Thu, 21 Aug 2008 07:02:03 BST CiteULike: eyliu's library [439 articles] http://www.citeulike.org/user/eyliu/order/to_read CiteULike.org en-gb Copyright © 2004-2008 citeulike.org http://www.citeulike.org/user/eyliu/article/783426 <i>Metrology, Inspection, and Process Control for Microlithography XIX, Vol. 5752, No. 1. (2005), pp. 237-247.</i><br /><br />Specular-mode spectroscopic scatterometry is currently being used as an in-line metrology tool for wafer-to-wafer process monitoring and control in lithography and etch processes. Experimental real-time, in situ demonstrations of critical dimension monitoring and control have been made for reactive ion etching. There have been no similar demonstrations of real-time control in the critical step of resist development. In this paper, we will show the results of a simulation study on the use of scatterometry in an immersion mode both to improve resolution and to act as a real-time monitor for photoresist topography evolution during development. We have performed realistic simulations of the experimental performance by using Prolith to generate developing resist profiles vs. time and a rigorous couple wave algorithm (RCWA) simulator (modified to include the immersion ambient) to generate simulated scatterometry data. We have examined several modes of operation of the proposed measurement including specular and 1st order scattered modes using spectroscopic ellipsometry and reflectometry. For our simulations, we have used pure water to approximate the developer refractive index. We have created realistic simulation data by adding appropriate amounts of random noise to perfect simulations, and then used regression analysis to extract profiles from these data. Water immersion increases feature shape resolution for small period gratings by increasing the scattering into real diffracted modes. Immersion scatterometry for improved feature resolution and high speed acquisition of resist profiles Fred Terry Joseph Bendik doi:10.1117/12.599135 Metrology, Inspection, and Process Control for Microlithography XIX, Vol. 5752, No. 1. (2005), pp. 237-247. 2006-08-02T20:07:10-00:00 2005 Metrology, Inspection, and Process Control for Microlithography XIX 5752 1 237 247 SPIE metrology scatterometry http://www.citeulike.org/user/eyliu/article/539126 <i>Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, Vol. 16, No. 1. (1998), pp. 80-87.</i><br /><br />The effort discussed here addresses the use of shorter incident wavelengths for characterizing sub-0.1 µm linewidths and the corresponding influence on scatterometry measurement sensitivity to linewidth variations. A sensitivity metric, based on the variance statistic, was developed using well-characterized, large-pitch (0.80 µm) photoresist grating structures on Si illuminated at 633 and 442 nm. The same metric was applied to short-pitch (0.20 µm), etched gratings on InP, with the result that appreciable scatterometry sensitivity was measured, even at the 633 nm incident wavelength. Modeling was used to estimate scatterometry sensitivity at three wavelengths for photoresist critical dimensions of 100 and 70 nm on Si. A significant increase in sensitivity was not found until the incident wavelength was reduced to 325 nm. We are presently investigating techniques to improve measurement sensitivity for short-pitch structures using the 633 nm incident wavelength. ©1998 American Vacuum Society. Scatterometry measurement of sub-0.1 mu m linewidth gratings Stephen Coulombe Babar Minhas Christopher Raymond Sohail John Mcneil doi:10.1116/1.589840 Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures, Vol. 16, No. 1. (1998), pp. 80-87. 2006-03-07T20:12:23-00:00 1998 Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures 16 1 80 87 AVS gratings metrology scatterometry http://www.citeulike.org/user/eyliu/article/531167 <i>Thin Solid Films, Vol. 468, No. 1-2. (1 December 2004), pp. 339-346.</i><br /><br />Spectroscopic, specular reflected light measurements (both ellipsometry-SE, and reflectometry-SR) of grating structures have relatively recently been shown to yield very accurate information on the critical dimensions, wall-angles and detailed wall shape of deep submicron features. The technique is often called ‘scatterometry’ or optical critical dimension (OCD) measurement. This technique has been moved rapidly from initial demonstrations to significant industrial application. In this paper, we will review the development of this technique for in situ and ex situ applications. When applied in situ, this technique opens up exciting new opportunities for studying the evolution of topography in semiconductor fabrication processes and for applying real-time control methods for nanometer level feature size accuracy. We will briefly comment on limitations and challenges for this measurement technique. Erratum to "Spectroscopic ellipsometry and reflectometry from gratings (Scatterometry) for critical dimension measurement and in situ, real-time process monitoring" [Thin Solid Films 455-456 (2004) 828-836] Hsu-Ting Huang Fred Terry doi:10.1016/j.tsf.2004.06.099 Thin Solid Films, Vol. 468, No. 1-2. (1 December 2004), pp. 339-346. 2006-03-05T21:24:25-00:00 2004 Thin Solid Films 468 1-2 339 346 metrology scatterometry http://www.citeulike.org/user/eyliu/article/1586437 <i>Journal of Research of the National Bureau of Standards, Vol. 20 (April 1938), pp. 419-477.</i> Refractive index and dispersion of distilled water for visible radiation, at temperatures $0$ to $60^\circ$ C Leroy Tilton John Taylor Journal of Research of the National Bureau of Standards, Vol. 20 (April 1938), pp. 419-477. 2007-08-23T17:00:08-00:00 1938 Journal of Research of the National Bureau of Standards 20 419 477 optical-properties water http://www.citeulike.org/user/eyliu/article/1072935 <i>Metrology, Inspection, and Process Control for Microlithography XVIII, Vol. 5375, No. 1. (2004), pp. 564-575.</i><br /><br />Scatterometry is a novel optical metrology that has received considerable attention in the silicon industry in the past few years. Based on the analysis of light scattered from a periodic sample, scatterometry technology can be thought of as consisting of two parts known as the forward problem and the inverse problem. In the forward problem, a scatterometer "signature" is measured. The signature is simply the measured optical response of the scattering features to some incident illumination, like laser light. In the inverse problem, the signature is analyzed in order to determine the parameters (such as linewidth, thickness, profile, etc) of the scattering features. Typically a rigorous electrodynamic model is used in the solution to the inverse problem, but due to the complexity of the model there is no direct analytic solution. Instead, a variety of numerical methods to solve the inverse problem have been proposed and utilized. The earliest widely used method of solution to the inverse problem involved the generation of a "library" of scatter signatures corresponding to discrete parameter combinations of the structure being measured. Once the library was generated, it was then searched in order to determine the best match to the measured signature. The parameters of the best match were then reported as the parameters of the measured signature. As the technology matured, other methods such as model optimization techniques also emerged. In fact, a variety of alternate techniques have been explored and reported, but a general study comparing the results (and hence the strengths and weaknesses) of the various techniques has yet to be performed. In this research, we shall report results from using several different solutions to the inverse problem on two applications (patterned resist and etched poly). The solution methods shall include the classic library search method as well as three common optimization methods. The results will show that each technique has strengths and weaknesses. For example, the library search methods are generally the most robust but also the most time consuming, and the optimization methods, while fast, are prone to reporting a local but not global minima. Comparison of solutions to the scatterometry inverse problem Christopher Raymond Michael Littau Andrei Chuprin Simon Ward doi:10.1117/12.538662 Metrology, Inspection, and Process Control for Microlithography XVIII, Vol. 5375, No. 1. (2004), pp. 564-575. 