Relativistic corrections in displacement measuring interferometry

Heilmann, Ralf K.; Konkola, Paul T.; Chen, Carl G.; Schattenburg, Mark L.

doi:10.1116/1.1313584

Cited by 13 publications

(14 citation statements)

References 4 publications

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“…The results derived in this paper agree well with results from [4] that have been derived with the Lorentz transformation. Reference [3] derives the Doppler shift at reflection by combining optical-path-length considerations together with the Lorentz transformation.…”

Section: Introductionsupporting

confidence: 91%

“…Although the Doppler effect can be considered to be well understood some recent publications [3,4,5] discuss the influence of the Doppler effect in displacement interferometers and it is claimed that relativistic corrections have to be taken into account to obtain correct results for high precision measurements. However, the first double-beam interferometer was realized by Albert Abraham Michelson to measure the ether drift [6] because the current light theory of that time claimed an ether as wave medium.…”

Section: Introductionmentioning

confidence: 99%

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Retardation effects in laser-Doppler measurements

Rembe

2008

Eighth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications

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Although the Doppler-effect is well known, some recent publications discuss the necessity of relativistic corrections in the measurements of two-beam interferometers. This is remarkable because sensor and detector are in the same reference frame and, therefore, it is not necessary to employ the Lorentz transformation. The whole consideration can be made in one inertial frame even if one reflector is moving in respect to the frame of source and detector. However, the commonly used equation for the Doppler-effect for a reflection at a moving surface is not correct because this equation is derived as a quasi-static solution by using optical path lengths. If the speed of light is considered as finite a different equation containing effects of wave propagation follows. Retardation effects in interferometers are discussed in this paper and its influences to laser-Doppler measurements are derived.

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Section: Introductionsupporting

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Retardation effects in laser-Doppler measurements

Rembe

2008

Eighth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications

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show abstract

“…[1]. The focus in the literature is typically on smooth surfaces, and as such the spreading rate has been modeled as limited either by bulk viscous forces in the core of the drop (for which n is predicted to be 0.1) or by molecular dynamics (limited by the rate of attachment of liquid "particles" to the solid surface, for which n = 0.14) (5,4).…”

Section: Background: Spreading Kineticsmentioning

confidence: 99%

“…Resolution in inkjet printing is directly related to the degree of liquid extension and spreading on the printing media after deposition. The presence of porosity in the media, either among the fibers in plain paper (attractive because of its low cost) or in a pigmented coating (i.e., a porous ceramic-containing layer) accelerates "drying" of the printed liquid through infiltration, but can also have a direct effect on final printed dot size (1)(2)(3). The current work examines droplet on demand (DoD) printing onto porous ceramic substrates, where 1 To whom correspondence should be addressed at 77 Massachusetts Ave., Rm.…”

Section: Introductionmentioning

confidence: 99%

Spreading and Infiltration of Inkjet-Printed Polymer Solution Droplets on a Porous Substrate

Holman¹,

Cima²,

Uhland³

et al. 2002

Journal of Colloid and Interface Science

150

160

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“…Ralf K. Heilmann [5] found for the first time, that an error can be introduced by the Doppler frequency shift caused by a velocity variation in high speed laser heterodyne interferometry. He founded a real-time measurement model considering an arbitrary stage motion in the interferometer arm.…”

Section: Introductionmentioning

confidence: 98%

Effect on the measurement precision of a multi-pass heterodyne interferometer by an acceleration and compensation method

2008

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To reduce the theoretical measurement error caused by a high acceleration in fast ultra-precision laser heterodyne interferometry, a model is proposed. This model is about how the displacement measurement precision is affected by the acceleration of the measuring prism in a multi-pass heterodyne interferometer. In the model, the integrals of Nv 2 /c and Nax/c are added on the basis of a conventional heterodyne interferometer model. It shows, that in the conventional model the measurement error increases with increasing measurement acceleration. An error compensation method is proposed, which uses numerical integration to obtain the real time speed and acceleration. Corrected data can be acquired by using an error correction formula. Simulation results show, that the measurement error can be reduced by this method from 10nm to 0.03nm when the displacement of the measuring prism is 500mm and the uniform acceleration of the measuring prism of a double pass interferometer equals g.

show abstract

Relativistic corrections in displacement measuring interferometry

Cited by 13 publications

References 4 publications

Retardation effects in laser-Doppler measurements

Retardation effects in laser-Doppler measurements

Spreading and Infiltration of Inkjet-Printed Polymer Solution Droplets on a Porous Substrate

Effect on the measurement precision of a multi-pass heterodyne interferometer by an acceleration and compensation method

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