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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

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September


Multi-Frequency Bayesian CS Methods for Microwave Imaging

  • Lorenzo Poli, Giacomo Oliveri, Ping Ping Ding, Toshifumi Moriyama, and Andrea Massa
  • received 07/22/2014; accepted 09/11/2014; posted 09/12/2014; Doc. ID 217433
  • [full text: PDF (490) KB)]
  • Abstract: The Bayesian retrieval of sparse scatterers under multi-frequency transverse magnetic illuminations is addressed. Two innovative imaging strategies are formulated to process the spectral content of microwave scattering data according to either a frequency-hopping multi-step scheme or a multi-frequency one-shot scheme. To solve the associated inverse problems, customized implementations of the single-task (ST) and the multi-task (MT) Bayesian Compressive Sensing (BCS) are introduced. A set of representative numerical results is discussed to assess the effectiveness and the robustness against the noise of the proposed techniques also in comparison with some state-of-the-art deterministic strategies.

Keywords (OCIS):

  • (110.0110) Imaging systems : Imaging systems
  • (280.0280) Remote sensing and sensors : Remote sensing and sensors
  • (110.1758) Imaging systems : Computational imaging
  • (110.6955) Imaging systems : Tomographic imaging
  • (110.3010) Imaging systems : Image reconstruction techniques
  • (100.3200) Image processing : Inverse scattering

Crossover from spherical particle Mie scattering to circular aperture diffraction

  • William Heinson, Amitabha Chakrabarti, and Christopher Sorensen
  • received 06/17/2014; accepted 09/08/2014; posted 09/08/2014; Doc. ID 214134
  • [full text: PDF (648) KB)]
  • Abstract: This paper demonstrates the manner in which the Mie results for light scattering by a three-dimensional sphere of arbitrary size and refractive index crosses over to Fraunhofer diffraction by a two-dimensional circular aperture of the same radius in the limit of very large radius. Demonstration is feasible only because the graphical results are plotted in the manner of the Q-space analysis which plots scattered intensity versus the logarithm of the magnitude of the scattering wave vector rather than linear versus the scattering angle.

Keywords (OCIS):

  • (050.1940) Diffraction and gratings : Diffraction
  • (050.1960) Diffraction and gratings : Diffraction theory
  • (290.0290) Scattering : Scattering
  • (290.4020) Scattering : Mie theory
  • (290.5825) Scattering : Scattering theory

Energy Redistribution Signatures in Transmission Microscopy of Rayleigh- and Mie-particles

  • Markus Selmke and Frank Cichos
  • received 05/23/2014; accepted 09/05/2014; posted 09/05/2014; Doc. ID 212638
  • [full text: PDF (2618) KB)]
  • Abstract: We describe the transmission characteristics for the interaction of an arbitrary beam with (possibly multilayered) particles of arbitrary size and electric permeability. Within the generalized Lorenz-Mie theory, expressions which generalize the total cross-sections to their fractional counterparts are presented which allow for an analytic quantification of transmission signals, both on-axis and off-axis. For Gaussian (Davis) beams, the relative angular domain of collection as compared to the beam's angle of divergence determines sensitively the shape and magnitude of the interference signal. Depending on the particle's position within the beam, the transmission signatures related to a pure energy redistribution as well as to accompanying absorption are discussed for Rayleigh particles in terms of their complex-valued polarizability. Implications for positioning, temperature control, spectroscopy and optimized extinction measurements are discussed.

Keywords (OCIS):

  • (110.0180) Imaging systems : Microscopy
  • (180.3170) Microscopy : Interference microscopy
  • (290.2200) Scattering : Extinction
  • (290.3030) Scattering : Index measurements
  • (290.4020) Scattering : Mie theory
  • (290.5825) Scattering : Scattering theory

Improved nonparaxial accelerating beams due to additional off-axis spiral phase

  • Wenguo Zhu and Weilong She
  • received 07/07/2014; accepted 09/05/2014; posted 09/05/2014; Doc. ID 216480
  • [full text: PDF (3555) KB)]
  • Abstract: The accelerating beam with Gaussian transverse profile can preserve its shape while propagating along a quarter of a circle. When an off-axis spiral phase is endowed, however, the beam will have an additional acceleration perpendicular to the circle. A 2D accelerating beam is constructed and is found that it accelerates along both x and y directions but its transverse intensity profile cannot keep well due to the interaction of accelerations along different directions. The intensity profile can be improved by imposing two off-axis spiral phases onto the input beam.

