Optical systems for photon management, that is the generation of tailored electromagnetic fields, constitute one of the keys for innovation through photonics. An important subfield of photon management deals with the transformation of an incident light field into a field of specified intensity distribution. In this paper we consider some basic aspects of the nature of systems for those light transformations. It turns out, that the transversal redistribution of energy (TRE) is of central concern to achieve systems with high transformation efficiency. Besides established techniques nanostructured optical elements (NOE) are demanded to implement transversal energy redistribution. That builds a bridge between the needs of photon management, optical engineering, and nanooptics.

The European Network of Excellence on Micro-Optics (NEMO) is a consortium of about 30 European institutes and companies which are working on micro-optics. The network is supported by the European Commission for a period of four years. One of its work packages is the Centre for Modelling and Design consisting of about 20 partners. In this work package a benchmark of the capabilities of commercial and internal software tools which are available among the partners will be made. The ten test systems which are used for the benchmarking range from seemingly simple things like calculating the intensity distribution in the focus of a microlens to complete systems like for example an optical interconnect system with microlenses, DOEs and a prism. The paper will present some of the benchmark systems. First results of the benchmarking itself cannot be presented in this proceeding because the benchmarking just ends at the end of August (after the deadline of this proceeding). But, hopefully first results can be presented during the talk.

In this contribution we present the accurate analysis and modeling of periodic optical structures that are finding wide application in photonics. The EM analysis is performed by two different 3D full-wave methods, the Transmission Line Matrix-Integral Equation (TLMIE) and the Generalized Transverse Resonance Diffraction (GTRD). TLMIE is a 3D full-wave hybrid technique in the time-domain which combines the advantages of the numerical TLM method and those of the analytical Green's functions representation for the free-space region, thus providing exact boundary conditions at optical frequencies. In GTRD the dyadic Green's function of a loaded box is used for the modeling of the layered structure, combined with Ohm's law formulation of the volume currents. By using the pre- and post-processing tools of TLMIE and GTRD methods, we investigate the dynamic of the EM field in and outside the structure and evaluate the frequency response of the laminated polarizer behaving as a negative uniaxial crystals. The calculated S-parameters are compared with measured data showing good agreement.

Depending on the specific application of a diffractive optical element (DOE), its polarization impact on the optical system must be taken into account. This may be necessary in imaging as well as in illumination optics, e. g., in miniaturized integrated optics or in high-resolution photolithographic projection systems. Sometimes, polarization effects are unwanted and therefore an exact characterization of their influences is necessary; in other cases a high polarization effect is the goal. It is well known how to calculate the point spread function (PSF) of a single diffractive micro-Fresnel lens. To do the same for a complete optical system with source, lenses, coatings, mirrors, gratings and diffractive elements, a 3D electrical field propagation along the geometric optical path is introduced into the ray-trace based optical systems design software in order to incorporate the entire electromagnetic polarization effects from the source to the image plane. Our software also considers the complex diffraction amplitudes including polarization effects from DOEs provided by rigorous electromagnetic methods. Together with a plane wave decomposition and with the local linear grating assumption, we are able to rigorously investigate the impact of e. g. polarization effects on the PSF of the whole optical system. Using this approach we analyze a hybrid diffractive-refractive microscope objective for mask inspection systems at 193 nm. Additionally we investigate focal properties of a sample diffractive blue laser disc pickup system.

In this paper we present a robust pseudo-random method for propagating an electromagnetic wavefront through an arbitrary optical system. The wavefront at an arbitrary plane is obtained by the discrete sampling of the wavefront in regular regions equally distributed on the entrance pupil and the appropriate modelling of the optical properties of the system. The discretization permits us to treat each region as a plane wave, so long as the area is small compared to the area of the pupil, therefore allowing us to apply the electromagnetic approximations of refraction and reflection during the transfer through an optical system. We can therefore account for amplitude and phase modulation of the wavefront due to the optical system, without making any assumptions about the shape of the optical elements. Furthermore, our numerical integration method on an arbitrary plane avoids singularities due to the classical analytical integrals, while still obtaining results comparable to rigorous electromagnetic theory. We have applied the method to simulating the propagation of both plane waves and spherical waves. The well known interference patterns of classical experiments such as Young's interference fringes or Newton's rings were reproduced accurately, with respect to results obtained applying analytical methods. We then successfully applied the method to analyze a Michelson interferometer set-up, demonstrating the robustness of the calculations. Since the propagation of the wavefront is possible with this method, in the future we plan to apply the method to simulating electrically large diffractive optical elements within a complex optical system, for which rigorous analytical methods may not be available, and other numerical methods generally require large computer resources.

During the last few years, the understanding of pupil plane manipulation capabilities to achieve an enhanced image formation process and its theoretical limitations becomes more and more important. Particularly the increased potential of computer calculations and digital signal detection makes it possible to simulate this kind of manipulations very fast and efficient. At the same time there is the opportunity to change the optical system such, that a digital reconstruction of the image gives a higher amount of information. An analysis of the optical transfer function as an important parameter of imaging quality with special interest in extended depth of focus is presented. The performance of different pupil plane masks is illustrated in comparison with standard optical systems. This means the basic features like depth of focus, resolution and contrast were derived and the limitations are shown. The mathematical principle of extended depth of focus with pupil manipulation is described and demonstrated with exemplary calculations. Furthermore, the relation between a given optical transfer function and the matching pupil function is shown. A robust and iterative algorithm is presented to calculate a pupil mask for a desired optical transfer function.

