the design process gives us the opportunity to use small computers. The complete zoom lens design procedure is presented from this standpoint with details of many important procedures.
An Expert System has been developed which will undertake the preliminary design of optical systems. During the preliminary design the optical designer considers the specification of an optical system and derives parameters such as lens type, focal length, etc. These parameters are then converted into power group layouts with curvatures, thicknesses, etc ready for optimisation by lens design software. The preliminary design will have been arrived at by utilising previous design knowledge and 'rules of thumb' acquired through experience. It is this stage of the design process which has been implemented by an expert system, and will hopefully prove a valuable aid to the optical designer during the important creative stage of the design process.
A nonsequential ray tracing method is described for treating systems where the order in which surfaces are hit depends on the ray being traced. These include systems with segmented mirrors and/or apertures, various types of prisms, e.g. corner cube reflectors and roof prisms, and systems containing concentrating collectors, waveguides, and resonators. Nonsequential (NS) surfaces are entered in any order using global coordinates, and can be nested with sequential surface subsystems. The material on both sides of each surface must be specified, as well as the refractive mode (i.e., whether a ray is to reflect, refract, or do either depending on whether or not the ray satisfies the conditions for total internal reflection). Analyses of selected systems using the Code VTM optical design program are presented as examples of this technique.
A new software product for computer-aided design of optical system has been worked out at the Data Storage Laboratory of the Bulgarian Academy of Sciences. It consists of three specialized modules. The first module - the Library or Optical Components can be used to define, actualize, and store in the external memory the data concerning the specific optical components organized in the respective functional classes. About ten thousand different components can be defined simultaneously, their exact number depending on the external memory capacity of the system. The second program module allows the user to construct various optical systems by specifying up to sixty model optical components of centerings and orientations which are physically acceptable though otherwise arbitrary. The optical system constructed in this way can be further subjected to various analyses. The third module of the package served to represent the connections between the variables involved either numerically or graphically.
A specialized software module for automated design of constructive details for optical system has been developed. It is a part of the OPTAL software package. In this way constructive elements with different applications can be defined. They can be integrated within a variety of optical systems and analysed separately or together with different Kinds of optical components.
At far Infrared wavelengths (45 to 180 micrometers) the energy losses by diffraction at the different optical surfaces of a spectrometer cannot be neglected. A specific optical software has been develooped to simulate the multiple diffraction effects existing in the Long Wavelength Spectrometer (LWS), one of the four scientific instruments of the ESA Infrared Satellite ISO. The optical design of the spectrometer is briefly described, the interest of the use of an off-axis aspherical grating for a compact and flexible design is demonstrated. The mathematical model based on the Fourier-Fraunhofer diffraction theory is explained. The diffraction effects due to the wavefront limitation, at the relevant levels, and the wavefront aberrations of the spectrometer are modelled. The main results are given and discussed. The emphasis is set on the study of the energy losses due to multiple diffractions. Finally this model has been used to optimise the LWS optics and to define tolerances for the manufacturing and the adjustment of the optical system.
This paper illustrates the use of modest aspheric surfaces and colour correcting elements made from materials other than germanium in cost effective optical designs for high performance thermal imagers. A number of optical design examples are given to show how aspheric surfaces and colour correcting elements are used to meet the space-volume requirements demanded by present day systems. The colour correcting materials considered are chalcogenide glasses, zinc selenide and zinc sulphide. The aspheric profile as measured from the best fit sphere departs by less than 15 micrometres and has local gradients less than one micrometre per millimetre of aperture. Such modest aspheric surfaces can be manufactured at relatively low cost on conventional lens polishing machines and can be easily tested using Newton fringes formed against a spherical test plate.