2007-01-28T20:45:59-00:00 2004 Metrology, Inspection, and Process Control for Microlithography XVIII 5375 1 564 575 SPIE scatterometry http://www.citeulike.org/user/eyliu/article/1044692 <i>Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications, Vol. 3450, No. 1. (1998), pp. 2-10.</i><br /><br />After presenting various grating problems which arise nowadays in modern physics, a review of the basic ideas of the main electromagnetic theories of gratings is given, pointing out their specific domains of validity, advantages and shortcomings. A user guide is given to help researchers and engineers to select the most appropriate theory to resolve their specific grating problem. Electromagnetic theory of gratings: review and potential applications Michel Neviere Evgueni Popov doi:10.1117/12.323403 Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications, Vol. 3450, No. 1. (1998), pp. 2-10. 2007-01-16T17:48:12-00:00 1998 Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications 3450 1 2 10 SPIE diffraction gratings http://www.citeulike.org/user/eyliu/article/572310 <i>Optics Letters, Vol. 2, No. 6. (1978), pp. 148-150.</i><br /><br />All 16 elements of the Mueller matrix of an optical system (sample) can be encoded onto, hence can be retrieved from a single detected signal using a class of photopolarimeters with modulated polarizing and analyzing optics. The general theory of operation of such polarimeters is presented. We also propose a specific new photopolarimeter whose polarizing and analyzing optics are modulated by synchronously rotating two quarter-wave retarders at angular speeds and 5. When the light flux leaving such polarimeter is linearly detected, a periodic signal =a0+12in = 1" align="middle"> (an cos nt+bn sin nft) is generated, with fundamental frequency f=2. From the Fourier amplitudes a0, an, bn, to be measured by performing a discrete Fourier transform (DFT) of the signal J, the 16 elements of the Mueller matrix are simply determined. PACS: 07.60.Fs        Additional Information Full Text: Access via Source Journal Abstract [ Previous / Next Abstract | Issue Table of Contents | Top of Page ] Source Journal Abstract [ Main Menu | Main Help ] Photopolarimetric measurement of the Mueller matrix by Fourier analysis of a single detected signal RMA Azzam Optics Letters, Vol. 2, No. 6. (1978), pp. 148-150. 2006-04-01T05:55:00-00:00 1978 Optics Letters 2 6 148 150 OSA metrology http://www.citeulike.org/user/eyliu/article/500887 <i>Journal of the Optical Society of America A: Optics, Image Science, and Vision, Vol. 22, No. 2. (2005), pp. 230-238.</i><br /><br />An extension of the recently developed method of intensity diffraction tomography is derived that assumes that the probing field is a spherical wave produced by a point source sufficiently far from the scatterer. A discussion of the method and numerical reconstructions of a simulated three-dimensional scattering object are presented. ©2005 Optical Society of America Spherical-wave intensity diffraction tomography Greg Gbur Mark Anastasio Yin Huang Daxin Shi doi:10.1364/JOSAA.22.000230 Journal of the Optical Society of America A: Optics, Image Science, and Vision, Vol. 22, No. 2. (2005), pp. 230-238. 2006-02-10T22:15:48-00:00 2005 Journal of the Optical Society of America A: Optics, Image Science, and Vision 22 2 230 238 OSA diffraction-tomography http://www.citeulike.org/user/eyliu/article/500884 <i>Journal of the Optical Society of America A: Optics, Image Science, and Vision, Vol. 19, No. 11. (2002), pp. 2194-2202.</i><br /><br />We introduce a hybrid tomographic method, based on recent investigations concerning the connection between computed tomography and diffraction tomography, that allows direct reconstruction of scattering objects from intensity measurements. This technique is noniterative and is intuitively easier to understand and easier to implement than some other methods described in the literature. The manner in which the new method reduces to computed tomography at short wavelengths is discussed. Numerical examples of reconstructions are presented. Hybrid diffraction tomography without phase information Greg Gbur Emil Wolf Journal of the Optical Society of America A: Optics, Image Science, and Vision, Vol. 19, No. 11. (2002), pp. 2194-2202. 2006-02-10T22:12:13-00:00 2002 Journal of the Optical Society of America A: Optics, Image Science, and Vision 19 11 2194 2202 OSA diffraction-tomography http://www.citeulike.org/user/eyliu/article/500217 <i>Ultrasonic Imaging, Vol. 7, No. 3. (July 1985), pp. 264-275.</i><br /><br />A generalized projection-slice theorem is derived for transmission fan beam diffraction tomography within the Born or Rytov approximations. The development is based on the use of the so-called paraxial approximation which requires that the object being probed subtend a small angle relative to the source point and to the measurement plane. Within this approximation it is shown that the transmitted field measured over a plane surface located on the opposite side of the object from the insonifying point source determines the three-dimensional spatial Fourier transform of the object profile over the surface of an ellipsoid of revolution in Fourier space. In the special case where the point source is in the far field of the object the semiaxes of the ellipsoid become equal and the surface degenerates to a sphere and the result reduces to the usual projection-slice theorem of plane beam diffraction tomography. Generalized projection-slice theorem for fan beam diffraction tomography Anthony Devaney doi:10.1016/0161-7346(85)90006-9 Ultrasonic Imaging, Vol. 7, No. 3. (July 1985), pp. 264-275. 2006-02-09T17:30:57-00:00 1985 Ultrasonic Imaging 7 3 264 275 diffraction-tomography http://www.citeulike.org/user/eyliu/article/2463448 <i>J. Opt. Soc. Am. A, Vol. 13, No. 4. (1 April 1996), 779.</i> Highly improved convergence of the coupled-wave method for TM polarization Philippe Lalanne Michael Morris J. Opt. Soc. Am. A, Vol. 13, No. 4. (1 April 1996), 779. 2008-03-04T07:21:57-00:00 1996 J. Opt. Soc. Am. A 13 4 779 OSA coupled-wave diffraction gratings http://www.citeulike.org/user/eyliu/article/2463424 <i>J. Opt. Soc. Am. A, Vol. 12, No. 5. (1 May 1995), 1077.</i> Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach MG Moharam Drew Pommet Eric Grann TK Gaylord J. Opt. Soc. Am. A, Vol. 12, No. 5. (1 May 1995), 1077. 2008-03-04T07:06:27-00:00 1995 J. Opt. Soc. Am. A 12 5 1077 OSA coupled-wave diffraction gratings http://www.citeulike.org/user/eyliu/article/2459994 <i>J. Opt. Soc. Am. A, Vol. 24, No. 9. (2007), pp. 2692-2700.