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Application of S-transform profilometry in eliminating nonlinearity in fringe pattern

APPLIED OPTICS 2012年第5期51卷 577-587页

作者： Zhong, Min Chen, Wenjing Jiang, Mohua Sichuan Univ Optoelect Dept Chengdu 610064 Peoples R China

The S-transform, conceptually viewed as an extension of the short-time Fourier transform and the wavelet transform, features a time-frequency representation known for its local spectral property and multiresolution strategy. It has been introduced in optical three-dimensional shape measurement based on a fringe projection technique recently. In this paper, an application of S-transform for demodulating fringe patterns affected by the nonlinearity has been discussed. Two methods based on the S-transform, called S-transform ridge method and S-transform filtering method, are used to eliminate the phase errors caused by nonlinear factors of the projector and CCD camera. The theoretical representations of S-transform ridge method and S-transform filtering method in fringe analysis are given. The computer simulation and experiment are carried out to verify our research. Compared with the reconstructions of the windowed Fourier transform, the wavelet transform and the S-transform ridge method, the S-transform filtering method gives a better result under considering the influence of the fringe nonlinearity. (C) 2012 Optical Society of America

关键词： abcd transforms Spectrum analysis Surface measurements figure Harmonic generation and mixing

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Ray matrix analysis of the fast Fresnel transform with applications towards liquid crystal displays

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APPLIED OPTICS 2012年第5期51卷 644-650页

作者： Davis, Jeffrey A. Cottrell, Don M. San Diego State Univ Dept Phys San Diego CA 92182 USA

We reexamine a previously published algorithm for performing a fast Fresnel diffraction calculation that uses two Fourier transform operations and is computationally much faster than the conventional approach. We analyze this technique using a ray matrix analysis and find explicit expressions for the maximum and minimum distances over which this algorithm is accurate. These distances coincide with the experimental distances that are appropriate when patterns are encoded onto liquid crystal displays. We show two examples that confirm our ideas. We expect that these results will be very useful for computational comparison with experimental studies of a variety of diffraction phenomena. (C) 2012 Optical Society of America

关键词： abcd transforms Matrix methods in paraxial optics Discrete optical signal processing

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Effect of abcd transformations on beam paraxiality

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OPTICS EXPRESS 2011年第27期19卷 25944-25953页

作者： Vaveliuk, Pablo Martinez-Matos, Oscar Serv Nacl Aprendizagem Ind SENAI Cimatec Fac Tecnol BR-41650010 Salvador BA Brazil Univ Complutense Madrid Fac Ciencias Fis Dept Opt E-28040 Madrid Spain

The limits of the paraxial approximation for a laser beam under abcd transformations is established through the relationship between a parameter concerning the beam paraxiality, the paraxial estimator, and the beam second-order moments. The applicability of such an estimator is extended to an optical system composed by optical elements as mirrors and lenses and sections of free space, what completes the analysis early performed for free-space propagation solely. As an example, the paraxiality of a system composed by free space and a spherical thin lens under the propagation of Hermite-Gauss and Laguerre-Gauss modes is established. The results show that the the paraxial approximation fails for a certain feasible range of values of main parameters. In this sense, the paraxial estimator is an useful tool to monitor the limits of the paraxial optics theory under abcd transformations. (C) 2011 Optical Society of America

关键词： abcd transforms First order optics Laser beams Optical elements Optical systems Paraxial wave optics

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Wigner functions in optics: describing beams as ray bundles and pulses as particle ensembles

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ADVANCES IN OPTICS AND PHOTONICS 2011年第4期3卷 272-365页

