This pdf file contains the front matter associated with SPIE Proceedings Volume 7652, including Title Page, Copyright information, Table of Contents, Introduction, and Conference Committee listing.

Many computational imaging technologies introduced in the last several years use optical, mechanical, sensor, illumination and computational degrees of freedom to enable special system characteristics. The general computational imaging framework will be discussed along with the value of some specific approaches. A more in-depth analysis of the extended depth of field class of solutions is described which includes a method for visualizing the efficiency and comparing the SNR of the many approaches, the value of extended depth of field solutions and a simplified design approach that does not require tools beyond what the designer is currently accustomed.

Canon Inc. released the new EF 24mm f/1.4L II USM lens with a subwavelength structure coating (SWC), a new type of high performance anti-reflective coating, in December 2008. The subwavelength structure, which is made from microcrystalline alumina, can be formed on large, curved surfaces using a simple sol-gel process. Furthermore, by inserting a thin-film layer with an intermediate refractive index between the lens and the microcrystalline alumina, it is possible to achieve superior anti-reflection performance matching various lens refractive indexes. This report presents the principles and performance of SWC and describes the application of SWC to imaging lenses.

In a highly corrected design the limiting aberrations are induced ones, not intrinsic. Their causes are explained, and some simple designs are shown which eliminate these aberrations. These designs have more negative lenses than usual.

This paper provides a derivation of two key formulas for wavefront propagation and stop shifting to sixthorder of approximation.

A source of illumination with good color properties, daylight or electric, should reveal a full range of colors, should enable good color discrimination between objects of similar spectral reflectance, and should not distort colors. We presently have only one recognized measure of color rendering in the lighting industry, color rendering index (CRI), developed in the early 1960s. However, CRI should not be used alone as a predictive measure of the color rendering properties of a light source. First, CRI is a poor predictor of color discrimination. Gamut area index (GAI), another measure of color rendering, is consistently better at predicting performance on the Farnsworth-Munsell 100 Hue test than is CRI. GAI is also better at predicting subjective judgments of "vividness" than CRI. On the other hand, when measuring the ability of a light source to display colors "naturally," neither the GAI nor the CRI performs consistently. In fact, sometimes GAI is a better predictor of "naturalness" than CRI, and sometimes the opposite is true. When GAI and CRI are used jointly in characterizing the color rendering characteristics of a light source used for illumination, high values on both metrics appear to ensure subjective impressions of both "naturalness" and "vividness." In general, this two-metric system appears to be predictive of an average individual's "preference." A priori tests of this two-metric system of color rendering were conducted, lending support to the validity of this approach for characterizing the color rendering properties of electric light sources.

Technical luminaries have to compete on an economic basis. Optics design plays a key role for the development of efficient products, providing unique light distributions and minimizing the total costs of ownership.

Light is not just for vision anymore! Illumination design should consider the needs of the visual and non-visual systems. Discussed are the lighting characteristics impacting these systems and the implications for designing light for architecture.

Good primary optics for LEDs are crucial for applications that work technically and economically. But what is "good"? For various optical design patterns, we look at the complex interplay between optics, manufacturing, tolerancing, lifetime and cost.

This paper presents the use of radial basis functions (RBF) for describing freeform optical surfaces. The RBF approximation framework along with preliminary optical design experiences will be summarized.

Adding keystone distortion (in addition to anamorphism) to an off-axis asphere dramatically improves the ability of the surface to correct aberrations. Analogously, using 1-theta and 3-theta terms are important when using Zernike surfaces.

Recent advances have made it viable to fabricate optical surfaces that are not rotationally symmetric using a new generation of diamond-turning machines. These surfaces can greatly extend the field of view of optical systems and provide compact solutions. Through the use of optimization and analysis methods that track aberration content throughout the field of view, two non-rotationally symmetric designs that provide a compact mirror based geometry with a 10 degree full field of view are presented and compared. It is shown that a φ-polynomial surface provides superior optical performance to an anamorphic asphere because the surface can be made comatic.

It is challenging to design a large field of view (FOV) and low F-number optical system, especially an eyepiece for head-mounted displays (HMD), which also demands compactness in size, lightness in weight and a large exit pupil distance. In this paper, we describe a novel design of a wide FOV free-form eyepiece by tiling multiple wedge-shaped free-form prisms. We compared our tiling method using the novel free-form prism eyepieces with a traditional tiling approach and the drawbacks of the traditional tiling method are analyzed. We further present a successive approximation method for designing a freeform surface and compare the accuracy of several surface conversion methods. An example design was also demonstrated.

Aspheric placement in the Double Gauss form is re-evaluated. Two aspheric configurations are considered and their resulting aberration balances are studied and compared to an all spherical design.

An innovative design for an anamorphic eyepiece is described, which uses a microlens array with complicated surface features used in conjunction with a modified microdisplay to provide a high resolution image with a panoramic field of view.

The design of a binocular visual system with long eye relief using the freeform profile is investigated in this paper. The surface parameters of the original profile were calculated upon its geometrical structure specification, and the tangential profile of the surface is described using the sample points. The astigmatism along the tangential plane can meet the system requirement.

The ATALST (Advanced Technology for Large Aperture Space Telescopes) effort has presented several design incarnations. Here we will discus the design process in detail and compare the design and performance of the 9.2m segmented, the 8m monolithic on-axis and 8m x 6m off-axis concepts.

Optical null tests for three lenses and two subsystems were incorporated into the optical design procedure for the Large-aperture Synoptic Survey Telescope [1]. The "skip surfaces" feature in the OSLO optical design program was crucial. The resulting optical tests were extremely simple, requiring only a retro reflecting spherical or flat mirror. This is only possible because the optical tests were simultaneously designed and optimized as the telescope was designed.