A general concept based on harmonic decomposition of pulses has been introduced to model ultra short pulse propagation through homogeneous and inhomogeneous dielectrics. This include propagation through free space, apertures and lens systems. This approach permits us to consider pulses of any arbitrary spatial and temporal characteristics. The pulse characteristics are found to be affected by angular and material dispersion. A computationally efficient method for the proper sampling of spectral phase has been introduced which requires only a minimum number of harmonic fields for the simulation. In the case of free space propagation, pulses maintains their shape but experience temporal and spectral shifts whose magnitudes depends on angular dispersion (diffraction angle). The pulse broadens, becomes asymmetric and chirped in dispersive media because of group velocity dispersion and higher order dispersion in the media. The pulse broadens due to radially varying group delay and group delay dispersion on propagation through focusing elements. The pulse energy at the focus is affected by the interplay of spherical and chromatic aberration by distributing the pulse energy over a large region on the axis.

Lens system design makes extensive use of optimization techniques to improve the performance of an optical system. We know that designing a lens system is a complex task currently done by experienced optical designers, using specialized optical design software tools. In order to contribute to this particular field, this paper presents a comparison between lens design done by optical designers and evolutionary algorithms lens based design. Evolutionary algorithms consist in population-based global search methods inspired by natural evolution. They are recognized to be particularly efficient for complex non-linear optimization problems. Given the non-linear nature of lens design as an optimization process, evolutionary algorithms are good candidates for automating this task. The evolutionary algorithms were applied to the monochromatic quartet that was presented to expert participants at the International Lens Design Conference in 1990 (a friendly competition). Comparative results demonstrate that the evolutionary approach is able to find solutions slightly better than those presented at the competition. Then a real-life imaging problem is tackled. Results show that an evolutionary algorithm is again able to discover lens systems comparable to design done after a reasonable effort by experts. This paper presents an analysis of this approach for automatic lens design from a real-life optical design point of view.

A variety of simulation tools, including optical design and analysis, have benefited by many years of evolution in software functionality and computing power, thus making the notion of virtual design environments a reality. To simulate the optical characteristics of a system, one needs to include optical performance, mechanical design and manufacturing aspects simultaneously. To date, no single software program offers a universal solution. One approach to achieve an integrated environment is to select tools that offer a high degree of interoperability. This allows the selection of the best tools for each aspect of the design working in concert to solve the problem. This paper discusses the issues of how to assemble a design environment and provides an example of a combination of tools for illumination design. We begin by offering a broad definition of interoperability from an optical analysis perspective. This definition includes aspects of file interchange formats, software communications protocols and customized applications. One example solution is proposed by combining SolidWorks¹ for computer-aided design (CAD), TracePro² for optical analysis and MATLAB³ as the mathematical engine for tolerance analysis. The resulting virtual tool will be applied to a lightpipe design task to illustrate how such a system can be used.

Specifics of non-imaging optical systems require special algorithms for automated optimization. We have implemented two methods into commercially available optical design software, which are robust and numerically effective. The first one is a modification of the edge-ray principle. In this case the optimization criterion should be expressed in geometrical terms (like, for example, collimation of an extended light source). This gives us the possibility to design not only CPClike collimators, but also rather complex refractive-reflective (RXI-like) devices. For the second (more general) case the optimization criterion is expressed in energetic terms. In this case stochastic behavior of the merit function due to Monte-Carlo ray-tracing procedure limits the applicability of standard optimization routines available in optical design software. We have realized a direct optimization algorithm, which does not calculate the derivatives of the merit function leading to reduced sensitivity with respect to local statistical deviations. The proposed algorithm is deterministic and does not suffer from redundant trials of random search. As a parametric description for the objects to be optimized we propose the use of piecewise Bezier splines. This allows relative strong shape bending but requires control for intersections. A "red-blue intersection reporting" algorithm is realized as a constraint for optimization.

In modern optical engineering the simulation of imaging and non-imaging optical systems on the basis of wave optics is of increasing importance. A simulation based on wave optics means on one hand to use everywhere in the optical system a wave-optical description of light. This allows the evaluation of more general merit functions for the description of the system quality which requires, for example, access to amplitude, phase, polarization, coherence information of light. On the other hand, including wave optics in optical simulations means to model the light propagation exact enough to describe wave-optical propagation effects. That means in general not to perform all simulations without physical approximations but to use light propagation models that work with sufficient physical precision within the optical system. The authors will discuss which needs follow for modern optical simulation software. This discussion includes a flexible handling of different models for simulation of light propagation, descriptions of different wave-optical light representations and considerations of numerical and physical simulation precision.

The main application of Monte Carlo methods in raytracing software lies in the field of scattering analysis. The basis for this simulation in raytracing software is the variation of the ray direction after refraction described by a Bidirectional Scattering Distribution Function (BSDF). In the simpliest case the scattering process is described by a BSDF which only depends on the scattering angle. We have extended this simple approach in different directions. One extension enables the simulation of different surface scattering effects. For example with a BSDF, which varies with the ray height on the surface, the local variation of the surface roughness due to fabrication effects can be simulated. Another extension allows the simulation of volume scattering. In this case the scattering properties of the material can be described by two functions: As before a scattering function determines the change in the ray direction due to local defects in the material. Additionally a function for the free path length is used e.g. to describe the density of local defects in the volume. The requirements and the limitations of the methods are shown and discussed. Several examples of typical applications are presented.

After having summarized the different methods in use to tolerance optical systems, with advantages and drawbacks, we present a new software, called TOLTRI, to post process the data's of tolerancing obtained with the TOR routine of CODE V and also introduce new features which are not possible in another way. This software accelerate the interpretation and discussions between the different disciplines involved, by presenting and sorting the results on separate EXCEL sheets and Matlab figures.

