Transient axial solution for plane and axisymmetric waves focused by a paraboloidal reflector

Tsai, Yi Te; Zhu, Jinying

doi:10.1121/1.4794367

Cited by 3 publications

(1 citation statement)

References 22 publications

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“…Revolution paraboloids have been widely used in large radio telescopes [1], radar antennas [2], and optics devices [3,4] because of their fine focusing and reflection properties. Owing to machining and deformation errors during manufacturing, the actual paraboloids are not always entirely consistent with their designs [5,6], and their performances are directly affected by these errors [7,8]. To determine precisely the actual surface error of a paraboloid, a best-paraboloid fitting is required for the deformed paraboloid.…”

Section: Introductionmentioning

confidence: 99%

Fitting and error evaluation for rotating paraboloid in arbitrary position using geometric iterative optimization algorithm

Tu¹,

Lei²,

Ma³

et al. 2019

Meas. Sci. Technol.

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To realize a more accurate fitting and error evaluation for a rotating paraboloid in an arbitrary position, a new fitting and error evaluation method based on the geometrical characteristics of the paraboloid is presented for rotating paraboloid in arbitrary positions. The proposed method is named the 'geometric iterative optimisation algorithm'. First, the initial reference vertex, focus and initial profile error of the measured rotating paraboloid are obtained based on coordinate transformations and the least-squares method, and a reference paraboloid is established by using the reference vertex and focus. Second, two regular hexahedrons are collocated by taking the reference vertex and focus as datum points, and the initial profile error as the side length. Eight auxiliary vertexes and focuses (that is, the vertexes of two regular hexahedrons) are obtained. Using the auxiliary vertexes and focuses, a series of auxiliary paraboloids defined by the auxiliary vertexes and focuses are established. Third, reference profile error and auxiliary profile errors of the measured rotating paraboloid are calculated by considering the reference paraboloid and the auxiliary paraboloids as ideal paraboloids. Fourth, the reference points are changed or the side lengths of the hexahedron are decreased by comparing the the reference profile error and the auxiliary profile errors. The minimum zone fitting and evaluation for the paraboloid profile are realized by repeating the above process. The principle and steps involved when using the proposed method to solve the rotating paraboloid profile error are described in detail, and mathematical formulas are presented. The simulation results show that this method can obtain not only accurate results but it is also stable.

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Section: Introductionmentioning

confidence: 99%

Fitting and error evaluation for rotating paraboloid in arbitrary position using geometric iterative optimization algorithm

Tu¹,

Lei²,

Ma³

et al. 2019

Meas. Sci. Technol.

View full text Add to dashboard Cite

show abstract

Broadband aberration-free focusing reflector for acoustic waves

Wang

et al. 2017

Physics Letters A

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Transient solutions for the angular dependence of acoustical transmitters and receivers employing paraboloidal reflectors

Cormack

Hamilton

2020

The Journal of the Acoustical Society of America

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Time-domain solutions are presented for the angular dependence of waveforms in the far field of a point source at the focus of a rigid paraboloidal reflector, and also for waveforms at the focus as a function of the direction of a plane wave incident on the reflector. The main restriction is that the wavelength is small in relation to both the radius of the aperture and the minimum radius of curvature of the reflector, conditions which are satisfied for reflectors with appreciable gain. The solution in the far field due to a point source at the focus is related by the principle of reciprocity to the solution at the focus due to an incident plane wave. Both solutions are expressed as the convolution of an explicit expression for the unit step response with the time derivative of the pressure waveform incident on the reflector. Results are presented illustrating the angular dependence of the reflected pressure waveforms at the focus due to incident N waves and tone bursts.

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Transient axial solution for plane and axisymmetric waves focused by a paraboloidal reflector

Cited by 3 publications

References 22 publications

Fitting and error evaluation for rotating paraboloid in arbitrary position using geometric iterative optimization algorithm

Fitting and error evaluation for rotating paraboloid in arbitrary position using geometric iterative optimization algorithm

Broadband aberration-free focusing reflector for acoustic waves

Transient solutions for the angular dependence of acoustical transmitters and receivers employing paraboloidal reflectors

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