METHOD FOR CALCULATING THREE-DIMENSIONAL SURFACE PROFILES BY INTERFERENCE

Abstract

A method for calculating three-dimensional surface profiles by interference, characterized in that it comprises the following steps: S1. Calibration of an interferometer using a standard mirror to determine a peak space displacement Δl of the interferometer; S2. Use of the interferometer to acquire a temporal interference image series for each pixel measurement point P(x) i , y j ) on an object to be measured, wherein the temporal interference image series consists of N interference images with interference fringes; S3. Obtaining a zero-level partial envelope and a potential zero-level partial envelope of the temporal interference image series; S4. Use of the zero-level partial envelope curve to determine a zero-level extremum point Z0(x) i , y j ) of the zero-level partial envelope curve; S5. Calculation of an altitude position Z d (x i, y j ) of the object to be measured based on the zero-level extremum point Z0(x i , y j ): Z d ( xi , yj ) = Δ l ( xi , yj ) + Z 0 ( xi , yj )

Description

[0001] The present application claims priority from the Chinese patent application dated November 18, 2021, application number 202111370114.1, entitled "Method for calculating three-dimensional surface profiles by interference". The entire content of the Chinese patent application is incorporated herein by reference. TECHNICAL AREA

[0002] The present invention belongs to the field of surface profile metrology and specifically relates to a method for calculating three-dimensional surface profiles by interference. STATE OF THE ART

[0003] Using existing technology, many scientists have conducted a number of research projects on the problem of calculating white-light interferograms. These projects can be summarized into three main areas of development: 1. Direct solution methods, including interpolation method, phase shift method, spatial frequency domain method; 2. Weighting methods, including center of gravity methods and coherent correlation methods; 3. Enclosure curve fitting methods, including polynomial fitting method, Gaussian fitting method, Fourier transform method, Hilbert transform method, wavelet transform method, and the method for calculating enclosure curve functions based on the sampling theorem.

[0004] With a perfect signal, each of these methods provides a near-ideal solution. However, if the spectrum of the reflected signal degrades, or if the signal reflected due to intensity degradation forms an interferogram with the reflected signal from the standard mirror, problems such as broadening of the interference signal enclosure curve and a decrease in signal contrast arise. Simultaneously, multi-level interference noise signals occur, resulting in a further degraded interferogram to be processed (as in Fig. 2a and Fig. (2b shown). Using the methods mentioned above, it is difficult to reconstruct the three-dimensional surface morphology of the target with high accuracy.

[0005] DE69426070T2 discloses a method for topographic profile measurement of the surface of a three-dimensional object.

[0006] CN113066083A discloses a method and electronic equipment for determining liquid Doppler parameters.

[0007] CN109163672A discloses a method for microtopography measurement based on a position selection algorithm with white light interference and zero optical path difference.

[0008] An article entitled “Efficient nonlinear algorithm for envelope detection in white light interferometry” was published by Kieran G. Larkin in the Journal of the Optical Society of America A, 1996, Vol. 13, No. 4, pp. 832-843 (https: / / doi.org / 10.1364 / JOSAA.13.000832). INVENTIONAL CONTENT

[0009] To overcome the shortcomings of existing technology, the present invention proposes a method for calculating three-dimensional surface profiles by interference. Since the multi-stage superimposed light field is generated inside the instrument, it is deterministic; the peak of the zeroth interference fringes on the same surface is unambiguous; and the spectral degradation effect does not affect the relative position of the peak of the enclosure curve. Therefore, the spatial distribution of the interference intensity of the measured object remains stable despite the effects of problems such as enclosure curve broadening and signal contrast degradation. By determining the position of the zeroth interference fringe Z0 and adding Z0 to the calibrated peak space shift Δl, the actual position Z can be determined. d of the object to be measured.