The history of lens design software is sadly littered with accounts of excellent programs which fell by the wayside for lack of support. Others evolved through various package formats to form the foundation of today's very successful commercial software. One example of this is the Imperial College lens design program developed throughout the 1960s, 1970s and 1980s by Charles Wynne, Michael Kidger, Prudence Wormell, and others. This program (best known as the Kidger Optics Ltd SIGMA) produced many excellent designs over the years. One reason was that the ray patterns and weighting factors for operands in the default merit function had been carefully honed through experience, to produce rapid convergence on the global optimum from a likely starting point. This paper describes a suite of optimisation raysets and weighted operands written in the C-like OSLO compiled macro language CCL, and modeled on the Imperial College tradition. It is available for free download from http://www.lambdares.com/techsupport/kb/index.phtml. Its prime function is to provide a fast, easily understood introduction to merit function construction for the beginner. One version is for use on OSLO EDU, the free version of OSLO, which is also available from the Lambda Research Corporation website. This paper demonstrates how OPIC can be used to locate, from a remote starting point, the global minimum of the "monochromatic quartet," the lens design problem from the SPIE 1990 International Lens Design Conference.

The use of a segmented merit functions in the optical design process is a good strategy to improve the optimization trajectories, however to reach good results it is necessary to change the segmentation of the merit function during the optimization. In this work we present a new application of the aplanatism condition, where it is used as a method to segment the merit function when extended objects are involved in the merit function definition. Our method begins with an equally distributed first sampling of the object to evaluate how far the sampled point is from the aplanatic condition. This initial value collection are used to obtain a second sampling of the object that provides the appropriate number of object field points that must be taken into account to use in the merit function. The use of the aplanatic condition to obtain dynamic merit function segmentation is especially important when large object fields are involved in the design process. We have tested the method using a wide field of view objective. The final objective configuration was obtained twice, one with a standard segmentation of the merit function (on axis, zonal point and full field) and two, with our method. The merit function, the optimization strategy, the variables and the initial system used are the same for both optimizations.

Because of the index change between water and air, dive masks with flat interfaces magnify by a factor of 1.34X, and the field of view (FOV) in water is restricted to about 60 degrees. In addition, the image suffers significant amounts of lateral color and distortion. For technical diving applications (e.g., underwater welding), these attributes reduce situational awareness, lead to poor hand-eye coordination and are highly undesirable. This paper describes the design issues and design solution of a unity magnification dive mask covering a full FOV of 140 degrees.

In this paper several techniques are described to perform the determination and correction of lens distortion in fringe projection systems for 3D object measurement. A new method to realise distortion determination for projection systems is introduced. It uses a plane surface and the projected fringe pattern as calibration tools and determines simultaneously the distortion of both projector and camera lens within an iterative procedure. The lens distortion calibration is performed in the state of the device "ready for measurement" which avoids errors by a later adjustment. A reduction of distortion errors up to 0.02 pixels in the projector chip and also in the camera chip is possible and leads to considerable improvements in the 3D measurements.

The effects of atmospheric differential refraction on astrophysical measurements are well known. In particular, as a ray of light passes through the atmosphere, its direction is altered by the effects of atmospheric refraction. The amount of this effect depends basically on the variation of the refractive index along the path of the ray. The real accuracy needed in the atmosphere model and in the calculation of the correction to be applied is of course, considerably worse, especially at large zenith angles. On the VLT Survey Telescope (VST) the use of an Atmospheric Dispersion Corrector (ADC) is foreseen at a wide zenith distance range. This paper describes the software design and implementation aspects regarding the analytical correction law discovered to correct the refraction effect during observations with VST.

Bi-directional Reflectance Distribution Function (BRDF) measurements that characterise the scattering properties of surfaces are extremely important to the design of optical instruments. Sophisticated codes require the characterisation of the scattering function of optically black and/or differently machined surfaces at several angle of incidence in a wide range of detector angles. These data can be used to develop processes to achieve desired BRDF patterns or to improve stray light suppression techniques. In this paper, we present the characteristics of an automatic, three dimensional, BRDF measurement set up that has been designed and developed at Galileo Avionica by the authors and the most significant experimental results of 3D BRDF data achieved on samples of aluminium alloys, gold and titanium, differently machined and/or black painted. The measurements have been taken at different illumination angles (from the normal incidence up to 45 degrees) at the wavelength of 650 nm. The wide variety of possible applications that can be explored through the proposed equipment, jointed to its flexibility, constitute a reference point for future investigations on the characterisation of the scattering properties of machined materials and paintings.

We have designed an ocular aberrometer based on the Hartmann-Shack (HS) type wavefront sensor for use in optometry clinics. The optical system has enhanced versatility compared with commercial aberrometers, yet it is compact and user-friendly. The system has the capability to sense both on-axis and off-axis aberrations in the eye within an unobstructed 20 degree field. This capability is essential to collect population data for off-axis aberrations. This data will be useful in designing future adaptive optics (AO) systems to improve image quality of eccentric retinal areas, in particular, for multi-conjugate AO systems. The ability of the examiner to control the accommodation demand is a unique feature of the design that commercial instruments are capable of only after modification. The pupil alignment channel is re-combined with the sensing channel in a parallel path and imaged on a single CCD. This makes the instrument more compact, less expensive, and it helps to synchronize the pupil center with the HS spot coordinate system. Another advantage of the optical design is telecentric re-imaging of the HS spots, increasing the robustness to small longitudinal alignment errors. The optical system has been optimized with a ray-tracing program and its prototype is being constructed. Design considerations together with a description of the optical components are presented. Difficulties and future work are outlined.

