This PDF file contains the front matter associated with SPIE Proceedings Volume 1780, including the Title Page, Copyright information, Table of Contents, and Conference Committee listing.

A basic relation in the diffraction theory of the image of a point source is that the distribution of complex amplitude in the PSF is given by the Fourier transform of the distribution of complex amplitude over a reference (or pupil) sphere at the exit pupil. For this relationship to be valid it is essential to express the complex amplitude over the reference sphere as a function of the rectangular coordinates of points on the exit pupil sphere, and not those of points in the exit pupil plane. I describe in what follows the advantages of using, also in geometrical optics, the reference spheres in the object and image spaces, respectively, as the surfaces of the entrance and exit pupils rather than the pupil planes.

Recent progress in global optimization has raised new interest in the application of global methods to lens design. This paper has several goals. We describe the attributes of a new global algorithm, Global Synthesis^TM (GS), and we distinguish it from previously reported methods on the basis of efficiency and the ability to handle many (i.e., > 50) variables and comparable numbers of active, nonlinear, equality, and inequality constraints. Many experienced designers doubt, often with good reason, that multiple minima exist for practical problems, so we present meaningful examples showing additional minima often do exist. These test cases, some with known optimal solutions, can be used to study and benchmark the performance of different methods, and we describe recent results with GS on these test problems. We discuss what is meant by `success' in global optimization, and point out the practical limits of current methods. Finally, we discuss what impact global optimization may have on optical design as it becomes a mainstream tool of designers.

The result of a lens optimization is critically dependent on the choice of the initial design, and this paper discusses ways in which starting points for optimization can be generated. Examples are given showing how, in some cases, an optimization program can obtain results that are very different from the initial design. In other cases, the choice of the initial design severely restricts the potentiality for optimization, and this is also discussed.

Practical resolution of optical lithography is often defined as the minimum feature size which can be fabricated with acceptable depth of focus. It can be predicted by calculating diffraction image contrast in various defocused planes. However, since a large volume of calculation is required to know image contrast under partially coherent illumination, evaluation of optical lithography systems with regard to use of the practical resolution is time consuming and does not give us a quick and clear forecast on optimum optical parameters for a given lithography specification. In this paper, we propose an analytical and intuitive method for getting image contrast in defocused planes, by use of the theory of interference fringe formation. By using this method, relations among defocus, numerical aperture, wavelength, coherence factor, and image contrast are derived analytically and these parameters can be optimized for given lithography methods, which employ not only the conventional but also various resolution- enhanced methods, such as annular illumination, phase-shift, illumination control, and others.

The image quality degradation due to atmospheric turbulence is one of the main limitations for imaging, laser propagation, and communication through the atmosphere. Adaptive optics is a technology to overcome these problems by real-time phase compensation. The main components for such systems, like wavefront correctors, wavefront sensors, and dedicated computers, are existing, and complete systems have been successfully tested. This article describes the principles of adaptive optics and concentrates on its applications to astronomical imaging, including some first observing results. The performance in image quality which can be expected from adaptive optics and the requirements for its application are discussed.

Computer integrated manufacturing (CIM) environment consists of several standalone software packages that are capable of transferring and receiving data from each other. The resulting data should be configured and controlled in a well defined format. Each of the separate software tools operates on various configurations of hardware platforms. Standards are required to enable networking all those platforms and other standards are essential to enable each individual user with his own hardware platform access to operate the various software tools that he needs. The latest trends in the development of numerically controlled (NC) lens production machines, innovative automated testing equipment, and the extension of CAE in CAD packages, are the major contributors for turning CIM in optics from theory to practice. Lack of the appropriate standards within the optical community as well as the status of other standards in computers and CNC, is partially responsible for its limited implementation. Recent developments, the current state, and the standards that are essential for CIM in the optical industry are presented.

This article considers the man-machine interface as it applies to optical design computing. The author makes every attempt to avoid commercialism, and applies praise and criticism as equally as possible.

The evolution of computer technology in the last decade produced a new computer category: the graphical workstation. These high performance computers, with multitasking graphical operating systems can increase the productivity of optical engineers significantly, however, the development of an optical design software which utilizes the extraordinary possibilities of these new environments requires special considerations. In this paper a new, highly interactive optical design software is introduced together with some useful methods which support the early stages of the design process.

We describe a novel method of determining potentially successful starting designs by utilizing an expert systems algorithm which operates on a database of previously well-designed optical systems. The database is composed of systems created by a `not-so-local' optimization algorithm, and a collection of previously well-designed systems. The expert system is unique in its ability to modify the number of optical elements to create new starting points. The `not- so-local' optimization algorithm combines the downhhll simplex method with a random multi- start algorithm which can create new optical systems for inclusion into the expert system database. This creates a diversity which can be used to synthesize unexpected starting designs.

A small expert system used in lens design is developed. With the help of it, a mass of initial configurations which may lead to local minima can be produced. The paper puts emphasis on the system architecture, inference engine, and certainty factor propagation.

We discuss how to solve the lens type of the optical system from the patent by using the virtual vertex back propagation (VVBP) network, and then apply the back propagation (BP) network to make lens optimization. The problem solving mechanism, such as the knowledge base of the neural network from our development, training the neural system, lens classification, and lens optimization, etc., makes that knowledge conveniently available to the user working in optical system planning. Therefore, the system can be applied to solving and planning the problems with both data driven and goal oriented methods.

A brief description of the algorithm and a program which can help the optical designer to choose the starting point of lens design is given. Examples are given of numerous features.

A new method to derive algebraic formulae for tracing skew rays in radial gradient-index media is described. We obtained power series for the ray position and direction, optical path length, and coordinates of the intersection point of the curved ray with the spherical end surface of the GRIN lens. All these formulae include the effects of terms up to the eighth power of the radius in the refractive index distribution.

The optical engineer can apply unit sphere methods, used to find geometrical configuration factors in radiant heat transfer calculations, to calculate similar factors for irradiance and illuminance distributions in many optical systems. This paper illustrates how using a dummy reference sphere of arbitrary radius, and direct ray trace analysis, can greatly simplify photoradiometric calculations while achieving accuracies of better than 1%. Uniform and non- uniform light sources are treated. Examples are presented using different optical configurations and light sources including projection systems, scanners, illuminators, and several imagers.

