In 1905 Karl Schwarzschild published three papers on optics, two of which revolutionized the field of reflecting telescope optics. In his first paper he developed a full theory of the aberrations of reflecting telescopes, generalizing the Eikonal of Bruns to take into account systems with an infinite long conjugate. In the second paper Schwarzschild applied his formulation to a masterful analysis of 2 mirror anastigmatic systems, along the way discovering the so called Ritchey-Chretien aplanat, 18 years Ritchey and Chretien's announcement. Numerous other innovations are given in what must be seen as being among the most important papers on the aberrations of optical systems ever written.

Simultaneous detection of the Stokes vector and Stokes images over a broad spectrum can be obtained from an achromatic division of amplitude imaging Stokes polarimeter. This is done through the use of a combination of beamsplitters, prisms and achromatic retarders to split the light into four different paths in collimated space and analyze each beam. Once each beam is focused onto the four quadrants of the camera, the Stokes vector, Stokes images and the degree of polarization across the scene can be obtained through the manipulation of the intensities for each image.

Many subtle effects arise when tracing polarization along rays that converge or diverge to form an image. This paper concentrates on a few examples that are notable for the challenges they pose in properly analyzing vector imaging problems. A striking example is the Federov-Imbert shift, in which coating phase-shifts cause a reflected beam to actually be deviated "sideways" out of the plane of incidence. A second example involving groups of coated surfaces is the correction of contrast loss from skew-angle depolarization in the optics of data projectors that use reflective polarization-modulating light valves. We show that phase-controlled coatings can collectively correct the contrast loss by exploiting a symmetry that arises when the coatings are operated in double-pass (due to use of reflective light valves). In lowest order, this symmetry causes any ellipticity that the coatings may introduce in the polarization of illuminating skew-rays to cancel in the return pass from the light valve back through the optics. Even beyond this first order reversibility result, we have shown elsewhere that, for NA less than about 0.2, the computation involved in calculating beam contrast can be reduced to the equivalent of tracing a single ray. We show here that the Federov-Imbert shift can be derived in a straightforward way using this formalism. Even a non-polarizing system will show vector effects when the numerical aperture is sufficiently high, as in photolithographic lenses. Wavefront quality in these deep-UV lenses is of order λ/100, and simulations to account for the complexities of the image transfer steps during IC manufacture must be accurate to better than a part in 1E2 or 1E3; hence small polarization distortions in the superposed image rays become very significant. An interesting source of such distortions is spatial dispersion in CaF₂ lens elements, which gives rise to intrinsic birefringence at the ppm level. Polarization ray tracing must then contend with the phenomenon of double refraction, wherein a given ray splits into two rays each time it passes through an element, giving rise in principle to an exponentially extended family of rays in the exit pupil. However, we show that it is possible to merge each coherent family of rays into a single plane-wave component of the image. (This is joint work with colleagues at Carl Zeiss SMT.¹) Generalizing beyond the analysis of birefringence, such a plane-wave component can be identified with the particular subset of rays that are converged through a common pupil point and transferred to the image after diffracting from the object points within an isoplanatic patch. Thin-film amplitude transfer coefficients implicitly take into account the prismatic change in beam-width that occurs when such a ray bundle refracts through a lens surface, but these coefficients do not include the focusing effect arising from power in the surfaces; hence polarization ray-tracing by sequential application of thin-film transfer coefficients does not by itself provide the correct amplitude distribution over the pupil.

Optical coatings are stratified media and, therefore, strongly anisotropic. The principal purpose of the stratification is to induce interference so as to yield the required spectral characteristics. At normal incidence the properties are largely insensitive to polarization, but at oblique incidence the sensitivity is significant. There may also be some birefringence in the material of the layers themselves, due to anisotropic strain or a directional microstructure, but, unless deliberately enhanced, their influence is normally small compared with that of the stratification. The effects are completely predictable and unambiguous, but, especially when coated components are combined into systems, they can be complicated and often unexpected. We normally divide optical coating materials into two major groups, metals and dielectrics. (Semiconductors are lumped with dielectrics.) These material classes behave differently. It is sometimes said that metals are insensitive to polarization. This is an oversimplification. Further, the surrounding media are usually dielectric, and so a coating incorporating a metal layer does exhibit a sensitivity to polarization, but of a somewhat different nature from that of a purely dielectric system. The polarization properties can be understood in terms of two linearly polarized eigenmodes defined in relation to the plane of incidence and designated as p- and s-polarization. Unfortunately, as is common in optics, there are several sign conventions, not always clearly defined when results are quoted.

