Weighted trapezoidal integral white light interference signal peak searching method

Abstract

The invention discloses a weighted trapezoidal integral white light interference signal peak searching method, which comprises the following steps of: acquiring a group of three-dimensional light intensity data through a white light interference measuring instrument, determining a self-adaptive integral parameter according to the central wavelength and the spectral width of a light source, selecting an integral weighting function, creating an integral window, and then carrying out weighted trapezoidal integral to obtain a white light interference signal peak searching result. And calculating a zero optical path position of the position, traversing each pixel position one by one, and calculating positions of all interference peak values to realize surface topography reconstruction. According to the method, the interference signal peak searching problem in white light interference measurement is solved, and the provided method has high anti-noise capability, high peak searching accuracy and high calculation speed, can be applied to different white light interference measurement instruments, and is wide in application range.

Description

Technical Field

[0001] The present invention relates to the field of optical metrology and testing, and in particular to a method for performing interference signal peak detection in a white light interferometer measurement instrument. Background Art

[0002] Optical precision measurement is widely used in various fields such as national defense, military, scientific research, aerospace, and precision manufacturing. White light interferometry, as a high-precision, non-contact, full-field measurement method, can quantitatively calculate and reconstruct the three-dimensional surface morphology of the measured object. White light interferometry is different from laser interferometry. The coherence length of the white light source is much smaller than that of the laser light source. Generally speaking, it is only a few microns to tens of microns. Near the zero optical path of the interference, the contrast of the interference fringes is high. As the optical path difference of the interference beam becomes larger and larger, the contrast of the interference fringes gradually decreases until the fringes disappear completely. According to this principle, in white light interferometry, as long as the measuring arm is moved and the scanning measurement is performed, and then the position with the highest contrast of the interference signal at each position is determined, the position of zero optical path difference can be determined, thereby reconstructing the three-dimensional surface morphology of the measured object.

[0003] In white-light interferometry, peak-finding of the interference signal is a key step. Chinese invention patent CN106767496A discloses a 3D topography recovery method that combines phase-shifting interferometry with vertical scanning interferometry. This method first acquires all interference images, then uses the extreme value method to calculate the position of zero optical path difference for each pixel, records the corresponding frame number, and then uses a five-step method to calculate the phase information of each pixel based on the frame number information. Finally, the two methods are combined to obtain the 3D topography.

[0004] Chinese invention patent CN108759709B discloses a white-light interferometry 3D reconstruction method suitable for surface topography detection. This method processes intensity and phase information separately. A Gaussian function is used to quickly generate an envelope curve from the interference curve. This envelope curve is then fitted to locate the zero optical path difference position where the peak occurs. The Carré algorithm is then used to obtain phase information. Finally, the two results are combined to obtain height information, enabling 3D topography reconstruction.

[0005] Chinese invention patent CN113091634A discloses a rapid microscopic topography measurement method suitable for white-light scanning interferometry. This method uses a host computer software program to control the expansion and contraction of a piezoelectric ceramic within a specified length for scanning measurement. Each movement captures and stores an interferogram. The stored interferogram is preprocessed, and a supersymmetric search method is used to locate the peak point in the interferogram. The frame number at the peak point is recorded, and height information is calculated. A seven-step phase shifting algorithm is used to extract phase information and perform phase unpacking.

[0006] With the continuous development of semiconductor chips, MEMS, metasurfaces and other fields, peak finding methods in white light interferometry have also been receiving widespread attention. How to solve the interference of measurement noise and improve the accuracy of peak finding and the speed of calculation processing are still problems to be solved. Summary of the Invention

[0007] The problem to be solved by the present invention is to provide a signal peak detection method for use in white light interferometry instruments. This method has high peak detection accuracy, strong noise immunity, and fast calculation processing speed. It can be widely applied to different types of instruments such as white light interferometer microscopes and white light interferometers. The technical solution adopted by the present invention is as follows: Step 1: Use a white light interferometer to collect a set of three-dimensional interference light intensity data I(y,x,z), where the x, y, and z axes are perpendicular to each other, x and y are two-dimensional spatial pixel coordinates, x ranges from 1 to Nx, y ranges from 1 to Ny, and Nx and Ny are pixel sizes; z is the scanning axis in the direction of the optical path difference, and a total of (Nz+1) interference light intensity images are collected in the z-axis direction. The interval between two adjacent collections is dz, and the total scanning length in the z-axis direction is L=Nz*dz.