</i><br /><br />The rigorous coupled-wave analysis (RCWA) is a method to compute diffraction of a field by a given grating structure. Within various applications, such as metrology, it is important to know how the field reacts to small perturbations in the grating. This behavior can be expressed by the field derivatives with respect to a certain parameter. Approximations of these derivatives can be found by using finite differences where the field is computed for a neighboring value of the parameter, and the difference gives the derivative. Unfortunately, RCWA involves solving eigenvalue systems that are computationally expensive. Therefore, a faster alternative is given that computes the derivatives by straightforward differentiation of the relations within RCWA. Solving additional eigensystems is replaced by finding derivatives of eigenvalues and eigenvectors, which is less computationally expensive. Computing shape parameter sensitivity of the field of one-dimensional surface-relief gratings by using an analytical approach based on RCWA NP van der Aa RMM Mattheij J. Opt. Soc. Am. A, Vol. 24, No. 9. (2007), pp. 2692-2700. 2008-03-03T09:29:18-00:00 2007 J. Opt. Soc. Am. A 24 9 2692 2700 OSA coupled-wave diffraction gratings scatterometry http://www.citeulike.org/user/eyliu/article/396567 <i>International Journal of Thermophysics, Vol. 26, No. 5. (September 2005), pp. 1495-1514.</i> Effect of Dissolved Air on the Density and Refractive Index of Water A Harvey S Kaplan J Burnett doi:10.1007/s10765-005-8099-0 International Journal of Thermophysics, Vol. 26, No. 5. (September 2005), pp. 1495-1514. 2005-11-16T12:40:31-00:00 2005 International Journal of Thermophysics 0195-928X 26 5 1495 1514 Kluwer Academic Publishers optical-properties water http://www.citeulike.org/user/eyliu/article/262254 <i>Science, Vol. 308, No. 5721. (22 April 2005), pp. 534-537.</i><br /><br />Recent theory has predicted a superlens that is capable of producing sub-diffraction-limited images. This superlens would allow the recovery of evanescent waves in an image via the excitation of surface plasmons. Using silver as a natural optical superlens, we demonstrated sub-diffraction-limited imaging with 60-nanometer half-pitch resolution, or one-sixth of the illumination wavelength. By proper design of the working wavelength and the thickness of silver that allows access to a broad spectrum of subwavelength features, we also showed that arbitrary nanostructures can be imaged with good fidelity. The optical superlens promises exciting avenues to nanoscale optical imaging and ultrasmall optoelectronic devices. Sub-Diffraction-Limited Optical Imaging with a Silver Superlens Nicholas Fang Hyesog Lee Cheng Sun Xiang Zhang doi:10.1126/science.1108759 Science, Vol. 308, No. 5721. (22 April 2005), pp. 534-537. 2005-07-22T06:21:54-00:00 2005 Science 308 5721 534 537 negative-refraction superresolution http://www.citeulike.org/user/eyliu/article/797055 <i>Physical Review Letters, Vol. 85, No. 18. (30 October 2000), 3966.</i><br /><br />With a conventional lens sharpness of the image is always limited by the wavelength of light. An unconventional alternative to a lens; a slab of negative refractive index material; has the power to focus all Fourier components of a 2D image; even those that do not propagate in a radiative manner. Such âsuperlensesâ can be realized in the microwave band with current technology. Our simulations show that a version of the lens operating at the frequency of visible light can be realized in the form of a thin slab of silver. This optical version resolves objects only a few nanometers across. Negative Refraction Makes a Perfect Lens JB Pendry doi:10.1103/PhysRevLett.85.3966 Physical Review Letters, Vol. 85, No. 18. (30 October 2000), 3966. 2006-08-11T09:29:01-00:00 2000 Physical Review Letters 85 18 3966 American Physical Society negative-refraction superresolution http://www.citeulike.org/user/eyliu/article/798165 <i>Semiconductor Manufacturing, IEEE Transactions on, Vol. 14, No. 2. (2001), pp. 97-111.</i><br /><br />Scatterometry is one of the few metrology candidates that has true in situ/in-line potential for deep submicrometer critical dimension (CD) and profile analysis. Most existing scatterometers are designed to measure multiple incident angles at a single wavelength on periodic gratings. We extend this idea by deploying specular spectroscopic scatterometry. Specular spectroscopic scatterometry (SS) is designed to measure the zeroth-order diffraction response at a fixed angle of incidence and multiple wavelengths. This mechanism allows the use of existing thin-film metrology equipment, such as spectroscopic ellipsometers, to accurately extract topographic profile information from one-dimensional (1-D) periodic structures. In this work, we developed the grating tool-kit (gtk), which implements several variants of rigorous coupled-wave analysis (RCWA) to accurately and efficiently simulate diffraction behavior of 1-D gratings. Theoretical simulations using this package show that specular spectroscopic scatterometry can be applied in the current semiconductor manufacturing technology, and can be easily extended to the 0.07-μm generation. We have also applied a library-based profile extraction methodology to resist and poly focus-exposure matrices patterned using 0.25and 0.18-μm lithography and etch technology, respectively, to extract their cross-sectional profiles. Discrepancies between CD-SEM, CD-AFM, and SSS measurements are discussed and explained Specular spectroscopic scatterometry Xinhui Niu N Jakatdar Junwei Bao CJ Spanos Semiconductor Manufacturing, IEEE Transactions on, Vol. 14, No. 2. (2001), pp. 97-111. 2006-08-12T02:43:57-00:00 2001 Semiconductor Manufacturing, IEEE Transactions on 14 2 97 111 metrology scatterometry http://www.citeulike.org/user/eyliu/article/709301 <i>(24 Mar 2006)</i><br /><br />Iterative projection algorithms are successfully being used as a substitute of lenses to recombine, numerically rather than optically, light scattered by illuminated objects. Images obtained computationally allow aberration-free diffraction-limited imaging and allow new types of imaging using radiation for which no lenses exist. The challenge of this imaging technique is transfered from the lenses to the algorithms. We evaluate these new computational “instruments” developed for the phase retrieval problem, and discuss acceleration strategies. A unified evaluation of iterative projection algorithms for phase retrieval S Marchesini (24 Mar 2006) 2006-06-23T20:53:07-00:00 2006 phase-retrieval http://www.citeulike.org/user/eyliu/article/670701 <i>Review of Scientific Instruments, Vol. 44, No. 12. (1973), pp. 1753-1762.</i><br /><br />A new light scattering instrument is described for measuring, as a function of scattering angle, the elements of the matrix describing light scattered from small particle systems. The instrument uses a piezo-optical birefringence modulator to modulate the polarization state of the incident light beam, and uses lock-in amplifier detection of the scattered light. The first and second harmonics of the modulation frequency are used with various combinations of filters and orientations to give the separate matrix elements. A treatment of a simple scattering experiment by means of Mueller calculus is carried through to illustrate the interactions of the light with the scattering system and with the various components of the measuring instrument. Evaluation of the instrumental performance is shown through measurements on two systems of monodisperse polystyrene spheres of average radius 550 and 3940 Å, compared with Mie calculations. Further measurements on sulfur colloids are presented, and suggestions of the value of this type of instrument in future work are given. ©1973 The American Institute of Physics A new polarization-modulated light scattering instrument Arlon Hunt Donald Huffman doi:10.1063/1.1686049 Review of Scientific Instruments, Vol. 44, No. 12. (1973), pp. 1753-1762. 