Keywords (OCIS):

  • (050.1970) Diffraction and gratings : Diffractive optics
  • (080.4865) Geometric optics : Optical vortices
  • (070.7345) Fourier optics and signal processing : Wave propagation

Propagation Evolution of the off-axis high-order cylindrical vector beam

  • Yang Li, Zhuqing Zhu, Xiaolei Wang, Liping Gong, Ming Wang, and Shouping Nie
  • received 06/17/2014; accepted 09/05/2014; posted 09/08/2014; Doc. ID 214067
  • [full text: PDF (942) KB)]
  • Abstract: The propagation characteristics of the off-axis high-order cylindrical vector beam (OHCVB) have been studied in this paper. The analytic expressions for the electric field and intensity distribution of OHCVB propagating in free space are presented for the first time. The transverse intensity of OHCVB, different from that of the input Gaussian beam, are not axially symmetric distribution owing to a slight dislocation between the polarization singularity located in vector field generator and the center point of Gaussian beam. Numerical results show that the intensity distribution in propagation strongly depends on propagation distance, dislocation displacement and topological charge. Accompanied by beam expansion, the intensity distribution of OHCVB tends to be steady eventually and the dark core of vector beam will disappear gradually in the process of propagation. Moreover, with the increase of the topological charge, more energy will be transferred from x-axis to y-axis and the annular intensity is split into two parts along the y-axis direction. The results help us to investigate the dynamic propagation behaviors of the high-order cylindrical vector beam under the off-axis condition, and also guide the calibration of the off-axis high-order cylindrical vector field in practice.

Keywords (OCIS):

  • (010.3310) Atmospheric and oceanic optics : Laser beam transmission
  • (260.5430) Physical optics : Polarization
  • (070.7345) Fourier optics and signal processing : Wave propagation

PAINTER: a spatio-spectral image reconstruction algorithm for optical interferometry

  • Antony Schutz, André Ferrari, David Mary, Férréol Soulez, Eric Thiebaut, and Martin Vannier
  • received 06/03/2014; accepted 09/04/2014; posted 09/04/2014; Doc. ID 213309
  • [full text: PDF (1437) KB)]
  • Abstract: Astronomical optical interferometers sample the Fourier transform of the intensity distribution of a source at the observation wavelength. Because of rapid perturbations caused by atmospheric turbulence, the phases of the complex Fourier samples (visibilities) cannot be directly exploited. Consequently, specific image reconstruction methods have been devised in the last few decades. Modern polychromatic optical interferometric instruments are now paving the way to multiwavelength imaging. This paper is devoted to the derivation of a spatio-spectral (3D) image reconstruction algorithm, coined PAINTER (Polychromatic opticAl INTErferometric Reconstruction software). The algorithm relies on an iterative process, which alternates estimation of polychromatic images and of complex visibilities. The complex visibilities are not only estimated from squared moduli and closure phases, but also differential phases, which helps to better constrain the polychromatic reconstruction. Simulations on synthetic data illustrate the efficiency of the algorithm and in particular the relevance of injecting a differential phases model in the reconstruction.

