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Isotropic two-dimensional high-order spline filtering method for surface metrology

An isotropic, high-order technology, applied in the field of isotropic two-dimensional spline filter design, can solve problems such as inability to derive robust algorithms and filters that do not satisfy isotropy, to eliminate edge effects and improve Utilization, Effect of Robust Algorithms

Active Publication Date: 2019-11-05
HARBIN INST OF TECH
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

[0003] The purpose of the present invention is to solve the problem that the existing two-dimensional spline filter does not satisfy isotropy, and the corresponding robust algorithm cannot be deduced, and proposes an isotropic two-dimensional high-order sample filter for surface measurement. bar filtering method

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  • Isotropic two-dimensional high-order spline filtering method for surface metrology
  • Isotropic two-dimensional high-order spline filtering method for surface metrology
  • Isotropic two-dimensional high-order spline filtering method for surface metrology

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specific Embodiment approach 1

[0017] The isotropic two-dimensional high-order spline filtering method for surface measurement in this embodiment, the method includes the following steps:

[0018] Step 1. Determine the minimum value of residual energy when the interpolation surface is bent and twisted under the action of the two-dimensional topography data of the surface to be measured, so as to extract the neutral plane of the surface filter;

[0019] Step 2, discretize the residual energy equation of step 1, seek the stagnation point of the discrete residual energy equation, obtain the recursive formula of the filter neutral plane, utilize the meaning of the Z transformation to determine the transfer function of the filter; and determine the filter coefficients;

[0020] Step 3, expressing the column vector central difference process involved in the minimum value of the residual energy in step 1 by matrix multiplication, and then writing the two-dimensional topography data matrix of the surface to be measu...

specific Embodiment approach 2

[0024] The difference from the first embodiment is that the isotropic two-dimensional high-order spline filtering method for surface measurement in this embodiment, in the first step, it is determined that under the action of the two-dimensional topography data of the surface to be measured The process of interpolating the minimum value of residual energy when the surface is bent and twisted to extract the neutral plane of the surface filter is as follows:

[0025] By solving the minimum value of the residual energy of formula (1), the neutral surface of the surface filter is extracted by using the condition satisfied when the residual energy function takes the minimum value:

[0026]

[0027] In the formula, E represents the residual energy; E is the order derivative of f(x,y) function, when E takes the minimum value, E is The derivative of is equal to 0, using this condition to obtain f(x, y); z represents the function of the measurement surface; f(x, y) represents the...

specific Embodiment approach 3

[0030] The difference from the specific embodiment 1 or 2 is that in the isotropic two-dimensional high-order spline filtering method for surface measurement in this embodiment, in the step 2, the residual energy equation in the step 1 is discretized, and the discrete The stagnation point of the residual energy equation, the recursive formula for obtaining the neutral plane of the filter, and the process of determining the transfer function of the filter using the Z transform are specifically:

[0031] First, the minimum value of the residual energy equation of formula (1):

[0032]

[0033] Changed to discrete form, expressed as:

[0034]

[0035] In the formula, {z i,j} indicates the measurement data of the measurement surface; {s i,j} represents the data of the neutral surface of the surface filter; Represents the k-order central difference operator, and takes the l-order central difference for x, and takes the (k-l)-order central difference for y; M, N indicates ...

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Abstract

The invention discloses an isotropic two-dimensional high-order spline filtering method for surface metering. The method belongs to the field of two-dimensional signal processing and surface metering.An existing two-dimensional spline filter does not meet isotropy and cannot derive a corresponding robust algorithm. The method comprises the following steps: determining the minimum value of the surface residual energy of the interpolation under the action of measurement data; determining a transfer function of the filter, and determining a filter coefficient; rewriting the minimum value of theresidual energy into a matrix form; solving a characteristic value and a characteristic vector of the real symmetry coefficient matrix, and carrying out orthogonal similar diagonalization processing on the coefficient matrix to obtain a fast filtering algorithm of the filter; weighting the deviation term of the residual energy minimum value expression of the filtering neutral surface to obtain a weighted filtering equation, and eliminating the influence of discrete points or blank points on the surface filtering central surface; And solving a weighted filtering equation to realize a robust algorithm. The calculation speed is improved by dozens of times to hundreds of times, meanwhile, a robust algorithm is achieved, and actual data containing discrete points or blank points can be processed.

Description

technical field [0001] The invention relates to the field of two-dimensional signal processing and surface measurement, in particular to a design method of an isotropic two-dimensional spline filter for surface measurement. Background technique [0002] In surface metrology and roughness measurement, the acquisition of contour filtering neutral line (one-dimensional measurement) or surface filtering neutral plane (two-dimensional measurement) is a crucial issue. For one-dimensional measurement, ISO 16610-21 and ISO 16610-22 stipulate two kinds of contour filters, Gaussian contour filter and spline contour filter, as standard filters for contour midline acquisition; at the same time, ISO 16610-31 and ISO16610 -32 respectively specifies the robust algorithm of Gaussian contour filter and spline contour filter. With the advancement of measurement technology and measuring instruments, surface metrology and roughness measurement of two-dimensional surfaces. For 2D filters, isot...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): H03H17/02G01B21/30
Inventor 佟明斯黄穗楚潘昀路赵学增
Owner HARBIN INST OF TECH