The options of the PRKH software are presented. The PRKH software is designed for the calculations of intensity distributions in partially coherent imaging of two-dimensional structures. The consistency check of the PRKH software was performed by comparison between PRKH-computed intensities and measurements in the image field of a projection lens. The achieved results were generalized, and adjustment rules were derived from them.

The degradation of image quality caused by asymmetric surface form errors is evaluated and analyzed in several types of lens systems, for example, the objective for a compact disc and the camera lenses. The asymmetric surface form error is expressed by the coefficients of Zernike's circle polynomial and applied to ray tracing. This simulation improves the efficiency of the analysis of the molded lenses and the setting of the fabrication tolerance in advance.

This work is a new approach for the design of start optical systems and represents a new contribution of artificial intelligence techniques in the optical design field. A knowledge-based optical-systems design (KBOSD), based on artificial intelligence algorithms, first order logic, knowledge representation, rules, and heuristics on lens design, is realized. This KBOSD is equipped with optical knowledge in the domain of centered dioptrical optical systems used at low aperture and small field angles. This KBOSD generates centered dioptrical, on-axis and low-aperture optical-systems, which are used as start systems for the subsequent optimization by existing lens design programs. This KBOSD produces monochromatic or polychromatic optical systems, such as singlet lens, doublet lens, triplet lens, reversed singlet lens, reversed doublet lens, reversed triplet lens, and telescopes. In the design of optical systems, the KBOSD takes into account many user constraints such as cost, resistance of the optical material (glass) to chemical, thermal, and mechanical effects, as well as the optical quality such as minimal aberrations and chromatic aberrations corrections. This KBOSD is developed in the programming language Prolog and has knowledge on optical design principles and optical properties and uses neither a lens library nor a lens data base, it is completely based on optical design knowledge.

We propose an iterative algorithm for computation of the radial phase function of an optical element (focusator), which formates the light segment along the optical axis and is characterized by a given length and the required intensity distribution on the segment. The algorithm is also applicable to computing the multi-focal lens so that the focusator is capable of focusing into a set of longitudinal light segments.

The knowledge of the index of refraction of optical materials is essential when dealing with optical instruments and problems. Different interpolation-formulas are used, the best known is the Laurent-formula as used in the Schott-catalogue. Unfortunately, the range of this formula is limited to 365 nm up to 1014 nm. But often problems must be solved, where a spectral region wider than the above one is used. In our company we introduced an interpolation which covers a wide range; not only usual glasses are well interpolated, but even special materials such as ZnS are described correctly. Some of the common formulas are compared, regarding the usable spectral range and the smoothness of the interpolation. For all Schott-glasses it is possible to interpolate at minimum a region of 365 nm up to 2335 nm, for some other materials (Zns, ZnSe, Saphir, Silicon, ...) much larger regions are usable.

A lens design optimization algorithm seeking for global minimum is discussed in this paper. In the design of a simple optical system, by using Monte Carlo random selection to produce a mass of initial configurations and using generalized simulated annealing and damped least square to perform optimization iteration on them, a group of local minima may be found and one global minimum can be determined among them.

Focus shift of lenses used in high power laser machining systems is a serious problem. Unavoidable energy absorption in lenses combined with cooling at the outer rims causes radial thermal gradients and ensuing optical distortion. An existing ray tracing program was adjusted to compute the influence of stationary radial temperature profiles on the performance of lenses. Three effects were taken into account: a change of the lens thickness and curvatures caused by thermal expansion, an alteration of the angles of refraction at both air-lens- interfaces, and a curved light path through the lens. The last two effects are caused by the thermally induced radial refractive index gradient. Major consequence is a shortening of the focal length. Reasonable agreement was obtained between measurements of the focal lengths of ZnSe-lenses and theoretical predictions based on measured power absorption.

The Laurent series expansion of low order used hitherto to describe the dispersion of the refractive index, n((lambda) ), of optical glasses typically in the range from 0.365 01 micrometers to 1.013 98 micrometers is no longer useful, if the range of wavelength is increased. A more appropriate equation to describe n((lambda) ) is a Sellmeier-type equation with several oscillator terms. We applied a three-term Sellmeier equation to experimental data of n((lambda) ) of optical glasses for a large interval of wavelength ranging from the absorption edge in the UV to 2.325 4 micrometers . The data can be fitted in the full range with an accuracy of some units in the sixth decimal place corresponding to the accuracy of the measurements. The change of the refractive index with the temperature has also been investigated. A dispersion formula, which has been developed recently, has been applied to experimental data of the temperature coefficient of n((lambda) ) in the range of wavelength between the UV absorption edge and 1.013 98 micrometers for the temperature range from - 100 degree(s)C to + 140 degree(s)C. This dispersion formula can be integrated to give directly the increments or decrements of the absolute refractive index with respect to n((lambda) ) at a given reference temperature, e.g., 20 degree(s)C. Based on a one-term Sellmeier equation we also developed and successfully tested dispersion formulae for the stress-optical coefficient and the Verdet constant.

We derive the general form of the light path function for corrected holographic concave gratings until the third order of the pupil coordinates. The waves used for recording and reconstruction deviate until the third order from spherical waves. From this we derive the transformation properties of the coma-parts of the wavefronts by grating diffraction and the propagation formula for deformed wavefronts in homogeneous media. These tools can be used for the correction of single gratings and systems containing gratings and as guidelines for intentions to correct diffractive elements with wavefronts deformed by synthetical holograms. The contributions of the third order terms to the ray tracing are given by analytic formulae. Applications are given. Deformed wavefronts can be recommended if there are external constraints by spatial arrangement to the grating configuration or if the spectral range is arranged below the recording wavelength.

Laser diodes emit a highly divergent beam with elliptical intensity profile and astigmatic wavefront. Conventional high quality collimators use up to seven elements to produce a plane wavefront free from astigmatism and with circular intensity profile. The same task can be accomplished by a system of only two holographic optical elements (HOE). Because of the strong dispersion of diffractive elements, it is necessary to achromatize the system. The design is based on Weingartner's iteration. The design algorithm and optical properties of the system are discussed.

Hybrid optics -- the combination of conventional lens elements and diffractive optical elements (DOE) -- offers new possibilities for optical system design due to its technological flexibility: the specific manufacturing processes allow fabrication of any arbitrary optical element surface shapes and it becomes possible to combine different optical functions in one single element. Furthermore, the technologies used are compatible with semiconductor manufacturing processes, which is a prerequisite for the development of highly integrated optronic devices. Since such aspects are very interesting for the design of space optical systems, a research project was initiated to investigate in detail the potential of hybrid optics for space applications. This paper presents some results of this project and describes the design, manufacture, and testing of a hybrid optical element for use in the visible, as an example.