Keywords (OCIS):

  • (100.3190) Image processing : Inverse problems
  • (100.5070) Image processing : Phase retrieval
  • (100.6890) Image processing : Three-dimensional image processing
  • (100.3175) Image processing : Interferometric imaging

Analysis of Scattering from Complex Dielectric Objects using the Generalized Method of Moments

  • Jie Li, Dan Dault, Naveen Nair, and Balasubramaniam Shanker
  • received 05/22/2014; accepted 09/03/2014; posted 09/04/2014; Doc. ID 212430
  • [full text: PDF (867) KB)]
  • Abstract: Integral equation based analysis of scattering from dielectric objects has been a topic of research for many decades. Different integral equation formulations, discretization methods, and comparative data of their relative advantages have been well studied. Traditional discretization methods typically rely on a tight coupling between the underlying geometry discretization and the approximation function space that is defined on this discretization. As a result, it is difficult to stitch together different approximation spaces or non-conformal domains or match basis sets to local physics. Furthermore, the basis sets most commonly used in discretizing dielectric boundary integral operators impose limits on the variety of integral equation formulations that can be employed. We recently presented a methodology \cite{Nair2011} that overcomes several of these bottlenecks. In the present paper, we introduce several extensions to these concepts for dielectric scattering problems. Specifically, we present a method that (i) uses mixed higher order local geometric descriptions, and (ii) mixes multiple basis sets defined on this geometry including higher order polynomials and classical Rao-Wilton-Glisson (RWG) functions. Furthermore, we provide a unified description of different integral equation formulations that can be used for analysis of scattering from dielectric objects and show that the present approach admits a larger range of formulations than existing methods. A number of results demonstrating the efficiency of the method (in terms of accuracy and capability) together with applicability to different formulations are presented.

Keywords (OCIS):

  • (000.4430) General : Numerical approximation and analysis
  • (290.0290) Scattering : Scattering
  • (050.1755) Diffraction and gratings : Computational electromagnetic methods

Comparative assessment of orthogonal polynomials for wavefront reconstruction over the square aperture

  • Jingfei Ye, Zhishan Gao, Shuai Wang, Jinlong Cheng, Wei Wang, and Wenqing Sun
  • received 06/11/2014; accepted 09/02/2014; posted 09/04/2014; Doc. ID 213727
  • [full text: PDF (2668) KB)]
  • Abstract: Four orthogonal polynomials for reconstructing a wavefront over a square aperture based on modal method are currently available, namely the 2D Chebyshev polynomials, 2D Legendre polynomials, Zernike square polynomials and Numerical polynomials respectively. They are all orthogonal over the full unit square domain. 2D Chebyshev polynomials are defined by the product of Chebyshev polynomials in x and y variables, so do 2D Legendre polynomials. Zernike square polynomials are derived by Gram-Schmidt orthogonalization process, where the integration region across the full unit square is circumscribed outside the unit circle. Numerical polynomials are obtained by the numerical calculation. The presented study is to compare these four orthogonal polynomials by theoretical analysis and numerical experiments from the aspects of reconstruction accuracy, remaining errors, and robustness. Results show that the Numerical orthogonal polynomial is superior to other three polynomials because of its high accuracy and robust even in the case of wavefront with incomplete data.

Keywords (OCIS):

  • (000.4430) General : Numerical approximation and analysis
  • (120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
  • (120.3940) Instrumentation, measurement, and metrology : Metrology

Localized input fields in the rigorous coupled-wave analysis

  • Maximilian Auer and Karl-Heinz Brenner
  • received 06/11/2014; accepted 09/02/2014; posted 09/04/2014; Doc. ID 213842
  • [full text: PDF (953) KB)]
  • Abstract: We introduce a new treatment for localized input fields in the coupled wave theory. Therefore, a combination of the angular spectrum decomposition (ASD) and a cyclic formulation of the rigorous coupled-wave analysis (RCWA) is used, which does not require the computation of several standard RCWA calculations. The cyclic approach especially concerns the definition of the convolution matrix of the permittivity and enables the processing of multiple input plane waves in a single RCWA calculation. At the same time it ensures physically meaningful simulation results for finite truncation limits and thus inherently conserves energy. By adapting the 3D-RCWA algorithm to efficiently simulate the effects of localized and arbitrarily polarized input fields to three-dimensional volume gratings, various advanced diffraction problems like fiber coupling, the influence of distorted plane waves or the effects of focused beams on diffraction gratings can be investigated. Therefore, the impact of this work should concern many fields of application.