[0010] To achieve the above-mentioned purpose, the technical solutions according to the present invention are: A method for calculating three-dimensional surface profiles by interference, comprising the following steps: S1. Calibration of an interferometer using a standard mirror to determine a peak space displacement Δl of the interferometer; S2. Use of the interferometer to acquire a temporal interference image series for each pixel measurement point P(x) i , y j ) on an object to be measured, wherein the temporal interference image series consists of N interference images with interference fringes; S3. Obtaining a zero-level partial envelope and a potential zero-level partial envelope of the temporal interference image series; S4. Use of the zero-level partial envelope curve to determine a zero-level extremum point Z0(x) i , y j) of the zero-level partial envelope curve; S5. Calculation of an altitude position Z d (x i , y j ) of the object to be measured based on the zero-level extremum point Z0(x i , y j ): Zd(xi,yj)=Δl(xi,yj)+Z0(xi,yj) Preferably, the standard mirror is an ideal standard planar reflector or a spherical or non-spherical mirror; where the standard mirror has the same spectral reflection properties as the object being measured.

[0011] Preferably, step S3 comprises the following steps: S31. Determine if N. Sample points P(n, x) i , y j ) at the same pixel position (x i , y j ) of the temporal interference pattern series extrema P e (n, x i , y j ) or transition points P t (n, x i , y j ) are, where n ∈ [1, M], M is a given value; S32. Obtaining the zero-level partial envelope curve and the potential zero-level partial envelope curve of the temporal interference image series based on the determined extreme value points P e (n,x i ,y j ).

[0012] Preferably, step S31 comprises the following steps: S311. Exposure of each sample point P(n, x) i ,y j ) on N. Interference patterns for recording intensity values ​​I(n, x) i , y j ) of each sample point P(n, x i , y j ) on the interference patterns; S312. Construction of a data cube S based on the intensity values ​​I(n, x) i , y j ) of the N. test points P(n, x i , y j ) on interference patterns, the N. sample points are located at the same position in the temporal interference pattern sequence, where the model for constructing the data cube S is as follows: S(n,i,j)=[I(n+1,xi,yj)−I(n,xi,yj)]×[I(n,xi,yj)−I(n−1,xi,yj)] where, I(n, x i , y j ) the intensity value of the sample point P(n, x) i , y j ) represented on the No. n image of the temporal interference pattern series; I(n+1 ,x i , y j ) the intensity value of the sample point P(n+1, x i , y j ) represented on the No. n+1 image of the temporal interference image series; I(n-1, x i , y j ) the intensity value of the sample point P(n-1, x i , y j ) represented on the No. n-1 image of the temporal interference image series; S313. Determine whether the sample point P(n, x) i , y j ) an extreme point of the temporal interference pattern series is: If S(n,i,j) ≤ 0, then the test point is P(n, x). i , y j ) an extremum point P e (n, x i , y j ); If S(n,i,j) > 0, then the test point is P(n, x). i , y j ) a transition point P r (n, x i , y j ) Preferably, step S32 is performed using the following method:

[0013] Sorting of each pixel measurement point P(x i , y j ) corresponds to an extremum point on the temporal interference pattern series, where at least three intensity values ​​are selected in descending order: a first extremum point P e (n a , xi, y j ), a second extremum point P e (n b , x i , y j ) and a third extremum point P e (n c , x i , y j ), where the following relationship exists: Ie(na,xi,yj) <Ie(nb,xi,yj); Ie(nb,xi,yj)>Ie(nc,xi,yj); where, I e (n a , x i , y j ) the intensity value of the first extreme point P e (n a, x i , y j ) is, I e (n b , x i , y j ) the intensity value of the second extreme point P e (n b , x i , y j ) is, I e (n c , x i , y j ) the intensity value of the third extreme point P e (n c , x i , y j ) is; then the second extremum point P e (n b , x i , y j ) on the zero-level partial envelope curve; where the first extremum point P e (n a , x i , y j ) and the third extremum point P e (n c , x i , y j ) lie on the potential zero-level partial envelope curve.

[0014] Preferably, step S4 comprises the following steps: S41. Use of the extremum points P e (n k , x i , yj ) and transition points P t (n a , x i , y j ) on the zero-level partial envelope curve to determine the zero-level extremum point Z0(x i , y j ) of the zero-level partial envelope curve.