We report the in situ characterization of a semiconductor saturable absorber mirror (SESAM) in an operating Yb:KGW mode-locked laser. The technique may be described as a pump-probe experiment in which the intracavity beam acts as a pump beam, while the output of the same laser is used as a test beam for the SESAM reflectivity. At zero delay, the probe pulse overlaps in time with the subsequent intracavity pulse. The method is an alternative to standard pump-probe measurements, in situations where the intracavity parameters such as energy fluence onto the SESAM, pulse length and center wavelength can not be simultaneously achieved with available lasers.

Nowadays optical design for microscopes encloses besides the classical approach many new ideas like implementation of new optical elements, the consideration of physical effects or digital image processing. All these things play an important role during the development of microscopes and microscopic components at Carl Zeiss. In this paper we present examples of the classical approach starting with the imaging theory of Ernst Abbe as well as the non-classical approach ranging from microscopic objectives with diffractive optical elements over the implementation of the propagation theory of short-time laser pulses in optical design software to digital image restoration and phase measurement.

When we design lenses, we always wonder if any better design exists than the current design. If the current design could be proved to be the global minimum under given conditions, we could be fully confident on our design. In this paper I would like to show an example of such a proof. The design example is the "reversible lens", 1985 International Lens Design Conference lens design problem. This problem requests the aberration control at the lateral magnifications -1/2 and -2 simultaneously. From the nature of light, the perfect imaging at the 2 magnifications can not be realized. Some researchers have been interested in the problem to predict the performance limit quantitatively, and to find the real design that realizes this performance limit. In 1992 Forbes and Jones applied a global optimization to this problem and showed some solutions with different element numbers. In 1995 Forbes and Wallace predicted a performance limit by the method of the optimization of the Eikonal function. But this prediction was much better than the performance of the ever-found solutions. In this paper I investigated the prediction of Forbes and Wallace and modified their prediction. I also designed a real lens that reaches the predicted performance limit.

Triggered by the roadmap of the semiconductor industry, tremendous progress has been achieved in the development of Extreme Ultraviolet (EUV) sources and high-quality EUV optical coatings in recent years, opening up also new fields of applications apart from microlithography, such as metrology, high-resolution microscopy, or surface analysis. In all these research areas the quality and imaging properties of the employed optics play a crucial role. In this contribution we present a comparison of different optical setups capable of guiding and imaging EUV radiation, which were tested in combination with a miniaturized laser-produced plasma source with high pulse energy (~ 3.5 mJ @ 13.5 nm) and a plasma size of about 300 μm. First, a modified EUV Schwarzschild objective with a numerical aperture of 0.44 and a demagnification factor of 10 was developed within the research project "KOMPASS". After adaptation to the table-top EUV source, a focus with a diameter < 30 μm at energy densities of several mJ/cm² could be produced. The setup is currently being used for comparative investigations of the interaction of EUV radiation with different materials, as e.g. the color center formation in LiF crystals. An attempt to use the Schwarzschild objective in reverse geometry as a EUV microscope will be part of future work. Second, a Kirkpatrick-Baez arrangement was realized, using the reflections from two curved silicon wafers under grazing incidence (about 5°). The cylindrical curvature is obtained by bending the thin substrates, allowing for a continuous tuning to the desired radii. Due to an Au coating a high reflectivity (theoretically ~ 80 % per reflection) over a broad EUV spectral range can be achieved. For reduction of aberrations the optical systems were fine-adjusted with the help of a Hartmann-Shack wavefront sensor both in the visible and in the EUV spectral range. The imaging properties in the EUV range were determined and compared to ray tracing calculations performed with ZEMAX.

Finding multiple local minima in the merit function landscape of optical system optimization is a difficult task, especially for complex designs that have a large number of variables. We discuss here a method that enables a rapid generation of new local minima for optical systems of arbitrary complexity. We have recently shown that saddle points known in mathematics as Morse index 1 saddle points can be useful for global optical system optimization. In this work we show that by inserting a thin meniscus lens (or two mirror surfaces) into an optical design with N surfaces that is a local minimum, we obtain a system with N+2 surfaces that is a Morse index 1 saddle point. A simple method to compute the required meniscus curvatures will be discussed. Then, letting the optimization roll down on both sides of the saddle leads to two different local minima. Often, one of them has interesting special properties.

The multidimensional merit function space of complex optical systems contains a large number of local minima that are connected via links that contain saddle points. In this work, we illustrate a method to construct such saddle points with examples of deep UV objectives and extreme UV mirror systems for lithography. The central idea of our method is that, at certain positions in a system with N surfaces that is a local minimum, a thin meniscus lens or two mirror surfaces can be introduced to construct a system with N+2 surfaces that is a saddle point. When the optimization goes down on the two sides of the saddle point, two minima are obtained. We show that often one of these two minima can be reached from several other saddle points constructed in the same way. The practical advantage of saddle-point construction is that we can produce new designs from the existing ones in a simple, efficient and systematic manner.

Weight optimization here stands for optic design, i.e. creation of a new optical system, on the assumption that weight should be a minimum! This will be done only by means of traditional design methods, that is excluding the use of aspherical surfaces, plastic materials, mirrors, diffractive or similar elements! This demand for lowest possible weight is important with systems, that must be transported for example into space, as well as with handheld systems, for instance binoculars, riflescopes, but also with photographic lenses. Up to now, no theory exists which describes how this problem can be solved. Here, the essay begins with the fundamentals, after that the basic facts related to the weight of a lens are discussed, as well as references made to publications. At the end, two design examples are given, the first being a binocular. The second example shows, that even in hopeless cases sometimes a solution can be found.