Keywords (OCIS):

  • (050.1950) Diffraction and gratings : Diffraction gratings
  • (090.7330) Holography : Volume gratings
  • (230.7370) Optical devices : Waveguides
  • (070.7345) Fourier optics and signal processing : Wave propagation

Vector Scattering from One Dimensional Periodic Perfectly Conducting Surface: TM Polarization

  • Qi Huang, Tian-lin Dong, Boyuan Chen, Qingxia Li, Jiasheng Tian, and Ping Chen
  • received 06/03/2014; accepted 09/02/2014; posted 09/03/2014; Doc. ID 213361
  • [full text: PDF (562) KB)]
  • Abstract: Abstract- Based on the Rayleigh hypothesis and the Floquet’s theorem, a vector method for studying electromagnetic wave scattering from one-dimensional periodic conducting surface with tapered transverse magnetic (TM) wave incidence is presented. The new formulation opens a new wide range of applications of the method, concerning not only gratings used in TM polarization but also conical diffraction, crossed gratings, two-dimensional problem, photonic band gaps, nonlinear optics, etc. The numerical results are consistent with the T-matrix method in the particular case when the plane of incidence is perpendicular to the generators of the surface. For the general case when the plane of incidence is not perpendicular to generators of the surface, the proposed method obtains significant results which reveal cross-polarized and anisotropic characteristics in the scattering while the energy balance is kept satisfactory. This straight forward approach is much more efficient than the T-matrix, thus suitable to be extended to other more involved periodic scattering problems.

Keywords (OCIS):

  • (050.0050) Diffraction and gratings : Diffraction and gratings
  • (050.1960) Diffraction and gratings : Diffraction theory
  • (290.5870) Scattering : Scattering, Rayleigh
  • (050.1755) Diffraction and gratings : Computational electromagnetic methods
  • (290.5825) Scattering : Scattering theory

August


Two dimensional Green's tensor for gyrotropic clusters composed of circular cylinders

  • Ara Asatryan, Lindsay Botten, Kejie Fang, Shanhui Fan, and Ross McPhedran
  • received 07/01/2014; accepted 08/25/2014; posted 09/03/2014; Doc. ID 214986
  • [full text: PDF (1729) KB)]
  • Abstract: The construction of Green's tensor for two-dimensional gyrotropic photonic clusters composed of cylinders with circular cross-sections using the semi-analytic multipole method is presented. The high efficiency and accuracy of the method is demonstrated. The developed method is applied to gyrotropic clusters which support topological chiral Hall edge states. The remarkable tolerance of chiral Hall edge modes toward substantial cluster separation is revealed. The transformation of chiral Hall edge states as the cluster separation increases is also presented. The excitation of chiral Hall edge modes for different source orientations is considered. Both gyro-electric and gyro-magnetic(ferrite) clusters are treated.

Keywords (OCIS):

  • (050.1940) Diffraction and gratings : Diffraction
  • (290.4210) Scattering : Multiple scattering
  • (050.5298) Diffraction and gratings : Photonic crystals

Tailorable optical scattering properties of the V-shaped plasmonic nano-antennas: a computationally efficient and fast analysis

  • M. Chryssomallis, D. Anagnostou, and Arash Rashidi
  • received 06/11/2014; accepted 08/25/2014; posted 08/26/2014; Doc. ID 213914
  • [full text: PDF (1065) KB)]
  • Abstract: We introduce an efficient computational scheme based on Macro Basis Function (MBF) method, to analyze the scattering of a plane wave by the V-shaped plasmonic optical nano-antennas. The polarization currents and the scattered fields for symmetric and anti-symmetric excitations are investigated. We investigate how the resonant frequency of the plasmonic V-shaped nanoantenna is tailored by engineering the geometrical parameters and by changing the polarization state of the incident plane wave. The computational model presented herein is faster by orders of magnitude than commercially available finite methods and is capable to characterize also other nano-antennas comprising of junctions and bends of nanorods.