New optical elements can be realized interferometrically by generating holographic diffractive structures. For lasers in the infrared spectral region the rulings of these structures need to be 2 to 5 times deeper than in common uses. By structuring photoresists holographically, varying different parameters, ruling depths of 24 microns and depth to grating constants of 1.5 could be performed. These structures had been applied as masks to reactive ion etching in glass and copper. For economic embossing replication techniques nickel stampers had been manufactured by electroforming the diffractive photoresist structures. Optimization of the embossing parameters has been carried out successfully regarding different thermoplastic materials and the achievable diffraction efficiency.

The beam propagation method (BPM) is used to assess the performance of a waveguide Fresnel lens with given parameters (f_# equals 4.6, (delta) n equals 0.08221 at (lambda) equals 830 nm) as a function of the support curve (i.e., of the front diopter of the lens). It is shown that the lenses having circular and parabolic front diopters (which almost coincide in the paraxial approximation) are corrected from third-order aberrations over a field of view of several degrees, wide enough to confirm the suitability of these lenses for integrated optical signal processing applications. The convenience of correcting its chromatic aberration is also discussed.

In this paper the design of a focusing grating coupler (FGC) is treated in the geometrical optics approximation for a rather general configuration. The guided mode may have an arbitrary phase profile and the free space wave which is generated by the FGC travels through an optical system before the final focal point is generated. This optical system does not need to have symmetry of revolution. The analysis uses the data of the ray fields coming from the free space and from the guided region at the location of a general point of the grating coupler. In this way an effective matching of the two ray fields is obtained without the need for time- consuming iterative ray-tracing. By using Lagrange's integral invariant, the optical pathlength function is obtained over the grating surface. The pathlength function is used to obtain the grating vector distribution when ray-tracing the designed FGC. The pathlength function also serves to construct the diffracted wavefront.

A description of wave aberrations is studied, calculated from a minimum number of ray tracings which allows the user to generate independent conditions for optimization processes.

Hamilton's method of characteristic functions can be used to calculate the effects of small system perturbations on image formation. In this paper we apply perturbation theory to the calculation of centering tolerances. We show how the aberrations caused by component shifts and tilts can be expressed as sums over surface contributions. We made up a computer program (called NODES) to calculate Eikonal coefficients of optical systems. With this program lens design can be optimized with regard to specific aberrations. Decentering aberrations can be included in the merit function. We give a few examples of optimization including centering tolerances.

The habit of teaching the movements of masses first, and propagation of light later, as an electromagnetic phenomenon was widespread. Looking further back into the history of physics, however, we see earlier the concepts for understanding light rays, and later their successful application to particle trajectories, leading to the highly developed celestial mechanics towards the end of the 19th century. And then, 1905, Karl Schwarzschild transferred the technique of `canonical coordinates,' named so by C.G.J. Jacobi in 1837, back to light rays in imaging systems. I would like to point to the chief steps in the evolution. The learning process for handling both particle and wave propagation aspects continues up to our time: Richard Feynman 1918 - 1988. We may judge each contribution: whether it opens our mind to a unifying theory, or whether it hardens partial understanding. And we can notice where the understanding of light propagation led the evolution, and how the theory for movement of masses caught up.

The dependence of the design performance on the dispersion property of radial GRIN materials is described. Also, a simple method based on the concept of the quasi-equivalent glass for the effective use of radial GRIN materials is presented, demonstrating a design example.

In a gradient index (GRIN) material, the index profile, in general, is given by a polynomial. The curved light rays are computed by a step-by-step integration method. Sharma et al., have given the details of the Runge-Kutta method; it is time-consuming and approximate. GRIN materials have now started being offered on the market place. When the gradient is axial (i.e., when the index varies with the depth in the lens, along the optical axis) it is the most useful for optical design of real-life large-aperture imaging systems. These axial gradients, that are offered for sale, are almost linear. Moore et al., have explained their efforts to obtain more linear profiles. When the gradient is exactly linear, the differential equation can be exactly integrated, which saves time for preliminary design through reduced computing time. This paper explains the details of this integration, gives the exact parametric equation of a light ray, and, hence, derives paraxial formulas for focal lengths.

Image plane in devices with dispersion contains a spatial coordinate and a wavelength coordinate. For the wavelength coordinate we define chromatic aplanatism in analogy with usual aplanatism. The feasibility of this definition is tested by ray tracing. A condition for color aplanatism is derived which can be used for the construction of color aplanatic surfaces. In the neighborhood of a color aplanatic point we find a very high spectral resolution in combination with a high aperture. In some cases of color aplanatism spatial aplanatism occurs along the spatial coordinate of imaging. This additional aplanatism can be a starting point for a combination of spatial with spectral resolution. This new task is interesting for remote sensing from satellites. We give variants of gratings with spectral aplanatism and with spatial resolution.

Spectral devices are frequently using holographic diffraction gratings as dispersing elements. The trend in developing such devices is going toward rather small and compact ones, which use CCD-detectors. Very useful for these purposes are imaging concave gratings. They realize an essential progress by the combination of dispersion with imaging properties. Mostly their imaging properties are priorly used in a single plane only. This means, a small area around the center point of the entrance slit is taken into account only in the performance of the grating. We have investigated some possibilities to design gratings with high spectral as well as high spatial resolution. The influence of several grating parameters on spectral and spatial resolution properties is discussed and ways to find new application possibilities by variation of chosen parameters are shown. Which improvements could be reached with the help of further optical surfaces are discussed.

The method has been proposed for computing Fresnel-type multi-focal lenses on the basis of special-type phase nonlinearity. Multi-focal lens is represented as a mathematical superposition of a thin lens and nonlinearity distorted Fresnel lens. Selection of the nonlinearity-type is reduced to the problem of the groove form determination for the phase diffraction grating with pre-set energy distribution between orders. In particular, bifocal lens and multi-focal lens have been investigated.

A method for calculating third order transverse aberrations of diffractive elements is presented. The vector grating diffraction equation, well known for its use in ray-tracing, is now used to directly obtain the angle Eikonal at unit magnification of the element in question. As an example, we consider the special case of an axially symmetric planar diffractive element. A single coordinate transformation yields not only the third order aberration coefficients but also the stop and object shift properties of the system.

