Surface reconstruction method of coherent scanning interferometer based on instrument three-dimensional transfer function

Abstract

The present invention relates to a coherent scanning interferometer surface reconstruction method based on the three-dimensional transfer function of the instrument, wherein the device includes an illumination system, an interference microscopic imaging system and an objective lens scanning system; the method includes the following steps: (1) obtaining a three-dimensional interference signal of the coherent scanning interferometer; (2) performing a three-dimensional Fourier transform on the signal to obtain a three-dimensional spectrum of the interference signal; (3) dividing the three-dimensional spectrum by the three-dimensional transfer function of the system to obtain the spectrum of the surface film model; (4) performing a three-dimensional Fourier inverse transform on the spectrum of the surface film model to obtain a reconstructed surface film model; (5) calculating the surface height by the position and phase of the reconstructed surface film model. The present invention utilizes the three-dimensional imaging theory of the coherent scanning interferometer to restore the surface film model of the surface to be measured in three-dimensional space and obtain the surface height, thereby achieving a microscopic surface morphology reconstruction capability with higher precision than traditional methods.

Description

Technical Field

[0001] The invention relates to the technical field of precision optical measurement engineering, and in particular to a coherent scanning interferometer surface reconstruction method based on a three-dimensional transfer function of the instrument. Background Art

[0002] With the development of high-end manufacturing fields such as optics, integrated circuits, aerospace, new energy vehicles, and medical devices, the requirements for the quality and manufacturing precision of high-end parts are constantly increasing, components are constantly miniaturized, and functional surfaces are constantly complicated, which puts higher requirements on the detection capability and accuracy of product surface morphology. In order to achieve high-efficiency measurement and avoid surface damage, optical methods are usually used to measure surface morphology, mainly coherent scanning interferometers, confocal microscopes, and zoom microscopes. Among them, coherent scanning interferometers (also known as scanning white light interferometers) are currently the only non-contact surface measurement technology that can achieve sub-nanometer longitudinal measurement accuracy within a centimeter-level field of view.

[0003] Modern coherent scanning interferometer technology has been developed for nearly 30 years and has become a widely used three-dimensional surface morphology measurement technology. However, since the imaging resolution is limited by the system transfer function and inherent optical aberrations, the measurement accuracy and spatial resolution of this technology have not made much progress in the past 20 years. The three-dimensional surface reconstruction method is one of the core technologies for coherent scanning interferometer to measure surface morphology, and is one of the main factors that determine the measurement accuracy and spatial resolution. The current surface reconstruction methods mainly include methods for calculating the peak or center of gravity position of the coherent envelope curve in the spatial domain, methods for analyzing the order and phase of the interference signal in the frequency domain, methods for extracting the coherent envelope by wavelet transform, and methods for judging the peak and phase of the low-coherence interference signal by the mutual coherence function. In order to simplify the method, these methods only consider the single-dimensional characteristics of the coherent scanning interferometer signal along the optical axis, and do not utilize the characteristics of the three-dimensional imaging of the instrument. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a coherent scanning interferometer surface reconstruction method based on the instrument's three-dimensional transfer function, which realizes the rapid and accurate restoration of the microscopic morphology of the surface to be measured.

[0005] The technical solution adopted by the present invention to solve the technical problem is: to provide a coherent scanning interferometer surface reconstruction method based on the instrument's three-dimensional transfer function, the steps of which are as follows:

[0006] (1.1) Obtaining three-dimensional interference signals from a coherent scanning interferometer;

[0007] (1.2) Preprocessing the acquired three-dimensional interference signal to constrain the background light intensity distribution in the longitudinal direction (i.e., the optical axis direction);

[0008] (1.3) performing a three-dimensional Fourier transform on the preprocessed three-dimensional interference signal to obtain a three-dimensional interference signal spectrum I(K), where K is a spatial frequency vector;

[0009] (1.4) obtaining the three-dimensional transfer function H(K) of the coherent scanning interferometer through experimental calibration or simulation;