Interest continues in dual waveband and wide waveband optical systems operating in the 3 -12.5 micron spectral region. In some cases, mirror optics will be preferred, in particular where large apertures are involved, precluding the use of refracting materials due to limitations on size. For other applications, catadioptric designs will offer the optimum solution. These approaches may not however, be able to satisfy every requirement. It is necessary therefore to consider design solutions using only refractive optics. A study has been undertaken to explore a range of optical material combinations that aim to provide chromatic correction over this large spectral waveband. Initially, candidate infra red transmitting materials were reviewed and the reliability of their optical and physical properties considered. A representative group of preferred materials was selected. Thin lens calculations were then performed to achieve common focus at several wavelengths, for different material combinations. Focal shift as a function of temperature was also modelled. The most promising combinations were then converted into thick lens design solutions. The performance of these solutions is presented. Apart from design .considerations, the practical suitability of the candidate materials for lens systems is discussed.
Many infra-red applications require a dual field of view telescope. Wide angle (low magnification) for general surveillance and narrow angle (high magnification) for concentrating on areas of interest and in particular for target recognition. A typical need is for a telescope for an airborne system that has very high magnification, low weight, compact size and quick magnification change time, along with a military environmental specification. These requirements, together with the high optical performance necessary, results in systems with very tight lens positioning tolerances. The design approach to solving these problems is described.
The quality of resonator mirrors still is a limiting factor of beam quality and output power for high power argon ion lasers. To compare the different coating and substrate materials and deposition methods it is necessary to measure the absorption of the mirrors. The absorption is of order 10-4. We use the high intracavity power of an argon ion laser to measure this absorption. An external interferometer records the mirror deformation while the 1aser is in operation. The laser mirror itself performs as a shearing interferometer. From the recorded interferogram we calculate the temperature distribution of the laser mirror and deduct its absorption.
Diamond machining of aspheric lenses can introduce manufacturing errors which are not found in conventionally finished optics. They have therefore not been addressed by conventional tolerancing and raytracing methods. This paper will show how some of these errors arise, and their appearance when examined interferometrically. Raytracing and experimental analysis of the effect of these errors on system performance is described, and diagnosis, with or without null test optics, is discussed.
Epoxy adhesives are widely used to bond prisms in cantilever fashion to mechanical mounting surfaces. Typically, the adhesive is applied in a prescribed thickness to a raised land on the mounting surface. This land then defines the area of contact with the prism. In order for the bond to survive, this area should equal or exceed some value related to the ass of the prism, the manufacturer's specified shear strength of the cured adhesive and the anticipated maximum acceleration due to shock and/or vibration during shipment, operation and mishandling by the user. In this paper, formulas relating prism clear aperture, material density and acceleration loading to minimum bond area for a representative commercially-available epoxy are derived for several common prism types. Since these computations are based on nominal conditions and some approximations, they should be regarded as guidelines for preliminary design purposes. Experimental verification of the choice of materials, application/cure methods and of the specific interface design is advisable in critical applications.
The distributions of illuminance and chromaticity on the point spread function (P.S.F.), and along the axis for optical systems with non uniform transmission filters are discussed. We consider both the aberration free system and systems with chromatic aberration with a standard achromatic correction. Filters that apodize the P.S.F., and also hyperresolving filters are studied. We also consider filters showing their most important effect along the axis.
This paper presents the effect of Ametropia on the laser interferometric visual acuity (LIVA) in the examination of human visual performance. The ocular correction is used as a means of measuring the refractive state of the eye and its accommodation. Theoretical expressions for the relationship between ametropia and the LIVA are derived in terms of geometrical optics. The transmissivity and the aberrations of the human eye, the ability of fringe pattern recognition and the difference between the LIVA and the usual geometrical figure visual acuity are discussed.
Holographic Head-Up Displays (HUDs) have major operational advantages over displays employing only conventional optics : principal among these are high display brightness for little attenuation of the outside world and the ability to cover wide angular fields of view. In addition, diffractive power can be used to give the effect of a shape other than that of the substrate on which the hologram is formed. There are limitations, however, particularly with regard to the amount of diffractive power that can be employed, the obliquity at which the hologram can operate and the vertical head movement over which high display brightness can be achieved. The paper considers both advantages and disadvantages of holographic HUDs and the application of this type of system to aircraft and, possibly, automobiles.
We have designed and manufactured a new concave, flat field, grating which permits to disperse simultaneously several spectra onto a matrix detector without any crosstalk between spectra and with a good resolution. Applications include absorption spectrophotometers, liquid chromatography detectors, blood analysers, colour measurement systems, etc... This paper describes the optimization and the performances of such a grating manufactured for being included in a blood analyser.