In the paper the third order aberrations of holographic lenses recorded on quadrics of revolution are investigated. Analytical results presented in previous works are verified numerically using collimating and imaging holographic lenses as an example. The numerical calculations are performed in two ways: geometrical (ray tracing) and diffraction. We show the very small difference between aberration spots of holographic lenses recorded on sphere, ellipsoid, and hyperboloid with the same value of main curvature.

A single holographic lens recorded with spherical waves can be used as a satisfactory Fourier transforming lens. By proper choice of the input pupil location where the object transparency illuminated with parallel light beam is placed a Fourier spectrum of this object free from spherical aberration and astigmatism can be obtained. The influence of the remaining coma is negligible if the relative aperture is not too high. It is also possible to diminish coma by recording the holographic lens on a spherical surface. However, full coma correction is not desirable, because compensation of distortion is then impossible. The uncompensated distortion leads to the deformation of the Fourier transform scale, but this fault is easy to correct by simple re-scaling at the recording step or subsequent image processing.

The manufacturing of glass lenses has always set exacting requirements on the finishing technique. If, in addition, the design deviates from the conventional geometry of plane and sphere, the standard manufacturing process of rough grinding with cup-wheels and subsequent precision grinding and polishing with reproductive techniques fails. In order to achieve highest form accuracies and surface qualities combined with a flexible surface shape, ductile single- point-grinding meets the requirements for the production of rotationally symmetric aspheres.

Modern aspheric design, computers, materials for molds and lenses, and advanced production and measuring equipment make possible accurate plastic lens elements that can meet requirements that used to need several elements. Reviewed are miniature TV camera lenses, laser diode collimator lenses and magnification with some detail regarding design, accuracy, and the low costs that can be achieved.

Curved rays in gradient index materials are described by differential equations. Numerical methods for solving these equations are compared. Attention is paid to the error estimation for step size control. These algorithms are used to trace rays in materials with an arbitrary refractive index field. This allows the application to the optical design of high power laser optics, where the absorption induced refractive index field is calculated by thermal FEM calculations.

An approximate method for the analysis of laser with a saturable absorber, taking into account longitudinal field dependence in the cavity, is presented. An approximate expression relating the small signal gain 2g_o to the output power normalized to the saturation power in the active medium P_out/P_sg, the saturable losses (alpha) _so, the ratio of the active medium length to the length of the nonlinear absorber, and to system parameters is derived. The characteristics revealing optimal output mirror reflectivity, which provides optimal power efficiency, are obtained as a function of the system parameters.

This paper explains a new optical recording unit with 80 semiconductor lasers ((lambda) equals 780 nm), and it can be used in the drum rotation type prepress equipment for film exposure. The optical system consists of three units: a unit composed of an off-axis paraboloid mirror and a stereographic projection lens, a both-side telocentric zoom lens unit, and an afocal reduction lens unit. A both side telocentrical optical design has been adopted for each of the units. The stereographic projection lens and the off-axis paraboloid mirror combine to keep the beam intervals regular. As a result, excellent imaging performance and telocentric characteristics at the exposure plane are now available for all magnification ranges.

The design of a simple two lens system for optical diffraction operating within a fixed bench distance is analyzed. Geometrical conditions for large size Fourier transforms, as needed when using light modulators, are deduced within paraxial theory. Different configurations using different lenses but giving the same input output magnification are studied in order to specify its practical usefulness. A ray tracing based numerical criterion for assessing the quality of the diffractive system is used. Preliminary experimental results are presented.

VNIR is an imaging spectrometer working in the 350 divided by 1050 nm spectral range. It simultaneously acquires multiple images of the same region, each in a different narrow spectral band. The resulting images provide a spectrum for each point in the scene. The VNIR spectrometer together with an infrared channel form the instrument OMEGA (Observatoire pour la Mineralogie, l'Eau, les Glaces et l'Activite') that will be used from a Russian orbiter to map the geochemical and mineralogical distribution of materials of the surface of Mars. The main purpose of VNIR is to extend the mapping capability towards short wavelengths, where a number of natural materials have their signatures, and to determine the location on the surface of spectral features mapped in the IR range. The instrument is composed of a lens objective and a concave holographic grating mirror based spectrometer. It can acquire images of 384 X N spatial pixels (N being the number of swaths, as the push broom technique is used) of 0.4 mrad each and 5 nm spectral resolution over 144 channels.

Scanning imaging absorption spectrometer for atmospheric chartography (SCIAMACHY) is an optical imaging spectrometer for atmospheric chemistry research. The instrument is selected by ESA for the Polar Platform mission. The optical system of SCIAMACHY consists of scanning mirrors, a telescope, and a complex spectrometer system. With the scanning mirrors the instrument can be directed in nadir or limb direction. The FOV is 2.3 X 0.023 degrees. With the spectrometer high spectral resolution (0.2 nm) measurements are simultaneously performed over a wide spectral range (0.24 to 2.4 micrometers ). Besides the polarization of the incoming radiation is measured with a polarization measurement device. For inflight calibration various possibilities are foreseen such as sun, moon, and on-board light sources.

Non-uniform transmission filters are used to modify the response of an optical system. Grey non-uniform filters produce important effects on the illuminance distributions both in the transverse and along the axis. Nevertheless, grey filters do not change the chromatic response significantly. So, we propose some types of annular color filters which modify the transverse and axial illuminance distributions, and they also modify the chromaticity distributions.

A number or applications (lithotripsy is among them) require a laser source with a variable pulse width in the range i'rom several hundreds nanoseconds to rew microseconds. Conventional technique al— lowing to generate Q-switched pulses or large duration is based upon introduction or negative loop in the oscillator scheme. This technique employs rast electronics which restrict reliability o the laser sys— tern and makes it rather complicated. Another approach to a solution or this problem includes scaling the resonator length o a Q—swltched oscillator. Large length or the resonator cavity in a compact conriguration can be obtained on a basis or either a oided resonator [1,2J or optical riber placed between one or the mirror and a laser rod 13 1 . To our knowledge [3 1 is the only paper in which a Nd:YAG rree-running operation with a riber - based resonator was described. Lack or works dealing with this approach is explained by a wide-spread opinion about parasitic nonlinear errects occurring in the riber. Indeed the nonlinear ertects (especially Sti— mulated BriIlouin Scattering) can result in pulse structure distortion and even in the damage or the riber. However update no investigations have been made revealing conditions which allow to generate stable pulses in Q-switch operation with optical riber in resonator. In experiment we investigated several laser schemes with a riber based resonator cavity.