2006-05-25T22:48:16-00:00 1973 Review of Scientific Instruments 44 12 1753 1762 AIP optical-polarization scattering http://www.citeulike.org/user/eyliu/article/583646 <i>SIGACT News, Vol. 27, No. 4. (December 1996), pp. 52-61.</i> Theoretical computer science cheat sheet Steve Seiden doi:10.1145/242581.242585 SIGACT News, Vol. 27, No. 4. (December 1996), pp. 52-61. 2006-04-12T12:22:07-00:00 1996 SIGACT News 0163-5700 27 4 52 61 ACM Press combinatorics mathematics http://www.citeulike.org/user/eyliu/article/550074 <i>Physical Review B (Solid State), Vol. 5, No. 12. (1972), pp. 4721-4729.</i><br /><br />The polarization properties of the various diffracted orders from a grating are determined ellipsometrically. The ratio m of the far-field complex reflection coefficients for the p and s polarizations for any order m is measured. This information is complementary to the data available from the partition of the scattered energy over the radiating orders. By examining the polarization of the specularly reflected zeroth-order beam at large angles of incidence the optical effect of surface roughness is established. The roughened surface layer is shown to be equivalent to a film whose index of refraction is the average of the indices of the material of the surface and the immersion medium, in accordance with the Maxwell Garnett theory. The film thickness is a measure of the surface roughness. To explain the ellipsometric results on the various orders we derived an expression for m starting from the Stratton-Silver-Chu integral using the physical-optics approximation. There is agreement between the gross features of the theory and experiment, but the exact magnitudes could not be compared. This points to the need for an exact solution of the grating-diffraction problem for both polarizations, including the effect of a finite conductivity at optical frequencies. Polarization Characteristics of Scattered Radiation from a Diffraction Grating by Ellipsometry with Application to Surface Roughness RMA Azzam NM Bashara doi:10.1103/PhysRevB.5.4721 Physical Review B (Solid State), Vol. 5, No. 12. (1972), pp. 4721-4729. 2006-03-13T22:13:56-00:00 1972 Physical Review B (Solid State) 5 12 4721 4729 APS diffraction gratings metrology http://www.citeulike.org/user/eyliu/article/548982 <i>(27 June 2002)</i> Mathematical Theory of Communication Claude Shannon Warren Weaver (27 June 2002) 2006-03-12T05:46:17-00:00 2002 University of Illinois Press communication-theory http://www.citeulike.org/user/eyliu/article/539128 <i>Journal of the Optical Society of America A: Optics, Image Science, and Vision, Vol. 16, No. 12. (1999), pp. 2880-2886.</i><br /><br />Synthetic aperture imaging is treated as a confocal process. The point-spread function of the synthetic aperture process is narrower than that of conventional imaging by a factor of 0.5, whereas the conventional confocal process offers resolution improvement of a factor of 0.72. The resolution in the regime between conventional confocal and conventional synthetic aperture is explored by computer simulation. Also, experimental results are given. ©1999 Optical Society of America Generalized confocal imaging and synthetic aperture imaging Emmett Leith Kurt Mills Patrick Naulleau David Dilworth Ignacio Iglesias Hsuan Chen Journal of the Optical Society of America A: Optics, Image Science, and Vision, Vol. 16, No. 12. (1999), pp. 2880-2886. 2006-03-07T20:20:27-00:00 1999 Journal of the Optical Society of America A: Optics, Image Science, and Vision 16 12 2880 2886 OSA confocal optical-sectioning synthetic-aperture http://www.citeulike.org/user/eyliu/article/539125 <i>Applied Optics, Vol. 19, No. 4. (1980), pp. 525-533.</i><br /><br />Test patterns in the form of diffraction gratings are used for testing and monitoring linewidths on integrated circuit structures. The first and second diffraction orders produced by a laser beam are evaluated to give the width of the grating lines. Measurements on chrome masks show that this technique is accurate to 5 down to linewidths of 0.5 µm. The design of a test set for factory type mask testing is presented. Also, experiments are reported on the testing of patterns on Si wafers directly after photoresist development and after various etching steps, and an automatic setup for rapid testing of wafers is described. PACS: 42.85.Fe, 85.40.-e, 42.10.Hc Linewidth measurements on IC masks and wafers by grating test patterns HP Kleinknecht H Meier Applied Optics, Vol. 19, No. 4. (1980), pp. 525-533. 2006-03-07T20:11:17-00:00 1980 Applied Optics 19 4 525 533 OSA gratings metrology http://www.citeulike.org/user/eyliu/article/531880 <i>Physical Review Letters, Vol. 70, No. 10. (1993), pp. 1409-1412.</i><br /><br />It is demonstrated that scattering by a rough surface can be described in terms of the coherent transfer function, which was first developed to describe the process of imaging. The two-dimensional (one transverse and one longitudinal) coherent transfer function for confocal imaging is presented for a high-angle theory. From this an effective transfer function for imaging of rough surfaces is developed, based on the Kirchhoff approximation. It is described how confocal imaging can be used to investigate various scattering mechanisms, and can be used for reconstruction of surface profiles in the Kirchhoff approximation. Scattering by a one-dimensional rough surface, and surface profile reconstruction by confocal imaging CJR Sheppard TJ Connolly Min Gu doi:10.1103/PhysRevLett.70.1409 Physical Review Letters, Vol. 70, No. 10. (1993), pp. 1409-1412. 2006-03-06T20:01:59-00:00 1993 Physical Review Letters 70 10 1409 1412 APS confocal metrology scattering http://www.citeulike.org/user/eyliu/article/531163 <i>Optics Communications, Vol. 117, No. 1-2. (15 May 1995), pp. 16-19.</i><br /><br />Using a generalization of results for scattering by stratified media and by rough surfaces, a new form of the scattering potential, for three-dimensional imaging in the reflection geometry, is proposed. The scattering potential for imaging in the reflection geometry CJR Sheppard TJ Connolly Min Gu doi:10.1016/0030-4018(95)00107-J Optics Communications, Vol. 117, No. 1-2. (15 May 1995), pp. 16-19. 2006-03-05T21:02:02-00:00 1995 Optics Communications 117 1-2 16 19 diffraction-tomography http://www.citeulike.org/user/eyliu/article/526151 <i>Journal of the Optical Society of America A: Optics, Image Science, and Vision, Vol. 20, No. 1. (2003), pp. 40-55.</i><br /><br />Several strategies in phase retrieval are unified by an iterative "difference map" constructed from a pair of elementary projections and three real parameters. For the standard application in optics, where the two projections implement Fourier modulus and object support constraints, respectively, the difference map reproduces the "hybrid" form of Fienup's input–output map when a particular choice is made for two of the parameters. The geometric construction of the difference map illuminates the distinction between its fixed points and the recovered object, as well as the mechanism whereby the form of stagnation encountered by alternating projection schemes is avoided. When support constraints are replaced by object histogram or atomicity constraints, the difference map lends itself to crystallographic phase retrieval. Numerical experiments with synthetic data suggest that structures with hundreds of atoms can be solved. ©2003 Optical Society of America Phase retrieval by iterated projections Veit Elser Journal of the Optical Society of America A: Optics, Image Science, and Vision, Vol. 20, No. 1. (2003), pp. 40-55. 