作者： Alonso, Miguel A. Univ Rochester Inst Opt Rochester NY 14627 USA

This tutorial gives an overview of the use of the Wigner function as a tool for modeling optical field propagation. Particular emphasis is placed on the spatial propagation of stationary fields, as well as on the propagation of pulses through dispersive media. In the first case, the Wigner function gives a representation of the field that is similar to a radiance or weight distribution for all the rays in the system, since its arguments are both position and direction. In cases in which the field is paraxial and where the system is described by a simple linear relation in the ray regime, the Wigner function is constant under propagation along rays. An equivalent property holds for optical pulse propagation in dispersive media under analogous assumptions. Several properties and applications of the Wigner function in these contexts are discussed, as is its connection with other common phase-space distributions like the ambiguity function, the spectrogram, and the Husimi, P, Q, and Kirkwood-Rihaczek functions. Also discussed are modifications to the definition of the Wigner function that allow extending the property of conservation along paths to a wider range of problems, including nonparaxial field propagation and pulse propagation within general transparent dispersive media. (C) 2011 Optical Society of America

关键词： Radiative transfer abcd transforms Wave propagation Quasi-probability distribution functions Matrix methods in paraxial optics Phase space methods of analysis

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Centroid propagation through optical systems with abcd kernels and non-uniform or finite apertures

Centroid propagation through optical systems with <i>ABCD</i...

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International Conference on Applications of Optics and Photonics

作者： Lancis, Jesus Martinez-Cuenca, Raul Ares, Jorge Bara, Salvador Univ Jaume 1 Dept Fis GROC UJI Castellon de La Plana 12071 Spain Univ Zaragoza Dept Fis Aplicada Zaragoza 50009 Spain Univ Santiago De Compostela Dept Fis Apl Santiago De Compostela 15782 Spain

ISBN: (纸本)9780819485755

Determining the precise location of irradiance centroids is a key step for optical triangulation and wavefront sensing based on wavefront slope measurements (as e.g. in Hartmann-Shack aberrometry). Since most aberrometers include some kind of optical relay system to reimage the irradiance distributions provided by the wavefront sampling element onto the irradiance detector, it is esential to ensure that the centroid position and momentum information is preserved along this operation. In optical systems with abcd difrraction kernels the centroids propagate according to an effective geometrical optics rule. However, the presence of finite apertures partially blocking the incoming beam or non-uniform transmittances unevenly altering its original irradiance distribution may give rise to potentially significant departures from this simple geometrical picture. The potential magnitude of this bias makes it advisable to take proper steps to counteract it in the design of aberrometric setups.

关键词： Diffraction abcd transforms Hartmann-Shack sensors wavefront sensing centroids

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General astigmatic transform of Hermite-Laguerre-Gaussian beams

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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION 2010年第11期27卷 2506-2513页

作者： Abramochkin, Eugeny Razueva, Evgeniya Volostnikov, Vladimir Russian Acad Sci PN Lebedev Phys Inst Samara branch Coherent Opt Lab Samara 443011 Russia

The general astigmatic transform, or two-dimensional non-separable linear canonical transform of a Hermite-Laguerre-Gaussian beam, is investigated by theoretical means. Some corollaries that apply to Hermite-Gaussian ... 详细信息

关键词： abcd transforms Cylindrical lenses First order optics Fourier transforms Light fields Light properties

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abcd formalism and attosecond few-cycle pulse via chirp manipulation of a seeded free electron laser

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OPTICS EXPRESS 2007年第20期15卷 12749-12754页

作者： Wu, Juhao Bolton, Paul R. Murphy, James B. Wang, Kelin Stanford Univ Stanford Linear Accelerator Ctr Stanford CA 94309 USA Brookhaven Natl Lab Natl Synchrotron Light Source Upton NY 11973 USA Univ Sci & Technol China Dept Modern Phys Anhua 230026 Peoples R China Southwest Univ Sci & Technol Sch Sci Mianyang 621010 Peoples R China

An abcd formalism is identified to characterize a seeded Free Electron Laser (FEL) with three chirps: an initial frequency chirp in the seed Laser, an energy chirp in the electron bunch, and an intrinsic frequency chirp due to the FEL process. A scheme of generating attosecond few-cycle pulses is proposed by invoking an FEL seeded by high-order harmonic generation (HHG) from an infrared laser. The HHG seed has generic attosecond structure. It is possible to manipulate these three chirps to maintain the attosecond structure via post-undulator chirped pulse compression. (C) 2007 Optical Society of America.

