Edward Charrier: Need to understand pattern roughness leads to computational metrology startup

SPIE Newsroom ◽  
2017 ◽  
Author(s):  
SPIE
Keyword(s):  
Computational Metrology

A Hull Normal Based Approach for Cylindrical Size Assessment

2011 ◽  
Vol 133 (1) ◽  
Author(s):  
Steven Turek ◽  
Sam Anand
Keyword(s):  
New York ◽  
Least Squares ◽  
Measured Data ◽  
Size Determination ◽  
Mathematical Definition ◽  
Dimensioning And Tolerancing ◽  
Normal Method ◽  
Computational Metrology ◽  
American Society ◽  
Definition Of

Digital measurement devices, such as coordinate measuring machines, laser scanning devices, and digital imaging, can provide highly accurate and precise coordinate data representing the sampled surface. However, this discrete measurement process can only account for measured data points, not the entire continuous form, and is heavily influenced by the algorithm that interprets the measured data. The definition of cylindrical size for an external feature as specified by ASME Y14.5.1M-1994 [The American Society of Mechanical Engineers, 1995, Dimensioning and Tolerancing, ASME Standard Y14.5M-1994, ASME, New York, NY; The American Society of Mechanical Engineers, 1995, Mathematical Definition of Dimensioning and Tolerancing Principles, ASME Standard Y14.5.1M-1994, ASME, New York, NY] matches the analytical definition of a minimum circumscribing cylinder (MCC) when rule no. 1 [The American Society of Mechanical Engineers, 1995, Dimensioning and Tolerancing, ASME Standard Y14.5M-1994, ASME, New York, NY; The American Society of Mechanical Engineers, 1995, Mathematical Definition of Dimensioning and Tolerancing Principles, ASME Standard Y14.5.1M-1994, ASME, New York, NY] is applied to ensure a linear axis. Even though the MCC is a logical choice for size determination, it is highly sensitive to the sampling method and any uncertainties encountered in that process. Determining the least-sum-of-squares solution is an alternative method commonly utilized in size determination. However, the least-squares formulation seeks an optimal solution not based on the cylindrical size definition [The American Society of Mechanical Engineers, 1995, Dimensioning and Tolerancing, ASME Standard Y14.5M-1994, ASME, New York, NY; The American Society of Mechanical Engineers, 1995, Mathematical Definition of Dimensioning and Tolerancing Principles, ASME Standard Y14.5.1M-1994, ASME, New York, NY] and thus has been shown to be biased [Hopp, 1993, “Computational Metrology,” Manuf. Rev., 6(4), pp. 295–304; Nassef, and ElMaraghy, 1999, “Determination of Best Objective Function for Evaluating Geometric Deviations,” Int. J. Adv. Manuf. Technol., 15, pp. 90–95]. This work builds upon previous research in which the hull normal method was presented to determine the size of cylindrical bosses when rule no. 1 is applied [Turek, and Anand, 2007, “A Hull Normal Approach for Determining the Size of Cylindrical Features,” ASME, Atlanta, GA]. A thorough analysis of the hull normal method’s performance in various circumstances is presented here to validate it as a superior alternative to the least-squares and MCC solutions for size evaluation. The goal of the hull normal method is to recreate the sampled surface using computational geometry methods and to determine the cylinder’s axis and radius based upon it. Based on repetitive analyses of random samples of data from several measured parts and generated forms, it was concluded that the hull normal method outperformed all traditional solution methods. The hull normal method proved to be robust by having a lower bias and distributions that were skewed toward the true value of the radius, regardless of the amount of form error.

scholarly journals Computing the Angularity Tolerance

1998 ◽  
Vol 08 (04) ◽  
pp. 467-482 ◽  
Author(s):  
Mark De Berg ◽  
Henk Meijer ◽  
Mark Overmars ◽  
Gordon Wilfong
Keyword(s):  
Restricted Problem ◽  
Dimensional Space ◽  
Similar Time ◽  
3 Dimensional ◽  
Computational Metrology ◽  
The Given ◽  
Time Bounds ◽  
Extract Information