[0008] Step 2: For each spatial pixel point (x, y), extract the interference light intensity signal of the pixel along the z-axis direction, denoted as I(z).

[0009] Step 3: Calibrate and measure the central wavelength and spectral curve of the light source of the white light interferometer measurement instrument to obtain the central wavelength l and spectral envelope width s of the light source, and calculate the wave number k0=2p / l of the light source.

[0010] Step 4: Calculate the center frequency nc = round(k0*L / (2p)), where the round() function rounds to the nearest integer. Then, based on nc as the center, symmetrically select several frequencies on both sides of nc to form a frequency index set nr. The number of selected frequencies is N.

[0011] Step 5: Calculate zc = round((Nz+1) / 2) and zh = round(L / (2*dz)). Create an integral window index set z_idx, which contains all integers from zc-zh to zc+zh as indices. Based on the index value z_idx, retrieve the corresponding z value sequence. The number of indices is M, and the corresponding z value set is denoted as z_win.

[0012] Step 6: Construct the integral auxiliary function p(zw j ), and the p(zw j )'s derivative pp(zw j ), , (Formula 1) , (Formula 2) Among them, mean() means taking the average value, the value range of zw is z_win, and the zw subscript represents the index value.

[0013] Step 7: Construct a complex exponential function , where i represents the imaginary unit, , n∈nr.

[0014] Step 8: Construct the integral auxiliary function, , (Formula 3) , (Formula 4) Using (Equation 3) and (Equation 4) to calculate the weighted trapezoidal integral, , (Formula 5) , (Equation 6) (Formula 7) Step 9: Calculate the peak position based on the integral value and the frequency index set nr. , (Equation 8) , (Equation 9) , (Equation 10) Wherein, conj() represents taking the conjugate of the complex number, Re() represents taking the real part of the complex number, and ze represents the peak position of the calculated light intensity signal I(z) at the current pixel position.

[0015] Step 10: Traverse each pixel position (x, y) in the light intensity data, repeat steps 2 to 9, and calculate the white light interference peak position of all positions. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The present invention will be further described below with reference to the accompanying drawings and examples.

[0017] Figure 1 It is a data processing flow chart of the white light interference signal peak finding method described in the present invention.

[0018] Figure 2 This is a graph of the interference light intensity at the pixel position (200, 200) in the present invention.

[0019] Figure 3 It is a distribution diagram of the calculation error between the peak position calculated by the peak-finding algorithm in the present invention and the set peak position. DETAILED DESCRIPTION

[0020] To help those skilled in the art better understand the technical solutions of the present invention, the following will provide a clear and complete description of the technical solutions of the present invention in conjunction with the accompanying drawings. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of them. The embodiments of the present invention and all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0021] Example 1: This embodiment provides a weighted trapezoidal integral white light interference signal peak finding method, comprising the following steps: Step 1: Simulate a white light interferometer measurement instrument to collect a set of three-dimensional interference light intensity data I(y,x,z), where the x, y, and z axes are perpendicular to each other, x and y are two-dimensional spatial pixel coordinates, x ranges from 1 to 400 (Nx=400), y ranges from 1 to 400 (Ny=400), and Nx and Ny are pixel sizes; z is the scanning axis in the direction of the optical path difference, and a total of 512 (Nz=511) interference light intensity patterns are collected in the z-axis direction. The interval between two adjacent collections is dz=0.02μm, and the total scanning length in the z-axis direction is L=511*0.02μm=10.22μm.

[0022] Step 2: For each spatial pixel point (x, y), extract the interference light intensity signal of the pixel along the z-axis direction, denoted as I(z). The data column contains a total of 512 data points.

[0023] Step 3: Use white light interferometry to measure the typical spectral distribution of the light source in the instrument. Assume that its central wavelength l = 0.6μm and the spectral curve is Gaussian. In actual experiments, the full width at half maximum (FWHM) of the spectral curve can be measured, and then the spectral envelope width s can be calculated based on the curve shape. In this example, s = 2.0μm is taken, and the wave number k0 = 2p / l of the light source is calculated.

[0024] Step 4: Calculate the center frequency nc = round(k0*L / (2p)) = 3, and then symmetrically select two frequencies on both sides of nc with nc as the center to form a frequency index set nr = {2, 3, 4}, where the number of selected frequencies is 3.

