The f/No. concept is extended to include image forming optical systems with non-circular aperture stops. The basic principles of classical radiometry, geometrical optics, and physical optics are described by a single simple formula that is used to derive f/No. definitions which account for effects from diffraction, aberrations, and arbitrary stop shapes. In general, the effective f/No. of an optical system is a strong function of stop shape if the stop is very narrow in one or more dimensions, with equivalent circular stop areas of f/No. 0.5 to 1. Practical methods for computing the effective f/No. are discussed.

Sources of error associated with Single Point Diamond Turning of rotationally symmetric aspheres are examined and mathematically dissected to yield equations in the form of a superposition of errors. The equations are derived from manufacturing process considerations involving CNC machining mechanics or operator observations. The types of errors reviewed here include geometry errors, displacement errors, and dynamic errors but do not include errors associated with thermal gradients.

We consider the problem of enhanced analyses to predict/visualize the level of color correction in projection lenses. Modern optical science describes all aspects of chromatic aberrations; however on the projection screen we can see not individual aberrations, but the cumulative effect of light propagation through the system. For example, a combination of spherochromatism and lateral color can create a result that is difficult to visualize. The purpose of this work is to fill the gap between aberration theory and image quality as it can be observed on the screen. One of the important parameters of image quality in the projection industry is the coloration of the border between wide black and white areas on the screen. We developed a computer model for full color image analyses. The output of such modeling is the edge function for individual (up to five) wavelengths or superposition of monochromatic edge functions with chosen waiting factors. It can be presented in graphical and color-coded formats. Basically, the computed superimposed edge function corresponds to what can be seen on the screen. The software supports calculations for a nominal system and for a disturbed system when any possible mechanical error is introduced. Nominal system analysis is useful at the stage of optical design evaluation. Analysis of a disturbed system is a very important instrument for the study of opto-mechanical sensitivity and optimization of the mechanical structure of the lens assembly.

Laser transmittion and scattering technique, including depolarization of wave applied to biological particles provide a sample way for diagnostic and treatment of skin lesion and breast cancer. Laser polarization imaging system is described for non invasive and non radioactive detection. The system described in this paper generates 16 full out put Mueller matrix for characterization of turbid medium. In this work we describe the scattering and depolarization of electromagnetic radiation through biological turbid medium. This research work provides a base work for designing quick model of polarized laser tissues imaging.

In the industrial environment of position-sensitive detectors' usage, the laser source used for position measurement is co-existing with different kinds of light sources along with their reflections and back-scatters from various surfaces. These randomly arising illumination noises may fall on the detector surface in different geometrical orientations and produce different unwanted effects. In this paper, we attempt to describe, model and analyze these stray noises with respect to the operation of PSDs. We also study how the presence of the spurious sources modifies the behaviour of these detectors. The experimental results obtained by using PSDs and signal beams along with the spurious sources are presented. The experimental data are compared with the results from the proposed mathematical model graphically.

The Amon-Ra instrument is the main optical payload of the EARTHSHINE satellite and a unique Earth reflectance monitor. It consists of two separate optical systems, one imaging photon fluxes over the visible waveband and the other bolometrically measuring global emissions while the satellite orbits about the L1-Lagrange point. Two optical systems were designed to share the same apertures to the Sun and Earth and view the same target along the same direction as the spacecraft rotates. This design approach is advantageous in minimising the optics alignment problem as well as the differential degradation of front-end optics and detectors between the two systems. Nevertheless, such an approach makes it diffcult to control stray-light separately in each system and the signal of one source may be corrupted due to the other. In this paper, we discuss the stray-light performance of the Amon-Ra instrument and report the analysis results.

This article describes a method for formal engineering design synthesis of various electro-optical devices. A formal description of the design synthesis is described here and in our previous work, that converges toward completely automated design synthesis. In the first example of design synthesis, which describes the design synthesis of threedimensional (3D) display, the optimization was performed with the goal of minimization of crosstalk and aberrations in the displayed image and maximization of the number of different views of the 3D image. The design of systems that need to be described by Quantum Optics / Quantum Mechanics is also studied, in an attempt to investigate the possibilities of description of light, that converge toward unified classical Physics and Quantum Mechanics description, as well as to create the corresponding unified design synthesis. Procedure for design of systems that need to be described by Quantum Mechanics / Quantum Optics methodology is elaborated as part of design synthesis methodology described here, and an example of its use is provided. Possibilities to perform formal design synthesis, such as to derive formal derivation of the transformation of the initial design to optimized version based on Quantum Optics / Quantum Mechanics, have also been elaborated.