The modern form of the refracting telescope advanced rapidly following its invention in 1608, but almost 300 years elapsed before practical prismatic binoculars became available. The evolution of binoculars and the associated manufacturing issues are discussed.

Design methods are described for unobstructed, plane-symmetric, anamorphic systems composed of three mirrors. Low order imaging constraints are used to reduce the dimensionality of the configuration space. Examples are presented from a specific class of systems with fixed packaging constraints.

Aspherical surfaces are difficult to manufacture, therefore we consider a possibility of using only spherical surfaces. Two optical designs for 800-mm F/4.5 seeing limited telescope are considered: Ritchey-Chrétien and a two-mirror Catadioptric system. The Ritchey-Chrétien system has a hyperboloidal primary mirror, a planoid aspheric secondary mirror, and a two-lens field corrector, whereas the all-spherical system contains a Mangin mirror and a meniscus corrector as the secondary group and a three-lens corrector. Our analysis of the image quality achieved in the two designs shows that the all-spherical catadioptric system is an acceptable alternative to the Ritchey-Chrétien design.

This paper was published in error and has been withdrawn. A correct version of the paper can be found at https://doi.org/10.1117/12.857310. The Publisher regrets the error.

A unique opportunity to test two antique refracting telescopes using interferometers and the surprising results that they meet modern standards, in terms of optical performance.

A design method of wide-angle three-mirror system with spiral optical axis is proposed. Asymmetric optical systems have more degrees of freedom than co-axial systems. The increased degrees of freedom can be applied for removal of ray obscuration by mirrors to achieve wide-angle and low F-number system design. The asymmetric system design requires three-dimensional comprehension of system structure and correction of asymmetric aberrations. In order to simplify the structure comprehension, a base sphere is introduced. The system structure can be changed into the two-dimensional structure of mirror interferences by the base sphere. The dominant asymmetric aberrations are spherical-like and astigmatism-like aberrations. The spherical-like aberration is eliminated by each mirror inidividualy and the astigmatism-like aberration is reduced by counterbalance of whole mirrors. An example of F/2 system with as wide angle as 30x24 degrees FOV is designed. The example system is fabricated by precision machining process for an infrared camera.

The SAFIRE, the Submillimeter and Far InfraRed Experiment, was designed for interstellar physics in the airborne Observatory SOFIA. SAFIRE is a cryogenic Echelle Grating spectrograph for covering 27 to 470 microns, with R ranging from 2-6,000. Here we will discuss the details of the optical design, the design process, and the performance of the instrument.

Following up on Cassini/CIRS, we are building the next-generation Composite InfraRed Spectrometer for deep-space planetary exploration. CIRS-Lite combines Mid & Far-IR channels into a single instrument with 4x the spectral sensitivity of CIRS. Here we discuss the instrument optical design, the design process, and the system performance.

We describe the optical design of a calibration unit for the off-axis laser guide stars at the Large Binocular Telescope's ARGOS facility. Artificial stars with the desired wavefront are created using a computer generated hologram.

The European Solar Telescope (EST) is a 4-m class solar telescope to be located in the Canary Islands which is currently in its conceptual design study. EST is a pan-european project (with 29 partners, plus 7 collaborating institutions, from 14 countries) promoted by the European Association for Solar Telescopes (EAST). In the current concept, the main telescope and its transfer optics assemblies 14 mirrors to provide a Science Coudé Focus with an F/50 telecentric beam. It is diffraction-limited in a FOV of 1 arcmin with an unvignetted FOV of 2'x2'. The whole system is being optimized in throughput for several instruments observing simultaneously in a spectral range from 0.39 μm to 2.3 μm. Its innovative concept integrates an optical transfer stage assembling multiconjugated adaptive optics with optical field de-rotation and with a perfect balance of the whole system in terms of polarization being also time and wavelength invariant.

A new method of optimization using the thru-focus MTF is described. Operands based on the thru-focus MTF peak and distance from the evaluation plane to the peak are investigated for their insensitivity to local minima in DLS optimization. The new optimization method is generally compared to conventional MTF optimization and demonstrates a significantly reduced optimization failure rate. The method is tested and shown to optimize a highly aspheric four element mobile lens design.

A significantly increased defocus tolerance can be obtained by combining pupil phase-modulation with digital demodulation in a hybrid imaging system. Designing the optimal pupil phase-modulation is however not a trivial task. We show how hybrid imaging fidelity can be predicted and used to compare arbitrary phase-modulations. The evaluations of two anti-symmetric and a symmetric phase-modulation yield initial design values that can be used for the optimization of specific hybrid designs.

We have developed an image processing algorithm that reduces lateral chromatic aberration. It has been implemented in Nikon digital single-lens-reflex cameras and application software. We have developed the aberration detection method which analyzes capture images and detect the aberrations of the image without lens information. Moreover, we have developed the aberration correction method optimized for raw images, which are mosaic images with Bayer color filter array. We also have developed the correction method optimized for in-camera processed images, whose color shift structures are distorted by in-camera processing.

In this work, we present the optical design of a tunable focus liquid lens composed with meniscus surfaces. The surfaces are elaborated of PDMS. Analysis of the opto-mechanical behavior of the lens is presented.

Illumination systems in microlithography have evolved from simple light mixing devices towards ultra-flexible contrast enhancement tools, enabling today's most advanced lithographic processes. A survey of the changing illumination requirements, design concepts and functionality is given.

