A. Papoulis, Systems and transforms with applications in optics, McGraw-Hill, 1968. Home/Search Document Not in Database Summary Related Articles Check |
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Fourier-Bessel Analysis of Mean and Maximum Bessel Beam . . . - Fox, Holm (1999) (Correct)
....for analysing the quantisation in a theoretical manner; in this article we apply the method numerically to study the mean and maximum quantisation methods already established. 2. Summary of Fourier Bessel Analysis The Fourier Bessel series expansion of order zero for a given function is given in [4] as (3) This is an orthogonal series in the range 0 , where is any desired value and represent the infinite set of solutions to = 0. For annular transducers the coefficients are given by (4) of the first kind of order one. Since must remain fixed for all to correctly implement the time ....
....= 1 at = if desired. However, the mean design still performs better after the rescaling, with a sum of squared coefficient errors relative to the ideal beam 24.45 larger for the maximum design than for the mean design. 4. Conclusions We have applied the Fourier Bessel method introduced in [4] to an equal area 4 annulus transducer with given design parameters. The mean design was superior in terms of coefficient error distribution in Fourier Bessel space. The numerical procedures involved in the analysis are easy to implement and allow us to determine exactly all the limited ....
A. Papoulis, Systems and transforms with applications in optics. Mc-Graw Hill, 1968.
Effects Of Parameter Mismatch In Ultrasonic Bessel Transducers - Fox, Holm (1999) (Correct)
....Bessel beam parameters and , in which is the axicon angle of an equivalent axicon transducer [1] This means that varies throughout the frequency spectrum and hence a mismatch exists between the ring radii and the various parameters in the desired X wave. 3. Fourier Bessel theory In [7], the Fourier Bessel series expansion of order = 0 for a given function is defined as an infinite sum of weighted Bessel terms Proc. IEEE Norwegian Signal Processing Symp. NORSIG 99, Asker (Oslo) Norway, Sep. 9 11, 1999, pp. 59 64 f(r) 9 # R i91 A i J 0 ( i r) ra a f(a) i J 0 ....
A. Papoulis, Systems and transforms with applications in optics. Mc-Graw Hill, 1968.
Analysis of Bessel Beam Quantisation in Annular Arrays - Holm, Fox (1999) (3 citations) (Correct)
....quantised Bessel beam as a = 0 and so = Transmission of the exact sum of finite aperture Bessel beams whose properties beam (1,3) therefore corresponds to the weighting are already understood from (1) 4) magnitudes = 1 and = 0. In practice however, 3. Application of Fourier Bessel Theory In [4], the Fourier Bessel series expansion of order = 0 for a given function is defined by (5) This is an orthogonal series in the range 0 , where is any desired value and represent the infinite set of solutions to = 0. The solutions to the Bessel equation = 0 may be computed numerically as = ....
A. Papoulis, Systems and transforms with applications in optics. Mc-Graw Hill, 1968.
Theory of Speckles in Diffractive Optics and Its.. - Aagedal, Schmid.. (1996) (Correct)
....beam shaping problems. The computeraided design of DEs offers a maximum in flexibility to find a transmission function fulfilling the specifications posed by the application. In some cases analytical solutions based on geometrical optics can be derived by applying the method of stationary phase [1] to find the transmission function of a DE [2, 3] performing the desired wave transformation. However, we will consider general beam shaping problems for which no analytical solutions exist. In this case, well known design algorithms such as iterative fourier transform algorithms (IFTAs) 4, 5, ....
Papoulis, A., 1968, Systems and Transforms with Applications in Optics, (McGraw-Hill).
Spatial-Domain Convolution/Deconvolution Transform - Subbarao (1991) (3 citations) (Correct)
....Based on this new spatial domain deconvolution formula, we have derived a new transform which is the subject of this report. The new transform is a linear transform. The forward part of the transform corresponds to convolution, and it is based on a convolution formula first derived by Papoulis [3, 4] in 1962. This formula was however derived independently by us in 1989. The inverse part of the transform corresponds to deconvolution, and it is based on a new deconvolution formula first derived by us and reported in [8] For images, the transform is expressed in the spatial domain. Therefore ....
....of the S transform. This will be referred to as the differential form of the definition of S transform due to the presence of the derivative term f k ( we shall also refer to it as the convolution formula. Note that, this formula holds even if h(t) is not a continuous function. Papoulis [3, 4] was the first to derive the convolution formula (9) in 1962 for N = 1. It was, however, derived independently by us in 1989. He has suggested that, when the series on the right hand side of Eq. 9) converges rapidly, the first few terms of the series can be used to numerically compute the ....
A. Papoulis, Systems and Transforms with Applications in Optics, McGraw-Hill, 1968, page 30.
Analytical Beam Shaping with Application to Laser.. - Aagedal, Schmid.. (1997) (1 citation) (Correct)
....here consists of two steps: First, find a purely geometrical distortion h of the plane which redistributes the intensity jf 1 j 2 into jf 2 j 2 . Then, realize the geometrical distortion h by a phase only element. In the second step the method of stationary phase is used to redistribute energy [15]. This approximation allows closed form solution for a number of practically important special cases. Before looking at the general setting in two dimensions, consider the plain 1d problem. In fact, it forms the basis of all solutions presented in this paper. The 1d Problem. Consider functions f 1 ....
A. Papoulis, Systems and Transforms with Applications in Optics, (McGraw - Hill, New York, 1968), Chap. 7.3, p. 234.
Design for Visually Servoed Microassembly - Bharath Mukundakrishnan.. (Correct)
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A. Papoulis, Systems and transforms with applications in optics, McGraw-Hill, 1968.
Multidimensional Systems and Signal Processing, 11.. - Bounds On Functions (Correct)
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A. Papoulis, Systems and Transforms with Applications in Optics, New York: McGraw-Hill, 1968.
On the Wigner distribution moments of rotationally.. - Bastiaans, Alieva (2000) (Correct)
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A. Papoulis, Systems and Transforms with Applications in Optics, McGraw--Hill, New York, 1968.
Fundamentals Of Image Processing - Young, Gerbrands, van Vliet (1995) (6 citations) (Correct)
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Papoulis, A., Systems and Transforms with Applications in Optics. 1968, New York: McGraw-Hill.
Fourier Spectrum of Radially Periodic Images - Isaac Amidror Laboratoire (Correct)
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A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968), pp. 158--160.
Pseudo-Nondiffracting Beams Generated By Radial Harmonic.. - Rosen, Salik, Yariv (1995) (Correct)
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A. Papoulis, Systems and Transforms with Applications in Optics ( McGraw-Hill, New York, 1968), Chap. 7, pp. 222 -- 254.
Three-Dimensional Electro-Optical Correlation - Rosen (1997) (Correct)
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A. Papoulis, System and Transforms with Applications in Optics, 1st ed. (McGraw-Hill, New York, 1968), Chap. 3, p. 61.
Fiber Fourier optics - Siegman (2001) (Correct)
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A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, 1968).
Pseudonondiffracting Slitlike Beam and Its Analogy to the.. - Rosen, Salik, Yariv (1995) (Correct)
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A. Papoulis, Systems and Transforms with Applications in Optics, 1st ed. (McGraw-Hill, New York, 1968), Chap. 7, p. 222.
Cross Talk of Wavelength-Multiplexed Quasi-Infinite Holograms - Mazurenko, Fainman (1998) (Correct)
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A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968), pp. 110, 226 -- 234.
A Unified Approach to Image Focus and Defocus Analysis - Liu (1998) (2 citations) (Correct)
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A. Papoulis, Systems and Transforms with Applications in Optics, McGraw-Hill, 1968, page 30. 139
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