In this experimental work, the SBS and SRS processes were used in order to produce UV laser beams of good optical quality and short duration time. An XeCl oscillator and a double-pass amplifier with a phase-conjugate mirror via stimulated Brillouin scattering, generate the laser beam at 308 nm to pump a Raman cell. The oscillator pulse was 11 nsec long, while the amplified phase-conjugate beam duration could vary from 3.3 to 1.5 nsec, by using the compression effect operated by the Brillouin mirror. When this last laser beam was focused into a Raman cell containing methane at 30 atm, the shortest backward stimulated Raman scattering pulse at 338.4 nm was 170 psec long with a brightness in excess of 10¹³ W(DOT)cm^-2(DOT)sr^-1. The 338.4 nm wavelength is interesting for the production of short bunches of cold electrons from Mg and Zn targets.

An approximate method of the modeling of nonlinear operation of the segment laser containing saturable absorber is presented. An analytical condition for the bistable operation as a function of the system parameters is derived beyond mean field approximation. The influence of the output mirror reflectivity, the linear losses, the saturable losses, the ratio of the active medium length to the saturable loss medium length on hysteresis loop is investigated. The results are compared to the predictions of the exact solutions, and they are found to be in qualitative agreement as well as in good quantitative agreement.

It is proposed to estimate lens quality for multi mode beam transformation by factor Q as a ratio of output to input beam parameter M². The quasi geometrical method of M² calculation is presented, and several examples are discussed. It is shown that for high M² beams, the requirements on lens quality are considerably lower than for diffraction limited systems.

We have designed a diode laser system that is capable of imaging more than 50 W to a spot of 0.4 mm with a numerical aperture NA equals 0.1. The theoretical limits of the efficiency and the beam quality of the system are discussed. For applications needing higher beam quality coupling optics for a longitudinally pumped Nd:YAG laser operated in the fundamental mode are presented.

The narcissus-effect is a well known phenomena in IR-scanning systems. Several methods of calculation have been proposed. Due to advances in IR-detector technology it is now possible to use detector line-arrays instead of single detectors for scanning systems. We have modified the model published by A. S. Lau. In our calculations the transmission of all optical components is taken into account, especially the transmission of the imager is also considered. We have developed a program based on this model. With this tool the calculations of the narcissus-equivalent temperature can be done by exact numerical ray-tracing for an array with up to twelve detectors. Separately for each of them you can see the exact narcissus-effect over the whole scan angle, showing a varying intensity over the detector array. The calculation can be done in arbitrary small steps over the whole scanning angle. Thus it is possible to take into account all effects of vignetting due to the mountings of the components or any other mechanical limitations. An example of such a scanning system is presented.

The sensitivity of electro-optical Earth surveillance systems within visual and near-IR bands is provided with the charge accumulation process in CCD matrices as image receivers. Efficiency of that process is affected by irregular image movement caused mostly by linear and angular fluctuations of an airplane or a space vehicle on the flight trajectory. Optical image stabilization systems under consideration compensate the movement and allow it to meet signal-to-noise requirement without space resolution degradation. Two constituents of the image stabilization system are measurement subsystem and compensation subsystem. Analog- digital compensation subsystems were investigated, the main compensation errors being estimated. In this report similar consideration of measurement subsystems is presented.

We constructed a Herriott multipass cell with one piezo driven mirror to reduce Fabry-Perot- interference fringes in a pulsed infrared tunable diode laser spectrometer. The applicability of the cell is demonstrated by measuring weak lines in the (nu) ₃-band of NO₂ with a pulsed tunable diode laser spectrometer. The reduction of the fringes is discussed in dependence to the frequency of laser excitation, the frequency of the piezo-element, and the elongation of the piezo driven mirror. The multipass cell should become a part of a high sensitive TDL spectrometer for environmental research.

This work concerns the analysis of errors induced on optical systems by mechanical stresses. These errors are a consequence of deformations induced by mounts, spacers, and similar things in contact with the optical surfaces. This analysis is essential to drive the mechanical design of very accurate optomechanical systems. The authors developed a method based on a finite elements modelling of the optical system and on interferometric measurement of the real surfaces deformation. The mechanical behavior of optomechanical items is evaluated by means of a structural analysis software package (ANSYS). The deformed finite elements model is transformed in a surface representation suitable for optical ray tracing, by means of a Zernike polynomial fitting. The mechanical stresses of real optical elements are measured by an interferometer and the surfaces are represented fitting the reflected or transmitted wavefront with the same method. The complete optical system under stress condition is then analyzed using an optical design program provided by a specialized ray tracing routine, supporting a Zernike polynomial representation of the optical surfaces. An application of this method was done on the optomechanical design of I..O. Star Sensor developed within an ESA program.

A compact design of a single-shot autocorrelator, including time-calibration, for the detection of low-repetition femtosecond laserpulses is presented. The conversion of the temporal duration of the laser pulse into a spatial distribution is obtained by noncollinear frequency doubling in a lithium-iodate crystal. The intensity distribution of the second harmonic signal is detected by a CCD-line-image sensor. The present crystal limits the resolution from 100 fs to 20 ps.

PFS is a two-channel Michelson interferometer operating in the infrared wavelengths between 1.25 and 45 micrometers . The instrument is mainly devoted to the study of the Martian atmosphere. The principal goals are the measurement of the atmospheric temperature and pressure, atmospheric constituents, aerosol and clouds, ground pressure for surface topography, and optical and thermophysical properties of the Martian soil. PFS will fly on the Mars 94 spacecraft which should be launched in 1994 and reach the planet in 1995. Essentially it consists of two different interferometers located in the same box which is divided in two parts. An edge filter placed on the PFS entrance is used to separate the spectral range into two parts. The reason for that is the different optical materials which have to be used in each spectral range. The optical layout of the experiment is very compact. Cubic mirrors are mounted on an L-structure pivoted on a stepping motor. The stepping motor moves the mechanics and permits the optical path difference between the arms to be varied. Each interferometer operates in a different spectral range between 1.25 - 4.8 micrometers (8000 - 2083 cm^-1) and 6 - 45 micrometers (1666 - 220 cm^-1), respectively. The spectral resolution is 2 cm^-1. The entrance aperture area is 30 cm² per channel and the field of view (FOV) 2 and 4 degs. Every measurement lasts about 4 s and the respective resolving power is 4166 and 1041. The time and, therefore, the relative optical path difference for the measurement of every point of the interferogram is given by a monochromatic reference channel at 1.2 micrometers which uses a laser diode as a source. The interferograms are double sided and have 16384 and 4096 points, respectively, corresponding to spectra of 6250 and 1823 points.