[0010] (1.5) The three-dimensional interference signal spectrum I(K) is divided by the three-dimensional transfer function H(K) to obtain the three-dimensional spectrum O(K) of the surface film model of the surface to be measured, and the formula is as follows:

[0011]

[0012] (1.6) performing a three-dimensional inverse Fourier transform on the three-dimensional spectrum O(K) of the surface film model of the surface to be measured to obtain a reconstructed surface film model of the surface to be measured;

[0013] (1.7) using the reconstructed surface membrane model, obtaining the surface height in the longitudinal direction pixel by pixel in the transverse direction;

[0014] (1.8) Reconstruct the three-dimensional surface morphology through the surface height obtained pixel by pixel.

[0015] In the step (1), a broad spectrum light source is used as an illumination light source to generate a low coherence interference signal.

[0016] The steps of obtaining the three-dimensional spectrum of the surface film model through the three-dimensional interference signal spectrum and the three-dimensional transfer function of the instrument in step (5) are as follows:

[0017] (a) Obtain the 3D transfer function of the coherent scanning interferometer experimentally, or calculate the theoretical 3D transfer function using formula (1):

[0018]

[0019] Where K is the spatial frequency vector, k0 is the wave number (i.e. 2π / λ, λ is the wavelength), S(k0) is the spectral power density,

[0020]

[0021] in is the three-dimensional pupil function of the optical imaging system limited by NA, δ() is the Dirac Delta function, h is the Heaviside step function, is the vertical unit vector, A N is the system numerical aperture;

[0022] (b) Divide the three-dimensional interference signal spectrum by the three-dimensional transfer function of the instrument to obtain the spectrum of the surface film model of the surface to be measured within the transfer function bandwidth. The spectrum outside the bandwidth is zero, which can be expressed by the following formula:

[0023]

[0024] Wherein, O(K) is the three-dimensional spectrum of the surface film model of the surface to be measured, I(K) is the three-dimensional interference signal spectrum, and H(K) is the three-dimensional transfer function of the instrument obtained in step (a);

[0025] The three-dimensional transfer function of the instrument in step (a) can be obtained through calibration or simulation.

[0026] In the step (b), the frequency spectrum outside the bandwidth is set to zero.

[0027] The step (7) of obtaining the surface height of the reconstructed surface membrane model pixel by pixel along the longitudinal direction is as follows:

[0028] (I) Calculate the amplitude and phase information of the surface film model at each pixel along the longitudinal direction;

[0029] (II) Determine the number of peak amplitudes of the surface film model at each pixel along the longitudinal direction;

[0030] If the number of peaks is 1, the amplitude of the surface film model is taken as a function of the height, the amplitude is fitted near the peak, and the corresponding surface height of the peak after fitting is obtained;

[0031] If the number of peaks is greater than 1, a fitting operation is performed on each peak, and the peak height is used as a weight to obtain the surface height after weighted average;

[0032] (III) obtaining the phase at the corresponding height according to the surface height obtained in step (II), and calculating the height correction value corresponding to the phase;

[0033] (IV) Subtracting the height correction value obtained in step (III) from the surface height obtained in step (II) to obtain the final surface height per pixel.

[0034] The height recovery method in step (7) is pixel-by-pixel calculation.

[0035] In the step (II), multiple peaks and single peaks must be distinguished.

[0036] In the step (V), the compensation height is obtained through the surface film model phase.

[0037] Compared with the prior art, the invention has the following beneficial effects: using the three-dimensional transfer function of the coherent scanning interferometer, the surface film model of the surface to be measured is restored in three-dimensional space and the surface height is obtained. Compared with the traditional method, it has the functions of three-dimensional transfer function correction and error compensation, which can improve the accuracy of measuring the surface morphology of three-dimensional objects, including surfaces with large height changes, and surfaces with large slopes and high-frequency surface textures. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of this application, and do not constitute a limitation of the embodiments of the present invention. In the drawings:

[0039] Figure 1 The coherent scanning interference surface reconstruction device and flow chart of the present invention

[0040] Figure 2 The central XZ cross-section of the collected 3D interference signal

[0041] Figure 3 The central XZ cross-section of the interference signal three-dimensional spectrum

[0042] Figure 4 The central XZ section of the spectrum of the surface film model

[0043] Figure 5 The central XZ section diagram of the amplitude of the surface film model

[0044] Figure 6 The vertical distribution of the amplitude of the surface film model

[0045] Figure 7 The surface morphology of the microsphere crown obtained by this invention is DETAILED DESCRIPTION

[0046] The present invention will be further described below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms fall within the scope limited by the appended claims of the application equally.