We present three designs for delivery of light in the oral cavity for photodynamic therapy (PDT) under the requirements of average irradiance of 50 mW/cm² and spatial non-uniformities well under 10% over a square area of 25 mm². The main goal is to design a device that avoids having to shield the oral cavity prior to irradiation for PDT. Illumination theory is instrumental in identifying an effective geometry for the device. The designs proposed build upon the technology that is already available for PDT and use illumination theory concepts to maximize the efficiency of the light delivery. One design combines a cylindrical diffusing fiber with a reflector derived from the edge-ray theorem while a second consists of a fiber illuminator coupled to a lightpipe device. Both designs are successful in delivering the light reducing the need of shielding and in providing the desired irradiance and uniformity. The two approaches performed comparably and provided a higher irradiance than needed, thus inspiring the design of a third, simpler design based on an off-axis cylinder reflector.

The National Ignition Facility (NIF) has a need for measuring gamma radiation as part of a nuclear diagnostic program. A new gamma-detection diagnostic uses 90° off-axis parabolic mirrors to relay Cherenkov light from a volume of pressurized gas. This nonimaging optical system has the high-speed detector placed at a stop position with the Cherenkov light delayed until after the prompt gammas have passed through the detector. Because of the wavelength range (250 to 700 nm), the optical element surface finish was a key design constraint. A cluster of four channels (each set to a different gas pressure) will collect the time histories for different energy ranges of gammas.

Micro-optical 5mm lenses in 50mm sub-arrays illuminate arrays of photovoltaic cells with 49X concentration. Fine tracking over ±10° FOV in sub-array allows coarse tracking by meter-sized solar panels. Plastic prototype demonstrated for 400nm<λ<1600nm.

This paper describes the design, assembly, and testing of a concentrating photovoltaic module which uses spectral splitting to achieve high system power efficiency. The assembly and testing of two prototype modules is also described. An efficiency of 37.5% was measured on the highest performing module.

A new method using a thin-film multilayer filter is described to couple light from high-power LEDs into a thin light guide such as an LCD backlight. Light emitted below the critical angle is reflected back to the LED and recycled. Largeangle emitted light passes the filter and is transported by total internal reflection in the light guide. The light guide can be as thin as 0.3mm for an LED of 1x1mm², and the best coupling efficiency is estimated to be around 80%. With this approach, a backlight system can be greatly simplified but also compact collimators can be realized. In this paper the optical design and testing of the filter is described, and a 1mm thick, 6.5mm diameter collimator is presented that emits in a cone of 2×13°. Measurements on prototypes show good agreement with the designed characteristics.

A polarization conversion and angular shaping LED module has been proposed to improve the efficiency and uniformity for direct type LCD backlighting. The design includes simulation based on nanostructure, polarization and geometrical optics.

We present a hybrid sunlight and light-emitting diode (LED) lighting system design for indoor illumination. Sunlight is collected by a set of sunlight concentrator and then split into visible and non-visible rays by a beam splitter. The visible rays pass through the light guide into a light box. The sunlight and LED light are combined and made uniform by the light box, if the sunlight is not bright enough, some of these 140 LEDs can be turned on to maintain indoor illuminance above the standard level. When nighttime comes, all the LEDs can be turned on to illuminate the indoor space. The lighting system can let the lighting environment green and comfortable. Our simulation of the illumination system shows that the efficiency of the sunlight and LED hybrid lighting combination is better than that of LED and traditional lighting systems.

This work presents a planar optical light guide design for concentrating solar power onto a photovoltaic cell. The design allows concentrated light injected into the guide to avoid interaction with other injection facets. The presented design has a HFOV of 1°, geometrical concentration of 112.5x at the output of the guide, and can achieve greater than 500x with secondary concentration.

A retrosphere (either a convex ball or a concave mirror) is a convenient element to use in the interferometric optical test of an objective. However, under some conditions the retrosphere can cause ambiguities in the interferogram due to the effects of Fresnel diffraction. This paper provides diffracted beam propagation analysis and results showing the magnitude of these effects for a range of system f- numbers and retrosphere radii. The paper also presents an alternative retroreflector design concept that avoids the ambiguities.

Most tolerances on optical elements can be derived or calculated from the application requirements using computeraided optical design programs. For surface quality and surface roughness, however, there are few guidelines or tools for calculating appropriate tolerances. Typically, we simply use a legacy specification (e.g. 60-40 and 3 A RMS) with little thought for either the cost of achieving the specification or the penalty for failing to achieve it. Often these legacy specifications are ambiguous, unnecessarily costly and in some cases completely meaningless. This paper provides some basic rules and equations for calculation of the real or perceived impact of these specifications, and some guidelines for the initiate (and for some of us veterans as well) as to how to compose a meaningful tolerance.

Structured mid-spatial frequency surface errors on aspheric optics can create ghost images and reduced contrast. This reduction in performance is shown to be non-linear with surface height using Fourier methods without small signal or statistical approximations. Tolerancing MSF errors can use traditional MTF metrics, and derives peak-to-valley limits on MSF surface height components.

Violation of Abbe's sine condition is well-known to cause coma in axisymmetric imaging systems, and generally any offense against the sine condition (OSC) will cause aberrations that have linear dependence on the field angle. A well-corrected imaging system must obey the Abbe sine condition. A misaligned optical system can have particular forms of the OSC which are evaluated here. The lowest order non-trivial effects of misalignment have quadratic pupil dependence which causes a combination of astigmatism and focus that have linear field dependence. Higher order terms can arise from complex systems, but the effects of misalignment are nearly always dominated by the lowest order effects which can be fully characterized by measuring images on axis and the on-axis offense against the sine condition. By understanding the form of the on-axis images and the OSC, the state of alignment can be determined.

The random phase screen transfer function is a useful tool to control the surface figure of optical components. Theory and proposed algorithms, tie in to lens design codes, and example specifications are reviewed.