Starting from the nonlinear Shroedinger equation describing the evolution of non-paraxial perturbations co-propagating with a strong background inside a nonlinear Kerr medium, we have deduced the small signal gain coefficient of the non-paraxial perturbation superimposed on the strong background wave. The results indicate that both the cut-off frequency and the asymptotic value of the gain coefficient of the non-paraxial perturbation are smaller than that of the paraxial counterpart. In addition, it is also shown that the gain coefficient degenerates to the nonlinear gain coefficient of paraxial perturbations under the paraxial approach. Furthermore, under the condition that the perturbation travels far enough inside the nonlinear medium, the gain coefficient degenerates further to the asymptotic gain coefficient predicted by the Bespalov and Talanov theory. The gain coefficient obtained in this work provides a more general solution to the study of perturbations.

Taking into account the effects of third-order nonlinear effects, transverse walk-off and diffraction etc., we have performed theoretical analysis and numerical simulation for third-harmonic generation (THG) in potassium dihydrogen phosphate (KDP). The results show that the efficiency of the THG decreases as the ratio of phase ripples of the input beam increases. The results also indicate that increasing the conversion efficiency of THG can improve the beam quality of the third-harmonic wave.

A model is developed to explain the hysteretic electric field dependence of the electrooptic coefficient in ferroelectric thin films. The reversible electric polarization and the tunable dielectric susceptibility of the ferroelectric thin film are proposed to explain the hysteretic ρ-E (electrooptic coefficient- applied electric field) loop. An empirical model used in ferroelectric capacitors to predict the high frequency C-V curve is utilized here to find the field dependence of the nonlinear susceptibility. The tunable susceptibility can also explain the peaked characteristics of the ρ-E loop. We also show that the linear electrooptic effect in ferroelectric thin films could produce the pseudo-quadratic electrooptic effect on field-induced birefringence as a result of the switchable spontaneous polarization of ferroelectrics. Thus, a careful interpretation of the field-induced birefringence is required to avoid misleading conclusions. This model provides a fundamental understanding to the tunability of the electrooptic coefficient and is useful for the electrooptic characterization of the ferroelectric thin films.

We have proposed a new application of an AWG for a compact planar spectroscopic sensor to meet both conditions for miniaturization and high-wavelength resolution in the sub-nanometer order. A liquid sample under test is poured into a groove (optical path length, 70μm: groove depth, 110μm) in the first slab region of the AWG. A preliminary experiment was carried out using water solution of sodium acetate with the fabricated near-infrared AWG sensor. Concentration of the sodium acetate solute could be determined with the average accuracy of ±0.25 wt%. As the next step of AWG-based sensor, we designed and fabricated a compact spectroscopic sensor using an AWG with an insertion loss of 4dB in the visible wavelength. For improving the sensitivity of visible AWG spectroscopic sensor, the optimal design of a groove for the liquid sample was carried out in consideration of the refractive index and transmittance of the chlorophyll a and b as various environmental indicators. We succeeded in discriminating chlorophyll solutions using the AWG sensor. And we obtained a transmittance difference of 1.4dB which is two times higher than that in the conventional scheme (0.7dB) by absorbency change of 1.0 (optical path: 1.0mm). From these theoretical and experimental investigations using a visible AWG, a compact AWG-based spectroscopic sensor has been confirmed to be effective in acquiring body information in bio-medical fields.

"Ivory" is a computer code that generates Optomechanical Constraint Equations (OCE) from the optical physical prescription data. The OCE predict the translation, rotation and size change of an optical image from the motions, temperature changes and other factors affecting the optical elements forming the image. An airborne optical image correlator has been designed and built for UAV applications. Commercially available optical components were used throughout. The centerpiece of the mechanical design was control of the manufacturing and assembly tolerances to assure precise alignment and stable image registration for high performance operation. Control was maintained during the design and manufacturing process by the use of optomechanical models based upon the Optomechanical Constraint Equations (OCE). The equations provided a comprehensive optomechanical model that related the critical optical functions (images and diffraction patterns) to the translation and rotation (dimensions and tolerances) of all the piece-parts. The equations also modeled the thermal and wavelength stability of the correlator. Engineers may generate the OCE by longhand calculations or in a computer spreadsheet. For larger optical systems this can be very time consuming. Ivory automates the generation of the OCE for the engineer making timely and accurate calculations of the image registration errors possible, even for very complex optical systems. This paper shows the application of the OCE to a variety of challenges in the optical image correlator: athermalization, alignment procedures, optical and mechanical tolerance budgets, optimizing the folded geometry and sizing alignment mechanisms.