A polarization ray trace model of the Laser Interferometer Space Antenna's (LISA) optical path is being created. The model will be able to assess the effects of various polarizing elements and the optical coatings on the required, very long path length, picometer level dynamic interferometry. The computational steps are described. This should eliminate any ambiguities associated with polarization ray tracing of interferometers and provide a basis for determining the computer model's limitations and serve as a clearly defined starting point for future work.

Biaxial ellipsometry measures the optical constants of materials, anisotropic films, and stacks of anisotropic films. Materials of interest include birefringent crystals, polarizing materials and films, and the complex multilayer anisotropic structures used in liquid crystal displays. An approach using Mueller matrix imaging polarimetry to simultaneously measure and angularly resolve reflection and transmission over large solid angles is presented. Biaxial materials have three refractive indices and three absorption coefficients in orthogonal directions but with arbitrary orientation. Determination of the dielectric tensor provides a succinct and suitable material representation, and its accurate determination is the focus of this investigation.

Novel optical design and engineering ideas are needed to build the large space telescopes for the direct detection and characterization of exo-solar system planets. For example, the Terrestrial Planet Finder Coronagraph requires a primary mirror 4 x 8 meters in size that is >10 x smoother than the 2.8 meter HST mirror and have a uniform reflectivity across the mirror to within 0.1%. The telescope system will need to control scattered light to within a part in 10 billion. The Terrestrial Planet Finder Interferometer will be a white-light, broadband infrared interferometer with a baseline in excess of 50 meters. In addition to direct imaging, planets masses and orbits can be derived from very precise measurements of the position of a star as it moves across the background. Interferometers provide the highest accuracy measurements of relative positions We will show that the optical design and the mechanical layout & configuration for these new telescopes need to be optimized for polarization as well as scattered light. Material science and coating technology plays an important role in the optimization of these systems. Stress across the surface of a mirror and stress within the optical thin film introduces polarization dependent scattered light. A new method to measure the anisotropy of the polarization-reflectivity of thin metal films on large astronomical mirrors is described.

To this day the standard method of imaging design is optimization. Recently we have introduced tailoring as a radically different paradigm of optical design. Tailoring determines the shape of optical surface, a priory free, by solving one or more differential equations. This method has proved successful in illumination design where a high level of detail needs to be accommodated and indeed a perfect solution is possible often with only one optical surface. The weakness of tailoring is first that it cannot adequately deal with weak requirement which need to be optimized, because they can not be precisely met or at least not met simultaneously. Examples range from manufacturability, to size, sensitivity to tolerances, but also includes imaging errors. Wassermann and Wolf showed in a classical paper how tailoring can be used in an imaging system in order to achieve aplanatism with the addition of two aspheres. In our contribution we present a synthesis which combines the virtues of optimization with those of tailoring for imaging design. It encompasses freeform surfaces and thus a huge number of effective parameters, however, only a few of these are subject to optimization. On the other hand our method can adequately use optimality criteria such as conflicting features in a figure of merit, which need to be compromised upon. Finally the result is a mathematically rigorous optimum with respect to whatever figure of merit is specified.

The design of high numerical aperture objective to be used as an optical data storage device was given out as a midterm exam in a lens design class consisting of twenty-nine students. The design space was restricted by the following constraints: the number of elements could not exceed three, only three material types were available, and the maximum overall length and the minimum working distance requirements were given. The students were allowed to pick their own starting point and were graded on both the maximum resolution they could achieve and the manufacturability of the design. The results were compiled into a design study. Although a few of the designs violated the specifications, the remainder could be grouped into three distinct design forms. The three different design forms were then analyzed for their ability to "stretch" the specifications (ex. working distance or resolution) while discussing the difference in tolerances between the design forms. The designs were also used to highlight the importance of controlling edge thicknesses and center thicknesses during the design process.