[0047] Embodiment 1:

[0048] like Figure 1 A coherent scanning interferometer device and a surface reconstruction method based on a three-dimensional transfer function of an instrument are shown. The coherent scanning interferometer device 1 includes an image acquisition CCD 3, a tube lens 4, a piezoelectric ceramic displacement stage 5, an interference objective lens 6, a test piece 7 and an illumination optical path 8. The piezoelectric ceramic scanning stage 5 can move along the optical axis. The surface reconstruction method 2 includes the following steps:

[0049] (1): A broad spectrum light source with a central wavelength of 560 nm is used as the illumination light source for the coherent scanning interferometric imaging system.

[0050] (2): Use the piezoelectric ceramic translation stage 5 to scan the front focal plane of the interference objective lens 6 along the optical axis through the surface to be measured 7. Every time the piezoelectric ceramic translation stage 5 moves one step, the image acquisition CCD 3 collects an interference pattern and adds it to the image stack. After the scanning is completed, the final three-dimensional interference signal is formed. The XZ cross-section diagram of the interference signal is shown as follows: Figure 2 As shown;

[0051] (3): Preprocessing the three-dimensional interference signal obtained in step (2) to constrain the background light intensity distribution in the longitudinal direction (i.e., the optical axis direction) to avoid frequency aliasing;

[0052] (4): Perform a three-dimensional Fourier transform on the three-dimensional interference signal preprocessed in step (3) to obtain a three-dimensional spectrum of the three-dimensional interference signal. The central XZ cross-section of the three-dimensional spectrum of the interference signal is as follows: Figure 3 As shown;

[0053] (5): The three-dimensional spectrum of the surface film model is obtained by using the three-dimensional interference signal spectrum obtained in step (4) and the system three-dimensional transfer function obtained by experimental calibration or simulation. The central XZ cross-sectional diagram of the spectrum of the surface film model is as follows: Figure 4 As shown;

[0054] (6): Perform a three-dimensional inverse Fourier transform on the spectrum of the surface film model in step (5) to reconstruct the surface film model to be tested, and obtain the central XZ cross-sectional view of the surface film model as shown in Figure 5 As shown;

[0055] (7): Using the surface membrane model reconstructed in step (6), the surface height along the longitudinal direction is obtained pixel by pixel in the transverse direction.

[0056] (8): Reconstruct the three-dimensional surface morphology by using the surface height obtained pixel by pixel in step (7), such as Figure 7 Shown is the measured surface morphology of the microsphere crown.

[0057] The steps of obtaining the three-dimensional spectrum of the surface film model through the three-dimensional interference signal spectrum and the three-dimensional transfer function of the instrument in step (5) are as follows:

[0058] (a) The three-dimensional transfer function of the coherent scanning interferometer is obtained experimentally or theoretically by calculation using formula (1):

[0059] 3D transfer function

[0060]

[0061] Where K is the spatial frequency vector, k0 is the wave number (i.e. 2π / λ, λ is the wavelength), S(k0) is the spectral power density,

[0062]

[0063] in is the three-dimensional pupil function of the optical imaging system limited by NA, δ() is the Dirac Delta function, h is the Heaviside step function, is the vertical unit vector, A N is the system numerical aperture.

[0064] (b) Divide the three-dimensional interference signal spectrum by the three-dimensional transfer function of the instrument to obtain the spectrum of the surface film model of the surface to be measured within the transfer function bandwidth. The spectrum outside the bandwidth is zero, which can be expressed by the following formula:

[0065]

[0066] Among them, O(K) is the three-dimensional spectrum of the surface film model of the surface to be measured, I(K) is the three-dimensional interference signal spectrum, H(K) is the three-dimensional transfer function of the instrument obtained in (a), and the central XZ section diagram of the spectrum of the surface film model obtained is shown in Figure 4 shown.