To fulfil the requirements of today's high performance cine lenses aspheres are an indispensable part of lens design. Among making them manageable in shape and size, tolerancing aspheres is an essential part of the development process. The traditional method of tolerancing individual aspherical coefficients results in unemployable theoretical figures only. In order to obtain viable parameters that can easily be dealt with in a production line, more enhanced techniques are required. In this presentation, a method of simulating characteristic manufacturing errors and deducing surface deviation and slope error tolerances will be shown.

New projection concepts based on OLED (organic light-emitting diode)-microdisplays will be presented. Up to now mostly all projection systems are based on reflective and/or transmissive microdisplays like digital micromirror devices (DMDs), nematic liquid crystals displays (LCDs) or liquid crystal on silicon displays (LCOS). But the size of necessary light source and illumination optics is a strong limitation for the miniaturization of the projection system itself or for system integration. Here we propose to use a high-brightness OLED-microdisplay as active element for image or pattern generation, giving the possibility to realize compact projection or imaging units. Optical parameters of the microdisplays are determined to get input data for optical system design. Based on these experimental results specially adapted optical systems are designed. First prototypes and realized projection systems for applications in optical 3Dshape detection are presented.

Recently, the development of high NA lenses for immersion lithography turned from dioptric concepts to catadioptric design forms. The introduction of mirrors involves the new challenge to deal with the inevitable obscuration of either field or pupil. We review the strategies used in this regard for microlithography, while focussing on the two most favored ones, folded and inline concepts. Although the vignetting situation is more complicated for inline systems, we report progress in this field of optical design yielding similar system performance for inline and folded designs. Since inline optical systems are much easier to realize, these are the concept of choice.

A wide-angle catadioptric lens with the rectilinear projection scheme has been designed and fabricated using an ultraprecision contouring machine. The completed imaging system has a wide field of view of 160°.

Last advances in optical design and manufacturing have helped to enlarge possibilities for optical solutions in any field that used optics elements. However, the useful solution is not always the best theoretical achievable one. Now, to find the right solution, the restrictions usually do not come from theoretical limits of optics, but from the feasibility of its practical implementations. This paper analyzes a set of important figures to be considered in the design of concentration optical system for photovoltaic solar energy applications. To illustrate it, the ISOFOTON optical concentration option will be presented. It is based in an innovative design methods of non-imaging optics and it is called TIR-R^[1]:a two stage concentrator with a primary lens, working mainly by total internal reflection, plus a secondary lens, working by refraction.

The control of optical distortion is useful for the design of a variety of optical system. The most popular is the F-theta lens used in laser scanning system to produce a constant scan velocity across the image plane. Many authors have designed during the last 20 years distortion control corrector. Today, many challenging digital imaging system can use distortion the enhanced their imaging capability. A well know example is a reversed telephoto type, if the barrel distortion is increased instead of being corrected; the result is a so-called Fish-eye lens. However, if we control the barrel distortion instead of only increasing it, the resulting system can have enhanced imaging capability. This paper will present some lens design and real system examples that clearly demonstrate how the distortion control can improve the system performances such as resolution. We present innovative optical system which increases the resolution in the field of view of interest to meet the needs of specific applications. One critical issue when we designed using distortion is the optimization management. Like most challenging lens design, the automatic optimization is less reliable. Proper management keeps the lens design within the correct range, which is critical for optimal performance (size, cost, manufacturability). Many lens design presented tailor a custom merit function and approach.

Stationary Fourier transform spectrometry is a well-known concept to build reliable field or embedded spectroradiometers, especially for the mid- and far- infrared. However, the quality of the interference pattern imaged on the focal plane array is crucial to obtain a good spectrum by Fourier transform. We describe here an accurate modeling of the interferometer behavior that takes into account the instrument aberrations and field of view in order to quantitatively predict, at each wavelength and for a spatially extended uniform incoherent source, the real interferogram defects, namely, fringe distortion, fringe blurring and illumination non-uniformity. To investigate these effects, we first derive the properties of the elementary interferograms built by each source point. For this purpose, we use ray-tracing to extract optical path and vignetting information with the help of a commercial optical design software package, and we reconstruct from them the two wavefronts that hit the detector using general numerical methods with the help of standard computing tools. The whole interferogram being formed by the incoherent superposition of all elementary interferograms, we next, compute the relevant quantities by appropriate numerical quadratures. We illustrate this method with two potential layouts of a Fourier transform spectrometer that we are currently designing for accurate radiometric measurements in the 2.9μm-9.6μm range with a spectral resolution better than 8cm^-1 on a 4.5°x0.6° field of view.

The axicon is an optical element which creates a narrow focal line along the optical axis, unlike the single focal point produced by a lens. The long and precisely defined axicon focal line is used e.g. in alignment, or to extend the depth of focus of existing methods such as optical coherence tomography or light sectioning. Axicons are generally manufactured as refractive cones or diffractive circular gratings. They are also made as lens systems or doublet lenses, which are easier to produce. We present a design in the form of a reflective-refractive single-element device with annular aperture. This very compact system has only two surfaces, which can be spherical or aspheric depending on the quality required of the focal line. Both surfaces have reflective coatings at specific zones, providing an annular beam suitable for generating extended focal lines. One draw-back of a normal axicon is its sensitivity to the angle of illumination. Even for relatively small angles, astigmatism will broaden the focus and give it an asteroid shape. For our design, with spherical surfaces concentric about the center of the entrance pupil, the focal line remains unchanged in off-axis illumination.