There has recently been an increased interest in being able to model optical systems that include sub-wavelength structures at one or more points in the system model. Software using the finite-difference, time-domain (FDTD) method can accurately model the interaction with the sub-wavelength structures, but cannot practically model the entire optical system. Therefore, in order to model the entire optical system including the sub-wavelength structures it is necessary to couple the FDTD software to optical system software. This type of coupling between macro and micro optical software codes has applications in a wide variety of fields including semiconductor lithography, optical data storage, telecom, biophotonics, metrology systems, and more. Conceptually all that is necessary to couple system software to a FDTD software is for each of the two optical software codes to be able to read in field files from the other and write out field files to the other. In practice several issues must be dealt with in order to ensure that this handing back and forth of fields is done correctly. This field handoff involves two major issues: (1) transferring an accurate and complete description of the field and (2) changing the sampling density of the field to be appropriate for further propagation inside of the other code. A brief explanation of the FDTD method is presented. This is followed by a listing of where the assumptions of scalar diffraction theory breakdown, requiring techniques such as FDTD. Lastly the steps involved in performing successful field transfers are presented.

The largest limitation of phase-shifting interferometry for optical testing is the sensitivity to the environment, both vibration and air turbulence. In many situations the measurement accuracy is limited by the environment and sometimes the environment is sufficiently bad that the measurement cannot be performed. Recently there have been several advances in dynamic interferometry techniques for reducing effects of vibration. This talk will describe and compare two dynamic interferometry techniques; simultaneous phase-shifting interferometry and a special form of spatial carrier interferometry utilizing a micropolarizer phase-shifting array.

With the upcoming of the next-generation large-capacity CDs and DVDs using a blue-violet laser, the track's pitch will continue to decrease. The conventional methods for pregrooves will have a technique challenge to meet tiny-pitch specs at low cost. In order to get an equispaced fringe pattern with concentric-ring structure by using optical interference lithography, a novel optical-interference method is proposed with the use of a plane wave plus a conical wave along the same optical-axis (Z) propagation. Based on the optical interference analysis with the two waves, plane and conical waves, the resulting intensity varies consinusoidally with the phase difference, as modulated by the optical path difference between the plane and conical waves. The constructive and destructive interference will occur in the interference light field, only depending on if in phase or out of phase for the two waves. The concentric-ring structure of equispaced fringe pattern can be produced, and the fringe period depends on the wavelength of the light beams and conical constant of the conical wavefront as well. The novel optical interference system has been modeled and simulated with a kind of Mach-Zender interferometer arrangement by commercial optical code. The optical simulation results are proved to have a good agreement with that as given by the theoretical analysis.

We present the first-order design details and preliminary lens design and performance analysis of a compact optical system that can achieve mutual occlusions. Mutual occlusion is the ability of real objects to occlude virtual objects and virtual objects to occlude real objects. Mutual occlusion is a desirable attribute for a certain class of augmented reality applications where realistic overlays based on the depth cue is important. Compactness is achieved through the use of polarization optics. First order layout of the system is similar to that of a Keplerian telescope operating at finite conjugates. Additionally, we require the image to lie on the plane of the object with unit magnification. We show that the same lens can be used as the objective and the eyepiece. The system is capable of having very close to zero distortion.

Head-mounted display (HMD) technologies find a variety of applications in the field of 3D virtual and augmented environments, 3D scientific visualization, as well as wearable displays. While most of the current HMDs use head pose to approximate line of sight, we propose to investigate approaches and designs for integrating eye tracking capability into HMDs from a low-level system design perspective and to explore schemes for optimizing system performance. In this paper, we particularly propose to optimize the illumination scheme, which is a critical component in designing an eye tracking-HMD (ET-HMD) integrated system. An optimal design can improve not only eye tracking accuracy, but also robustness. Using LightTools, we present the simulation of a complete eye illumination and imaging system using an eye model along with multiple near infrared LED (IRLED) illuminators and imaging optics, showing the irradiance variation of the different eye structures. The simulation of dark pupil effects along with multiple 1^st-order Purkinje images will be presented. A parametric analysis is performed to investigate the relationships between the IRLED configurations and the irradiance distribution at the eye, and a set of optimal configuration parameters is recommended. The analysis will be further refined by actual eye image acquisition and processing.

