Bessel functions: parallel display and processing

Lohmann, Adolf W.; Ojeda‐Castañeda, J.; Serrano-Heredia, Alfonso

doi:10.1364/ol.19.000055

Cited by 9 publications

(4 citation statements)

References 8 publications

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“…Based on the fact that the complex caustic structures are expressed in terms of polynomial phase functions, we adopt an optical technic similar to that employed by Lohmann et al [2] [3] for implementing Airy, Bessel and Laguerre functions. The proposed setup is a Fourier transformer whose schematic diagram is given in Figure 1 Substituting from Equation (19) into Equation (20a) and using the integral property of the Dirac function yields…”

Section: Generation Of the Elementary Optical Catastrophes With K = 1mentioning

confidence: 99%

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Generation of Some Catastrophes in Optics by Binary Screens

Belafhal¹,

Hricha²,

Halba³

2019

OALib

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In this paper, the artificial generation of elementary catastrophe optics having odd codimensions K = 1, 3 and 5 such as the Fold, the Swallowtail and the Wigwam diffraction caustics is investigated theoretically. It is shown that the integral catastrophes with odd polynomials phase functions can be reduced to the well-known Airy-Hardy cosine integrals. In this connection, the caustic functions of the Fold, Swallowtail and Wigwam caustic beams are expressed in closed-form in terms of Airy-Hardy cosine functions. An optical method based on the Fourier transform similar to that described by Lohmann et al. [Optics Comm. 109 (1994) 361-367] is proposed for the generation of the Fold, Swallowtail and Wigwam caustic beams. The displaying of the catastrophe patterns with K = 1, 3 and 5 is optically implemented in the Fourier transform device by using simple binary screens with tailored polynomials transmission.

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Section: Generation Of the Elementary Optical Catastrophes With K = 1mentioning

confidence: 99%

“…For K = 1, the phenomenon is called Fold diffraction caustic, we have 1 3 . 3 a C = (2) and the structure function…”

Section: Introductionmentioning

confidence: 99%

Generation of Some Catastrophes in Optics by Binary Screens

Belafhal¹,

Hricha²,

Halba³

2019

OALib

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“…Shivakoti [9] et al investigated the selection of optimal laser beam micromarking process parameters using the fuzzy TOPSIS [10] method in the GaN laser beam [11] marking process and concluded that small pulse frequency [12], high current, and scanning speed lead to increased mark intensity. Some people have explored this area through Bessel curves [13]. And a connected Fermat spiral area lling algorithm (CFS) [14] has also been proposed, but its study has not been deeply applied to laser marking technology and cannot be applied for complex graphics [15].…”

Section: Introductionmentioning

confidence: 99%

Exploration of Laser Marking Path and Algorithm Based on Intelligent Computing and Internet of Things

Liu

Xue

et al. 2022

Computational Intelligence and Neuroscience

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Nowadays, laser processing technology is being used more and more in various fields, and the requirements for laser control procedures are getting higher and higher. This paper aims to study the path generation problem of laser marking technology in order to improve the efficiency of laser marking as well as the protection of the marking material. Therefore, we creatively propose two-path generation methods, namely, sawtooth parallel and contour parallel, and design the boundary curve offset algorithm and domain partition intersection algorithm for the computer simulation of the two marking paths, respectively. Through the simulation, we discussed the efficiency and marking quality of the two path generation methods and gave the conclusion that the efficiency of the sawtooth parallel path generation method is greater than that of the contour parallel path generation method under specific parameters.

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“…1987 年美国罗切斯特大学 Durnin [1] 首次提出无衍射光束(Bessel 光束)概念. 无衍射光束具有中心光斑小、光强高度集中、方向性好、最大无衍射距离远等特点, 可以应用在高精度定向或准直光学系统、非线性光学等领域中, 因此研究人员对无衍射光束的传输特性和应用进行了大量的研究 [2][3][4][5][6][7][8] . 例如, 研究人员发现在激光光镊应用中, 无衍射光束可以克服高斯光多方面的限制 [8] ; 近年来, 人们又发现了衍射光束的自重建特性 [9][10][11] , 这一特性使得无衍射光束同时操作多个粒子成为可能, 因而有望在多平面光学微操作中得到应用 [12] , 特别是高阶无衍射光束的自重建特性在新型光镊系统中具有极高的应用价值 [13] .…”

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