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Beam stabilization system is one of the most important units for lithography, which can accomplish displacement and pointing detection and control and includes beam measurement unit(BMU) and beam steering unit(BSU). Our group has set up a beam stabilization system and verified preliminarily beam stabilization algorithm of precise control beam position and angle. In the article, we establish beam delivery mathematic model and analyze the system inherent error. This shows that the reason why image rotation effect arises at the output plane of beam stabilization is the fast steering mirror (FSM) rotation of BSU in the process of beam stabilization. Two FSMs rotation around 45 o axis of FSM make the most contribution to image rotation which rotates 1.414 mrad as two FSMs rotation angle difference changes 1 mrad. It is found that error sources include three key points: FSM accuracy; measurement noise and beam translation by passing through of beam splitters changing as the ambient temperature changing. FSM accuracy leads to the maximum 13.2μm displacement error and 24.49μrad angle error. Measurement inaccuracy as a result of 5μm measurement noise results in the maximum 0.126mm displacement error and 57.2μrad angle error. Beam translation errors can be negligible if temperature is unchanged. We have achieved beam stability of about 15.5μrad for angle and 28μm for displacement (both 1σ) after correcting 2mm initial displacement deviation and 5mrad initial angle deviation with regard to the system rebuilt due to practical requirements.

Point spread function (PSF) defines the intensity of the diffraction image formed by the optical system for a point source. The PSF of an optical system varies with the field of the point source and such variance generally cannot be neglected. This paper proposes a realization method of full-field PSF—incorporating field dependence into the PSF matrix. Two practical optical systems with distinct degree of aberrations are chosen and the PSF using the method proposed with that obtained by direct integration are compared. The result and analysis suggest this method can obtain the PSF in any desired field at a fast speed and with relatively high accuracy.

We introduce a new approach for spline-based elastic registration using both point landmarks and intensity information. With this approach, both types of information and a regularization based on the Navier equation are directly integrated in a single energy minimizing functional. For this functional, we have derived an analytic solution, which is based on matrix-valued non-radial basis functions. Our approach can cope with monomodal and multimodal images. For the latter case, we have integrated a computationally efficient analytic similarity measure. We have successfully applied our approach to synthetic images, phantom images, and MR images of the human brain.

The Rayleigh-Sommerfeld formula(RS) has proved accurate for evaluating diffraction of the optical field from a planar aperture. Thus the FFT based direct integration method for the RS(FFT-DIRS) can provide a more exact reconstructed image from sampling points of the diffraction field of the object than the numerical method for the Fresnel formula(FR) that is an approximation of the RS. Although the FFT-DIRS has been proposed and studied in some literatures, an important problem remains to be solved, that is the effect of sampling on it. Sampling of the object diffracted field leads to a periodic or quasi periodic shifting of the reconstructed image. If these spatial replicas overlap, the desired image can not be recovered without the aliasing noise. So the overlapping period plays an important role in employing the FFTDIRS for the practical applications. In this paper, a formula of this overlapping period is obtained through the relationship between the RS and the FR. Then the validity of this formula at different distances is investigated by the experimental results.

To give optical designers the innovative capabilities that CAD users already have, OPTIS has created the first optical design program fully integrated into a CAD program. This technology called OPTISWORKS Optical Design is available as a plug-in to SolidWorks. It presents multiple advantages for opto-mechanical designers working on projection display systems.

We propose a waveguide based surface plasmon resonance optical biosensor for portable applications. Numerical results show that direct integration of a wire-grid polarizer is not only difficult, but also has poor polarization filtering performance. Our initial efforts focus on a waveguide based structure with prism coupling and the use of baculovirus as model pathogen.

A novel technique is presented which integrates the capacity of a laser tweezer to optically trap and manipulate objects in three-dimensions with the resolution-enhanced imaging capabilities of a solid immersion lens (SIL). Up to now, solid immersion lens imaging systems have relied upon cantilever-mounted SILs that are difficult to integrate into microfluidic systems and require an extra alignment step with external optics. As an alternative to the current state-of-art, we introduce a device that consists of a free-floating SIL and a laser optical tweezer. In our design, the optical tweezer, created by focusing a laser beam through high numerical aperture microscope objective, acts in a two-fold manner: both as a trapping beam for the positioning and alignment of the SIL and as an near-field scanning beam to image the sample through the SIL. Combining the alignment, positioning, and imaging functions into a single device allows for the direct integration of a high resolution imaging system into microfluidic and biological environments.

We report the comparison between two methods to evaluate optical systems. The flux-tracing method is an extension of the classical ray-tracing methods with additional energetic features. The direct integration method involves the calculation of the integral appearing in the diffraction theory of aberrations. We give a brief outline of the two methods and compare the results on a standard optical system. This will help to put in common the two methods to try to formulate new algorithms for the design of optical systems.

An algorithm for diffraction-based modeling of optical systems for laser devices has been developed. The direct integration is used for the Rayleigh-Sommerfeld formula throughout the system, so optical elements with non-plane surfaces may be adequately treated. The integration is based on the modified Cotes quadrature formula and ensures both high accuracy and speed. A method for the diffraction-based search for an initial scheme for optimization is also proposed. Thus the whole synthesis procedure for a laser optical system may be performed on the basis of diffraction theory.