This paper deals with illumination assessment for IR devices: a skill software has been developed to predict image non-uniformities, including Narcissus effect. Built upon real raytraces, special algorithms have been carried out to reduce the computation time and to increase the accuracy. Some tutorial examples are provided.

Optical seekers are an emerging subsystem for endoatmospheric defensive interceptor application because of their potential advantages in target acquisition and track. Seeker performance is degraded by the aerodynamic flow through which the signal must pass and the window that allows the signal to pass onto the optical seeker. Various optical design considerations for the aero-optical subsystem are presented to include coolants, window materials, flow fields, impacts of interaction effects, and test results.

In order to reduce the cost of manufacturing optical systems with aspherical surfaces due to accuracy requirements, we perform systematic investigations for finding the best arrangement of aspherics in optical systems. Since the change of image quality is very sensitive to aspherics parameters differential ray tracing is needed and interpolating aberration techniques are used to evaluate the contributions of higher order aberrations (examples are given).

By using a number of aspheric surfaces in a novel afocal arrangement, a new binocular system has been designed which avoids the use of erecting prisms and provides a very wide horizontal field of view. The method uses spherical reflecting surfaces to re-fold the light path so that the field curvature is substantially corrected. This allows larger than normal eyepiece lenses giving a greater eye-relief in spite of the wide field of view. The concept logic impinges heavily on the optimization procedure and necessitates careful choice of parameters and constraints. Designs for magnification from X4 to X10 are discussed. The aspheric surfaces suggest the use of plastic elements for ease of manufacture and these give a potentially lightweight instrument with considerable user appeal.

Lens systems having external pupil positions are mainly used in connection with optical scanners. In consequence, these so-called f-(Theta) lenses show barrel distortion. This paper, however, is considering the front stop lenses (FS-lenses) poor in distortion and, therefore, suitable for photographic purposes.

Many people all over the world suf1er from eyediseases. According to the information of physicians there is I billion of' myopic sick people in the world, 69 million in Russia , 2 million 125 thousand in Moscow. Modern ophthalmology has a large arsenal o means or treating such patients. For using some methods o sight correction it is necessary to know the exact shape o the anterior surface or a cornea ( or the cor— neal topography ). For example, there exist microsurgical ope— rations o keratotomy, contact lens fitting etc. In order to use these methods successfully it is necessary to determine the optical power distribution and the radius o a cornea with the precision o 0.25 dioptre and 0.01 mm respectively. For this purpose at present special devices — kerato— scopes are usually used, for example, Topographical Modeling System (TMS ) [ 3 ] , Photokeratoscope PKS—1 000 [2 1 , Corneascope [4] , K—O1 [1 ] . All these instruments realize so called method of keratometry. The cornea to be examined is illuminated by the light from the mire, which looks like a series of the shining rings. The light is reflected by the cornea and a virtual image of the mire is created. This virtual image is projected by the lens to the image plane where the photo— or TV camera is placed. Usually the telecentric projected system is applied. The recorded image (keratogramm) is then processed by means of special algorithms. In all the above mentioned devices the shining rings must be located at a defined distance from the eye. If the longitudinal or lateral 'lisplacernents or the eye relative to the devioe take place the shape of the mire image at the keratogramrn will be distorted. This distortion leads to the errors oi the measurement results. There±ore, in these kerato— scopes the eye should be boated relative to the apparatus very accurately, with the error less than 0.25 mm. To provide such an aoouraoy o1 looation special arrangements are used, Lor example, a laser system or the eye alignment in Topogra— phical Modeling System,a changeable aperture stop in PKS—i000. An essetial disadvantage limiting the possibilities of the keratosoopes is the dependence of the measured oorneal topo— graphy precision results from the aoouraoy of the eye align— ment. This disadvantage deoreases the possibilities o the keratosoopes. For example, acoording to the results o the experimental research [6], TMS provides the necessary preci— sion for determining the optical power distribution of 0.25 dioptre 70% of the whole corneal area only. That is why the main problem o the keratosoopes optical system design is to eliminate the influence ot the eye align— ment on the measurement precision.

The development of the 35 - 70 mm f/3.4, 80 - 200 mm f/4, and 28 - 85 mm f/3.3 - 4 Vario- Sonnar lenses for the 24 X 36 mm format has been centered on finding means of design which ensure image quality equivalent to or at least approaching the image quality of fixed focal-length lenses. The structure and the performance of the lenses are described, and the development process of the Vario-Sonnar lens with focal length doubling is discussed in greater detail.

A long focal length close focusing zoom lens for the visible waveband which rivals the performance of fixed long focal length lenses is described. Particular areas of discussion include, the utilization of anomalous glasses to control secondary color and the choice of focus system configuration to minimize breathing, provide continuous close focusing to macro magnifications and the reduction of the number of large diameter elements required.

For best results and the highest speed of cutting sheet metal by high power lasers, the numerical aperture of the focussed beam must be properly matched to the material thickness. To alleviate the need for frequent changes of fixed-focal-length lenses a zoom lens system which allows fast and continuous adaptation is desirable. Requirements include near diffraction limited performance in a range of at least f/3 to f/8 and a back focus in excess of the focal length for lens protection against fumes and spatters. Four zoom lens designs for use with CO₂-lasers in the 1 to 2 kW range are presented, which differ in technical complexity (use of an aspheric surface versus an additional lens element) and in the ranges of numerical apertures (f/2.8 to f/8 and f/2 to f/7). Only one of these has so far been built and measured, and cutting tests have shown slightly better performance at the short focal lengths over that of single (ZnSe) lenses of (optimized) meniscus shape.

In this paper, several collimator systems that may be used in the IR region with no central obscuration are discussed. One of them is a two-mirror asymmetrical system with the secondary of high order asymmetrical surface. The system has been realized in practice. Optical design shows that the image spot is diffraction limited at the center of field, and is about 1.8 arcsec at the margin of +/- 0.6 degree(s) field. Due to technological defect, the real image spot is about 1.8 arcsec at the center and 4.2 arcsec at the margin of field.