Sensors operating in the 8-12 micron long wave infrared (LWIR) portion of the electromagnetic spectrum have long been used to extend the useful range of operating conditions beyond those of sensor systems operating in the visual spectral band. Infrared systems must cover widely varying fields-of-view (FOV) depending on application, at fast f/numbers compared to systems operating in the visible band. Typical FOVs for LWIR sensors run the gamut from < 1 degree to >50 degrees for large focal planes, necessitating the use of long focal lengths. When the focal length of the optics increases, the sensitivity to defocus caused by thermal effects also increases. Optical materials with useful transmission in the infrared region exhibit larger changes (> 400X) in refractive index with temperature (dN/dT) than optical glass. This in turn introduces larger changes in focus over temperature for infrared systems compared to comparable focal length visual systems. Thermal expansion and contraction of the materials also contribute to changes in system performance and the coefficient of thermal expansion (CTE) is generally larger for infrared materials than for visual band optical glasses. The thermal performance problem is exacerbated with low f-numbers systems. The ability to detect targets having a small temperature difference from ambient is proportional to the light collecting ability of the optics, especially when uncooled detectors are used. It is typical to require f-numbers in the f/1 regime for the LWIR for uncooled applications. Methods have been developed to find optical designs with reduced thermal sensitivity for these applications.

The injection lens of the high power solid laser facility built soon was designed as double lens. The tolerance of the double lens was analyzed, and the optical performance of which was detected in experiment.

We proposed a modified testing equipment for adjusting the back focal length of compact camera module (CCM). The advantages of this modified testing equipment with conversion lens were testing space saving, small size testing chart, high speed chart changing, and variable object distances. The testing chart displacement of 0.17 mm in the modified testing equipment can produce the equivalent testing chart displacement of 1000 mm in the conventional testing equipment. At the regular object distance of 2000 mm, both total track and testing chart size of the modified test equipment were 1.6% of that of the conventional testing equipment.

We present a novel method to diffractive null lens designs to test parabolic mirrors. The phase coefficients control the diffracted ray which hits normally the aspheric surfaces. The spherical and coma aberrations are corrected. The equations are exact and optimization process is not required.

In the manufacturing process of an optical surface with rotational symmetry the ideal ronchigram is simulated and compared with the experimental ronchigram. From this comparison the technician, based on your experience, estimated the error on the surface. Quantitatively, the error on the surface can be described by a polynomial e(ρ²) and the coefficients can be estimated from data of the ronchigrams (real and ideal) to solve a system of nonlinear differential equations which are related to the Malacara formula of the transversal aberration. To avoid the problems inherent in the use of polynomials it proposed to describe the errors on the surface by means of cubic splines. The coefficients of each spline are estimated from a discrete set of errors (ρ_i,e_i) and these are evaluated by means of genetic algorithms to reproduce the experimental ronchigrama starting from the ideal.

Transflective LCDs use both reflective and transmissive elements in order to remain readable under strong ambient light conditions through light recycling. A transflective LCD illumination system based on the dual cell gap structure is simulated and compared to a regular LCD to assess contrast performance under influence of ambient light in terms of a user viewable image. Previous studies in the literature have not developed full system model simulations that include image output, glare and light leakage due to both microstructure geometry and polarization. The overall contrast performance is evaluated for a wide range of ambient source strengths using three different contrast metrics (ANSI, NIST and a proposed illuminance distribution contrast method). Three ambient source types (planar Lambertian, planar isotropic and a parabolic reflector) are used to simulate both office and outdoor environments. The sources were selected to simulate both specular and diffuse components of ambient lighting. The proposed contrast performance relationship between the different components of polarization leakage, microstructure leakage, and glare for both ambient and nominal backlight sources was verified in the Monte Carlo simulation models. The proposed contrast performance relationship provides a new understanding into the proper design of transflective LCD devices as control of the dark feature or black level illuminance is highly important. The proposed distribution contrast method proved to be more accurate and sensitive in assessing contrast performance than the NIST and ANSI methods. The transflective system was able to attain an average contrast performance of 10X beyond that of the regular LCD.

Software Configurable Optical Test System (SCOTS)[1], a computerized "reverse Hartmann test", can rapidly, robustly and quantitatively measure complex 3-dimensional specular surfaces, for instance large segmented solar collectors, faceted automotive headlight reflector or other free-form surfaces.

Tailoring of secondary optics, especially in short distances to the light source, requires appropriate, point source based, primary optic models which provide adequate accuracy. We propose a method to generate such models for complex, even non-smooth, primary optics by using spatial radiation patterns and applying backward tailoring. Furthermore, we demonstrate the scope of this method and the improvements on the secondary optic design process.

Solar concentrators using wedge prism with diffractive grating or sawtooth profile mirror are proposed and studied. The concentrator length-to-thickness ratio can exceed 7 and the maximum concentration ratios exceed 3.5 for these designs.

A key factor in the manufacturing difficulty of a precision optic, and therefore a key cost factor, is the surface quality (scratch-dig) specification. On the other hand, surface quality usually has little or no significant impact on the performance of the finished optical system, but rather is included in tolerancing for cosmetic purposes only. From a manufacturing standpoint, center thickness, radius, irregularity, glass type and cosmetic quality are all inter-related. When more importance is placed on any one of these, there is a tendency for the others to be negatively impacted. This paper makes the case that when surface quality is over-emphasized, not only is it a cost driver but also the average "as built" optical performance of the optical system will be lower because performance based tolerances are more likely to be pushed to their limit.

The classic method of design centering commonly used to increase the yield of electronic circuits is employed to improve manufacturability of complex lens designs. The approach uses the results of Monte Carlo (MC) statistics to iteratively center the nominal design on a new point that shows an improved yield. Rather than just employing the MC lens run for routine as-built performance forecast, the results of the simulation are re-used to find the changes in the nominal design parameters values which will increase the yield. The centers-of-gravity (COG) algorithm is selected as a quick and easy method of shifting the nominal design point in the multidimensional parameter space to the new location. The classic COG algorithm is modified to avoid situations when the position of either "pass" or "fail" center of gravity is difficult to determine. Examples of application, which include a wide-angle IR lens and a plan-apochromat objective for a digital microscope show that such method of lens design centering is promising, and even a single iteration may result in significantly improved yield.