Four flight models and a spare of the Solar X-ray Imager (SXI) telescope mirrors have been fabricated. The first of these is scheduled to be launched on the NOAA GOES- N satellite on July 29, 2005. A complete systems engineering analysis of the "as-manufactured" telescope mirrors has been performed that includes diffraction effects, residual design errors (aberrations), surface scatter effects, and all of the miscellaneous errors in the mirror manufacturer's error budget tree. Finally, a rigorous analysis of mosaic detector effects has been included. SXI is a staring telescope providing full solar disc images at X-ray wavelengths. For wide-field applications such as this, a field-weighted-average measure of resolution has been modeled. Our performance predictions have allowed us to use metrology data to model the "as-manufactured" performance of the X-ray telescopes and to adjust the final focal plane location to optimize the number of spatial resolution elements in a given operational field-of-view (OFOV) for either the aerial image or the detected image. The resulting performance predictions from five separate mirrors allow us to evaluate and quantify the optical fabrication process for producing these very challenging grazing incidence X-ray optics.

The implementation plan for the "return-to-flight" of the space shuttle after the spectacular Columbia disaster upon re-entering the earth's atmosphere on February 1, 2003 included significant upgrades to the Ground Camera Ascent Imagery assets at Kennedy Space Center (KSC) and Cape Canaveral Air Force Station. The accident was due to damage incurred when a piece if insulating foam debris from the external fuel tank struck the left wing during take-off. The Ground Camera Ascent Imagery Project encompasses a wide variety of launch vehicle tracking telescopes and cameras at the Eastern Range. Most of these launch vehicle imaging telescopes are manually tracked and fitted with video and 35 mm film cameras, and many of them are fixed-focus (i.e., focused at the hyperfocal distance for the duration of the launch). In this paper we describe a systems engineering analysis approach for obtaining performance predictions of these aging launch vehicle imaging telescopes. Recommendations for a continuing maintenance and refurbishment program that closes the loop around the KSC photo-interpreter are included.

Techniques and formulas will be presented that demonstrate an effective means of characterizing the rigid body motions of optical elements from their nominal positions as caused by manufacturing tolerances and thermal effects. These techniques allow accurate prediction of the final position of a mechanically held lens element to be determined relative to mechanical datums. Even a single lens element with entirely nominal dimensions often needs to be positioned relative to a mechanical reference; the effects of any inherent inaccuracy of the mounting process can be over-looked and/or over-simplified. Tolerances on lens seats, element radii, bore diameters as well as thermal effects need to be accounted for in a design in order to accurately predict the final optical performance of a system in an "as built" condition. The differences in accounting for the mounting tolerances of edge mounted, cell mounted, and surface-centered elements are discussed. The work presented will aid in linking the tools available to the optical engineer in the form of optical design software, with the data available to the mechanical engineer in the form of manufacturing and fabrication tolerances.

The accuracy of optical modeling techniques to represent finite element derived surface displacements is evaluated using commercial software tools. Optical modeling methods compared include the Zernike polynomial surface definition, surface interferogram files, and uniform arrays of data in representing rigid-body and elastic surface errors. Methods to create surface normal displacements and sag displacements from FEA displacement data are compared. Optical performance evaluations are performed as a function of surface curvature (f/#). Advantages and disadvantages of each approach are discussed.

Many of the upcoming telescope projects propose to provide new levels of imaging performance thereby driving the optical design to larger and higher precision optics. This translates into tighter error budgets on the allowable image motion due mechanical disturbances. Much work has been published in this area and especially with the advances in computational capabilities, system or integrated models have been developed which allow end-to-end performance assessment. However, many of the design decisions are still based on subsystem performance metrics or only weakly consider system information in the subsystem design. A specific example is that optical design is done from a static perspective in that the sensitivities are normally evaluated separately without the inclusion of phasing information between the coefficients. This phase information is contained in the structural dynamics model in the form of the eigenvectors. Eigenvectors and perturbations of the eigenvectors can have a large effect on computed jitter because the induced optical tilts are sensitive to derivative functions. This information is ignored for several reasons - one being that complex optical design for a telescope and instrument, even with the advanced tools, still requires an experienced designer and secondly, it requires an integrated model to take advantage or even fully understand how to use this information - it requires cross-disciplinarian tools. We use two space-based systems as examples to illustrate how perturbations to these eigenvectors, due to design changes or uncertainty in the design, can have large impact on image motion.

