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Adolf W. Lohmann

Other affiliations: AT&T, Tel Aviv University, Weizmann Institute of Science  ...read more
Bio: Adolf W. Lohmann is an academic researcher from University of Erlangen-Nuremberg. The author has contributed to research in topics: Fourier transform & Spatial filter. The author has an hindex of 39, co-authored 152 publications receiving 5859 citations. Previous affiliations of Adolf W. Lohmann include AT&T & Tel Aviv University.


Papers
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Journal ArticleDOI
TL;DR: The theory of speckle masking is presented; it makes use of triple correlations and their Fourier counterparts, the bispectra, and shows algorithms for the recovery of the object from genuine astronomical Bispectra data.
Abstract: Due to the turbulent atmosphere the resolution of conventional astrophotography is limited to ∼1 sec of arc. However, the speckle-masking method can yield diffraction-limited resolution, i.e., 0.03 sec of arc with a 3.6-m telescope. Speckle masking yields true images of general astronomical objects. No point source is required in the isoplanatic field of the object. We present the theory of speckle masking; it makes use of triple correlations and their Fourier counterparts, the bispectra. We show algorithms for the recovery of the object from genuine astronomical bispectra data.

610 citations

Journal ArticleDOI
TL;DR: A quasi-geometrical representation of the space–bandwidth product in the Wigner domain is claimed to be more useful than a pure number that counts the degrees of freedom of the system.
Abstract: The space–bandwidth product (SW) is fundamental for judging the performance of an optical system. Often the SW of a system is defined only as a pure number that counts the degrees of freedom of the system. We claim that a quasi-geometrical representation of the SW in the Wigner domain is more useful. We also represent the input signal as a SW in the Wigner domain. For perfect signal processing it is necessary that the system SW fully embrace the signal SW.

391 citations

Journal ArticleDOI
TL;DR: Binary phase elements in photoresist have been implemented which transform a uniform beam of light into an array of output light spots by means of the fractional Talbot effect.
Abstract: Binary phase elements in photoresist have been implemented which transform a uniform beam of light into an array of output light spots by means of the fractional Talbot effect. Arrays of more than 30 x 30 light spots with varying spot shapes have been achieved with compression ratios of up to 1:9.

306 citations

Journal ArticleDOI
TL;DR: In this article, a rigorous definition of the local spectrum is proposed based on the Wigner distribution function, and optical methods for producing this local spectrum are developed for sound pattern analysis.

243 citations

Journal ArticleDOI
TL;DR: The Hilbert transform is generalized by defining the fractional Hilbert transform (FHT) operation, which is characterized by two parameters.
Abstract: We have generalized the Hilbert transform by defining the fractional Hilbert transform (FHT) operation. In the first stage, two different approaches for defining the FHT are suggested. One is based on modifying only the spatial filter, and the other proposes using the fractional Fourier plane for filtering. In the second stage, the two definitions are combined into a fractional Hilbert transform, which is characterized by two parameters. Computer simulations are presented.

218 citations


Cited by
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Journal Article
TL;DR: In this article, a fast Fourier transform method of topography and interferometry is proposed to discriminate between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour generation techniques.
Abstract: A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

3,742 citations

Journal ArticleDOI
TL;DR: The Navier-Stokes equations are well-known to be a good model for turbulence as discussed by the authors, and the results of well over a century of increasingly sophisticated experiments are available at our disposal.
Abstract: It has often been remarked that turbulence is a subject of great scientific and technological importance, and yet one of the least understood (e.g. McComb 1990). To an outsider this may seem strange, since the basic physical laws of fluid mechanics are well established, an excellent mathematical model is available in the Navier-Stokes equations, and the results of well over a century of increasingly sophisticated experiments are at our disposal. One major difficulty, of course, is that the governing equations are nonlinear and little is known about their solutions at high Reynolds number, even in simple geometries. Even mathematical questions as basic as existence and uniqueness are unsettled in three spatial dimensions (cf Temam 1988). A second problem, more important from the physical viewpoint, is that experiments and the available mathematical evidence all indicate that turbulence involves the interaction of many degrees of freedom over broad ranges of spatial and temporal scales. One of the problems of turbulence is to derive this complex picture from the simple laws of mass and momentum balance enshrined in the NavierStokes equations. It was to this that Ruelle & Takens (1971) contributed with their suggestion that turbulence might be a manifestation in physical

3,721 citations

Journal ArticleDOI
Leon Cohen1
01 Jul 1989
TL;DR: A review and tutorial of the fundamental ideas and methods of joint time-frequency distributions is presented with emphasis on the diversity of concepts and motivations that have gone into the formation of the field.
Abstract: A review and tutorial of the fundamental ideas and methods of joint time-frequency distributions is presented. The objective of the field is to describe how the spectral content of a signal changes in time and to develop the physical and mathematical ideas needed to understand what a time-varying spectrum is. The basic gal is to devise a distribution that represents the energy or intensity of a signal simultaneously in time and frequency. Although the basic notions have been developing steadily over the last 40 years, there have recently been significant advances. This review is intended to be understandable to the nonspecialist with emphasis on the diversity of concepts and motivations that have gone into the formation of the field. >

3,568 citations

Journal ArticleDOI
10 Jun 2009
TL;DR: The current performance and future demands of interconnects to and on silicon chips are examined and the requirements for optoelectronic and optical devices are project if optics is to solve the major problems of interConnects for future high-performance silicon chips.
Abstract: We examine the current performance and future demands of interconnects to and on silicon chips. We compare electrical and optical interconnects and project the requirements for optoelectronic and optical devices if optics is to solve the major problems of interconnects for future high-performance silicon chips. Optics has potential benefits in interconnect density, energy, and timing. The necessity of low interconnect energy imposes low limits especially on the energy of the optical output devices, with a ~ 10 fJ/bit device energy target emerging. Some optical modulators and radical laser approaches may meet this requirement. Low (e.g., a few femtofarads or less) photodetector capacitance is important. Very compact wavelength splitters are essential for connecting the information to fibers. Dense waveguides are necessary on-chip or on boards for guided wave optical approaches, especially if very high clock rates or dense wavelength-division multiplexing (WDM) is to be avoided. Free-space optics potentially can handle the necessary bandwidths even without fast clocks or WDM. With such technology, however, optics may enable the continued scaling of interconnect capacity required by future chips.

1,959 citations

Journal ArticleDOI
01 Mar 1991
TL;DR: A compendium of recent theoretical results associated with using higher-order statistics in signal processing and system theory is provided, and the utility of applying higher- order statistics to practical problems is demonstrated.
Abstract: A compendium of recent theoretical results associated with using higher-order statistics in signal processing and system theory is provided, and the utility of applying higher-order statistics to practical problems is demonstrated. Most of the results are given for one-dimensional processes, but some extensions to vector processes and multichannel systems are discussed. The topics covered include cumulant-polyspectra formulas; impulse response formulas; autoregressive (AR) coefficients; relationships between second-order and higher-order statistics for linear systems; double C(q,k) formulas for extracting autoregressive moving average (ARMA) coefficients; bicepstral formulas; multichannel formulas; harmonic processes; estimates of cumulants; and applications to identification of various systems, including the identification of systems from just output measurements, identification of AR systems, identification of moving-average systems, and identification of ARMA systems. >

1,854 citations