Error contributor of defocus and quadratic caustic in line scale measurement

Takahashi, Akira; Takigawa, Yuichi; Miwa, Nobuharu

doi:10.1088/0957-0233/22/1/015302

Cited by 6 publications

(4 citation statements)

References 15 publications

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“…The length measurement system used for this experiment was a one-dimensional, laser-interferometric line scale calibration system named Standard Scale Calibrator SSC-05 developed by Nikon [21,22]. The specifications of the scale calibration system are shown in table 2.…”

Section: Length Measurement Systemmentioning

confidence: 99%

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Long-term dimensional stability of a line scale made of low thermal expansion ceramic NEXCERA

Takahashi

2012

Meas. Sci. Technol.

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Length measurement was carried out on line scales made of the ultralow-expansion ceramic NEXCERA™ and synthetic quartz for 13 months. 550 mm long precision line scales made of the two materials were manufactured and their changes in length were measured over the same period, using a high-precision laser-interferometric line scale calibration system. NEXCERA was used to evaluate its long-term dimensional stability. Synthetic quartz was used because of its long-term stability to ensure the stability of the long-term length measurement, including the line scale calibration system and measurement procedure. The long-term stabilities of relative length expressed in terms of 2σ over 13 months were 1.1 ± 1.1 × 10−8 for NEXCERA and 4.2 ± 6.3 × 10−8 for synthetic quartz. The experimental results were within the estimated measurement error. No significant secular change in length was observed for the line scale made of NEXCERA.

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Section: Length Measurement Systemmentioning

confidence: 99%

“…The line-detecting microscope used in the line scale calibration system has an objective lens with a reduced NA, and the optical system is specially adjusted to reduce the measurement error due to the defocus of a line scale and the microscope optics [22].…”

Section: Length Measurement Systemmentioning

confidence: 99%

Long-term dimensional stability of a line scale made of low thermal expansion ceramic NEXCERA

Takahashi

2012

Meas. Sci. Technol.

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“…A fundamental error source in line scale metrology is the tilt of the optical axis of the line detector combined with a non-flat surface of the line scale. This causes a sine error combined with the error caused by focus variation [21] of the line marks. However, these errors can easily and quite effectively be eliminated by turning the scale 180 • horizontally, repeating the measurement and averaging the directions.…”

Section: Characterization Of Error Sources and Uncertainty Budgetmentioning

confidence: 99%

MIKES fibre-coupled differential dynamic line scale interferometer

Lassila

2012

Meas. Sci. Technol.

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An instrument developed for high accuracy calibration of line scales up to 1.16 m is described. The instrument is based on an earlier design from the early 1990s. Since then, in order to improve performance and achieve smaller uncertainty, large portions of software, mechanics and optics have been redesigned and several uncertainty components better characterized. The software has been developed to be less sensitive to imperfections of the line mark. In order to decrease noise and deformation coupling in interferometric measurement, the interferometer operating principle has been designed to use a fibre-coupled laser light, interferometer optics have been improved for better phase adjustment and detection and a differential interferometer principle has been taken into use. In order to minimize the effects due to deformations of the stone table rail with moving heavy carriage, a separate bed has been designed under line scale supports. The bed with fixed differential reflector prevents deformations of the table from affecting the line scale versus interferometer position. The main properties of the instrument are described and an uncertainty estimate is presented. The expanded uncertainty (k = 2) for line distance calibration of high-quality low-thermal-expansion line scale is U = [(4.5 nm)2 + (43 × 10−9 L)2]½, where L is the measured length. The results of international comparisons support the uncertainty estimate.

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“…This method is simple and can resist the Abbe offset, which is extensively adopted by metrological institutes and manufacturing enterprises [23][24][25][26][27][28]. But the accuracy of the method is usually affected by the tilt of the target retroreflectors and the dissymmetry of the optical paths during the calibration.…”

Section: Introductionmentioning

confidence: 99%

Influence of tilt on collinear calibration of a laser interferometer

et al. 2013

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Collinear calibration is a typical and common method for a laser (heterodyne) interferometer, but it usually suffers from the influence of the tilt of the target retroreflectors and the dissymmetry of the optical paths during the calibration. This paper mainly analyzes and models the calibration error caused by the tilt error of the target retroreflectors and reveals the error source that is the disturbance from the rotary error of the guideway slider pair. Experimental results prove the validity of the analysis and model of the calibration error. The calibration error is up to 0.5 μm when the tilt error is 0.36°, which is large enough to equal the maximum tolerance of laser interferometer (0.5 μm) in use.

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Error contributor of defocus and quadratic caustic in line scale measurement

Cited by 6 publications

References 15 publications

Long-term dimensional stability of a line scale made of low thermal expansion ceramic NEXCERA

Long-term dimensional stability of a line scale made of low thermal expansion ceramic NEXCERA

MIKES fibre-coupled differential dynamic line scale interferometer

Influence of tilt on collinear calibration of a laser interferometer

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