Deformation of rotating liquid surfaces by laser heating is experimentally and theoretically studied. A horizontal plate containing the liquid sample (crude oil with highly temperature-dependent viscosity and surface tension) turns around a vertical axis fixed in the inertial reference frame at an angular speed continuously variable between 0 and 60 rpm. The liquid surface then adopts a classic parabolic profile which works as a convergent mirror for incoming light beams. The liquid surface is smooth and quite insensitive to external vibrations due to its high viscosity. In the next step a CW, CO₂ laser beam parallel to the rotation axis and also at rest in the inertial frame impinges the rotating liquid surface at a given distance from the rotation axis. While the liquid turns, a circular groove is thus ploughed in the liquid surface as a result of the surface tension temperature dependence. The resulting surface profile adopts an axisymmetric stationary shape after a transient heating stage. Its 3D shape at varying turning speed and laser power is experimentally studied by classic fringe-projection techniques. In spite of the low light-reflectivity of the liquid sample, which impedes its practical application in image-forming instruments, the device is useful to build up prototypes of rotating mirrors and to investigate the optical effect of axisymmetric perturbations in their surface profiles.

In compressible flows particle imaging, as done in Particle Image Velocimetry (PIV), is far from trivial. The inhomogeneous refractive index field can cause aero-optical aberrations including blurring of the image, especially near optical interfaces such as shock waves. The understanding of the process causing particle image blur (or blurring of the point spread function of the imaging system) is important in order to assess the measurement accuracy of optical measurement systems, such as PIV. A model for imaging through a shock wave is presented to determine the characteristic shape of blurred particle images when imaged across shock waves. The conjectured model is validated through a PIV experiment, where particle image recordings of the flow across a steady oblique shock wave are obtained in a supersonic wind tunnel. The parametric study focuses on two dominating parameters: 1) the angle between the viewing axis and the shock wave; 2) the numerical aperture of the imaging optics.

Prediction of optical performance for large, deployable telescopes under environmental conditions and mechanical disturbances is a crucial part of the design verification process of such instruments for all phases of design and operation: ground testing, commissioning, and on-orbit operation. A Structural-Thermal-Optical-Performance (STOP) analysis methodology is often created that integrates the output of one analysis with the input of another. The integration of thermal environment predictions with structural models is relatively well understood, while the integration of structural deformation results into optical analysis/design software is less straightforward. A Matlab toolbox has been created that effectively integrates the predictions of mechanical deformations on optical elements generated by, for example, finite element analysis, and computes optical path differences for the distorted prescription. The engine of the toolbox is the real ray-tracing algorithm that allows the optical surfaces to be defined in a single, global coordinate system thereby allowing automatic alignment of the mechanical coordinate system with the optical coordinate system. Therefore, the physical location of the optical surfaces is identical in the optical prescription and the finite element model. The application of rigid body displacements to optical surfaces, however, is more general than for use solely in STOP analysis, such as the analysis of misalignments during the commissioning process. Furthermore, all the functionality of Matlab is available for optimization and control. Since this is a new tool for use on flight programs, it has been verified against CODE V. The toolbox' functionality, to date, is described, verification results are presented, and, as an example of its utility, results of a thermal distortion analysis are presented using the James Webb Space Telescope (JWST) prescription.

We describe a tool to analyze the effects of gravity induced deflections on a telescope structure with segmented primary mirror optics. An objective of the telescope structural design process is to minimize image quality degradation due to uncorrectable static deflections of the optics under gravity, while ensuring that the overall system meets several requirements including limits of maximum primary mirror actuator stroke, segment rotation and decenter, and secondary mirror actuation. These design and performance criteria are not readily calculated within a finite element program. Our Merit Function routine, implemented in MATLAB and called by ANSYS, calculates these parameters and makes them available within ANSYS for evaluation and design optimization. In this analysis, ANSYS outputs key structural-model nodal displacements to a file, which are used to determine the 6 degree of freedom motion of the telescope's optical surfaces. MATLAB then utilizes these displacements, along with a database containing coordinate system transforms and a linear optics model derived from ZEMAX, to calculate various performance criteria. The values returned to ANSYS can be used to iteratively optimize performance over a set of structural design parameters. Optical parameters calculated by this routine include the optical path difference at the pupil, RMS wavefront, encircled energy and low order Zernike terms resulting from primary mirror segment rotation and decenter. Also reported are the maximum actuator strokes required to restore tip-tilt and piston of the primary mirror segments, and the deflection of the secondary mirror under gravitational load. The merit function routine is being used by the Thirty Meter Telescope (TMT) project to optimize and assess the performance of various telescope structural designs. This paper describes the mathematical basis of the calculations, their implementation and gives preliminary results of the TMT Telescope Structure Reference Design.