We propose a novel conceptual design for a Head-Mounted Projection Display (HMPD) with Eye-Tracking (ET) capabilities. We present a fully integrated system that is robust, easy to calibrate, inexpensive, and lightweight. The HMD-ET integration is performed from a low-level optical configuration in order to achieve a compact, comfortable, easy-to-use system. The idea behind the full integration consists of sharing the optical path between the HMD and the Eye-Tracker. Along with lens design and optimization, system level issues such as eye illumination options, hardware alternatives are discussed.

In this paper further developments [1,2] of a passive matrix projection/direct view display are presented. The device uses micromachined and electrostatic actuated Fabry-Perot filters. Applications are surface topology measurements (stereographic projection) in small cavities, laser beam writing and pattern projection e.g. in Head-Mount-displays, automotive or information panels. The display pixels with diameters in the order of 100 μm consist of a layer stack fabricated by LPCVD. The stack embeds an air gap which his created by a sacrificial etch process and a thin membrane which can be deflected electrostatically. The fabrication process has already been described elsewhere [2]. By membrane actuation the gap thickness is lowered and the interference spectrum generated by the layer stack is varied. The careful adjustment of the layer parameters like thickness and refractive index determines the design wavelength of the switches. They are assembled in rows and columns, resulting in an n^*m-display matrix, where n^*m actually is 4800. In principle the display may either be fabricated for transmission or reflection mode, depending on the substrate material (quartz or silicon). This paper focuses on transmissive displays. For pattern generation, an electric potential scan is applied on the n line contacts, and a video potential, which carries the image information, is addressed on the m column contacts. After each scan cycle, the potential polarities are reversed in order to avoid charge effects and to lower cross-talk between adjacent pixels. The response time is 100 μs, which is at least an order of magnitude faster than for common LCD technology. Further advantages are high temperature stability, low power consumption and low production costs, since only five mask layers are used in the present process. In this paper especially the electrical characteristics are evaluated and an addressing scheme for future active matrix addressing is derived.

We present experimental demonstration of a novel full-color three-dimensional microscopy method. A white-light high-brightness LED illuminates a Michelson interferometer. A color CCD camera records the color image of an object in superposition with the reference beam. The short-coherence interferometric process is applied to each of the three color channels to extract tomographic contour images of the object. The set of three images are recombined as RGB channels to construct a color tomographic image of a section of the object. The reference mirror is scanned over a range of axial distances to construct a three-dimensional tomographic image of the object with full natural color representation. The technique is applied to imaging of artificial color objects as well as colorful biological objects with about 10 um axial resolution, about 100 ~ 200 um penetration depth, and 50 ~ 60 db dynamic range. In contrast to most existing three-dimensional microscopy methods, the present technique allows monitoring of tissue structures close to its natural color, which may be useful in various physiological and pathological applications.

Based on electro-optic effect in crystal, a novel laser ranging method is proposed. A special designed mono-block LiNbO₃ crystal is laid after the laser transmitter. The CW-laser emitted from the transmitter propagates through the crystal and travels forward to the measured target. After being reflected by the target, the laser goes back and crosses the same crystal. Electric pulses with the steep enough edges are loaded on the crystal. Based on electro-optic effect, double refraction and internal double reflection effect in crystal, the crystal cuts off the round-trip light beams, and reflects a light pulse cut out by the crystal to a detector aside from the original beam path. The pulse width T is the period that laser goes forward and back between the crystal and the target. From the T one can get the measured range R. The feasibility of this method is proved by our experiments and a brand-new way for the laser ranging is provided.