Dioptric systems are usually the first choice for the design of an optical system, e.g. a projection lens or a microscope. But in some cases refractive designs suffer from serious drawbacks like chromatic aberration or material problems (cost, quality, absorption, birefringence, etc.). In such cases reflective systems are an attractive alternative. Reflective systems can be subdivided into two classes: on one hand there are systems with central pupil obscuration, e.g. reflective microscopes or telescopes in astronomy, which have a high aperture but only a small field size, on the other hand there are unobscured systems, e.g. reflective relay systems or EUV projection lenses, which have a large field but only small aperture. By the combination of an unobscured and an obscured mirror system one obtains systems with large field and high numerical aperture. We present new designs, which prove this design principle.

Depth of focus can be enhanced with cubic phaseplates located at the exit pupil of an optical system without significant loss of resolution. The enhancement factor is proportional to the strength of the phaseplate. The digital image is inversely filtered. The stronger the phaseplate is the stronger the inverse filter function must be. This causes increasing noise for high spatial frequencies in the restored image. Therefore, an optimum strength of the cubic phaseplate has to be chosen for the respective situation. A variable phaseplate system has been realized and tested. The performance of the setup has been experimentally studied. Applications and practical aspects are discussed in particular regarding barcode readers.

In a conventional particle tracking system, the depth of field is usually very small because of the use of high power imaging lens. The tracking accuracy may also be affected by the smearing of spot image, caused by focal shift. Increasing the focal depth and keeping uniform spot size in the focal region is highly desirable for a high accurate tracking system. In this report, we study the design of phase apdodizer that could be used to increase the focal depth of a tracking lens. The design is based on the requirements by highly accurate tracking that the point-spread function (PSF) of the lens keep an even and concentrated energy distribution when the lens is defocused. To achieve this purpose, a pure phase-shifting apodizer is introduced on the pupil plane of the lens. The function of the apodizer is to control the energy distribution of the 3D diffraction pattern near the focal region and make the effective spot size uniform or minimum variation along optical axis. The pattern of the 3D PSF of the lens with the apodizer shapes closed to a cylinder. New method used to search and optimize the design of the phase apodizer that meet the requirements of a particle tracking system will be studied. Theoretical analysis and numerical simulation are given in support of the method.

Numerous optical systems, such as telescopes, adaptive optics systems, and aberrometers, are equipped with wavefront sensors, which often use sampling devices measuring the slope of the wavefront at discrete points across the pupil (e.g. Shack-Hartmann sensors). The accuracy of the sampled output signal is always affected by the fabrication and alignment tolerances of the wavefront sensing optical system. Typically, it is a requirement to express the measurement error in terms of input wavefront, so the optical ray intercept error has to be converted into wavefront measurement error. This conversion cannot be obtained directly from a conventional tolerance analysis because of the wavefront breaking by the sampling device. The tolerancing method proposed in this paper solves the problem of converting conventional merit function degradation into input wavefront measurement error. The proposed method consists of two parts. First, a Monte Carlo tolerance analysis based on a specific merit function is performed, and a 90% border system is selected. Then, an optimization is applied to the 90% border system, by varying a "dummy" phase surface introduced at the entrance pupil of the system. A concrete example is presented.

For gaining a deeper understanding of the diffraction processes that take place in deep dielectric transmission gratings, a phenomenological explanation has been developed on the basis of a modal field, which propagates vertically through the grating region. The excitation of these modes by the incident wave, their propagation constants and how they couple to the diffraction orders determines the diffraction efficiency of the transmitted orders. The explicit modal analysis discloses the description of the highly efficient diffraction for polarized or unpolarized light by a very simple interference mechanism, which will be the subject of this paper.

Projection lenses for high resolution lithography have high NA and work at small wavelengths. In the wavelength regime of VUV (e.g. 193nm), there is a very limited number of optical glasses available, namely fused silica and calcium fluoride. The latter is very expensive and used only sparely, leading to limited possibilities for chromatic correction. In addition to catadioptric approaches, another way to deal with chromatic aberrations is the use of diffractive optical elements (DOEs). They have negative dispersion coupled with positive power and they do not contribute to the Petzval sum. Moreover, it is easy to integrate an aspherical functionality into the structure of the DOE. Usually a DOE is placed close to the aperture stop to correct axial color. The stop of a lithographic projection lens often is located at the largest diameter, causing some serious fabrication difficulties for the DOE. For this reason a class of lenses with intermediate image is of interest. Here, the accessible conjugate of the aperture stop enhances the possibilities to arrange the stop and the DOE. This allows a convenient tradeoff between fabrication challenges and aberration correcting properties. We present different lens designs that take advantage of the named properties of DOEs at high numerical aperture.

Micro and nano optics enable the control of light for producing intensity distributions with given profiles, propagation properties and polarization states. The higher the requirements on the optical function, the more complicated will be its realizing with a single element surface or a single element class. Combinations of refractive and diffractive, both diffractive or sub-wavelength structures with each other give the ability to link the advantages of different element classes or different element functions for realizing the optical functionality. In the paper we discuss two different examples of combinations for DUV applications. In detail we present a diffractive - diffractive beam homogenizer with NA of 0.3 that show no zero order. A binary phase grating for polarization control combined with a beam shaping element will be presented. The polarized order of this grating shows an efficiency of about 90% with a degree of polarization better than 90%. Wave optical and rigorous design strategies and simulations as well as the optical measurements will be discussed for the given examples.