Tolerancing has long been identified as a crucial part in the development of optical systems. It aims at finding the best balance between quality and cost as tolerances closely tie together manufacturing expenses and performance. Tolerance effects have been included into the optimization function (merit function) by some lens designers to find insensitive designs^1-5 and frequently compensators are employed to further improve the performance of assembled lenses. Compensators are limited to a small number of system parameters, but selective assembly of components can extend the number of parameters available for compensation. It can be employed to reduce tolerance effects of disturbed parameters by finding the best matches out of a set of components. In this work we discuss how desensitization and selective assembly can be combined to loosen tolerances and increase as-built performance. The investigations concentrate on tolerance insensitive design forms under the presence of selective assembly compensators. In contrast to desensitizing a given lens or introducing new design means we focus on introducing new assembly strategies into the design procedure and investigate how using selective assembly as a compensator while desensitizing the remaining design parameters can lead to even less sensitive designs.

An automated procedure for lens manufacturing tolerance assignment is described. The procedure makes direct use of Monte Carlo sampling to obtain tolerance assignments. Tolerances are specified so as to minimize manufacturing cost, subject to a constraint on minimum acceptable lens performance. A simulation evaluates the cost-effectiveness of the program and provides quantitative evidence on the cost savings it can provide.

We provide an overview of the design drivers for mobile camera phone cameras, with particular attention paid to aspheric order. The designer is often tempted to use high order aspheres (e.g. 18th order). However, better as-built performance can often be obtained at lower orders.

We propose two parameters CS and AS for fast estimating sensitivities to constant coma and linear astigmatism in a misaligned lens system. We show that these figures correlate well with actual tolerancing of some lens systems.

We performed measurement of the HHG (High-order Harmonics Generation) beam wavefront by the PDI (Point Diffraction Interferometer) sensor recently. The XUV HHG beam operates at wavelength 30nm with 1kHz pulse frequency delivering average energy 1nJ in the beam. This beamline is located in the PALS laser centre facility in Prague. The PDI sensor is a self-referencing monolithic device and it consists of a thin foil and a very small pinhole. The foil is semi-transparent for the XUV radiation and it is used as a density filter. The pinhole is located on the axis of the XUV beam focal spot and works as a diffraction aperture generating a reference spherical wave. If the XUV detector is placed behind the PDI sensor interferogram can be captured. It represents an interference between the spherical reference wave and the original measured wave which passed the thin foil. From the information encoded in this pattern it is possible to sequentially reconstruct the beam wavefront profile. In this paper we will discuss obtained results as well as design and setup of the XUV PDI sensor.

Algorithms for polarization ray tracing biaxial materials and calculating the directions of ray propagation and energy flow, the refractive indices, and the coupling coefficients for all four resultant reflected and transmitted rays are presented. Examples of polarization state maps, retardance maps and diattenuation maps are generated as a function of angle of incidence for comparing plane parallel plate systems with uniaxial and biaxial materials.

Low polarization, high numerical aperture microscope objectives ideal for polarization sensitive applications are designed, fabricated, and measured. A microscope objective is designed to meet the application requirements using Code V. Performance of typical AR coatings is examined and determined to be insufficient to meet the polarization performance desired. Custom AR coatings are optimized using an in house polarization ray tracing program to reduce the objectives diattenuation. The resulting microscope objectives perform about 5 times better than our low polarization Nikon objectives.

Orientation Zernike Polynomials have been shown to provide a complete and systematic description of polarized imaging using the polar decomposition of the Jones pupil. We use this concept to predict the polarization performance of high NA lithography lenses.

New polarization methods allow the ray tracing simulation of polarization critical components, including multilayer biaxial films, anisotropic and gyrotropic crystals, electro-optical, and magneto-optical materials bring many new challenges.

We explore polarization distribution in point spread functions and Stokes parameter signatures of pupil aberrations. With the aid of stress-engineered optical elements, we explore how pupil aberrations map onto Stokes parameters in the focal plane.

The retardance associated with a three-by-three polarization ray tracing matrix is analyzed. The retardance of the polarization ray tracing matrix contains both a geometrical transformation and the polarization properties of diattenuation and retardance associated with a ray path through the optical and polarization elements. A method using parallel transport of transverse vectors is able to separate the geometrical transformation from the "physical" retardance, allowing the retardance to be calculated. A non-polarizing ray tracing matrix provides proper local coordinates to calculate the physical retardance without the geometrical transformation.

A three-by-three polarization ray tracing matrix method for polarization ray tracing in optical systems is presented for calculating the polarization transformations associated with ray paths through optical systems. The method is a three dimensional generalization of a Jones matrix. Diattenuation of the optical system is calculated via singular value decomposition.

A class of optical surfaces called 'Swept Conics' or 'Conical Spheroids' can be used to transform wavefronts from point sources to diffraction limited line or arc images, and vice versa.

We show that both edge-ray and aplanatic concentrators are special cases of generalized functional designs. The formulas associated with the generalized functional method provide a convenient means of generating the shape profiles of such concentrators.

New ultra-thin optical designs are presented. They are formed by optical sections (called channels) working in parallel (multichanneling) to provide the desired optical function. The phase-space representation of the bundle of rays going from the source to the target is discontinuous between channels. This phase-space ray-bundle flow is divided in as many branches as channels there are but it is a single trunk at the source and at the target. Typically, these multichannel devices are at least formed by three optical surfaces: two of them have discontinuities (in the shape or in the shape derivative) while the last one is smooth. The discontinuities of the optical surfaces are causing the separation of the flow in branches (in the phase space). The number of discontinuities is the same in the two first surfaces: Each channel is defined by the smooth surfaces in between discontinuities, so the surfaces forming each separate channel are all smooth. No diffractive analysis is done.

