“…The latter propagation law is an easy equivalent for the input-output relation (6). To see the strong resemblance between the intrinsically isotropic case and the one-dimensional case, we remark that the relations M rr t .…”
Section: ͑32͒mentioning confidence: 89%
“…This approach has recently been generalized [2][3][4][5][6] to the case of Gaussian-type modes, which may possess orbital angular momentum. In the present paper we propose to use this formalism for the description of an arbitrary scalar two-dimensional signal, which might be deterministic or stochastic (i.e., completely coherent or partially coherent).…”
Section: Introductionmentioning confidence: 99%
See 1 more Smart Citation
Bastiaans
1
,
Alieva
2
2010
J. Opt. Soc. Am. A Self Cite
Based on the analysis of second-order moments, a generalized canonical representation of a two-dimensional optical signal is proposed, which is associated with the angular Poincaré sphere. Vortex-free (or zero-twist) optical beams arise on the equator of this sphere, while beams with a maximum vorticity (or maximum twist) are located at the poles. An easy way is shown how the latitude on the sphere, which is a measure for the degree of vorticity, can be derived from the second-order moments. The latitude is invariant when the beam propagates through a first-order optical system between conjugate planes. To change the vorticity of a beam, a system that does not operate between conjugate planes is needed, with the gyrator as the prime representative of such a system. A direct way is derived to find an optical system (consisting of a lens, a magnifier, a rotator, and a gyrator) that transforms a beam with an arbitrary moment matrix into its canonical form.
“…The latter propagation law is an easy equivalent for the input-output relation (6). To see the strong resemblance between the intrinsically isotropic case and the one-dimensional case, we remark that the relations M rr t .…”
Section: ͑32͒mentioning confidence: 89%
“…This approach has recently been generalized [2][3][4][5][6] to the case of Gaussian-type modes, which may possess orbital angular momentum. In the present paper we propose to use this formalism for the description of an arbitrary scalar two-dimensional signal, which might be deterministic or stochastic (i.e., completely coherent or partially coherent).…”
Section: Introductionmentioning confidence: 99%
Bastiaans
1
,
Alieva
2
2010
J. Opt. Soc. Am. A Self Cite
Based on the analysis of second-order moments, a generalized canonical representation of a two-dimensional optical signal is proposed, which is associated with the angular Poincaré sphere. Vortex-free (or zero-twist) optical beams arise on the equator of this sphere, while beams with a maximum vorticity (or maximum twist) are located at the poles. An easy way is shown how the latitude on the sphere, which is a measure for the degree of vorticity, can be derived from the second-order moments. The latitude is invariant when the beam propagates through a first-order optical system between conjugate planes. To change the vorticity of a beam, a system that does not operate between conjugate planes is needed, with the gyrator as the prime representative of such a system. A direct way is derived to find an optical system (consisting of a lens, a magnifier, a rotator, and a gyrator) that transforms a beam with an arbitrary moment matrix into its canonical form.
“…In recent times, the interpolation representations in the linear canonical transform (LCT) domain have become one of the important areas in different theoretical and practical disciplines. For instance, it has an important role in signal and image processing [1][2][3][4], optics [5][6][7][8], filter design [9,10], radar system analysis [11,12], and many others (see, e.g., [13,14]). The LCT of a function f ðzÞ is defined as follows [15][16][17]:…”
Section: Introductionmentioning confidence: 99%
Al-Abdi1
2022
Computational and Mathematical Methods
There has been several Lagrange and Hermite type interpolations of entire functions whose linear canonical transforms have compact supports in ℝ . There interpolation representations are called sampling theorems for band-limited signals in signal analysis. The truncation, amplitude, and jitter errors associated with the Lagrange type interpolations are investigated rigorously. Nevertheless, the amplitude and jitter errors arising from perturbing samples and nodes are not studied before. The aim of this work is to establish rigorous analysis of their types of perturbation errors, which is important from both practical and theoretical points of view. We derive precise estimates for both types of errors and expose various numerical examples.
Bastiaans
1
,
Alieva
2
2016
Springer Series in Optical Sciences
No abstract