Keywords (OCIS):

  • (290.0290) Scattering : Scattering
  • (160.3918) Materials : Metamaterials
  • (250.5403) Optoelectronics : Plasmonics

FDTD-Based Quantitative Analysis of Terahertz Wave Detection for Multilayered Structures

  • Wanli Tu, Shuncong Zhong, Yao-Chun Shen, Qing Zhou, and Ligang Yao
  • received 07/03/2014; accepted 08/25/2014; posted 08/27/2014; Doc. ID 215285
  • [full text: PDF (873) KB)]
  • Abstract: Experimental investigations have shown that terahertz pulsed imaging (TPI) is able to quantitatively characterise a range of multilayered media (e.g., biological issues, pharmaceutical tablet coatings, layered polymer composites, etc.). Advanced modelling of the interaction of terahertz radiation with a multilayered medium is required to enable the wide application of THz technology in a number of emerging fields, including non-destructive testing. Indeed, there have already been many theoretical analyses performed on the propagation of terahertz radiation in various multilayered media. However, to date, most of these studies used one-dimensional or two-dimensional models, and the dispersive nature of the dielectric layers was not considered or was simplified. In the present work, the theoretical framework of using terahertz waves for the quantitative characterisation of multilayered media was established. A three-dimensional (3D) model based on finite difference time domain(FDTD) method is proposed. A batch of pharmaceutical tablets with a single coating layer of different coating thicknesses and different refractive indices was modelled. The reflected THz wave from such a sample was computed using the FDTD method, assuming that the incident THz wave is broad-band, covering a frequency range up to 3.5THz.The simulated results for all of the pharmaceutical coated tablets considered were found to be in good agreement with the experimental results obtained using a commercial TPI system. In addition, we also studied a three-layered medium to mimic the occurrence of defects in the sample.

Keywords (OCIS):

  • (120.4290) Instrumentation, measurement, and metrology : Nondestructive testing
  • (080.1753) Geometric optics : Computation methods
  • (110.6795) Imaging systems : Terahertz imaging

Comparison of the rigorous coupled-wave approach and the finite element method for photovoltaic devices with a periodically corrugated metallic backreflector

  • Manuel Solano, Muhammad Faryad, Akhlesh Lakhtakia, and Peter Monk
  • received 06/25/2014; accepted 08/25/2014; posted 08/25/2014; Doc. ID 214651
  • [full text: PDF (453) KB)]
  • Abstract: Optimal design of photovoltaic devices with a periodically corrugated metallic back\-reflector requires a rapid and reliable way to simulate the optical characteristics for wide ranges of wavelength and angle of incidence. Two independent numerical techniques are needed for confidence in numerical results. We compared the rigorous coupled-wave approach (RCWA) and the finite element method (FEM), the former being fast and flexible, but the latter having predictable convergence even for discontinuous constitutive properties. Depending on the shape of the corrugation and the constitutive properties of the metal and dielectric materials making up the device, both methods can exhibit slow convergence rates for p-polarized light. The chosen model problem in this paper is of this type. As rapid spatial variations of the fields are the underlying cause, suitable selective refinement of the FEM mesh can overcome this slow convergence. Therefore, it would be desirable to have a self-adaptive scheme for choosing the mesh in the FEM. This will slow down the algorithm, but will give a reliable way to check the RCWA results.