Diffuser technology is known in diffractive optics for several decades and was mainly used together with coherent monochromatic light sources. In the last years diffusers play a more important role for illumination and homogenization task of partial coherent light sources, for example, Excimer lasers and LED's. In difference to illumination systems using lenses and micro lens arrays diffusers can be used to freely redistribute the intensity of the light source with a high homogeneity. Using diffuser technology for partial coherent illuminations needs an understanding of the characteristics of the light sources as coherence, wavelength bandwidth, divergence, radiation characteristic/intensity distribution. Since these characteristics are different for coherent and partial coherent light sources, these must be taken into account during the design of diffuser. This leads to new design concepts and surface structures. The authors will explain concepts of diffuser design for LED's and Excimer lasers and will show practical results.

To study the quantitative impact of diffractive optical elements on lens design and glass selection, a Zeiss Tessar lens (f/6) with and without a diffractive optical element is optimized with respect to the wavefront performance by a Zemax(R) Hammer routine. Optimization includes the selection of glasses as well as the geometry of the optical elements. In a first run, these are all refractive elements. In a second run, one refractive element is replaced with one diffractive surface. In a third run, the diffractive surface is introduced as an additional feature. It is found that one refractive element can be replaced with a diffractive surface at a moderate loss of lens performance. This holds, however, only for an optimized glass selection, which is found to be particularly important. In the case of four refractive elements plus diffractive surface, an according result is obtained. The diffractive surface will improve the overall system performance if and only if the glass selection is appropriate.

Established phase contrast methods in microscopy use the phase-shifted zeroth order Fourier component of an image-carrying light wave as a reference wave for interferometric superposition with the remaining part of the image wave. Our method consists of a spatial Fourier filtering of the image wave with a spiral phase element which leads to an edge enhancement of both amplitude and phase objects. The spiral phase element is realized by displaying a high resolution phase hologram on a computer-controlled reflective spatial light modulator. The edge enhancement is isotropic which means that all edges are highlighted simultaneously. Controlling the phase of the central area of the hologram leads to an interference image that has a 3-dimensional appearance of the object. In order to allow for white light imaging, the dispersion is compensated by a special double-diffraction setup.

A homogeneous illumination of a microscope requires a homogeneous intensity distribution in the field plane and in the pupil plane. An inhomogeneity in the pupil gives rise to a distortion in the image. This distortion is more clearly seen in defocused image planes and is commonly misinterpreted as classical aberration. An inhomogeneous intensity distribution in the field plane causes for example a line thickness variation of an imaged structure. In classical microscopy which operates with classical light sources, for example spiral-wound filaments, the task of designing a homogenised illumination can be solved using geometrical optics. Using instead of an incoherent a partial coherent light source may lead to interferences in the pupil and in the field plane which represent the major problem of such illumination systems. We present simulated results concerning the propagation of partial coherent light. The lateral and temporal coherence of a multimode laser was determined experimentally. With these results simulations were done using partial coherent beams. The considered optical components include lenslet arrays and diffractive optical elements.

A 21x Schwarzschild microscope lens for the EUV spectral range with a numerical aperture of 0.2 was designed and fabricated. The mechanical design of the lens had to comply with high requirements on surface figure amounting to 0.4 nm r.m.s. error for both mirrors. An optimized mirror mount was developed which is based on solid state hinges. In particular, gravity load, intrinsic stresses of the multilayer reflective coating as well as mounting forces and possibilities for mirror adjustment had to be considered. To provide a completely hydro-carbon free design the hinges were connected to the mirror by flux-less soldering.

In a number of applications the high precision microscopes are indispensable and rather complex instruments, which have afocal optical systems. The magnification of afocal optical systems is independent of the object distance. Therefore we can form a real image with a constant height of an object from a comparatively big object distance range [1]. Our aim is to develop an afocal optical system with a relatively big numerical aperture that facilitates the description of the vectorial calculation of electromagnetic field propagation from the object to the image [2]. The preconditions of these vectorial calculations will be achieved by a complex rear and a single front elements special afocal optical system, of which the following are strictly true: The object is in the front focal plane of the front element, the image is in the rear focal plane of the rear element, the aperture stop is in the rear focal plane of the front element and in the front focal plane of the rear element on the adjacent coincidental focal planes. Consequently, the raytracing is telecentrical in both the object and image space. The presentation shows the design of the afocal optical system that satisfies the above conditions and specifications.

The Space Infrared Telescope for Cosmology and Astrophysics (SPICA) mission is the third Japanese astronomical infrared satellite project of a 3.5m cooled telescope optimized for mid- to far-infrared observations, following the Infrared Telescope in Space (IRTS) and the ASTRO-F missions. It will employ mechanical coolers and an efficient radiative cooling system, which allow us to have a cooled (4.5K) telescope of the aperture much larger than previous missions in space. The SPICA will attack a number of key problems in present-day astrophysics, ranging from the origin of the universe to the formation of planetary systems, owing to its high spatial resolution and unprecedented sensitivity in the mid- to far-infrared. The large aperture size for cryogenically use is, however, a great challenge and demands substantial technology developments for the telescope system. We adopt monolithic mirror design in the baseline model because of the technical feasibility and reliability. We set the optical performance requirement as being diffraction limited at 5μm at the operating temperature of 4.5K. The total weight attributed to the telescope system is 700kg, which requires a very light 3.5m primary mirror together with the mirror support structure. At present we are working on two candidate materials for the SPICA telescope: silicon carbide (SiC) and carbon-fiber reinforced silicon carbide (C/SiC). This presentation gives a general overview of the SPICA mission and reports the current design and status of the SPICA telescope system, including recent progress of the development of C/SiC mirrors.