In computational metrology one needs to compute whether an object satisfies specifications of shape within an acceptable tolerance. To this end positions on the object are measured, resulting in a collection of points in space. From this collection of points one wishes to extract information on flatness, roundness, etc. of the object. In this paper we study one particular feature of objects, the angularity. The angularity indicates how well a plane makes a specified angle with another plane. We study the problem in 2-dimensional space (where the planes become lines) and in 3-dimensional space. In 2-dimensional space the problem is equivalent to computing the smallest wedge of the given angle that contains all the points. We give an O(n2 log n) algorithm for this problem. In 3-dimensional space we study the more restricted problem where one of the planes is known (a datum plane). In this case the problem is equivalent to asking for the smallest width 3-dimensional strip that contains all the points and makes a given angle with the datum plane. We give an O(n log n) algorithm to solve this version. We also show that in the case of uncertainty in the measured points, upperbounds and lowerbounds on the width can be computed in similar time bounds.

Computational metrology and inspection (CMI) in mask inspection, metrology, review, and repair

2012 ◽  
Vol 1 (4) ◽  
Author(s):  
Linyong Pang ◽  
Danping Peng ◽  
Peter Hu ◽  
Dongxue Chen ◽  
Lin He ◽  
...  
Keyword(s):  
Computational Metrology ◽  
Mask Inspection

scholarly journals Culling a Set of Points for Roundness or Cylindricity Evaluations

2003 ◽  
Vol 13 (03) ◽  
pp. 231-240 ◽  
Author(s):  
Olivier Devillers ◽  
Franco P. Preparata
Keyword(s):  
Cross Sections ◽  
Input Data ◽  
Linear Time ◽  
Programming Approach ◽  
Fixed Size ◽  
Recent Approach ◽  
Data Points ◽  
Surface Measurements ◽  
Computational Metrology ◽  
Set Of Points

Roundness and cylindricity evaluations are among the most important problems in computational metrology, and are based on sets of surface measurements (input data points). A recent approach to such evaluations is based on a linear-programming approach yielding a rapidly converging solution. Such a solution is determined by a fixed-size subset of a large input set. With the intent to simplify the main computational task, it appears desirable to cull from the input any point that cannot provably define the solution. In this note we present an analysis and an efficient solution to the problem of culling the input set. For input data points arranged in cross-sections under mild conditions of uniformity, this algorithm runs in linear time.

Eliminating the offset between overlay metrology and device patterns using computational metrology target design

2016 ◽  
Author(s):  
Jianming Zhou ◽  
Sarah Wu ◽  
Craig Hickman ◽  
Ewoud van West ◽  
Maurits van der Schaar ◽  
...  
Keyword(s):  
Computational Metrology ◽  
Target Design

Efficient approximation and optimization algorithms for computational metrology

1999 ◽  
Vol 21 (2) ◽  
pp. 189-190
Author(s):  
Christian A. Duncan ◽  
Michael T. Goodrich ◽  
Edgar A. Ramos
Keyword(s):  
Optimization Algorithms ◽  
Computational Metrology ◽  
Efficient Approximation

In-situ repair qualification by applying Computational Metrology and Inspection (CMI) technologies

2013 ◽  
Author(s):  
C. Y. Chen ◽  
Ivan Wei ◽  
Laurent Tuo ◽  
C. S. Yoo ◽  
Dongxue Chen ◽  
...  
Keyword(s):  
Computational Metrology ◽  
In Situ Repair

Computational Metrology for the Design and Manufacture of Product Geometry: A Classification and Synthesis

2006 ◽  
Vol 7 (1) ◽  
pp. 3-9 ◽  
Author(s):  
Vijay Srinivasan
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Design Specification ◽  
Combinatorial Optimization Problems ◽  
The Past ◽  
Manufactured Products ◽  
Measurement Tools ◽  
The Status ◽  
Computational Metrology ◽  
Design And Manufacture

The increasing use of advanced measurement tools and technology in industry over the past 30 years has ushered in a new set of challenging computational problems. These problems can be broadly classified as fitting and filtering of discrete geometric data collected by measurements made on manufactured products. Collectively, they define the field of computational metrology for the design specification, production, and verification of product geometry. The fitting problems can be posed and solved as optimization problems; they involve both continuous and combinatorial optimization problems. The filtering problems can be unified under convolution problems, which include convolutions of functions as well as convolutions of sets. This paper presents the status of research and standardization efforts in computational metrology, with an emphasis on its classification and synthesis.

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