Keywords (OCIS):

  • (050.1950) Diffraction and gratings : Diffraction gratings
  • (050.1755) Diffraction and gratings : Computational electromagnetic methods
  • (050.5298) Diffraction and gratings : Photonic crystals

Human gesture recognition using 3D Integral Imaging

  • Pedro Latorre-Carmona, V. Traver, Eva Salvador-Balaguer, Filiberto Pla, and Bahram Javidi
  • received 05/02/2014; accepted 08/25/2014; posted 09/03/2014; Doc. ID 211272
  • [full text: PDF (3379) KB)]
  • Abstract: Three-dimensional Integral Imaging allows one to reconstruct a 3D scene, including range information, and provides sectional re-focused imaging of 3D objects at different ranges. This paper explores the potential use of 3D passive sensing Integral Imaging for human gesture recognition tasks from sequences of reconstructed 3D video scenes. As a preliminary testbed, the 3D Integral Imaging sensing is implemented using an array of cameras with the appropriate algorithms for 3D scene reconstruction. Recognition experiments are performed by acquiring 3D video scenes of multiple hand gestures performed by ten people. We analyze the capability and performance of gesture recognition using 3D Integral Imaging representations at given distances and compare its performance with the use of standard 2D single-camera videos. To the best of our knowledge, this is the first report on using 3D Integral Imaging for human gesture recognition.

Keywords (OCIS):

  • (100.5010) Image processing : Pattern recognition
  • (100.6890) Image processing : Three-dimensional image processing
  • (110.6880) Imaging systems : Three-dimensional image acquisition
  • (150.6910) Machine vision : Three-dimensional sensing

Theoretical analysis and applications on nano-block loaded rectangular ring

  • Shiping Zhan, Hongjian Li, Guangtao Cao, Zhihui He, Boxun Li, and Hui Xu
  • received 06/27/2014; accepted 08/22/2014; posted 08/25/2014; Doc. ID 214835
  • [full text: PDF (404) KB)]
  • Abstract: We propose compact and switchable optical filters based on the nano-blocks loaded rectangular rings, and investigate the selecting property numerically and theoretically. A simple and convenient phase model is established for the theoretical analysis. The dependent factors, such as the number, size and positions of the loaded blocks, are discussed in details. It is found that longer wavelength can be obtained without increasing the device dimension, and the selected wave is more sensitive to length of the loaded blocks. The loading positions play key roles for the realization of separating the second order modes. Finally, applications of this proposed structure are simply discussed. We find that the loaded filter device guarantees a more compact size than the unloaded one on same property, and a tunable plasmon induced transparency (PIT) based switch effect is also achieved. These findings suggest potential applications in compact filter, tunable slow light devices and sensor field

Keywords (OCIS):

  • (140.4780) Lasers and laser optics : Optical resonators
  • (230.7370) Optical devices : Waveguides
  • (250.5403) Optoelectronics : Plasmonics
  • (230.7408) Optical devices : Wavelength filtering devices

Invisibility assessment: a visual perception approach

  • Ivan Moreno, Yessenia Jauregui-Sánchez, and Maximino Avendaño Alejo
  • received 03/18/2014; accepted 08/22/2014; posted 08/25/2014; Doc. ID 208362
  • [full text: PDF (1839) KB)]
  • Abstract: Determining how invisible an optical cloak intended to hide something is becoming a real problem in recent times. There are many invisibility mechanisms, the performance is quite different from technique to technique, and it is desirable to have a precise metric for their comparison. Here we propose a simple metric that assesses the invisibility in a similar way as humans do. This invisibility index is based on the fact that the human visual system (HVS) is highly sensitive to spatial frequencies, and then uses the Fourier transform and the contrast sensitivity function of the HVS to assess invisibility.

Keywords (OCIS):

  • (070.0070) Fourier optics and signal processing : Fourier optics and signal processing
  • (330.5000) Vision, color, and visual optics : Vision - patterns and recognition
  • (100.4995) Image processing : Pattern recognition, metrics
  • (230.3205) Optical devices : Invisibility cloaks

Nonparaxial propagation of elliptical Gaussian vortex beams in uniaxial crystal orthogonal to the optical axis

