Cosine Error Elimination Method for One-Dimensional Convex and Concave Surface Profile Measurements

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Xiangyu Guo ◽  
Jaemin Han ◽  
ChaBum Lee
Keyword(s):  
Convex Surface ◽  
Spherical Surface ◽  
Surface Profile ◽  
Surface Measurement ◽  
Profile Measurement ◽  
Optical Surface ◽  
Large Area ◽  
One Dimensional ◽  
The One ◽  
Error Motion

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.

APPLICATION OF A ONE-DIMENSIONAL POSITION SENSITIVE CHAMBER ON SYNCHROTRON RADIATION

2014 ◽  
Vol 27 ◽  
pp. 1460142
Author(s):  
HUIRONG QI ◽  
MEI LIU
Keyword(s):  
Synchrotron Radiation ◽  
Low Cost ◽  
Large Area ◽  
Position Resolution ◽  
One Dimensional ◽  
X Ray ◽  
High Position ◽  
Standard Data ◽  
Wire Chamber ◽  
The One

In the last few years, wire chambers have been frequently used for X-ray detection because of their low cost, large area and reliability. X-ray diffraction is an irreplaceable method for powder crystal lattice measurements. A one-dimensional single-wire chamber has been developed in our lab to provide high position resolution for powder diffraction experiments using synchrotron radiation. There are 200 readout strips of 0.5 mm width with a pitch of 1.0 mm in the X direction, and the working gas is a mixture of Ar and CO2 (90/10). The one-dimensional position of the original ionization point is determined by the adjacent strip's distribution information using the center of gravity method. Recently, a study of the detector's performance and diffraction image was completed at the 1W1B laboratory of the Beijing Synchrotron Radiation Facility (BSRF) using a sample of SiO2. Most of the relative errors between the measured values of diffraction angles and existing data were less than 1%. The best position resolution achieved for the detector in the test was 71 μm (σ value) with a 20 μm slit collimator. Finally, by changing the detector height in incremental distances from the center of the sample, the one-dimensional detector achieved a two-dimensional diffraction imaging function, and the results are in good agreement with standard data.

A New Three-Dimensional Profilometer for Surface Profile Measurement Using Digital Fringe Projection and Phase Shifting

2005 ◽  
Vol 295-296 ◽  
pp. 471-476
Author(s):  
Liang Chia Chen ◽  
S.H. Tsai ◽  
Kuang Chao Fan
Keyword(s):  
High Speed ◽  
Structured Light ◽  
Three Dimensional ◽  
Surface Profile ◽  
Phase Shifting ◽  
Fringe Projection ◽  
Surface Measurement ◽  
Profile Measurement ◽  
Digital Fringe Projection ◽  
Fringe Patterns

The development of a three-dimensional surface profilometer using digital fringe projection technology and phase-shifting principle is presented. Accurate and high-speed three-dimensional profile measurement plays a key role in determining the success of process automation and productivity. By integrating a digital micromirror device (DMD) with the developed system, exclusive advantages in projecting flexible and accurate structured-light patterns onto the object surface to be measured can be obtained. Furthermore, the developed system consists of a specially designed micro-projecting optical unit for generating flexibly optimal structured-light to accommodate requirements in terms of measurement range and resolution. Its wide angle image detection design also improves measurement resolution for detecting deformed fringe patterns. This resolves the problem in capturing effective deformed fringe patterns for phase shifting, especially when a coaxial optical layout of a stereomicroscope is employed. Experimental results verified that the maximum error was within a reasonable range of the measured depth. The developed system and the method can provide a useful and effective tool for 3D full field surface measurement ranging from µm up to cm scale.

ONLINE SURFACE MEASUREMENT WITH DIGITAL SHACK–HARTMANN WAVEFRONT SENSOR

2010 ◽  
Vol 09 (03) ◽  
pp. 123-133
Author(s):  
XIAOMING YIN ◽  
LIPING ZHAO ◽  
XIANG LI ◽  
ZHONGPING FANG
Keyword(s):  
Good Accuracy ◽  
Focal Spot ◽  
Detection Method ◽  
Surface Profile ◽  
Wavefront Sensor ◽  
Surface Measurement ◽  
Profile Measurement ◽  
Practical Applications ◽  
Centroid Detection ◽  
3D Profile

Shack–Hartmann wavefront sensor splits the incident wavefront into many subsections and transfers the distorted wavefront detection into the centroid measurement. The accuracy of the centroid measurement determines the accuracy of the SHWS. In this paper, we have presented an automatic centroid measurement method based on the image processing technology for practical applications of the digital SHWS in surface profile measurement. The method can detect the centroid of each focal spot accurately and robustly by eliminating the influences of various noises. Based on this centroid detection method, we have developed a digital SHWS system which can automatically detect centroids of focal spots, reconstruct the wavefront, and measure the 3D profile of the surface. The experimental results demonstrate that the system has good accuracy, repeatability and compatibility to optical misalignment. The system is suitable for online applications of surface measurement.

scholarly journals A geodesical approach for the harmonic oscillator

2020 ◽  
Vol 17 (1 Jan-Jun) ◽  
pp. 6
Author(s):  
Rodrigo Sánchez-Martínez ◽  
Alvaro Lorenzo Salas-Brito ◽  
Hilda Noemí Núñez-Yépez
Keyword(s):  
Harmonic Oscillator ◽  
Kepler Problem ◽  
Spherical Surface ◽  
Free Particle ◽  
Theoretical Physics ◽  
Canonical Transformations ◽  
Canonical Coordinates ◽  
One Dimensional ◽  
Particle Form ◽  
The One

The harmonic oscillator (HO) is present in all contemporary physics, from elementary classical mechanicsto quantum field theory. It is useful in general to exemplify techniques in theoretical physics. In this work,we use a method for solving classical mechanic problems by first transforming them to a free particle formand using the new canonical coordinates to reparametrize its phase space. This technique has been used tosolve the one-dimensional hydrogen atom and also to solve for the motion of a particle in a dipolar potential.Using canonical transformations we convert the HO Hamiltonian to a free particle form which becomestrivial to solve. Our approach may be helpful to exemplify how canonical transformations may be used inmechanics. Besides, we expect it will help students to grasp what they mean when it is said that a problemhas been transformed into another completely different one. As, for example, when the Kepler problem istransformed into free (geodesic) motion on a spherical surface.

On-Machine Optical Surface Profile Measuring System for Nano-Machining

2011 ◽  
Vol 5 (3) ◽  
pp. 369-376 ◽  
Author(s):  
Hiroshi Sawano ◽  
◽  
Motohiro Takahashi ◽  
Hayato Yoshioka ◽  
Hidenori Shinno ◽  
...  
Keyword(s):  
Error Detection ◽  
Machine Surface ◽  
Detection Method ◽  
Surface Profile ◽  
Optical Probe ◽  
Measuring System ◽  
Profile Measurement ◽  
Optical Surface ◽  
Increasing Demand ◽  
Surface Profile Measurement

There has been an increasing demand for machining of precision parts recently. In order to meet such requirements, nano-machining systems with on-machine surface profile measuring function are required. This paper presents a newly developed on-machine shape measuring system with an optical probe. In this system, an astigmatic focus error detection method is applied to the optical probe. In addition, the influence of the uneven reflection from the surface can be reduced by using two quadrant photodiodes. The results of surface profile measurement confirm that the system developed provides a resolution of 1 nm scale and a repeatability of approximately 50 nm.

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