The Far-Infrared and Sub-millimeter Space Telescope (FIRST) Astronomy Mission, is a cornerstone of the ESA science program for space observations in the 0.1 to 1 mm wavelength band. A very high accuracy star tracker has to be developed for the pointing and stabilization functions of the FIRST spacecraft. This paper deals with the optics trade-off analysis of this new star tracker VHPA, acronym derived from `very high pointing accuracy.' The optics trade-off consists of a comparative analysis of the following configurations: dioptric, catadioptric, Schmidt and Ritchey-Chretien telescopes. The results are shown and the polychromatic tests of image quality are reported, including centroid error function. A table of merit is provided in order to select the configuration proposed as baseline.

As leader in the design, manufacturing, and testing of electro-optical systems for space applications, Lockheed Missiles and Space Company is committed to the development of technology driven and competitively priced high quality products. In view of this commitment of improving quality and reducing cost, several designs for unobscured, off-axis, high performance, reflective optical telescopes for IR applications have been developed. The designs presented in this paper have been modeled and analyzed using state-of-the-art optical and mechanical design computer programs to determine their effectiveness in achieving very good optical characteristics, light weight, and low manufacturing cost. In particular a three mirror system is described which is capable of optical performance close to diffraction limit over a circular field of view of 20 degrees at f/4.

In this paper a new optical system for large astronomical telescopes is proposed. The center part of the primary mirror of a Cassegrain or R-C system is utilized to build a third mirror. Should we exchange the secondary of a Cassegrain or R-C system with another second mirror, the optical system becomes a powerful three-mirror system with good image quality and a relatively wide field. General equations for eliminating spherical aberration, coma, and astigmatism are given. An example of a 2-meter telescope system of this type is calculated and optimized.

A relatively large aperture (375 mm) optical system working at f/1.6 for a low-light-level movable TV camera has been designed. In the process of designing, advantages and defects of a catadioptric system with all spherical surfaces and three kinds of aspherical systems have been compared. The optical system we finally adopted is a reflecting system with two aspherical surfaces. Its primary mirror is hyperboloid and the secondary is a high order planary aspherical surface. Maximal asphericity is 0.048 mm and 0.007 mm, respectively. There are also two small correcting lenses (crown and flint glass) near focus in order to correct curvature of field and astigmatism. Within 2.4 degree(s) field of view, spot diagrams show that the maximal image is 0.035 mm in diameter with a flat focal plane over the wavelength 4861 angstrom to 6563 angstrom. The total weight of the optical elements is about 14 Kg. The optical tube length is about 277 mm and its T/Number is 2.

In general, the correction of cemented doublets is based on the convergence condition and the correction of spherical and chromatic aberrations. This can be achieved by a suitable assignation of values to the lenses radii. Moreover, if during the correction process a change of glass is introduced, it is possible for another aberration to be in tolerance. The result is a two lens system which, in spite of its simplicity, is free of many aberrations. The current presentation describes a method to obtain aplanatic cemented doublets, with the spherical, coma, and chromatic aberrations in tolerance, by an appropriate selection of glasses before the project. Some maps of glasses with lines which provide this election are presented. These lines are valid for both telescope and microscope objectives. Besides, with this method it is possible to easily project aplanatic cemented doublets with a residual value of the spherical aberration. Finally, it is also shown that certain combinations of glasses are impossible to be corrected simultaneously of spherical and chromatic aberrations.

The task of correcting wavefront aberrations in large telescopes is split nowadays between active and adaptive optics. This paper defines the requirements for an active optics system and discusses the advantages and disadvantages of different types of primary mirrors from the point of view of active optics.

Following the successful astronomical runs of the Come-On adaptive optics prototype on the ESO 3.6 m telescope in La Silla, Chile an upgraded version called Come-On-Plus is currently being constructed and was set up in December 1992. This paper describes the main improvements of this new system. In particular, the 52 actuator deformable mirror with 30 Hz closed loop bandwidth, the modal control, the high detectivity wavefront sensor channel, and the infrared imaging channel are presented. Finally, the laboratory tests of each subsystem are analyzed. This second prototype is dedicated to routine astronomical observing as well as providing design parameters for the adaptive optics for the ESO Very Large Telescope (VLT).

Algorithms of wavefront reconstruction and phase distortions compensation by an adaptive optical system of phase conjugation in the presence of measurement noises and errors of phase corrector control within statistics view on a base of variational and matrix methods are presented. Reconstruction and compensation of phase distributions use information about statistical characteristics of wavefront, measurement noises, and control errors. Equations for orthogonal Karhunen-Loeve type modes, providing minimum phase distortions compensation error, while the number of modes is fixed, and realized by phase corrector with fixed response functions without approximation error, are received and researched. Results of calculations of residual error of reconstruction and compensation of wavefront disturbed by atmosphere in an adaptive system with a different number of Gartman sensor channels and a different number of actuators via the value of measurement noises and control errors are presented.

Laserdot has at first been involved in the adaptive optics field under French government military programs. It has allowed the achievement of very high-performance systems. Impressive results have been obtained in this specific field. In this paper we first remind the reader how an adaptive optics system runs and we review the main components used in such a system. Second, we briefly describe the Come-On-Plus experiment and relative components. As a description of the different strategies that can be explored for astronomical applications, we also present the Adaptive Optics Bonnette of the CFHT 3.6 m telescope. At last, we describe the peculiar adaptive mirror that has been achieved for the ESRF x-ray beam line as well as the sensor which is being used in this experiment. It shows that it is possible to extend the concept of adaptive optics to other domains than military or astronomical applications.

The paper defines the concept of optimized modal correction for adaptive optics systems. The objective is to achieve the best image quality versus the disturbances to be corrected and the level of light coming from the observed object. Examples of optimized modal correction effects on optical transfer functions are given and compared to the results obtained without optimization. This work has been supported by DRET (Direction des Recherches, Etudes et Techniques) and CFH Corp. (Canada France Hawaii Corp.).

The a-priori knowledge of the availability of active optics in a telescope can be advantageous in the design, optimization, and specification of tolerances for auxiliary devices of such a telescope. A modification of the merit function to be used into the optimization process is given, together with some considerations about the design procedure. The different effects of aberrations typically depending upon the position of the field of view (like coma or astigmatism), with those typically constant over the whole field of view (like spherical aberration) are explicitly taken into account in the mathematical treatment. A possible range of applications (prime focus corrector, off-axis field corrector, field flattener, reducing camera, and so on) is discussed. A case study for a field flattener is shown. The general result that can be derived from this paper is that tolerances are generally strongly relaxed, while a significant improvement of the nominal performances can be obtained only in particular cases or assuming a high dynamic range of the active optics correction.