By linking predictive methods from multiple engineering disciplines, engineers are able to compute more meaningful predictions of a product's performance. By coupling mechanical and optical predictive techniques mechanical design can be performed to optimize optical performance. This paper demonstrates how mechanical design optimization using system level optical performance can be used in the development of the design of a high precision adaptive optical telescope. While mechanical design parameters are treated as the design variables, the objective function is taken to be the adaptively corrected optical imaging performance of an orbiting two-mirror telescope.

The Herzberg Institute of Astrophysics has developed Integrated Modeling tools for the Thirty Meter Telescope (TMT) project. This simulation software, implemented in MATLAB, models the telescope optical system, structural dynamics, and the segmented primary mirror and secondary mirror active optical control systems. For the TMT project, the integrated model was used to assess the effect of wind loading on the telescope in terms of delivered image quality. The simulation includes a state-space model of the telescope structural dynamics derived from an ANSYS finite element model, a linear optics model derived from a ZEMAX prescription, and wind loading forces derived from PowerFLOW computational dynamics software. The overall complexity of the model necessitates rigorous validation and verification procedures to ensure that the simulation data structures properly represent the original design, and that the calculations performed by the system are reliable. In this paper we discuss the validation and verification of the model data structures, structural configuration, optical configuration, coordinate system transforms, linear optics model, Zernike calculations, and wind loading model. As a case study, we present the verification, validation, and simulation results of the Thirty Meter Telescope Reference Design.

An effective multi-field wavefront control (WFC) approach is demonstrated for the James Webb Space Telescope (JWST) on-orbit optical telescope element (OTE) fine-phasing using wavefront measurements at the NIRCam pupil, and the optical and computational implications of this approach are discussed. The integration of a Kalman Filter as an optical state estimator into the JWST wavefront control process to further improve the robustness of the fine-phasing JWST OTE alignment will also be discussed. Through a comparison of WFC performances between the JWST on-orbit and ground-test optical system configurations, the connection (and a possible disconnection) between WFC and optical system alignment under these circumstances are analyzed. Our MACOS-based [2] computer simulation results will be presented and discussed.

The James Webb Space Telescope (JWST) is a key component of NASA's Origins Program to understand the origins and future of the universe. JWST will be used to study the birth and formation of galaxies and planets. The mission requires a large (25m² aperture) but extremely stable (150 nm RMS wave front error) optical platform, where performance is a tightly coupled function of numerous physical processes. Distortion due to thermal loading is a significant error source. The process by which predicted heat loads are mapped to optical error is termed Structural-Thermal-Optical Performance (STOP) modeling. Thermal-optical performance is a function of heat loads, thermal properties (conductivities, radiative coupling coefficients), structural properties (moduli, geometry, thermal expansion coefficients, ply layup angles), and optical sensitivities. Sensitivities, the gradients of performance with respect to design parameters, give a direct way to identify the parameters that have the largest influence on performance. Additionally, gradients can identify the largest sources of uncertainty, and thus contribute to improving the robustness of the design, either via redesign or by placing requirements on parameter variability. The paper presents a general framework for developing the analytical sensitivities of the STOP prediction using the Chain Rule. The paper focuses on solving for the sensitivities of the steady-state, conduction-only, problem, using discipline modeling tools (thermal, structural, and optical) to compute the terms in the STOP gradients. The process is demonstrated on the SDR2 Rev. 1 cycle of the JWST modeling effort.