We propose a design method for freeform reflectors based on source-target maps. The necessity for maps to fulfill the integrability condition to obtain a continuous reflector surface is discussed and demonstrated with various reflector geometries. We also review the advantages and drawbacks of reflectors with step discontinuities that do not require the integrability condition to be satisfied.

A method to design isotropic inhomogeneous refractive index distribution is presented, in which the scalar wave field solutions propagate exactly on an eikonal function (i.e., remaining constant on the Geometrical Optics wavefronts). This method is applied to the design of "dipole lenses", which perfectly focus a scalar wave field emitted from a point source onto a point absorber, in both two and three dimensions. Also, the Maxwell fish-eye lens in two and three dimensions is analyzed.

Using the Simultaneous Multiple Surface method in 2D (SMS2D), we present a fast catadioptric objective with a wide field of view (125°×96°designed for a microbolometer detector with 640×480 pixels and 25 microns pixel pitch.

We simulate the predicted Gouy phase anomaly near astigmatic foci of Gaussian beams using a beam propagation algorithm integrated with lens design software and compare computational results with experimental data.

We discuss general mathematical ideas arising in the problems of laser beam shaping and splitting. We give examples illustrating how formulating and analyzing the problem in its initial stages can lead to insight into how to use more general purpose design tools. We will be particularly concerned with questions concerning the scaling and symmetry of such systems.

Airy beams are a new class of nondiffracting beams predicted in 1979 and observed in 2007. In this paper, we show that beam propagation methods are an effective way to study the behavior of those beams in propagation and to design such beams. A lens design software integrated beam propagation feature is implemented to design an Airy beam generation setup based on Fourier transform in a coherent optical system. The setup was reproduced in the lab for experimental validation using a "cubic-shaped" mirror. The resulting monochromatic Airy beam presents a main lobe FWHM of approximately 30 μm over a diffraction-free distance of 15 mm. Computational results show excellent agreement with experimental data as well as with analytical predictions expressed in terms of the optical setup geometrical parameters.

Imaging diffractive optical elements (DOEs), randomly distributed microlenses and sub-λ-structures allow the improvement of the performance of Excimer-based imaging and illumination systems. Here we present the concept study of a hybrid imaging system for Excimer laser high power application at a working wavelength of 308 nm. In this hybrid approach a focus has to be put onto the impact of the non-desired diffraction orders to the optical performance and also to the amount of light remaining in the system and causing lens heating. Hereby the diffraction efficiency of the DOE is of enormous importance. Especially the influence of the passive facet of blazed transmission gratings has to be considered. For illumination systems we discuss the transfer of the uneven raw profile of an Excimer-laser into a Gaussian far-field distribution by introducing a microlens array with a 2-dimensional Voronoi-pattern. The holographic record of the microlens array allows additionally to influence the coherence parameters.

The paper details a square core fiber beam delivery design utilizing a unique micro lens array launch method. The paper includes the resulting performance of a prototype created to verify the design and its stability with an emphasis on homogenization as the fiber is articulated.

NFIRAOS (Narrow Field InfraRed Adaptive Optics System, pronounced nefarious) is the first light adaptive optics system for the Thirty Meter Telescope (TMT). It is a near-IR, diffraction limited, multi-conjugate adaptive optics (MCAO) system that uses two deformable mirrors to correct aberrations due to atmospheric turbulence. The f/15 beam delivered by the telescope, with a two arc-minute field of view, is relayed to one of three client instrument ports. Wavefront sensing is accomplished with six high order sodium laser guide star (LGS) wavefront sensors (WFSs) and three visible natural guide star (NGS) wavefront sensors. Plus, the control system uses two tip/tilt and one focus infrared WFSs located in the instruments. In this paper, we describe several optical design challenges we have faced. The science optics have been redesigned to meet evolving specifications, and the LGS WFS design has undergone multiple iterations. We present an overview of the optical systems and design drivers, including the current state of each design.

We present the definition, design, and construction of a 3.3X continuous-zoom short-wave infrared (SWIR) telephoto lens. Compared to visible and mid-wave infrared lenses, defining the appropriate lens requirements of short-wave lenses have some different trade-offs in terms of balancing radiometry and optimum focal plane sampling. In addition, the design process of optimizing a visible zoom design form of given first-order properties to work in the SWIR band reveals some challenges in glass selection and subsequent aberration balancing. A comparison of the actual measured MTF performance of a prototype lens shows reasonable performance compared to the design.

Significant advances have been made in recent years in the development of lithography optics. The resolution of structures smaller than 45 nm demanded a new class of catadioptric objective lenses whose design and construction is the result of decades of development in lithography optics. This article describes the best-performing lens types and design principles of the catadioptric concept of these lenses.

A custom optical microscope with an integrated liquid lens to enable an extended depth imaging in biological tissue has been fabricated and shown to provide subcellular resolution using Gabor image fusion in an optical coherence tomography setup. In this paper, we report on the development and assessment path of this technology over the last few years. Specifically, we report on the optical design as well as the MTF prediction and experimental measurements of the new optical microscope head. The microscope head was integrated in a custom optical coherence microscopy setup that is presented. Images of an African frog tadpole, ex vivo human breast excised tissue, and in vivo skin images, acquired with the integrated instrument, are presented.

We analyze the focusing of 20fs, 15fs and 10fs ultrashort pulses using achromatic lenses by expanding the wave numbers of the pulse around the center frequency of the incident pulse up to the third order.