In January 1987 we presented a paper "Spherical aberration - some fascinating observations."1 In that paper we presented a parametric analysis of f/2, one through four element lenses, relating monochromatic axial performance (spherical aberration) to refractive indices from 1.5 to 2.0. In this paper we extend our prior work to include parametric analyses relating the same one through four element lenses over the same refractive index range to the sensitivity to element decentration. In this paper we will review the prior paper for continuity in addition to the new material.
New lenses are presented for film scanning on line array sensors. Structure and image forming properties of the lenses are discussed. Also the performance of the lenses is demonstrated by MTF values for the green, red and blue channel with respect to the 13 x 13 μm pixels of the solid-state line array sensors.
Using the 'thin lens' equations in Argentieri's notation a relation between third-order coma and Petzval-curvature is derived, which holds for symmetric shaped simplets and which for its part is not influenced by bending both of two symmetrical components symmetrically. Third-order coma of the spherical mirror can be rewritten, to make it accessible to the same relation. Thus a tool is given to analyse the space of Cassegrainians or Gregorians composed out of such catadioptric simplets having predetermined values for each of the existing five third order aberrations. Zeroing all such aberrations conveys to a funktion in a two-dimensional space relating the necessary power of the first member and the necessary distance of the second member at unit power of the entire system, where such systems can be achieved. Some particular points of this function show congeniality with well known optical systems in astonomical instruments.
The VLT which will become operational in the late 90's is a 16 m equivalent diameter telescope. retained is a linear array of four 8 m unit telescopes. Unit telescopes can be used individual the full collecting power of the array is not required. The beams of the four telescopes c recombined in a fixed central station where very large instruments will be located.
Low expansion glasses offer many advantages as mirror blank materials due to their thermal and mechanical properties as well as the flexility they offer in design and fabrication. Fused Silica, Corning Code 7940 and ULE titanium silicate, Code 7971, produced by the flame hydrolysis process, are high purity and homogeneous glasses. Determination of the average and the variation pattern of pie Coefficient of thermal expansion (CTE) within ULE mirror blanks (nominally 0 x 10-'/°C over the 5°C to 35°C temperature interval) is readily accomplished to an accuracy of + 2 parts per billion per degree centigrade (ppb/°C) by ultrasonic measurements. The ability to fusion seal each of the glasses offers mirror manufacturing design freedom of shape, size and weight. Solid monolithic mirror blanks have been successfully manufactured by the hex-seal method up to 4 meters diameter and 10 meter blanks are an extension of the proven fusion techniques. Lightweight fusion bonded ULE mirrors, such as the primary used in the Hubble Space Telescope, are fabricated by first "welding" selected glass pieces together to form a structurally rigid core and then fusing it between two plates. Ultralightweight (10% solid weight) low expansion mirrors produced by "frit bonding" a fusion core between two precision machined plates, maintain an optical figure when exposed to thermal cycling and mechanical abuse environments.
For about 20 years Schott has been supplying the glass ceramic ZERODUR, a material with very low thermal expansion. Besides many other applications ZERODUR is excellently suited for the manufacture of mirror substrates for telescopes. About 80 % of all telescopes in the western world with mirror diameters p1.8 m have been equipped with ZERODUR during the last 10 years. The development of modern astronomical telescopes is aimed at larger primary mirrors and extremely lightweighted secondary mirrors. New techniques have been developed by Schott for the manufacture of thin monolithic mirror blanks of more than 8 m in diameter. The development of thin meniscus shaped shells using the spin casting technique was successfully completed last year. During a test production several mirror substrates up to 4.1 m in diameter and down to 57 mm in thickness could be produced. The know-how has been acquired for the fabrication of mirror substra-tes of more than 8 m in diameter by the spin casting technique. Schott has also performed considerable developmental work in the field of lightweighted ZERODUR mirror substrates which can be generated using different techniques: forming of the lightweighted structure during casting, fusion of individual components to a total structure and lightweighting of a massive block by various mechanical machining methods. Several samples have been produced with diameters up to 0.7 m and weights per unit area down to approximately 60 kg/m2.