2006-03-02T03:55:59-00:00 2003 Journal of the Optical Society of America A: Optics, Image Science, and Vision 20 1 40 55 OSA convex-optimization phase-retrieval http://www.citeulike.org/user/eyliu/article/526145 <i>Journal of the Optical Society of America A: Optics, Image Science, and Vision, Vol. 7, No. 3. (1990), pp. 394-411.</i><br /><br />Phase problems occur in many scientific disciplines, particularly those involving remote sensing using a wave field. Although there has been much interest in phase retrieval in optics and in imaging in general over the past decade, phase retrieval has a much longer history in x-ray crystallography, and a variety of powerful and practical techniques have been developed. The nature of crystallography means that crystallographic phase problems are distinct from those in other imaging contexts, but there are a number of commonalities. Here the principles of phase retrieval in crystallography are outlined and are compared and contrasted with phase retrieval in general imaging. Uniqueness results are discussed, but the emphasis is on phase-retrieval algorithms and areas in which results in one discipline have, and may, contribute to the other. Phase retrieval in crystallography and optics RP Millane Journal of the Optical Society of America A: Optics, Image Science, and Vision, Vol. 7, No. 3. (1990), pp. 394-411. 2006-03-02T02:39:33-00:00 1990 Journal of the Optical Society of America A: Optics, Image Science, and Vision 7 3 394 411 OSA crystallography phase-retrieval http://www.citeulike.org/user/eyliu/article/526142 <i>Acta Crystallographica Section A, Vol. 60, No. 2. (2004), pp. 134-141.</i><br /><br />In this paper, an extremely simple structure solution method termed charge flipping is presented. It works ab initio on high-resolution X-ray diffraction data in the manner of Fourier recycling. The real-space modification simply changes the sign of charge density below a threshold, while in reciprocal space the moduli Fobs are retained resulting in an Fobs map without weighting. The algorithm is tested using synthetic data for a wide range of structures, the solution statistics are analysed and the quality of reconstruction is checked. Finally, mathematical aspects of the algorithm are considered in detail, and these show that in this chaotic iteration process the solution is a limit cycle and not a fixed point. Ab initio structure solution by charge flipping Gabor Oszlanyi Andras Suto doi:10.1107/S0108767303027569 Acta Crystallographica Section A, Vol. 60, No. 2. (2004), pp. 134-141. 2006-03-02T02:30:12-00:00 2004 Acta Crystallographica Section A 60 2 134 141 crystallography phase-retrieval http://www.citeulike.org/user/eyliu/article/526133 <i>Physical Review, Vol. 56, No. 1. (1939), pp. 99-107.</i><br /><br />It has been shown by Larmor, Kottler and others that the classical method of calculating diffraction from the Kirchhoff formula in terms of a scalar light function cannot be applied directly to the electromagnetic field since it takes into account neither the vector character of the field nor the effect of charges along the contour of the opening. The field equations are integrated directly by means of a vector analog of Green's theorem. The results are applied to the calculation of diffraction of electromagnetic waves from a rectangular slit in a screen of infinite conductivity. The results are compared with an exact solution obtained recently by Morse and Rubenstein. Diffraction Theory of Electromagnetic Waves JA Stratton LJ Chu doi:10.1103/PhysRev.56.99 Physical Review, Vol. 56, No. 1. (1939), pp. 99-107. 2006-03-02T02:08:08-00:00 1939 Physical Review 56 1 99 107 APS diffraction http://www.citeulike.org/user/eyliu/article/518787 <i>Acoustics, Speech, and Signal Processing [see also IEEE Transactions on Signal Processing], IEEE Transactions on, Vol. 37, No. 12. (1989), pp. 2131-2147.</i><br /><br />The authors derive the fundamental strip-mapping SAR (synthetic aperture radar) imaging equations from first principles. They show that the resolution mechanism relies on the geometry of the imaging situation rather than on the Doppler effect. Both the airborne and spaceborne cases are considered. Range processing is discussed by presenting an analysis of pulse compression and formulating a mathematical model of he radar return signal. This formulation is used to obtain the airborne SAR model. The authors study the resolution mechanism and derive the signal processing relations needed to produce a high-resolution image. They introduce spotlight-mode SAR and briefly indicate how polar-format spotlight processing can be used in strip-mapping SAR. They discuss a number of current and future research directions in SAR imaging A signal processing view of strip-mapping synthetic aperture radar DC Munson RL Visentin Acoustics, Speech, and Signal Processing [see also IEEE Transactions on Signal Processing], IEEE Transactions on, Vol. 37, No. 12. (1989), pp. 2131-2147. 2006-02-23T19:05:13-00:00 1989 Acoustics, Speech, and Signal Processing [see also IEEE Transactions on Signal Processing], IEEE Transactions on 37 12 2131 2147 synthetic-aperture http://www.citeulike.org/user/eyliu/article/518782 <i>Proceedings of the IEEE, Vol. 71, No. 8. (1983), pp. 917-925.</i><br /><br />Spotlight-mode synthetic aperture radar (spotlight-mode SAR) synthesizes high-resolution terrain maps using data gathered from multiple observation angles. This paper shows that spotlight-mode SAR can be interpreted as a tomographic reeonstrution problem and analyzed using the projection-slice theorem from computer-aided tomograpy (CAT). The signal recorded at each SAR transmission point is modeled as a portion of the Fourier transform of a central projection of the imaged ground area. Reconstruction of a SAR image may then be accomplished using algorithms from CAT. This model permits a simple understanding of SAR imaging, not based on Doppler shifts. Resolution, sampling rates, waveform curvature, the Doppler effect, and other issues are also discussed within the context of this interpretation of SAR. A tomographic formulation of spotlight-mode synthetic aperture radar DC Munson JD O'Brien WK Jenkins Proceedings of the IEEE, Vol. 71, No. 8. (1983), pp. 917-925. 2006-02-23T18:52:25-00:00 1983 Proceedings of the IEEE 71 8 917 925 synthetic-aperture tomography http://www.citeulike.org/user/eyliu/article/515251 <i>Physical Review, Vol. 131, No. 6. (1963), pp. 2766-2788.