[0067] The steps for obtaining the surface height of the reconstructed surface membrane model pixel by pixel along the longitudinal direction are as follows:

[0068] (I) Calculate the amplitude and phase information of the surface film model at each pixel along the longitudinal direction. The amplitude is as follows: Figure 6 As shown;

[0069] (II) determining the number of amplitude peaks of the surface film model at each pixel point along the longitudinal direction;

[0070] If the number of peaks is 1, the amplitude of the surface film model is taken as a function of the height, the amplitude is fitted near the peak, and the corresponding surface height of the peak after fitting is obtained;

[0071] If the number of peaks is greater than 1, a fitting operation is performed on each peak, and the peak height is used as a weight to obtain the surface height after weighted average;

[0072] (III) obtaining the phase at the corresponding height according to the surface height obtained in step (II), and calculating the height correction value corresponding to the phase;

[0073] (VI) Subtracting the height correction value obtained in step (III) from the surface height obtained in step (II) to obtain the final surface height per pixel.

Claims

1. A coherent scanning interferometer surface reconstruction method based on the instrument three-dimensional transfer function, characterized in that: The steps include: (1.1) Obtaining three-dimensional interference signals from a coherent scanning interferometer; (1.2) Preprocessing the acquired three-dimensional interference signal to constrain the background light intensity distribution in the longitudinal direction, i.e., the optical axis direction; (1.3) performing a three-dimensional Fourier transform on the preprocessed three-dimensional interference signal to obtain a three-dimensional interference signal spectrum I(K), where K is a spatial frequency vector; (1.4) The three-dimensional transfer function H(K) of the coherent scanning interferometer is obtained by experimental calibration or simulation, and the formula is as follows: Where K is the spatial frequency vector, k0 is the wave number, i.e. 2 / , λ is the wavelength, S(k0) is the spectral power density, in is the three-dimensional pupil function of the optical imaging system limited by NA, δ() is the Dirac Delta function, h is the Heaviside step function, is the vertical unit vector, A N is the system numerical aperture; (1.5) The three-dimensional interference signal spectrum I(K) is divided by the three-dimensional transfer function H(K) to obtain the three-dimensional spectrum O(K) of the surface film model of the surface to be measured, and the formula is as follows: (1.6) performing a three-dimensional inverse Fourier transform on the three-dimensional spectrum O(K) of the surface film model of the surface to be measured to obtain a reconstructed surface film model of the surface to be measured; (1.7) Using the reconstructed surface membrane model, the surface height along the longitudinal direction is obtained pixel by pixel in the transverse direction, specifically including: (7.1) calculating the amplitude and phase information of the surface membrane model along the longitudinal direction at each pixel point; (7.2) Determine the number of peak amplitudes of the surface film model at each pixel along the longitudinal direction: If the number of peaks is 1, the amplitude of the surface film model is taken as a function of the height, the amplitude is fitted near the peak, and the corresponding surface height of the peak after fitting is obtained; If the number of peaks is greater than 1, a fitting operation is performed on each peak, and the peak height is used as a weight to obtain the surface height after weighted average; (7.3) acquiring the phase at the corresponding height according to the acquired surface height, and calculating the height correction value corresponding to the phase; (7.4) subtracting the obtained height correction value from the obtained surface height to obtain a final surface height per pixel; (1.8) Reconstruct the three-dimensional surface morphology through the surface height obtained pixel by pixel.

2. The method for surface reconstruction of a coherent scanning interferometer based on a three-dimensional transfer function of an instrument according to claim 1, characterized in that: In step (7.2), multiple peaks and single peaks must be distinguished.

3. The method for surface reconstruction of a coherent scanning interferometer based on a three-dimensional transfer function of an instrument according to claim 1, characterized in that: The compensation height in step (7.3) is obtained through the surface film model phase.

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