[0015] Preferably, the method for determining the zero-level extremum point Z0 (x) includes i , y j ) the following steps: Selection of at least two first transition points P t (n k+1 , x i , y j ) and second transition points P t (n k-1 ,x i , y j ), which are located near the extremum point P e (n k , x i , y j ) of the zero-level partial envelope curve; use of a fitting method to fit the extremum point P e (n a , x i , y j ), of the first transition point P t (n k+1 , x i , y j) and the second transition point P t (n k-1 , x i , y j ) of the zero-level partial envelope curve to determine the zero-level extremum point Z0(x i , y j ).

[0016] Preferably, the adjustment method includes at least one of the following methods: adjustment, center of gravity method or interpolation method.

[0017] Preferably, step S4 also includes the following steps: S42. Adjustment of the zero-level extremum point Z0'(xi,yj) of the potential zero-level partial envelope curve, using preconditions to replace erroneous zero-level extremum point Z0(x) i , y j ); where the prerequisite is: Continuous surface measurement data of the object to be measured show no height jumps.

[0018] Preferably, step S1 comprises the following steps: S11. Use of a standard mirror with known surface shape for calibrating the interferometer and obtaining the standard surface distribution Z(x) i , y j ) of the standard mirror; S12. Performing a temporal interference image series at each pixel measurement point on the standard mirror with the interferometer to determine a deformation distribution Z(x) i , y j ) of the standard mirror to calculate; S13. Calculation of the peak space shift Δl (x) caused by light path inequality inside the interferometer i , y j ): Δl(xi,yj)=Z(xi,yj)−Z¯(xi,yj)

[0019] Preferably, the interferometer is a broadband white light interferometer or a narrowband laser interferometer.

[0020] The present invention achieves the following technical effects: 1. The present invention is carried out in the spatial frequency domain to avoid complex calculations such as Fourier transform and convolution, which improves the real-time capability of the algorithm. 2. The present invention exhibits a high degree of accuracy in its adaptation of the partial envelopment curve and can be used to calculate three-dimensional surface profiles of surfaces with low reflectance. 3. The present invention is suitable for samples with low reflectance and has prospects in practical applications such as industrial measurement and scientific research. EXPLANATION OF THE DRAWINGS Fig. Figure 1 is a schematic representation of a method for calculating three-dimensional surface profiles according to an embodiment of the present invention; Fig. Figure 2a shows a schematic interference signal measured using a state-of-the-art Michelson interferometer. Fig. Figure 2b shows a schematic interference signal of the same system in the prior art, which leads to a change in the interference pattern due to spectral degradation. Fig. Figure 3 shows a diagram of the relative positions of the maximum point Z0 of the zeroth interference fringes, the peak position Z d and the displacement distance Δl of the transition curve peak in the reference state. Fig. Figure 4a shows a diagram for calculating three-dimensional surface profiles on a step according to an embodiment of the present invention. Fig. 4b shows a centroid section view of Fig. 4a. Fig. Figure 5a shows a diagram for calculating three-dimensional surface profiles at a step, obtained using the Fourier transformation method. Fig. 5b shows a centroid section view of Fig. 5a. Fig. Figure 6a shows a diagram for calculating three-dimensional surface profiles on a step, obtained using the center of gravity method. Fig. 6b shows a centroid section view of Fig. 6a. SPECIFIC EXECUTION FORMS

[0021] To clarify the objectives, technical solutions, and advantages of the present invention, the invention is explained in more detail below in conjunction with the drawings and specific embodiments. It should be understood that the specific embodiments described here serve only to illustrate the present invention and do not constitute a limitation of the invention.

[0022] The object of the present invention is to provide a method for calculating three-dimensional surface profiles by interference. This method is explained in detail below using specific embodiments.

[0023] In conventional white light interferometers, peak values ​​Z overlap due to influences such as "multiple interference superposition effects" and "spectral degradation effects". d the outer transition curve and the center position Z0 of the zero-level interference fringes (partial envelope curve) are often not, as in Fig. Figure 3 shows. Therefore, the proposed method for calculating three-dimensional surface profiles by interference according to the present invention enables the determination of the actual position Z by accurately calculating the center Z0 of the zero-level interference fringes and the peak space displacement Δl in the calibrated state. d of the object to be measured.