</i><br /><br />Methods are developed for discussing the photon statistics of arbitrary fields in fully quantum-mechanical terms. In order to keep the classical limit of quantum electrodynamics plainly in view, extensive use is made of the coherent states of the field. These states, which reduce the field correlation functions to factorized forms, are shown to offer a convenient basis for the description of fields of all types. Although they are not orthogonal to one another, the coherent states form a complete set. It is shown that any quantum state of the field may be expanded in terms of them in a unique way. Expansions are also developed for arbitrary operators in terms of products of the coherent state vectors. These expansions are discussed as a general method of representing the density operator for the field. A particular form is exhibited for the density operator which makes it possible to carry out many quantum-mechanical calculations by methods resembling those of classical theory. This representation permits clear insights into the essential distinction between the quantum and classical descriptions of the field. It leads, in addition, to a simple formulation of a superposition law for photon fields. Detailed discussions are given of the incoherent fields which are generated by superposing the outputs of many stationary sources. These fields are all shown to have intimately related properties, some of which have been known for the particular case of blackbody radiation. Coherent and Incoherent States of the Radiation Field Roy Glauber doi:10.1103/PhysRev.130.2529 Physical Review, Vol. 131, No. 6. (1963), pp. 2766-2788. 2006-02-22T02:16:19-00:00 1963 Physical Review 131 6 2766 2788 APS coherent-states optical-coherence quantum-optics http://www.citeulike.org/user/eyliu/article/515250 <i>Proceedings of the Physical Society, Vol. 80, No. 6. (1962), pp. 1269-1272.</i><br /><br />It is shown that the analytic properties of the temporal complex degree of coherence &gamma;(&tau;) in the complex time plane (&tau; complex) impose a relationship between|&gamma;(&tau;)| and arg &gamma;(&tau;) on the real time axis. This relationship involves, in general, the location of the zeros of the degree of coherence in the lower half of the complex &tau; plane. It is suggested that the analytic continuation of the temporal degree of coherence of many spectral distributions has no zeros at all in this half plane. The spectral profiles of such distributions could be uniquely determined from measurements of|&gamma;(&tau;)| alone. This possibility is of interest in connection with Michelson's well-known method of visibility curves. It is also of interest in connection with the recently proposed correlation and coincidence techniques (employing square-law detection) for determining narrow spectral profiles, such as those found in the output from an optical maser. Is a Complete Determination of the Energy Spectrum of Light Possible from Measurements of the Degree of Coherence? E Wolf doi:10.1088/0370-1328/80/6/307 Proceedings of the Physical Society, Vol. 80, No. 6. (1962), pp. 1269-1272. 2006-02-22T02:11:46-00:00 1962 Proceedings of the Physical Society 80 6 1269 1272 optical-coherence http://www.citeulike.org/user/eyliu/article/515249 <i>Reviews of Modern Physics, Vol. 37, No. 2. (1965), pp. 231-287.</i><br /><br />This article presents a review of coherence properties of electromagnetic fields and their measurements, with special emphasis on the optical region of the spectrum. Analyses based on both the classical and quantum theories are described. After a brief historical introduction, the elementary concepts which are frequently employed in the discussion of interference phenomena are summarized. The measure of second-order coherence is then introduced in connection with the analysis of a simple interference experiment and some of the more important second-order coherence effects are studied. Their uses in stellar interferometry and interference spectroscopy are described. Analysis of partial polarization from the standpoint of correlation theory is also outlined. The general statistical description of the field is discussed in some detail. The recently discovered universal "diagonal" representation of the density operator for free fields is also considered and it is shown how, with the help of the associated generalized phase-space distribution function, the quantum-mechanical correlation functions may be expressed in the same form as the classical ones. The sections which follow deal with the statistical properties of thermal and nonthermal light, and with the temporal and spatial coherence of blackbody radiation. Later sections, dealing with fourth- and higher-order coherence effects include a discussion of the photoelectric detection process. Among the fourth-order effects described in detail are bunching phenomena, the Hanbury Brown-Twiss effect and its application to astronomy. The article concludes with a discussion of various transient superposition effects, such as light beats and interference fringes produced by independent light beams. Coherence Properties of Optical Fields L Mandel E Wolf doi:10.1103/RevModPhys.37.231 Reviews of Modern Physics, Vol. 37, No. 2. (1965), pp. 231-287. 2006-02-22T02:08:26-00:00 1965 Reviews of Modern Physics 37 2 231 287 APS optical-coherence http://www.citeulike.org/user/eyliu/article/515246 <i>Reports on Progress in Physics, Vol. 17, No. 1. (1954), pp. 35-100.</i><br /><br />A critical review is presented of recent progress in classical diffraction theory. Both scalar and electromagnetic problems are discussed. The report may serve as an introduction to general diffraction theory although the main emphasis is on diffraction by plane obstacles. Various modifications of the Kirchhoff and Kottler theories are presented. Diffraction by obstacles small compared with the wavelength is discussed in some detail. Other topics included are: variational formulation of diffraction problems, the Wiener-Hopf technique of solving integral equations of diffraction theory, the rigorous formulation of Babinet's principle, the nature of field singularities at sharp edges, the application of Mathieu functions and spheroidal wave functions to diffraction theory. Reference is made to more than 500 papers published since 1940. Diffraction Theory CJ Bouwkamp doi:10.1088/0034-4885/17/1/302 Reports on Progress in Physics, Vol. 17, No. 1. (1954), pp. 35-100. 2006-02-22T02:00:17-00:00 1954 Reports on Progress in Physics 17 1 35 100 diffraction http://www.citeulike.org/user/eyliu/article/515184 <i>American Journal of Physics, Vol. 32, No. 12. (1964), pp. 919-926.</i><br /><br />A quasithermal, quasmonochromatic lamp is described which serves as a highly degeneratelight source with adjustable coherence time between 10–5 sec and 1 sec. This lamp is used forseveral demonstration experiments concerning the relations between coherence and fluctuations:The intensity interferometer of Hanbury Brown and Twiss is applied to measure the correlationsbetween intensity fluctuations. The double slit experiment of Young serves to stressthe role of fluctuations for classical interferometry. Interference patterns from two independentquasithermal lamps are presented. ©1964 American Association of Physics Teachers Coherence and Fluctuations in Light Beams W Martienssen E Spiller doi:10.1119/1.1970023 American Journal of Physics, Vol. 32, No. 12. (1964), pp. 919-926. 2006-02-21T21:46:31-00:00 1964 American Journal of Physics 32 12 919 926 AAPT optical-coherence http://www.citeulike.org/user/eyliu/article/511860 <i>(01 January 1986)</i><br /><br /><P>The latest mathematical and numerical techniques of diffraction theory are used in this book to give a full and richly illustrated description of waves in focal regions. Dr Stamnes has taken the unusual but comprehensive step of treating electromagnetic, acoustic and water waves in one volume. For researchers, practitioners and graduate students in the fields of wave propagation, diffraction, asymptotics, image formation and focusing.