The JWST Observatory currently under development for NASA and it's international partners contains a 6.5 meter diameter cryogenic telescope and a suite of 4 highly sensitive instruments which will collect imagery and spectroscopic data over the spectral range of 0.6 to 30 micrometers. The Observatory architecture contains a number of innovative and aggressive technologies including a light-weight primary mirror made up of 18 individually controllable segments, a large sunshield to permit stable low temperature operation, and a nested multi-loop pointing and tracking subsystem to establish milli-arc second line of sight stability. Detailed analytical models are being developed for each of the individual elements of the Observatory. The work described in this paper draws on these models so as to create a high level end-to-end model for the total Observatory. The principal thrust of this end-to-end model (OPTOOL) is to verify that the Observatory meets its overall image quality requirements. These requirements are codified in terms of Strehl ratio, encircled energy, and image anisotropy, and are applied at wavelengths of 1,2, and 5.6 micrometers. OPTOOL is implemented through Matlab (Version 7.0.1) with a Fourier optics based approach for PSF calculations, and uses a direct integration calculation to permit high spatial sampling of the PSF. Polychromatic PSFs are calculated using the Observatory band pass characteristic and an assumed constant Jansky level target. The focal plane arrays of each of the 4 instruments are also included in the model so that realistic signal with noise imagery can be simulated. Exit pupil optical path difference (OPD) maps can be generated using combinations of Zernike polynomials or shaped power spectral densities. Aberrations can be applied to the entire pupil or to the individual segments which make up the pupil. Global exit pupil OPD maps can also be imported and used to generate predicted Point Spread Functions (PSFs). Sample results are presented.

The Terrestrial Planet Finder Coronagraph (TPF-C) is conducting pre-formulation design and analysis studies based on a 8x3.5m elliptical aperture, light-weight primary mirror feeding an internally occulted (Lyot) coronagraph. The primary mirror has challenging static and dynamic performance requirements. We report on recent trade studies and concepts including open- and closed-back mirror blank designs and comparisons of thermal and mechanical performance; aperture shape alternatives to better match the coronagraph application with weight, packaging, and fabrication constraints; and mirror material trades.

Terrestrial Planet Finder (TPF) is a mission to locate and study extrasolar Earthlike planets. The TPF Coronagraph (TPF-C), planned for launch in the latter half of the next decade, will use a coronagraphic mask and other optics to suppress the light of the nearby star in order to collect visible light from such planets. The required contrast ratio of 5e-11 can only be achieved by maintaining pointing accuracy to 4 milli-arcseconds, and limiting optics jitter to below 5 nm. Numerous mechanical disturbances act to induce jitter. This paper concentrates on passive isolation techniques to minimize the optical degradation introduced by disturbance sources. A passive isolation system, using compliant mounts placed at an energy bottleneck to reduce energy transmission above a certain frequency, is a low risk, flight proven design approach. However, the attenuation is limited, compared to an active system, so the feasibility of the design must be demonstrated by analysis. The paper presents the jitter analysis for the baseline TPF design, using a passive isolation system. The analysis model representing the dynamics of the spacecraft and telescope is described, with emphasis on passive isolator modeling. Pointing and deformation metrics, consistent with the TPF-C error budget, are derived. Jitter prediction methodology and results are presented. Then an analysis of the critical design parameters that drive the TPFC jitter response is performed.

The Terrestrial Planet Finder mission will search for Earth-like, extrasolar planets. The Coronagraph architecture option (TPF-C) will use contrast imaging to suppress the bright starlight in order to detect reflected visible light from the planet. To achieve the required contrast ratio stability of 2e-11, the payload pointing stability must be maintained to better than 4 milli-asec (1σ). The passive TPF-C pointing architecture uses a 3-stage control system combined with a 2-stage passive isolation system to achieve the required pointing accuracy. The active pointing stage includes reaction wheels used for coarse pointing of the spacecraft, a position controlled secondary mirror that provides intermediate alignment, and a Fine Guidance Mirror that provides fine steering control. Each stage of the Pointing Control System (PCS) introduces some pointing inaccuracy due to actuator non-idealities that cause the physical commands to deviate by some amount from the ideal command, by sensor noises that are fed back through that stage's actuators to produce physical motions, and by modeling errors that arise because of imprecise knowledge of the dynamics of the system. The PCS must demonstrate the required accuracy of pointing performance in the presence of all of these effects. This paper presents the baseline PCS design and preliminary performance results. These results are compared to the TPF-C error requirements in order to assess the viability of the flight baseline design.