Dual band focal plane arrays enable the simultaneous imaging of the MWIR and LWIR onto the same detector. Each spectral band is read out independently providing a separable MWIR and LWIR image. The development of this technology has necessitated the further development of dual band optics. Although reflective solutions simplify the need for color correction, multiple field of view reflective optics do not package nearly as well as refractive or catadioptric solutions. Dual band optical systems require that both bands focus at the same image plane at the same time. The challenge lies with the very broad spectral band of 3.5 - 11.0 microns, the different partial dispersions between the MWIR and LWIR, and the need to minimize the number of lenses to maximize transmission. This paper looks at the development of refractive and catadioptric concepts for designing continuous zoom lenses for dual band detectors.

We present a lens with a constant total field of view and real-time variable resolution in certain zones of interest. This smart imaging lens uses an active optical element to modify as desired the local distortion. This way, while keeping the total field of view constant, the resolution can be increased in a zone of interest, at the expense of decreasing it somewhere in the remaining part of the field of view. We first present the concept of this lens, using a deformable mirror as the active surface. Computer simulations are done with Zemax in which a magnifying power of 2 in a zone of interest representing 10% of the full field of view is achieved, using a f=12.5 mm lens and a F/# of 18. Different combinations of theses parameters would allow different performances and results. We then present experimental results of this lens with a prototype built using a ferrofluidic deformable mirror as the active element. Experimental results of a zone of increased resolution with a magnification of 1.32 and a zone of decreased resolution with a magnification of 0.80 are obtained.

For practical quantum computing, it will be necessary to detect the fluorescence from trapped ions using microscale ion trap chips. We describe the first design, fabrication and assembly of a set of diffractive optics for intimate integration into the trap chip and for coupling this fluorescence into multimode fibers. The design is complicated by the constraints of the ion trap environment. In addition, the choice of available materials is restricted to those compatible with ultrahigh vacuum. The completed optics-ion trap assembly has successfully demonstrated ion trapping, as well as ion shuttling, with no necessary modifications to the trapping and shuttling voltage levels.

The alignment method of a fast catadioptric optical module with very large field of view is presented in this paper. The module is made of three aspheric optical components: a primary mirror, a secondary mirror and a field lens. To achieve the 22.6 degrees field of view, the secondary mirror makes a large obscuration requiring an F/0.75 working f-number to achieve the effective F/1.05. The catadioptric optical module was integrated with the IRXCAM-640 uncooled camera module made by INO. System spatial resolution is improved with the use of a 4-position microscan mechanism.

The lens design problem for the 2010 IODC is to design a 100 mm focal length lens in which every optical surface has the same radius of curvature, positive or negative, or is plano. The lens is used monochromatically at 532 nm and is made of only Schott N-BK7 glass. The goal of the problem is to maximize the product of the semi-field of view and the entrance pupil diameter while holding the distortion to within ±5% and the RMS wavefront error to ≤ 0.07 wave within the field of view. There were 37 entries from eight different countries. Four different commercial lens design programs were used, along with two custom, in-house programs. The number of lens elements in the entries ranged from 3 to 64. The overall length of the lenses varied from 105 mm to 3.6 km. The winning entry had an entrance pupil diameter of 81.3 mm and a semi-field of view of 43.5° for a merit function product of 3537.

Problem definition: Transfer maximum monochromatic flux from a 1-mm-square Lambertian source in air to an equal-étendue nonimmersed target. The target surface is rectangular with a 16:9 aspect ratio. The surface area of the target must be at least 4 mm². The target is defined such that only rays incident on the target surface at angles of θmax or less, relative to the surface normal, are considered to be within the phase space of the target, where the value of θmax is determined by the equal-étendue requirement.

Moment of Illumination data is shown to be a useful optimization target in illumination systems, yielding smooth merit functions, swift calculation and good noise tolerance.

Illumination design often involves the tailoring of optical surfaces to provide a desired illuminance distribution. Tailoring algorithms often make simplifying assumptions, like assuming a point or Lambertian source, and that results in a difference between the actual output and the desired output. By using the virtual prototyping capability of illumination software, simulations can be used to accurately predict distributions with simplifying assumptions removed. In addition, optimization algorithms can be used to adjust the tailored surface so that the match without simplifying assumptions is improved. One optimization approach uses the (simulated illuminance)/(desired illuminance) ratio to compensate the distribution used by the tailoring algorithm. This type of iterative compensation approach can be effective when the difference between simulated and desired distributions is small, but becomes less effective when the simulated and desired illuminance distributions have different sizes or are shifted with respect to one another. These limitations can be overcome by using the difference in position of the simulated and desired cumulative flux distributions instead of the ratio of the simulated and desired illuminance distributions.

The development of a flexible tolerancing tool for illumination systems based on Matlab® and Zemax® is described in this paper. Two computationally intensive techniques are combined, Monte Carlo tolerancing and non-sequential ray tracing. Implementation of the tool on a computer cluster allows for relatively rapid tolerancing. This paper explores the tool structure, describing the splitting the task of tolerancing between Zemax and Matlab. An equation is derived that determines the number of simulated ray traces needed to accurately resolve illumination uniformity. Two examples of tolerancing illuminators are given. The first one is a projection system consisting of a pico-DLP, a light pipe, a TIR prism and the critical illumination relay optics. The second is a wide band, high performance Köhler illuminator, which includes a modified molded LED as the light source. As high performance illumination systems evolve, the practice of applying standard workshop tolerances to these systems may need to be re-examined.

We report our experiences on the optimization of illumination systems and discuss how to take advantage of multi CPU computers. As an example, the design of a LED airfield lamp is shown.

A method for performing optical beam shaping in the near-field region using diffractive optical elements generated by Fresnel based Phased Optimised General Error Diffusion algorithm (POGED) was developed and investigated by means of numerical simulations. POGED was found to deliver significantly higher signal to noise ratio than iterative Gerchberg-Saxton type algorithm.