</P> Waves in Focal Regions: Propagation, Diffraction and Focusing of Light, Sound and Water Waves (Series on Optics and Optoelectronics) Stamnes (01 January 1986) 2006-02-19T21:56:59-00:00 1986 Taylor & Francis book diffraction http://www.citeulike.org/user/eyliu/article/510714 <i>Microwave Theory and Techniques, IEEE Transactions on, Vol. 32, No. 8. (1984), pp. 860-874.</i><br /><br />In this paper, the results of computer simulations used to determine the domains of applicability of the first-order Born and Rytov approximations in diffraction tomography for cross-sectional (or three-dimensional) imaging of biosystems are shown. These computer simulations were conducted on single cylinders, since in this case analytical expressions are available for the exact scattered fields. The simulations establish the first-order Born approximation to be valid for objects where the product of the relative refractive index and the diameter of the cylinder is less than 0.35 lambda. The first-order Rytov approximation is valid with essentially no constraint on the size of the cylinders; however, the relative refractive index must be less than a few percent. We have also reviewed the assumptions made in the first-order Born and Rytov approximations for diffraction tomography. Further, we have reviewed the derivation of the Fourier Diffraction projection Theorem, which forms the basis of the first-order reconstruction algorithms. We then show how this derivation points to new FFT-based implementations for the higher order diffraction tomography algorithms that are currently being developed. Limitations of Imaging with First-Order Diffraction Tomography M Slaney AC Kak LE Larsen Microwave Theory and Techniques, IEEE Transactions on, Vol. 32, No. 8. (1984), pp. 860-874. 2006-02-18T20:49:44-00:00 1984 Microwave Theory and Techniques, IEEE Transactions on 32 8 860 874 born-approximation diffraction-tomography rytov-approximation http://www.citeulike.org/user/eyliu/article/500896 <i>Applied Optics, Vol. 41, No. 28. (2002), pp. 5951-5955.</i><br /><br />Phase can be retrieved from intensity measurements with the intensity transport equation. Three-dimensional image formation of weak phase objects based on this method is investigated. It is shown that, although the refractive index of a thin object can be measured, the three-dimensional variation of refractive index of an arbitrary object cannot, in general, be reconstructed, as spatial frequencies with a zero-axial component are not detected. However, this may not be a problem if regions with known refractive index are present in the sample. ©2002 Optical Society of America Three-dimensional phase imaging with the intensity transport equation Colin Sheppard Applied Optics, Vol. 41, No. 28. (2002), pp. 5951-5955. 2006-02-10T22:32:25-00:00 2002 Applied Optics 41 28 5951 5955 OSA transport-of-intensity http://www.citeulike.org/user/eyliu/article/500890 <i>Journal of the Optical Society of America A: Optics, Image Science, and Vision, Vol. 21, No. 11. (2004), pp. 2173-2179.</i><br /><br />Deterministic phase retrieval is reinterpreted in terms of phase-space optics. A novel derivation of the transport-of-intensity equation is presented based on the Wigner distribution function and the ambiguity function. The phase retrieval problem is formulated as estimating the local first-order moment of the Wigner function from intensity information. A comparison with phase-space tomography suggests a generalization of deterministic phase retrieval that provides larger flexibility for signal recovery. In addition, one particular numerical implementation of generalized deterministic phase retrieval is presented. Simulated intensity data are used to validate the method. ©2004 Optical Society of America Phase-space interpretation of deterministic phase retrieval Andrey Semichaevsky Markus Testorf Journal of the Optical Society of America A: Optics, Image Science, and Vision, Vol. 21, No. 11. (2004), pp. 2173-2179. 2006-02-10T22:25:54-00:00 2004 Journal of the Optical Society of America A: Optics, Image Science, and Vision 21 11 2173 2179 OSA ambiguity-function phase-retrieval phase-space transport-of-intensity wigner-distribution http://www.citeulike.org/user/eyliu/article/500889 <i>Journal of the Optical Society of America A: Optics, Image Science, and Vision, Vol. 22, No. 12. (2005), pp. 2651-2661.</i><br /><br />A reconstruction theory for intensity diffraction tomography (I-DT) has been proposed that permits reconstruction of a weakly scattering object without explicit knowledge of phase information. We investigate the I-DT reconstruction problem assuming an incident (paraxial) spherical wave and scanning geometries that employ fixed source-to-object distances. Novel reconstruction methods are derived by identifying and exploiting tomographic symmetries and the rotational invariance of the problem. An underlying theme is that symmetries in tomographic imaging systems can facilitate solutions for phase-retrieval problems. A preliminary numerical investigation of the developed reconstruction methods is presented. ©2005 Optical Society of America Image reconstruction in spherical-wave intensity diffraction tomography Mark Anastasio Daxin Shi Yin Huang Greg Gbur doi:10.1364/JOSAA.22.002651 Journal of the Optical Society of America A: Optics, Image Science, and Vision, Vol. 22, No. 12. (2005), pp. 2651-2661. 2006-02-10T22:18:39-00:00 2005 Journal of the Optical Society of America A: Optics, Image Science, and Vision 22 12 2651 2661 OSA diffraction-tomography image-reconstruction http://www.citeulike.org/user/eyliu/article/500885 <i>Journal of the Optical Society of America A: Optics, Image Science, and Vision, Vol. 18, No. 9. (2001), pp. 2132-2137.</i><br /><br />The relationship between computed tomography (CAT) and diffraction tomography (DT) is investigated. A simple condition with a clear physical meaning is derived for the applicability of CAT. Corrections due to scattering are incorporated into CAT, and it is shown that the effect of scattering may be characterized by a two-dimensional fractional Fourier transform. The implications of these results for the three-dimensional imaging of weakly scattering objects are also discussed. ©2001 Optical Society of America Relation between computed tomography and diffraction tomography Greg Gbur Emil Wolf Journal of the Optical Society of America A: Optics, Image Science, and Vision, Vol. 18, No. 9. (2001), pp. 2132-2137. 2006-02-10T22:13:23-00:00 2001 Journal of the Optical Society of America A: Optics, Image Science, and Vision 18 9 2132 2137 OSA computed-tomography diffraction-tomography http://www.citeulike.org/user/eyliu/article/500416 <i>Circuits and Systems, IEEE Transactions on, Vol. 25, No. 9. (1978), pp. 694-702.</i><br /><br />We adopt a view that suggests that many problems of image restoration are probably geometric in character and admit the following initial linear formulation: The original<tex>f</tex>is a vector known a priori to belong to a linear subspace<tex>cal P_b</tex>of a parent Hilbert space<tex>cal H(</tex>, but all that is available to the observer is its image<tex>P_a f</tex>, the projection of<tex>f</tex>onto a known linear subspace<tex>cal P_a</tex>(also in<tex>cal H</tex>). 