Monitoring of the oceans from satellite requires frequent updates - preferably with global coverage in one day, excluding effects of cloud. This demands optics covering swath widths up to about 3000km, within which spatial resolution in the order 250m or less is desirable for observation of coastal zones. Wide field angles, typically around 90°, are needed for optical systems operating from altitudes that are typical for polar orbiting satellites. At least 15 resolved spectral bands are needed in the visible and near-IR regions, requiring wide-field imaging spectrometers or designs using multiple filters. Other constraints on optical design include requirements for radiometric calibration, precise spatial registration of spectral bands, good control on stray light, and insensitivity to polarisation. The paper describes two design forms in which a single optical channel provides the complete wide-angle field, with appropriate allowances for calibration etc. In the first design, a wide angle telescope is followed by a spectrometer and an area-array detector. The spectrometer uses refractive dispersion for stray light control, and gives good spatial and spectral registration. In the second design, spectral resolution is provided by a set of filters with linear array detectors. In-field separation of detectors is used to avoid a need for dichroic beam splitters or dispersive optics; spatial registration in this case demands exceptional distortion correction, that takes account of Earth curvature. Both designs provide an external entrance pupil for location of calibration hardware.

The Ozone Monitoring Instrument (OMI) was launched on 15 July 2004 on NASA's EOS AURA satellite. The OMI instrument is an ultraviolet-visible imaging spectrograph that uses two-dimensional CCD detectors to register both the spectrum and the swath perpendicular to the flight direction with a 115 degrees wide swath, which enables global daily ground coverage with high spatial resolution. This paper presents a number of in-flight radiometric and spectral instrument performance and calibration results.

For the increasing market of low-cost multispectral pushbroom scanners for spaceborne Earth remote sensing the Jena-Optronik GmbH have developed the JSS product line. They are typically operated on micro-satellites with strong resources constraints. This leads to instrument designs optimised with respect to minimum size and mass, power consumption, and cost. From various customer requirements, Jena-Optronik has derived the JSS product line of low-cost optical spaceborne scanners in the visible wavelength range. Three-mirror anastigmat (TMA) telescope designs have become a widespread design solution for fields of view from 2 to 12 deg. The design solution chosen by Jena-Optronik is based on all-aluminium telescopes. Novel ultra-precision milling and polishing techniques now give the opportunity to achieve the necessary optical surface quality for applications in the visible range. The TMA telescope optics design of the JSS-56 imager will be accommodated onboard the RapidEye spacecraft. The JSS-56 TMA with a F-number of 4.3 realised a swath width of 78km with a Ground pixel resolution of 6.5m × 6.5m. The aluminium mirrors are Ni coated to achieve a suitable surface polish quality. This paper discusses typical requirements for the thermal design the bimetallic effects of the mirrors. To achieve a nearly diffracted limited imaging the typical surface irregularities due to the turning process have to be addressed in the ray tracing models. Analysis and integration of real mirror data in the ZEMAX design software are demonstrated here and compared with build-in standard tolerance concepts.

This paper presents an analysis of the requirements for instruments for meteorological applications, presents different implementation options with their prime benefits and drawbacks and discusses the optimization space. The different scanner options with their influence on the architecture of the optical system and the focal plane assembly are addressed. This leads to different candidate implementations. For those the optimization space is described leading to a preferred solution in form of a rotating reflective optics, an in-field spectral separation and a matrix based focal plane assembly. The main advantages of such a system are its flexibility with respect to the possible number of spectral channels, the possible radiometric resolution, and the variability of the geometrical resolution. It is shown that results of a first design iteration demonstrate the feasibility of the chosen approach.

This paper describes the optical design criteria and expected image quality of the High Resolution Imaging Channel (HRIC), which is part of the Spectrometers and Imagers for Mercury Planetary Orbiter (MPO) BepiColombo Integrated Observatory SYStem (SIMBIO-SYS) suite, for imaging and spectroscopic investigation of Mercury. SIMBIO-SYS has been selected by ESA as part of the scientific payload of the ESA BepiColombo mission to Mercury. HRIC has the main objective of characterising Mercury surface features with a very high spatial resolution in the visible. The optical design has been optimised to achieve the stringent scientific requirement of 5 m ground pixel size at 400 km from the planet surface. The adopted catadioptric optical configuration provides a resolution of 2.5"/pixel for a pixel size of 10 micron. The focal ratio is F#8 in order to be diffraction limited at 400 nm and to optimise radiometric flux and overall mechanical dimensions. The optical design solution includes two hyperbolic mirrors optimized with a dioptric camera, in order to correct the field of view of 1.47°, covered by a detector of 2k x 2k pixels. The mixed (reflective + refractive) solution guarantees a good balance of achieved optical performances and optimisation of resources (mainly volume and mass). The adopted configuration corrects and transmits well over the whole band of observation (400 - 900 nm).

The Heliospheric Imager (HI) is part of the SECCHI suite of instruments on-board the two STEREO spacecrafts to be launched in 2006. Located on two different orbits, the two HI instruments will provide stereographic images of solar coronal plasma and coronal mass ejections (CME) over a wide field of view (~90°), ranging from 13 to 330 solar radii (R₀). These observations complete the 15 R₀ field of view of the solar corona obtained with the other SECCHI instruments (2 coronagraphs and an EUV imager). The HI instrument is a combination of 2 refractive optical systems with 2 different multi-vanes baffle system. The key challenge of the instrument design is the rejection of the solar disk light, with total straylight attenuation of the order of 10^-13 to 10^-15. The optics and baffles have been specifically designed to reach the required rejection. This paper presents the SECCHI/HI opto-mechanical design, with the achieved performances. A test program has been run on one flight unit, including vacuum straylight verification test, thermo-optical performance test and co-alignment test. The results are presented and compared with the initial specifications.