Integrated Modeling is currently being used to assess the feasibility of a baseline design concept (pre-phase A), developed for the Coronagraph version of the Terrestrial Planet Finder (TPF) mission. This design concept incorporates many challenging design elements for a space-born observatory: including a monolithic 8 by 3.5 meter elliptical primary mirror; a 12 meter long deployable secondary mirror support structure; as well as a 14 meter long deployable, tensioned-membrane, V-groove sunshield. Unprecedented thermal and dynamic stability is required by this flight system to allow observation of enough contrast between planets and their parent stars. This stringent performance requirement necessitates a balanced system, designed to optimize the various interacting disciplines: optical, thermal, structural & control. To support design feasibility studies, a MATLAB-environment-based integrated modeling tool (IMOS: Integrated Modeling of Optical Systems) was employed for analyzing the end-to-end system performance for typical in-orbit maneuvers. Our integrated modeling goal is to use a single model definition file to specify the thermal, structural, and optical modeling and analysis parameters, improving results accuracy, configuration control and data management. In working towards that goal, we have had parallel efforts in IMOS capability development, as well as design concept modeling and analysis. Typical system performance metrics studied include the relative motions of the optical elements, as well as the deformation of individual optics, decomposed into best-fitting Zernike polynomials.

The Johns Hopkins University Applied Physics Laboratory (JHU/APL) is currently developing a prototype star scanner design incorporating a variation on the V-slit design concept, called the N-slit, which is intended for deployment on future NASA spacecraft missions, such as the Radiation Belt Storm Probe (RBSP). In order to effectively test and evaluate alternative designs, including optics, sensors, and tracking algorithms, we have developed a laboratory testbed that simulates celestial objects, including stars down to a specified magnitude. We do this by creating a light-hermetic dome-shaped projection environment using light emitting diodes of specified brightness coupled to the dome exterior via fiber-optic patch cords, which can be adjusted by current bias and selected for color, if necessary, to simulate stars over a particular range of magnitudes required for the desired system accuracy. We also simulate the spacecraft platform spin dynamics using a two-axis servo-actuated mount for the star tracker test unit within the dome. This same actuator or a similar assembly can then be transitioned to actual field tests for sensor down-select and full functionality demonstrations prior to follow-on spacecraft-qualified design. We will describe the design, construction, calibration, and operation of this simulator and preliminary results of star scanner sensor evaluation using a photomultiplier-based N-slit sensor.

In this paper, we theoretically prove the fractional self-imaging effect of the two-dimensional array with arbitrary shape and symmetry, using scalar diffraction theory and the known periodic self-Fourier-Fresnel transform function comb(x , y). As a result, we also got a general equation to calculate the phase of the fractional Talbot image of the two-dimensional array. As an example, we numerically evaluate the intensity distribution of the diamond array in triangular symmetry in the fractional Talbot plane using Matlab, The result is a good agreement with the theory.

This paper presents an IIR (infinite impulse response) structure for an optical interleaver to deliver simultaneously three channels of 2π/3 shifted passband transmissions. Using the proposed structure, the phase responses and the spectral response of the IIR interleaver can be designed separately. Therefore, the design of an IIR interleaver is simplified, and the obtained interleaver can achieve a better performance than that of an FIR (finite impulse response) interleaver in terms of wider passband bandwidth, higher channel isolation, and lower insertion loss. A numerical design example is given to demonstrate the effectiveness of the proposed IIR interleaver design scheme.

The core diameter of the single-mode fiber is about 0.006mm to 0.009mm. Any slight misalignment or deformation of the optical mechanism will cause signification optical losses during connections. Previous studies often concentrated on improving the manufacturing process to obtain high precision components. Although the precision can be controlled, misalignment may still occur due to the contact stress on the connecting interface. This study uses the finite element method to simulate the contact status, and takes the MT series connectors for examples. The MT series connectors use the guide-pin structure to align the both contact surface, and use the spring or clip to keep tight contact. Because the MT ferrules are made of plastic materials, they are softer than ceramic ones and the deformation strains are more significant. For the finite element analysis, the solid model of the MT ferrule can be constructed according to the fiber protrusion, oblique angle, physical contact (PC) radius, and JIS C5981 standard. Using the ANSYS software, simulation result showed that, the fiber center displacement would be 0.9μm for the usually used oblique PC connectors. It will significantly affect the eccentricity values for the single-mode applications because only 1.5μm can be accepted. Using this new standard (eccentricity < 0.6μm) to select ferrules, and making them into connectors, it is found that the insertion losses of 98% connectors are less than 0.3 dB. This result satisfies the requirement for single-mode applications.