  • Xun Wang, Liu Zhirong, and Daomu Zhao
  • received 06/11/2014; accepted 08/22/2014; posted 08/25/2014; Doc. ID 213751
  • [full text: PDF (5867) KB)]
  • Abstract: Analytical expressions for the three components of nonparaxial propagation of a polarized elliptical Gaussian vortex beam in uniaxial crystal orthogonal to the optical axis are derived. Intensity and phase distributions of the three components of a polarized elliptical Gaussian vortex beam propagating in a uniaxial crystal orthogonal to the optical axis are illustrated by numerical examples. Influences of the initial beam’s parameters and the parameters of the uniaxial crystal on the evolution of the beam’s intensity and phase distributions in the uniaxial crystal are examined in detail. Results show that the statistical properties of an elliptical Gaussian vortex beam nonparaxial propagating in uniaxial crystal orthogonal to the optical axis are closely determined by the initial beam’s parameters and the parameters of the crystal: the beam waist width not only affects the size of the beam profile in uniaxial crystal, but also determines the nonparaxial effect of an elliptical Gaussian vortex beam; the profile of an elliptical Gaussian vortex beam in the uniaxial crystal becomes twisted and tilted, whether the elliptical factor α is greater or smaller than unity; the beam profile is tilted to the left in positive crystal, in contrast, it is inclined to the right in negative crystal. The results indicate that uniaxial crystal provides a convenient method to modulate the intensity and phase distributions of an elliptical Gaussian vortex beam, which is beneficial to optical manipulation of microscopic particles and nonlinear optics involving in special beam profile and phase.

Keywords (OCIS):

  • (260.1180) Physical optics : Crystal optics
  • (260.1960) Physical optics : Diffraction theory
  • (350.5500) Other areas of optics : Propagation

(LITH2014) Robust and efficient inverse mask synthesis with basis function representation

  • Xiaofei Wu, Shiyuan Liu, Wen Lv, and Edmund Lam
  • received 07/07/2014; accepted 08/18/2014; posted 09/02/2014; Doc. ID 216337
  • [full text: PDF (2683) KB)]
  • Abstract: Mask optimization is essential in the resolution scaling of optical lithography due to its strong ability to overcome the optical proximity effect. However, it often demands extensive computation in solving the nonlinear optimization problem with a large number of variables. In this paper, we use a set of basis functions to represent the mask patterns, and incorporate this representation into the mask optimization at both the nominal plane and various defocus conditions. The representation coefficients are updated due to the gradient to the coefficients, which can be easily obtained from the gradient to the pixel variables. To ease the computation of the gradient, we use an adaptive method that divides the optimization into two steps, in which a small number of kernels is used as the first step, and more kernels are used for fine optimization. Simulations performed on two test patterns demonstrate that this method can improve the optimization efficiency by several times, and the optimized patterns have better manufacturability compared with regular pixel-based representation.

Keywords (OCIS):

  • (110.5220) Imaging systems : Photolithography
  • (110.1758) Imaging systems : Computational imaging
  • (110.4235) Imaging systems : Nanolithography

Local transformation leading to an efficient Fourier Modal Method for perfectly conducting gratings

  • Simon Félix, Agnes Maurel, and Jean François Mercier
  • received 06/27/2014; accepted 08/13/2014; posted 08/20/2014; Doc. ID 214623
  • [full text: PDF (1765) KB)]
  • Abstract: We present an efficient Fourier modal method for the wave scattering by perfectly conducting gratings (in the two polarizations). The method uses a geometrical transformation, similar to the one used in the C-method, which transforms the grating surface into a flat surface, thus avoiding to question the Rayleigh hypothesis; also, the transformation only affects a bounded inner region which naturally matches the outer region; this allows to apply a simple criterion to select the ingoing and outgoing waves. The method is shown to satisfy the reciprocity and the energy conservation and it has an exponential rate of convergence for regular groove shapes. Besides, it is shown that the size of the inner region, where the solution is computed, can be reduced to the groove depth, that is to the minimal computation domain.

Keywords (OCIS):

  • (050.1950) Diffraction and gratings : Diffraction gratings
  • (050.2770) Diffraction and gratings : Gratings
  • (050.1755) Diffraction and gratings : Computational electromagnetic methods

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