The V.L.T. mirror characteristics : - a huge size, - a great flexibility, calls for an improvement of conventional techniques previously used for polishing, figuring and testing. These mirrors must be free of : - high frequency defects, - non axisymmetric defects not correctable by the active optic system. Fortunately, thanks to their active shape control, a given amount of low frequency defects can be tolerated.
The evolution of traditional polishing techniques and a new method developed at Carl Zeiss are reviewed with respect to their suitability to figure large and fast primaries of the 8m class. The role of fast metrology techniques in the figuring process is demonstrated with the ESO NTT primary mirror. The figuring scenario for an 8m mirror as a synthesis of advanced tool technology and fast metrology methods is presented as state of the art at Carl Zeiss. For handling and figuring support of large mirrors new concepts have to be applied. Solutions for the critical steps are outlined.
This paper discusses the principles of adaptive optics, its performance, and its requirements for applications in astronomy to overcome limitations due to atmospheric turbulence. Guidelines for the implementation of these devices in telescopes are given in particular for the Very Large Telescope (VLT) of the European Southern Observatory. It is intended to equip each (me of the four 8-meter telescopes of the ESO- VLT, which are arranged in a linear array with an independent adaptive optical system. These systems will serve the individual and the combined Coude foci. In a first approach diffraction limited imaging for 3.5μm and longer is envisaged resulting a resolution of a few hundredths of an arcseconds. Currently, a small scale prototype adaptive system is under development. It is equipped with a 19 piezoelectric actuator deformable mirror, a Shack-Hartmann type wavefront sensor, and a dedicated wavefront computer for closing the feedback loop. This system is based on a polychromatic approach, i.e. it senses the wavefront in the visible but the adaptive correction loop works for the infrared wavelength range from .1 to 5 μm. The experience with this system will be used for the development of the final VLT systems, requiring a minimum of 150 to 200 subapertures. To solve the reference source problems experiments to generate artificial reference stars by scattering a laser pulse in the upper atmosphere are in preparation. Major developments are still necessary to solve the data processing problems which are associated with large numbers of subapertures and high correction bandwidth, especially if one plans later to extend the wavelength range towards the visible. In the VLT project adaptive optics is of particular importance for its synthetic aperture observation mode as a long baseline interferometer with resolutions in the range of a few milliarseconds on the sky. In this application a complete phasing of the telescope array is required in order to have the full gain of the large telescopes.
We consider optical systems with residual peak to valley wavefront errors below 150 nm. The interference figure for λ = 633 am may then be adjusted and photographed as to hold out at every point of the image of the pupil a one to one rolaionship betwonn the optical density of the interferogram and the magnitude of the wavefront error. An enduring interference figure is secured by means of a tiny reflecting aluminized spot on a hare substrate located on the image of a distant point source. We investigate how subsequent photoreproduction of an interferogram upon a photoresist coating may act as a transmitting or reflecting wavefront corrector.
The central-axis reflector (LAS) , the design principle which is pre-sented below is a segmented-mirror telescope.The inventions relate main-ly to the optical system and to the tracking apparatus. A large number of small individual mirror bodies , ground off-axis (hexagonal/polygonal) produce one primary mirror with closed circular aperture when joined together. The overall design of the tracking apparatus results directly-and thus without unnecessary adornment- from the two planes of motion which have been reduced to a minimum but which are required for tracking of the telescope.
This paper describes three simple methods for improving convenience and reducing memory requirements during the optimisation of complex optical systems, without significant penalty in terms of computer time. Such optical systems will typically involve surfaces of unusual shape (e.g. aspherised toric), tilted and decentred surfaces, many linked parameters, and multiple configurations (e.g. zoom systems, or removable components). The three methods have all been employed to good effect in the authors' optimisation program. They are (i) a scheme of equation building with small partitioned matrices, (ii) a simple but highly efficient method for the storage of constructional data, and (iii) the diagonalisation of a quadratic variance-based merit function into a simple sum of squares.