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Abstract This paper presents a novel method to eliminate cosine error in precision concave and convex surface measurement by integrating a displacement probe in a precision spindle. Cosine error in surface profile measurement comes from an angular misalignment between the measurement axis and the axis of motion and negatively affects the measurement accuracy, especially in optical surface measurements. A corrective multiplier can solve this problem for spherical surface measurement, but cosine error cannot be eliminated in the case of complex optical surface measurement because current tools do not measure such surfaces along the direction normal to the measurement plane. Because the displacement probe is placed on the spindle axis, the spindle error motion will affect the shape precision and surface roughness measurement of optical components such as mirrors and lenses, and the displacement probe will measure a combination of the spindle error motion and the geometry of optical surfaces. Here, the one-dimensional concave, convex, and hollow measurement targets were used, and cosine error was fundamentally eliminated by aligning the probe on the spindle always normal to the measured surface, and compensation was made for the aerostatic bearing spindle rotational error obtained by the reversal method. The results show that this proposed measurement method cannot only eliminate cosine error but also scan the large area quickly and conveniently. In addition, measurement uncertainty and further consideration for future work were discussed.
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Cosine Error-Free Metrology Tool Path Planning for Thickness Profile Measurements
Abstract This paper presents a novel thickness profile measuring system that measures double-sided thin pipe wall surfaces in a non-contact, continuous, cosine error-free, and fast manner. The surface metrology tool path was developed to align the displacement sensors always normal to the double-sided surfaces to remove cosine error. A pair of capacitive-type sensors that were placed on the rotary and linear axes simultaneously scans the inner and outer surfaces of thin walls. Because the rotational error of the rotary axis can severely affect the accuracy in thickness profile measurement, such error was initially characterized by a reversal method. It was compensated for along the rotational direction while measuring the measurement target. Two measurement targets (circular and elliptical metal pipe-type thin walls) were prepared to validate the developed measurement method and system. Not only inner and outer surface profiles but also thin-wall thickness profiles were measured simultaneously. Based on the output data, the circularity and wall thickness variation were calculated. The thickness profile results showed a good agreement with those obtained by a contact-type micrometer (1-µm resolution) at every 6-deg interval. The uncertainty budget for this measuring system with metrology tool path planning was estimated at approximately 1.4 µm.
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- Award ID(s):
- 1902697
- PAR ID:
- 10217881
- Date Published:
- Journal Name:
- Journal of Manufacturing Science and Engineering
- Volume:
- 143
- Issue:
- 4
- ISSN:
- 1087-1357
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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This paper presents a novel method to eliminate cosine error in precision concave and convex surface measurement by integrating a displacement probe in a precision spindle. Cosine error in surface profile measurement comes from an angular misalignment between the measurement axis and the axis of motion and negatively affects the measurement accuracy, especially in optical surface measurements. A corrective multiplier can solve this problem for spherical surface measurement, but cosine error cannot be eliminated in the case of complex optical surface measurement because current tools do not measure such surfaces along the direction normal to the measurement plane. Because the displacement probe is placed on the spindle axis, the spindle error motion will affect the shape precision and surface roughness measurement of optical components such as mirrors and lenses, and the displacement probe will measure a combination of the spindle error motion and the geometry of optical surfaces. Here, the one-dimensional concave, convex, and hollow measurement targets were used, and cosine error was fundamentally eliminated by aligning the probe on the spindle always normal to the measured surface, and compensation was made for the aerostatic bearing spindle rotational error obtained by the reversal method. The results show that this proposed measurement method cannot only eliminate cosine error but also scan the large area quickly and conveniently. In addition, measurement uncertainty and further consideration for future work were discussed.more » « less
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Abstract This short article describes the major findings from the CVB experiment performed in the LMM on the International Space Station from 2010–2012. CVB was the first experiment to run in the new facility and focused on understanding the heat transfer and fluid mechanics occurring inside a wickless miniature heat pipe. The LMM was used to map the location of the vapor-liquid interface inside the device and to measure the film thickness profile on the walls of the device. Several interesting and unexpected phenomena were observed in microgravity including flooding of the heater end with liquid as the heat input increased, explosive nucleation of vapor bubbles at the heater end in the shortest version of the heat pipe tested, condensation on highly superheated surfaces, and the spontaneous formation of rip currents as the device tried to enhance the contact line area available for evaporation of the liquid.more » « less
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A displacement thickness based inflow generation method, for simulation of a developing turbulent boundary layer, is proposed. Following existing rescaling/recycling methods, velocities from a plane sufficiently downstream of the inlet are recycled back and used as the inflow after re-scaling based on inner and outer length-scales. The inner length-scale is based on the viscous length-scale (for smooth walls) or surface specific scales (for rough walls). Prior recycling methods for smooth and rough boundary layers typically use d99 as the outer length-scale. Since d99 is a threshold based quantity, it is strongly dependent on the mean velocity profile and can have large undesired fluctuations, particularly if the profile shape is atypical or unsteady. Here, we propose the use of profile integrated quantities such as the displacement thickness (d1) to obtain a ‘surrogate’ for d99 in order to mitigate the adverse effects of having to determine the outer scale from a point-wise measurement of the mean velocity profile. The outer length- scale at the downstream plane is determined based on the local displacement thickness and higher-order moments of the integrated velocity profile. The inlet displacement thick- ness is fixed at a desired value and the outer length-scale at the inlet is determined through an iterative method. The use of high-order moments of the velocity profile is tested a- priori on DNS data for a developing boundary layer. Also, an initial application to LES over a surface with roughness elements is presented.more » « less
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Purpose To investigate relationships between blood pressure and the thickness of single retinal layers in the macula. Methods Participants of the population-based Beijing Eye Study, free of retinal or optic nerve disease, underwent medical and ophthalmological examinations including optical coherence tomographic examination of the macula. Applying a multiple-surface segmentation solution, we automatically segmented the retina into its various layers. Results The study included 2237 participants (mean age 61.8±8.4 years, range 50–93 years). Mean thicknesses of the retinal nerve fibre layer (RNFL), ganglion cell layer (GCL), inner plexiform layer, inner nuclear layer (INL), outer plexiform layer, outer nuclear layer/external limiting membrane, ellipsoid zone, photoreceptor outer segments (POS) and retinal pigment epithelium–Bruch membrane were 31.1±2.3 µm, 39.7±3.5 µm, 38.4±3.3 µm, 34.8±2.0 µm, 28.1±3.0 µm, 79.2±7.3 µm, 22.9±0.6 µm, 19.2±3.3 µm and 20.7±1.4 µm, respectively. In multivariable analysis, higher systolic blood pressure (SBP) and diastolic blood pressure (DBP) were associated with thinner GCL and thicker INL, after adjusting for age, sex and axial length (all p<0.0056). Higher SBP was additionally associated with thinner POS and higher DBP with thinner RNFL. For an elevation of SBP/DBP by 10 mm Hg, the RNFL, GCL, INL and POS changed by 2.0, 3.0, 1.5 and 2.0 µm, respectively. Conclusions Thickness of RNFL, GCL and POS was inversely and INL thickness was positively associated with higher blood pressure, while the thickness of the other retinal layers was not significantly correlated with blood pressure. The findings may be helpful for refinement of the morphometric detection of retinal diseases.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4048433