In general, most conventional three-dimensional moving image capturing device uses two cameras for capturing the right and left video signals of an object. But this system has many disadvantages in that it essentially requires two cameras each having various accessories, and in that it is difficult and takes much time to integrate the moving images. Also, some calibration and rectification processes must be needed in the practical applications, because the operational characteristics of these two cameras can't be made to be same. On the other hand various camcorder adapters for capturing 3D moving image have been developed in order to eliminate the disadvantages of this two-camera system. But in this system, an entrance pupil point is formed inside the 3D moving image capturing device, so that when a wide moving image having a wider picture angle is to be captured, it is necessary to greatly increase the sizes of the total reflecting mirrors, which causes the adapter housing having the total reflecting mirrors mounted therein to be increased in size. Accordingly, in this paper, a new compact electro-optical 3D camcorder adapter for effectively capturing three-dimensional image having any picture angles is proposed and its performance is analyzed by comparing with those of the conventional ones. Some experimental results also confirm the superiority of the proposed system and its usefulness in the practical applications.

In recent years, fiber optics has found major applications in sensor technology. In this paper, we develop a theoretical analysis on different configurations of couples of fibers, in order to determine the optimal configuration for a position sensor, which allows us to measure displacements in the order of microns. This sensor is based on intensity modulated sensor and can be used in Scanning Electrochemical and Photoelectrochemical Microscopy for control of the tip-sample distance. Finally, we presented a novel design of a displacement sensor on the basis of this analysis.

A spatial light modulator, using a liquid crystal display (LCD), has been developed to be implemented in a measurement system which is based on the heterodyne interferometry. This interferometric device can be applied to the study of the mean roughness of reflective objects and phase distributions in transparent objects. An infinite moving grating is simulated on the LCD spatial modulator, on a screen with 128 x 240 pixels, which is handled by a microcontroller program in which the direction and velocity of the displacement, and also the fill factor and spatial period, can be defined. We show our first experimental results using this modified heterodyne interferometer to measure the profile of transparent and reflective objects.

In this work we propose the optical design of Galilean telescopes for low vision people using hybrid optical components. By use of these new optical components we have obtained compact and lightweight optical systems without detriment of the optical quality of the images. We present the optical design of telescopes for three different magnifications, as well as the evaluation of the image quality using the eye model proposed by Bruce H. Walker.

In this work an alternative is presented to design a noncontact profiler using diffractive optical elements in substitution of the traditional optical elements (refractive, reflective). With these elements is possible to have lenses with large numerical aperture and high control of the spherical aberration that is most important in the case of the profilers. Also, the optical design of a profiler that we are presenting, it will be used in a large coordinate measuring machine allowing us to scan surfaces in a continuous way. We also present the algorithms for recover the form of the surface starting from the date obtained with the profiler.

A polarimeter designed for measuring small rotation angles on the polarization plane of light is described. The experimental device employs one fixed polarizer and a rotating analyzer. The system generates a periodical intensity signal, which is then Fourier analyzed. The coefficients of Fourier Transform contain information about rotation angles produced by organic compounds that exhibited optical activity. The experimental device can be used to determine the sugar concentration in agave juice.

It has recently been proposed a new application of optical thin films as one-dimensional filters for spatial frequencies (Opt. Lett. 30, p. 914). Some possible applications include detection of extrasolar planets, high-sensitivity angle sensors, and beam-splitter cubes for special purposes. In this paper, the performance of thin-film spatial filters toward changes in wavelength is studied to characterize their behavior in optical systems that involve polychromatic light. We show how the performance of these devices under white-light illumination is influenced by the selection of design parameters.

Liquid crystal displays (LCDs) or thin-film transistor (TFT) LCDs have been regarded as a promising technology in flat panel displays (FPDs). To meet the demands of the mass production and quality control, the development of automatic electro-optical characteristics measurement systems for LCDs is very important. To achieve this, we propose a generalized spectroscopic ellipsometry (GSE) based technique to measure the characteristics of LCDs. Our approach involves two primary steps. First, we review a theoretical basis for generalized spectroscopic ellipsometries for the LCD measurement. Those are mainly categorized into two classes of ellipsometries: the transmission variable angle spectroscopic ellipsometry (VASE) and the spectroscopic ellipsometry (SE) using a photoelastic modulator (PEM), called PEM SE. Second, on the basis of the VASE and PEM SE, we present a GSE-based system to measure the electro-optical characteristics for twisted nematic liquid crystals (TNLCs) and super twisted nematic liquid crystals (STNLCs). In this paper, the simulation results indicate the feasibility of this technique. Finally, the automatic GSE-based system is presented for measuring the LCD electro-optical characteristics.