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
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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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