[0024] Regarding the in Fig. The procedure for calculating three-dimensional surface profiles by interference, as shown in Figure 1, comprises the following steps: S1. Calibration of an interferometer with a standard mirror to obtain the peak space displacement Δl of the interferometer, which is described by the following expression: Δl(xi,yj)=Z(xi,yj)−Z¯(xi,yj) where Z(x i , y j ) is a standard surface distribution of the standard mirror obtained by the interferometer; where Z(x i , y j ) a deformation distribution of the standard mirror, which was generated by applying a method for calculating three-dimensional surface profiles by interference according to the present invention. S2. Use of the interferometer to acquire a temporal interference image series for each pixel measurement point P(x) i , y j) on an object to be measured.

[0025] In a preferred embodiment of the present invention, we take the object to be measured as a stage, use a calibrated white light interferometer and acquire a temporal interference image series for each pixel measurement point P(x). i , y j ) within the detection range of the stage. The temporal interference pattern series consists of N interference patterns with interference fringes, where each pixel on the interferograms exhibits "spatial intensity" variations.

[0026] S3. Obtaining a zero-level partial envelope and a potential zero-level partial envelope of the temporal interference image series, including the following steps: S31. Determine if N sample points P(n, x) i , y j ) at the same pixel position (x i , y j ) in the temporal interference pattern series, extreme value points P e (n, x i , y j) or transition points P(n, x) i , y j ) are, where n ∈ [1, M], and M is a given value.

[0027] Within a detection range of one stage, each pixel measurement point corresponds to P(x i , y j ) a recorded sample point P(n, x i , y j ) in the temporal interference pattern series for this stage, and it is checked whether this sample point P(n, x) i , y j ) an extremum point P e (n, x i , y j ) or a transition point P t (n, x i , y j ) is.

[0028] Steps S31 include in particular the following steps: S311. Expose each sample point P(n, x i , y j ) on N interference patterns to determine intensity values ​​I(n, x i , y j ) of each test point P(n, x i , y j ) to obtain on the interference patterns; where i, j represents the position, n represents the sampling time, where n ∈ [1,M], M is a preset value determined based on the height difference of the object to be measured and the sampling interval. S312. Build a data cube S based on the intensity values ​​I(n, x). i , y j ) of each Nth sample point P(n, x) i , y j ) on interference patterns, the N sample points are located at the same position in the temporal interference pattern sequence.

[0029] For any given sample point (x1, y1), since the temporal interference pattern consists of N interference patterns, the sample points (x1, y1) correspond to the same positions in the N interference patterns P(1, x1, y1), P(2, x1, y1),..., P(n, x1, y1), P(n+1, x1, y1),..., P(N, x1, y1). The corresponding intensity values ​​are I(1, x1, y1), I(2, x1, y1),..., I(N, x1, y1).

[0030] Similarly, for the same position (x i , yj ) the intensity values ​​I(n, x i , y j ) of all test points P(n, x i , y j ) are obtained at different times, and the following model of the data cube S is created: S(n,i,j)=[I(n+1,xi,yj)−I(n,xi,yj)]×[I(n,xi,yj)−I(n−1,xi,yj)] where I (n,x i , y j ) the intensity value of the sample point P(n, x) i , y j ) represented in interference pattern no. n of the temporal interference pattern series; where I(n+1, x i , y j ) the intensity value of the sample point P(n+1, x i , y j ) represented in interference pattern no. n+1 of the temporal interference pattern series; where I(n-1,x) i ,y j ) the intensity value of the sample point P(n-1,x) i , y j ) represented in interference images No. n-1 of the temporal interference image series.

[0031] S313. Determine whether the test point P(n, x)i , y j ) is an extremum point in the temporal interference pattern series, otherwise it is a transition point: If S(n,i,j) ≤ 0, then the test point is P(n, x). i , y j ) an extremum point P e (n, x i , y j ); If S(n,i,j) > 0, then the test point is P(n, x). i , y j ) a transition point P t (n, x i , y j ).