We shall consider the compensation for thermal distortions of laser beams propagated through the atmosphere on horizontal and vertical paths. It is found that the critical power of the source can be increased about ten times when going over from horizontal to vertical paths. The efficiency of different adaptive correction algorithms, namely program correction, phase- conjugate, and amplitude-phase control, are studied.

Recent advances in adaptive optics control techniques have demonstrated the interest of modal control in astronomical applications in comparison with a nodal control. This paper describes the advantages to use such a control for the Come-On-Plus project. The different steps of nodal and modal control algorithms used for this experiment are given.

Laser guide star (LGS) adaptive optics systems can dramatically improve the resolution of ground-based astronomical telescopes but introduce a variety of novel optical engineering requirements. We describe how these requirements have been addressed in the Starfire Optical Range (SOR) Gen II adaptive optics system and review sample experimental results illustrating the degree of atmospheric turbulence compensation achieved with natural and laser guide stars. Although adequate for a 1.5 m aperture diameter telescope, the level of compensation possible with a single low altitude LGS is limited by anisoplanatism and will not be adequate for larger aperture telescopes operating at visible wavelengths. We evaluate these limitations numerically for a sample problem involving a four meter aperture diameter telescope and estimate the performance improvements possible through the use of mesospheric sodium guide stars, multiple guide stars, and multiple deformable mirrors. Implementing these advanced concepts introduces new challenges in the areas of laser guide star generation, wavefront sensing, and beam train optical design.

We analyze the use of a single laser or natural guidestar to correct atmospheric distortion for a wide field of view (WFOV) imaging system. We concentrate on the absolute system limits without regard to radiometrics or compensation method by evaluating the best system OTF possible at field points in and beyond the isoplanatic patch. The improvement of OTF at mid- spatial frequencies is several decades over the non-corrected OTF even at field angles of one arc minute, and we conclude that post processing should be able to recover much more information in adaptive optics systems even at wide FOVs than uncompensated systems.

The Berlin Lens Design Problem, the first problem posed at a European conference, differs slightly from the problems posed at the large international lens design conferences held in the USA. The problem: Decentered Center Element, created by Hannfried Zugge and myself, stresses the practical aspect of lens design. It is well known by experienced lens designers: image degradation is mainly due to decentering tolerances. Therefore, the knowledge of what happens if a lens-element is decentered is essential for the practical success of a lens which is to be manufactured. Of course, such a problem is handled today by a tolerancing program. But tolerancing an existing design is a post-process which doesn't change the design. On the other hand, up to today, no design procedure is known (at least in the literature) which makes sure that the design-process will create a lens, which can be manufactured easily. Also the Berlin Lens Design Problem doesn't change this state of the art. But dealing with the problem indeed may increase the knowledge about a decentered system, either reoptimized or not. The solutions received show that there is a practical value as well as a scientific one. In addition, we really hope that every contributor was, and hopefully every reader of this paper is, fascinated by this unusual problem.

The application of the program DEMOS for design and modeling of IR optical systems is considered. The principles of the multiconfigurational optimization for IR and multispectral systems design are worded. The analysis of the kinoform elements (KE) application for the systems of this group is given. Besides, the methods of the image quality improvement by means of optical system optimization taking into account the surface errors are described. The examples of IR systems design are presented.

The current two major non-numerical design methods, equivalent layers and polynomial synthesis, are reviewed and compared. The equivalent layer method works well when only a small number of fixed refractive indices is available. This is the case when the coating is manufactured by evaporation. Polynomial synthesis generates a priori better designs but does not allow predetermination of refractive indices. So, for evaporation, the designs have to be translated from many refractive indices to a few. This process generally downgrades the design. This translation is not necessary when sputtering or chemical vapor deposition is being used. Here, in-between refractive indices can easily be generated by mixing or flip-flopping. As a consequence, superior designs can be implemented.

A report is given on the contents and the structure of ISO DIS 10110 "Preparation of drawings for optical elements and systems", including a comprehensive selection of important details. This future International Standard gives rules for the indication of quality characteristics of optical elements and subsystems.

An outline is given of how advantages of conventional magnetic recording have been combined with those of compact disc technology to establish a method of high density magneto-optical recording, where information can be erased and freshly recorded at potentially very high superficial density and data rates. Application of the principles of thin film optics to the design of multilayer recording media with optimised magneto-optical "read" characteristics are emphasised, and possible future developments discussed.

In recent years a lot of efforts were made to characterize laser beams and to describe their propagation in optical systems. More than two years one working group of the International Organization for Standardization (ISO) worked in this field and has proposed a procedure to measure beam width and beam divergence1. The Optical and Quantum Electronics Journal will publish a special issue on laser beam quality this year2. What a waste of time for a single parameter one might think. What are the problems, then?

The properties of multiple-layer dielectric systems of low absorption are considered. The possibility is demonstrated of application of conducting surface model for the cases when absorption is concentrated near the layer boundaries. The formulas for calculation of such systems are presented. Special attention is paid to the calculation of quarter-wavelength slightly absorbing mirrors, including the case of oblique light incidence.

As a consequence of advancements in Inertial Confinement Fusion research, LLNL is developing plans for a new 1.5 to 2 mega-joule solid-state Nd:glass laser designed to achieve fusion ignition. The new design is possible in part due to advances in optical coatings suitable for highpower laser systems. High damage threshold mirrors and polarizers are comprised of electronbeam deposited dielectric multilayers. Subthreshold illumination, or laser conditioning, of the multilayer coatings results in an increase in the damage thresholds by factors of 2 to 3 at 1.06pm, thus meeting the fluence requirements of the advanced architecture. For anti-reflective coatings, protective organic coatings for non-linear crystals and phase plates for beam smoothing, sol-gel films provide high damage thresholds coatings at low cost.

The requirement of not just survival but high performance operation in a hostile environment is a fundamental consideration in some optical systems. The paper details the effects of - and compensation for - deep-sea immersion, variable air-pressure and humidity, and a variety of thermal perturbations. The deleterious effects on optical materials resulting from a selection of hostile environments, including that of high radiation levels, are also considered and suggestions made concerning the optimum choice of materials.