[0025] Step 5: Calculate zc = 256, zh = 50, create an integral window index set z_idx, containing all integers from 206 to 306 as indices, and retrieve the corresponding z value sequence based on the index value z_idx. The number of indices is 101, and the corresponding z value set is recorded as z_win from -1.01μm to +0.99μm, with a length interval of 0.02μm.

[0026] Step 6: Construct the integral auxiliary function p(zw j ), and the p(zw j)'s derivative pp(zw j ), , , Among them, mean() means taking the average value, the value range of zw is z_win, and the zw subscript represents the index value.

[0027] Step 7: Construct a complex exponential function , where i represents the imaginary unit, , n∈nr.

[0028] Step 8: Construct the integral auxiliary function, , , Using (Equation 3) and (Equation 4) to calculate the weighted trapezoidal integral, , , .

[0029] Step 9: Calculate the peak position based on the integral value and the frequency index set nr. , , , Where conj() represents the conjugate of the complex number, Re() represents the real part of the complex number, and ze represents the peak position of the calculated light intensity signal I(z) at the current pixel position. In this example, the calculation result at the pixel coordinate (x,y)=(200,200) is selected. The estimated peak position ze=0.1894μm, and the actual peak position is 0.1902μm. At the same time, the white light interference intensity curve at this position is as follows Figure 2 shown.

[0030] Step 10: Traverse each pixel position (x, y) in the light intensity data and repeat steps 2 to 9 to calculate the white light interference peak position at all positions. In this example, the deviation distribution of the estimated peak value and the set peak position at all 400*400=16000 pixel positions is calculated as follows Figure 3 shown.

Claims

1. A weighted trapezoidal integral white light interference signal peak finding method, characterized in that: The following steps are involved: Step 1: Use a white light interferometer to collect a set of three-dimensional interference light intensity data I(y,x,z), where the x, y, and z axes are perpendicular to each other, x and y are two-dimensional spatial pixel coordinates, x ranges from 1 to Nx, y ranges from 1 to Ny, and Nx and Ny are pixel sizes; z is the scanning axis in the direction of the optical path difference, and a total of (Nz+1) interference light intensity images are collected in the z-axis direction. The interval between two adjacent collections is dz, and the total scanning length in the z-axis direction is L=Nz*dz; Step 2: For each spatial pixel point (x, y), extract the interference light intensity signal of the pixel along the z-axis direction, denoted as I(z); Step 3: Calibrate and measure the central wavelength and spectral curve of the light source of the white light interferometer measurement instrument to obtain the central wavelength l and spectral envelope width s of the light source, and calculate the wave number k0=2p / l of the light source; Step 4: Calculate the center frequency nc = round(k0*L / (2p)), where the round() function rounds to the nearest integer. Then, based on nc as the center, symmetrically select several frequencies on both sides of nc to form a frequency index set nr. The number of selected frequencies is N. Step 5: Calculate zc = round((Nz+1) / 2) and zh = round(L / (2*dz)). Create an integral window index set z_idx, which contains all integers from zc-zh to zc+zh as indices. Based on the index value z_idx, retrieve the corresponding z value sequence. The number of indices is M, and the corresponding z value set is recorded as z_win. Step 6: Construct the integral auxiliary function p(zw j ), and the p(zw j )'s derivative pp(zw j ), , (Formula 1) , (Formula 2) Among them, mean() means taking the average value, the value range of zw is z_win, and the zw subscript represents the index value; Step 7: Construct a complex exponential function , where i represents the imaginary unit, , n∈nr; Step 8: Construct the integral auxiliary function, , (Formula 3) , (Formula 4) Using (Equation 3) and (Equation 4) to calculate the weighted trapezoidal integral, , (Formula 5) , (Equation 6) ; (Formula 7) Step 9: Calculate the peak position based on the integral value and the frequency index set nr. , (Equation 8) , (Equation 9) , (Equation 10) Where conj() represents taking the conjugate of a complex number, Re() represents taking the real part of a complex number, and ze represents the peak position of the calculated light intensity signal I(z) at the current pixel position. Step 10: Traverse each pixel position (x, y) in the light intensity data, repeat steps 2 to 9, and calculate the white light interference peak position of all positions.

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