1) Find necessary and sufficient conditions under which<tex>f</tex>is uniquely determined by<tex>P_a f</tex>and 2) find necessary and sufficient conditions for the stable linear reconstruction of<tex>f</tex>from<tex>P_a f</tex>in the face of noise. (In the later case, the reconstruction problem is said to be completely posed.) The answers torn out to be remarkably simple. a)<tex>f</tex>is uniquely determined by<tex>cal P_a</tex>iff<tex>cal P_b</tex>and the orthogonal complement of<tex> cal P_a</tex>have only the zero vector in common. b) The reconstruction problem is completely posed iff the angle between<tex>cal P_b</tex>and the orthogonal complement of<tex>cal P_a</tex>, is greater than zero. (All angles lie in the first quadrant.) c) In the absence of noise, there exists in both cases a) and b) an effective recursive algorithm for the recovery of<tex>f</tex>employing only the operations of projection onto<tex>cal P_b</tex>and projection onto the orthogonal complement of<tex>cal P_a</tex>These operations define the necessary instrumentation. Generalized Image Restoration by the Method of Alternating Orthogonal Projections D Youla Circuits and Systems, IEEE Transactions on, Vol. 25, No. 9. (1978), pp. 694-702. 2006-02-10T04:14:25-00:00 1978 Circuits and Systems, IEEE Transactions on 25 9 694 702 convex-optimization image-restoration http://www.citeulike.org/user/eyliu/article/500221 <i>(29 October 1999)</i><br /><br />This book gives a clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory and explains how to use these methods to obtain approximate analytical solutions to differential and difference equations. These methods allow one to analyze physics and engineering problems that may not be solvable in closed form and for which brute-force numerical methods may not converge to useful solutions. The objective of this book is to teaching the insights and problem-solving skills that are most useful in solving mathematical problems arising in the course of modern research. Intended for graduate students and advanced undergraduates, the book assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations; develops local asymptotic methods for differential and difference equations; explains perturbation and summation theory; and concludes with a an exposition of global asymptotic methods, including boundary-layer theory, WKB theory, and multiple-scale analysis. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach the reader how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions; over 600 problems, of varying levels of difficulty; and an appendix summarizing the properties of special functions. Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Carl Bender Steven Orszag (29 October 1999) 2006-02-09T17:50:35-00:00 1999 Springer asymptotic-methods book perturbation-theory http://www.citeulike.org/user/eyliu/article/228152 <i>(24 January 1997)</i><br /><br />Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book. Optimization by Vector Space Methods (Series in Decision and Control) David Luenberger (24 January 1997) 2005-06-15T04:19:22-00:00 1997 Wiley-Interscience book optimization http://www.citeulike.org/user/eyliu/article/500218 <i>Ultrasonic Imaging, Vol. 4, No. 4. (October 1982), pp. 336-350.</i><br /><br />A reconstruction algorithm is derived for parallel beam transmission computed tomography through two-dimensional structures in which diffraction of the insonifying beam must be taken into account. The algorithm is found to be completely analogous to the filtered backprojection algorithm of conventional transmission tomography with the exception that the backprojection operation has to be replaced by a backpropagation process whereby the complex phase of a field measured over a line outside the object is made to propagate back through the object space. The algorithm is applicable to diffraction tomography within either the first Born or Rytov approximations. Application of the algorithm to three-dimensional structures is also discussed. A filtered backpropagation algorithm for diffraction tomography AJ Devaney doi:10.1016/0161-7346(82)90017-7 Ultrasonic Imaging, Vol. 4, No. 4. (October 1982), pp. 336-350. 2006-02-09T17:31:47-00:00 1982 Ultrasonic Imaging 4 4 336 350 diffraction-tomography http://www.citeulike.org/user/eyliu/article/497321 <i>SIAM Rev., Vol. 44, No. 2. (2002), pp. 169-224.</i> Optical Wavefront Reconstruction: Theory and Numerical Methods Russell Luke James Burke Richard Lyon doi:10.1137/S003614450139075 SIAM Rev., Vol. 44, No. 2. (2002), pp. 169-224. 2006-02-07T20:53:32-00:00 2002 SIAM Rev. 0036-1445 44 2 169 224 Society for Industrial and Applied Mathematics phase-retrieval http://www.citeulike.org/user/eyliu/article/497197 <i>Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 253, No. 1274. (1959), pp. 358-379.</i><br /><br />An investigation is made of the structure of the electromagnetic field near the focus of an aplanatic system which images a point source. First the case of a linearly polarized incident field is examined and expressions are derived for the electric and magnetic vectors in the image space. Some general consequences of the formulae are then discussed. In particular the symmetry properties of the field with respect to the focal plane are noted and the state of polarization of the image region is investigated. The distribution of the time-averaged electric and magnetic energy densities and of the energy flow (Poynting vector) in the focal plane is studied in detail, and the results are illustrated by diagrams and in a tabulated form based on data obtained by extensive calculations on an electronic computor. The case of an unpolarized field is also investigated. The solution is not restricted to systems of low aperture, and the computational results cover, in fact, selected values of the angular semi-aperture α on the image side, in the whole range 0 ≤α≤ 90 degrees. The limiting case α→ 0 is examined in detail and it is shown that the field is then completely characterized by a single, generally complex, scalar function, which turns out to be identical with that of the classical scalar theory of Airy, Lommel and Struve. The results have an immediate bearing on the resolving power of image forming systems; they also help our understanding of the significance of the scalar diffraction theory, which is customarily employed, without a proper justification, in the analysis of images in low-aperture systems. Electromagnetic Diffraction in Optical Systems. II. Structure of the Image Field in an Aplanatic System B Richards E Wolf Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 253, No. 1274. (1959), pp. 358-379. 2006-02-07T19:24:55-00:00 1959 Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 253 1274 358 379 diffraction http://www.citeulike.org/user/eyliu/article/497196 <i>Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 253, No. 1274. (1959), pp. 349-357.</i><br /><br />An integral representation is obtained for the electromagnetic field in the image space of an optical system. This representation, which is not restricted to systems of low angular aperture, is in the form of an angular spectrum of plane waves, and is closely related to that introduced by Luneberg (1944) as a vector generalization of well-known formulae of Debye (1909) and Picht (1925). It is shown that the representation has a simple physical interpretation in terms of a modified Huygens-Fresnel principle which operates with secondary plane waves rather than with secondary spherical waves. Electromagnetic Diffraction in Optical Systems. I. An Integral Representation of the Image Field E Wolf Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 253, No. 1274. (1959), pp. 349-357. 2006-02-07T19:24:26-00:00 1959 Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 253 1274 349 357 diffraction