关键词： abcd transforms Attosecond pulses Fourier transforms Free electron lasers Infrared lasers Pulse compression

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Cartesian beams

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OPTICS LETTERS 2007年第23期32卷 3459-3461页

作者： Bandres, Miguel A. Gutierrez-Vega, Julio C. Tecnol Monterrey Photon Math Opt Lab Monterrey 64849 Mexico CALTECH Pasadena CA 91125 USA

A new and very general beam solution of the paraxial wave equation in Cartesian coordinates is presented. We call such a field a Cartesian beam. The complex amplitude of the Cartesian beams is described by either the parabolic cylinder functions or the confluent hypergeometric functions, and the beams are characterized by three parameters that are complex in the most general situation. The propagation through complex abcd optical systems and the conditions for square integrability are studied in detail. Applying the general expression of the Cartesian beams, we also derive two new and meaningful beam structures that, to our knowledge, have not yet been reported in the literature. Special cases of the Cartesian beams are the standard, elegant, and generalized Hermite-Gauss beams, the cosine-Gauss beams, the Lorentz beams, and the fractional order beams. (c) 2007 Optical Society of America.

关键词： abcd transforms Beam structure First order optics Gaussian beams Optical fields Optical systems

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Phase reconstruction from intensity measurements in linear systems

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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION 2003年第6期20卷 1046-1049页

作者： Bastiaans, MJ Wolf, KB Tech Univ Eindhoven Fac Elektrotech NL-5600 MB Eindhoven Netherlands Univ Nacl Autonoma Mexico Ctr Ciencias Fis Cuernavaca 62251 Morelos Mexico

The phase of a signal at a plane is reconstructed from the intensity profiles at two close parallel screens connected by a small abcd canonical transform, this applies to propagation along harmonic and repulsive fibers and in free media. We analyze the relationship between the local spatial frequency (the signal phase derivative) and the derivative of the squared modulus of the signal under a one-parameter canonical transform with respect to the parameter. We thus generalize to all linear systems the results that have been obtained separately for Fresnel and fractional Fourier transforms. (C) 2003 Optical Society of America.

关键词： abcd transforms Fractional Fourier transforms Phase retrieval Power spectra Refractive index Spatial frequency

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Wigner formulation of optical processing with light of arbitrary coherence

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APPLIED OPTICS 2001年第2期40卷 249-256页

作者： Pe'er, A Wang, DY Lohmann, AW Friesem, AA Weizmann Inst Sci Dept Phys & Complex Syst IL-76100 Rehovot Israel Beijing Polytech Univ Dept Appl Phys Beijing 100022 Peoples R China Univ Erlangen Nurnberg Lab Nachrichtentech D-91058 Erlangen Germany

A unified mathematical formulation for designing and analyzing even the most general optical processor is presented. It exploits the Wigner distribution function to characterize the illumination, the input, the inherent filter, and the output results. To characterize the propagation of the light through the optical processor setup, we exploit the Wigner matrix formalism, which is appealing because it allows simple geometric analysis. The Wigner distribution function was extended to include illumination of arbitrary coherence so that processors using either coherent light or partially coherent light can be designed and analyzed with the same Wigner formalism. The basic principles, design, and analysis of the imaging and Fourier-transform operations and use of the Wigner formalism to evaluate the performance and tolerances of optical processors are presented. (C) 2001 Optical Society of America OCIS codes: 070.4550, 080.2730, 030.1640, 030.4280, 070.2580.

关键词： abcd transforms Light fields Optical processing Optical processing devices Physical optics Spatial frequency

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