A brief review of the classical theories for modeling of wire grid-based polarizing element is given. A method based on the exact Green's function approach is chosen, with additional features from recent scattering theory developed for periodic structure modeling. At the heart of it are closed-form analytic expressions specially derived here for the computations of the lattice sums coefficients, first in the normal incidence case and then generalized to any incidence. An algorithm is drawn and implemented in a numerical code to compute the amplitude and intensity reflection and transmission coefficients, for both p and s polarization orientation, as function of incident radiation wavelength. Only physical parameters (wire diameter and spacing, wire material complex index and wavelength), which are the main design variables for such components, are needed as inputs with the exception of the number of cylindrical harmonics used to describes the local field around each wire. It is checked that the resulting code is stable with this extra numerical parameter and convergence is fast leading to reduced overall computation time even in broad spectral range case. Application of the method is illustrated with examples taken from the design of polarizing grids and polarizing beamsplitters for both mid/far-infrared earth observation instrument and sub-mm ground based instrumentation.

A novel paraxial propagation scheme for two-dimensional optical field wave-fronts is proposed, in Cartesian and cylindrical coordinate systems. This is achieved by extending the method originally proposed by Ladouceur [Opt. Lett. 21, 4 (1996)], for boundary-less one-dimensional beam propagation, to two-dimensional optical wave-fronts. With this formulation the arbitrary choice of physical window size is avoided by mapping the infinite transverse dimensions into a finite-size domain with an appropriate change of variables, thus avoiding the energy loss through the artificial physical boundary that is usually required for the absorbing or the transparent boundary approach. Comparison of analytical solution of propagating wave-fronts and those obtained with the proposed algorithm is given, a discussion of the method advantages and limitations is also provided.

We investigated analytically and numerically the occurrence of modulation instability in fibers with periodic changes both in dispersion and gain. Previously, it has been known that the modulation instability is suppressed in dispersion managed solitons where dispersion is managed in such a way that the local dispersion alternates between the normal and the anomalous regimes. In this work, we enhanced the advantage of the dispersion management scheme by additionally introducing proper gain/loss profiles in fibers. The gain/loss profile is given by Γ(z)=0.5/D(z)*(dD/dz), where D(z) represents the dispersion profile. The fundamental gain spectrum of the modulation instability in the dispersion and gain managed fibers have been derived analytically and confirmed by numerical calculation. Our investigation reveals that in the dispersion and gain fibers the modulation instabilities are always much more suppressed compared to the case that only dispersion managed. In practical dispersion management schemes, dispersion profiles show discontinuity, and thus, the corresponding gain/loss profiles tend to finite. In these cases, the gain/loss profiles were approximated by lumped gains/losses of finite values. Our numerical calculations confirm that this approximation also works well.

In this paper, we design a subwavelength binary grating working as a diffractive polarizing beamsplitter. The polarizing beamsplitter is then optimized by using a genetic algorithm to increase its extinction ratios up to as high as 238 and 82. We use the rigorous coupled-wave analysis method to calculate the parameters of the beamsplitter during the optimizing process.

The National Ignition Facility (NIF), currently under construction at the University of California's Lawrence Livermore National Laboratory (LLNL) is a stadium-sized facility containing a 192-beam, 1.8 Megajoule, 500-Terrawatt, 351-nm laser system together with a 10-meter diameter target chamber with room for nearly 100 experimental diagnostics. NIF is being built by the National Nuclear Security Administration and when completed will be the world's largest laser experimental system, providing a national center to study inertial confinement fusion and the physics of matter at extreme energy densities and pressures. NIF's 192 energetic laser beams will compress fusion targets to conditions where they will ignite and burn, liberating more energy than required to initiate the fusion reaction. The commissioning of the first four beamlines (a quad) was completed in October 2004 -- a two-year period where a wide variety of energetic laser pulses were propagated through the laser system. Success on many of the NIF laser's missions depends on obtaining precisely specified energy waveforms from each of the 192 beams over a wide variety of pulse lengths and temporal shapes. A computational system, the Laser Performance Operations Model (LPOM) has been developed and deployed during NIF commissioning to automate the laser setup process, and accurately predict laser energtics. For each shot on NIF, the LPOM determines the characteristics of the injection laser system required to achieve the desired main laser output, provides parameter checking for equipment protection, determines the required diagnostic setup, and supplies post-shot data analysis and reporting. LPOM was deployed prior to the first main laser shots in NIF, and has since been used to set up every shot in NIF's first quad (four beamlines). Real-time adjustments of the LPOM energetics model allows NIF to routinely deliver energies within 3%, of requested and provide energy balance within the four beamlines to within 2% for shots varying from 0.5 to 26 kJ (1.053 μm) per beamline. The LPOM has been a crucial tool in the commissioning of the first four beamlines (a quad) of NIF.