An effort to model the dynamic motion of an ionic-polymer metal composite elestic beam was undertaken. Development of the static portion of the model was begun by assuming the beam behaves in accordance with the nonlinear equation used to describe large-angle deflection of elastic cantilever beams. A Simulink simulation was developed to estimate the final deflection of a beam due to a constant moment. The dynamic portion of the model was developed by assuming that each segment of the beam could be represented as a simple second-order system. Future efforts to more accurately model beam motion - by modifying the method used to model the forcing moment, by expanding the model to predict the performance of beams of all dimensions, and by validating model performance against actual beam motion - were recommended.© (2002) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A novel device to directly integrate mechanical motion with electronics on a chip for system integration is designed and fabricated. The device is a laterally movable gate field effect transistor. Here the gate moves parallel to the substrate surface rather than perpendicular to its as in the moving gate transistors reported earlier. Lateral motion results in linear response of device drain current with gate motion. It also makes large motion possible. The device has a variety of applications in smart sensors, actuators and integrated smart systems. A simple fabrication process is developed that is compatible with fabrication of high-aspect ratio structures. The latter give distinct performance improvement. The basic principles of operation of the LMGFET is demonstrate din initial measurements. This, to our knowledge, is the first report on the operation of such a device.

The charging of the workpiece in electron beam direct writing processes has been identified as a problem that disturbs the electron beam and causes pattern displacement error. In this paper the electron beam deflection caused by surface charging is evaluated by the SIMION and MATHEMATICA simulation programs. Isolated charged patterns of different geometry are simulated as electrodes with given potentials in SIMION to calculate the extent of beam deflection, while secondary electron emission yield and beam dosage are assigned in MATHEMATICA programming for determination of surface potential and spatial field, from which the beam deflection is then calculated. The simulation results are in good agreement with each other and they are compared with values available in literature. The initial charge content along with the pattern dimensions chosen in simulation are found to be the major factors that determine the extent of beam deflection. The limitation of SIMION simulation on the beam deflection is also discussed.

Band edge effects such as increased density of modes, large field enhancement, and low group velocity will provide highly efficient parametric amplification if the proper phase matching conditions can be established. We derive the phase matching conditions for 1D-photonic band gap structures. Direct integration of Maxwell's equations in the time domain confirms these conclusions, and show that parametric amplification in 1D-photonic band gap structures provide much larger conversion efficiencies compared with quasi-phase-matching.

Analytical formulas are derived for integrals of phase function of large particles, namely for light fluxes scattered singly within an arbitrary angular range and mean scattering angle squared. The relations of the first kind are obtained via direct integration, by the scattering angle, of the Fresnel's reflectivities weighted with some angular function. The Fraunhofer's diffraction and geometrical optics parts are taken into account. As a result, the light flux is expressed as a sum of elementary functions. The formulas can be obviously converted to the known relations for the single-scattering albedo and mean cosine of the phase function for a particular case of the integration over full range from) to 180 degrees. The mean scattering angle squared is used, for example, by the small- angle diffusion approximation to compute light propagation. The corresponding formula is derived by comparing the solutions to the radiative transfer equation with the said approximation and with the small-angle one. The mean scattering angle squared is particularly shown to be inversely proportional to the effective size parameter squared of particles. The proportionality coefficient is found.

A simple and elegant method to determine unambiguously the phase from several phase-shifted interferograms (intensity fringe patterns) is presented. Instead of calculating the arc- tangent, a line integral of the phase gradient is evaluated. The ambiguities introduced due to the multiple values of the arc-tangent function are avoided, eliminating the necessity for the complex methods of phase unwrapping. This method works effectively even in the regions of high intensity gradients, is insensitive to the profile of the illuminating beam and to the shape of the domain boundaries. The algorithm is applied to the special case of four phase-shifted interferograms to demonstrate the phase determination procedure.

A finite element (FE) formulation is presented for modeling the dynamical response of smart structures with embedded piezoelectric ceramic devices subjected to transient loading. The FEM formulation presented is based on a variational principle using the concept of virtual work. An unconditionally stable method ((alpha) -method) is utilized for the direct integration of the equations of motion and can be put in the form of a 3-step linear multistep method of second order equations. A thin cantilever plate with piezoelectric devices is investigated to show the feasibility of the analysis and numerical simulation. The code employs 20 node isoparametric 3D piezoelectric elements, flat-shell elements and transition elements at the interface of the piezoelectric devices and the plate. Under a given external loading, the structure and the embedded sensors deform and the voltage response of the sensor can be calculated as a function of time. Such calculations can be useful as a design tool for smart structures.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A finite element formulation is presented for modeling microelectromechanical systems (MEMS) to predict the behavior of dynamic response of piezoelectric ceramics subjected to both mechanical and electrical loadings. The FEM formulation presented is based on variational principle using the concept of virtual work. An unconditionally stable method for direct integration of the equations of piezoelectric material is introduced and can be put in the form of 3-step linear multistep method of second order equations. A thin cantilever plate with PZT sensor mounted on it, is investigated to show the feasibility of analysis using 20 node isoparametric 3D piezoelectric elements, flat-shell elements, transition elements which are implemented for the numerical analysis. Under a given initial loading, a structure would deform accordingly, and the distributed sensor outputs could be calculated at each time step. Such calculation can be used as design tool for MEMS structures containing sensors and actuators.

For very sensitive applications, it may be necessary to adjust the spatial power spectral density (PSD), obtained by measuring any line figure on an optical surface, to eliminate the effect due to ground vibration. This is possible only if we know how to relate the standard random vibration output-numerous pointwise temporal PSDs-to spatial PSDs measured by interferometers. This paper serves as such a link. Two methods are presented here. The first uses direct integration starting from the mathematical definition of the spatial PSD of a function. The second borrows the relationship between two-dimensional spatial PSD and temporal PSD from atmospheric disturbance. As expected, both methods give nearly identical results.

We detail the use of an optical linear algebra processor for a finite element processing application. A linear time-varying structural mechanics finite element earthquake case study is described. The structure response under earthquake loading is considered, and the solution is obtained with the Newmark direct integration algorithm. The optical architecture for performing the required computationally burdensome banded matrix-vector operations is reviewed. The case study was solved on a laboratory version of the optical processor, and the results are presented.