The aspherics is effective to reduce the number of lenses and to improve the performance of the optical system. The lens designer determines the surfaces to be aspheric and executes the optimization. But it is unknown a priori which surfaces should be aspheric. If the designer tries all the combination of the aspheric surface numbers, the number of the combination is very large. One method to solve this difficulty is to extend the aspheric surface number to a continuous variable and include it in the variables of the optimization. I would call it the traveling aspherics. The best surface number of the aspherics is determined through the optimization. The global optimization is necessary to get the best surface number of the aspherics. In section 1, the definition of the traveling aspherics is explained. In section 2, the design procedure with the traveling aspherics is explained. In section 3, the effect of the traveling aspherics is examined through a practical lens design problem. The method of the traveling aspherics can be applied to any complicated cases and requires no special experience of the lens design.

Nodal Aberration Theory (NAT) was discovered in 1977 and was last presented at this conference 25 years ago. This paper presents recent discoveries and why this theory is gaining in relevance for the future.

We describe a tool that analyzes the characteristics of an existing lens, and then determines which surfaces should be made aspheric for optimal results. We apply this tool to several problems, and discuss the results.

Forbes introduced the usage of Gaussian quadratures in optical design for circular pupils and fields, and for a specific visible wavelength band. In this paper, Gaussian quadrature methods of selecting rays in ray-tracing are derived for noncircular pupil shapes, such as obscured and vignetted apertures. In addition, these methods are generalized for square fields, and for integrating performance over arbitrary wavelength bands. Integration over wavelength is aided by the use of a novel chromatic coordinate. These quadratures achieve low calculations with fewer rays (by orders of magnitude) than uniform sampling schemes.

Diffractive optical elements (DOE) are well-suited for the correction of longitudinal and transverse chromatic aberrations in broadband optical systems such as photographic lenses, HMDs or infrared lenses. Unfortunately, the diffraction efficiency η for the working order of DOEs is often clearly below 100% which causes stray light from unwanted diffraction orders and prevents a more frequent use of DOEs in practice. The main reasons for the decrease of diffraction efficiency η are spectral bandwidth, variation of the incidence angle of impinging light and manufacturing errors of the DOE. In the present paper, several scalar approximations for the diffraction efficiency η as a function of these parameters are compared with rigorous electromagnetic calculations. The validity of these formulae are shown to extend over a surprisingly large range of parameters.

Coddington Equations are used to calculate the astigmatic images of a small bundle of rays centered on a ray commonly known as the principal ray. Some authors generalize it such that for a refractive or reflective surface of any shape to the 2^nd order, and an incident wavefront of any shape to the 2^nd order, the refracted or reflected wavefront can be calculated to the 2^nd order. We extend it further such that it applies to the diffractive surface as well. The derivation is based on the general Snell's law and differential ray tracing approach. We present these generalized Coddington Equations in two forms: matrix formalism and explicit expressions. The equations are verified with explicit ray tracing using a commercial lens design program. The relations are applied to evaluate the imaging performance for null testing of aspheric surfaces using computer generated holograms.

Optical systems with a reflected light condition, e.g. microscopes with reflected light illumination or fundus cameras, need to have weak first order ghosts or even to be completely free from them. Sequential ray tracing can be used to control optical performance and reflections on a ray basis during optimization. This is significantly more efficient in computation time and convergence than the usual approaches with non-sequential ray tracing or reconfigured optical systems to cover all critical ghosts. An ophthalmic lens for a fundus camera was designed with first order reflections stripped out by applying sequential ray tracing. The merit-function only had to be completed under certain conditions guaranteeing the absence of any reflections. No additional reconfiguration of the optical system in the design software was necessary.

It is shown how undergraduate Physics students were introduced to spectrographs optics through laboratory sessions and computer simulations. Simulation and evaluation of two equivalent spectrographs corresponding to a real commercial spectrograph were performed. Evaluation of the real spectrograph was also performed. A comparative work on spectrographs linear dispersion and their resolution was also performed.

Third-order aberrations need the paraxial raytracing of a marginal as well as principal ray through the entire system to be determined. When the optical system has GRIN media, even the paraxial raytrace could be cumbersome. This work presents the use of the ABCD matrix for obtaining the raytracing of those rays and, thus, it could ease the calculation of the third-order aberration coefficients, i.e. contribution of GRIN to surface refraction and transfer, for each individual surface of GRIN optical elements. A procedure to be implemented in any modern commercial optical software has been presented and evaluated for simple systems.

Optimization of a mobile imaging lens, which is for 5-megapixel, 1.4μm, CMOS image sensor, with multiple configurations to reduce flare is presented. The most severe flare, which could cause artifacts such as "purple flare" in images, is due to totally internal reflection (TIR) from optical surfaces in a mobile phone camera lens. We illustrate how to optimize the lens for good performance and manufacturable tolerances to reduce flare due to TIR. The MTF, distortion, relative illumination, lateral color, cumulative probability function for lens with tolerances and flare amount is shown for the starting lens. An optimization method for lens design to reduce TIR flare is proposed and described. The resulting optimized lens performance, tolerances and flare are compared with that of the starting lens.

We present an illustrating method for triplet prisms combination that can minimize the chromatic aberration. The apochromatic aberration equation, relation between relative partial dispersion and glass V-number can be quickly analyzed and found the combination.

The Optical Plate Diagram of C. R. Burch has been generalized to allow the calculation of third-order perturbation aberrations for nominally axially symmetrical optical systems. The plate method has the advantage of simplifying the third-order analysis of optical systems by removing the first-order considerations that complicate traditional approaches. This development is shown to be directly analogous to the original derivation of Shack and Thompson.