[0032] S32. Obtain the following using the extremum point P e (n, x i , y j ) the zero-level partial envelope curve and the potential zero-level partial envelope curve of the temporal interference image series.

[0033] In a preferred embodiment of the invention, the obtained extreme value points for each pixel measurement point P(x) are i , y j ) in the temporal interference pattern series sorted in descending order of intensity, and a first extremum point P e(n a , x i , y j ), a second extremum point P e (n b , x i , y j ) and a third extremum point P e (n c , x i , y j ) are selected.

[0034] There is the intensity value I e (n a , x i , y j ) of the first extremum point P e (n a , x i , y j ) smaller than the intensity value I e (n b , x i , y j ) of the second extremum point P e (n b , x i , y j ); at the same time the intensity value I e (n b , x i , y j ) of the second extremum point P e (n b , x i , y j ) greater than the intensity value I e (n c , x i , y j ) of the third extremum point P e (n c, x i , y j ).

[0035] Then the zero-level partial envelope curve is the transition curve that passes through the second extremum point P. e (n b , x i , y j ) proceeds;

[0036] And the transition curves that pass through the first extreme value point P e (n a , x i , y j ) and the third extremum point P e (n c , x i , y j ) are potential zero-level partial envelope curves.

[0037] For the selection of any number of odd previous extremum points with the highest intensity values, the transition curve passing through the extremum point with the medium intensity value is the zero-level partial envelope curve, and the other extremum points lie in potential zero-level partial envelope curves.

[0038] In another embodiment of the invention, two of the four extreme value points P(n) can also be f , x i , y j ) and the fifth extremum point P(n g , x i , y j ) with the highest intensity values ​​are selected, where the intensity relationship is as follows: Ie(nf,xi,yj) <Ie(ng,xi,yj);

[0039] Then the transition curve passes through the extremum point with the highest intensity value P(n) g , x i , y j ) the zero-level partial envelope curve;

[0040] And the transition curve through the extremum point P(n) f , x i , y j ) is the potential zero-level partial envelope curve.

[0041] For the selection of any number of previous even extremum points with the highest intensity values, the transition curve through the extremum point with the highest intensity value is the zero-level partial envelope, and the other extremum points lie in potential zero-level partial envelopes.

[0042] In the case of a multilayer film structure, as in Fig. As shown in 2b, the transition curve of the group with the highest intensity peak in the outer transition curve can be selected as the zero-level partial envelope curve, depending on requirements.

[0043] S4. Use of the zero-level partial envelope curve to determine a zero-level extremum point Z0(x) i , y j ) of the zero-level partial envelope curve.

[0044] Step S4 includes the following steps: S41: Obtain the zero-level extremum point Z0(x) i , y j) of the zero-level partial envelope curve based on the extreme value points P e (n k , x i , y j ) and transition points P t (n a , x i , y j ) through adaptation.

[0045] In a preferred embodiment of the invention, the second extreme value point P e (n b , xi, y j ) and a first transition point P e (n b-2 , x i , y j ), a second transition point P e (n b-1 , x i , y j ), a third transition point P e (n b+1 , x i , y j ) and a fourth transition point P e (n b+2 , x i , y j ) near the second extreme value point P e (n b , x i , y j ) jointly adjusted to find the zero-level extremum point Z0(x i , y j) to obtain the zero-level partial envelope curve.

[0046] Furthermore, the relative accuracy of the fit can be improved by selecting a more precise fitting method for the second extreme value point P. e (n b , x i , y j ), the first transition point P e (n b-2 , x i , y j ), the second transition point P e (n b-1 , x i , y j ), the third transition point P e (n b+1 , x i , y j ) and the fourth transition point P e (n b+2 , x i , y j ) improved. Through calculations, a continuous mathematical curve is obtained to find the zero-level extremum Z0(x). i , y j to obtain. The adjustment method is a well-known technique and will not be explained in detail here.

[0047] In another embodiment of the invention, methods such as center of gravity methods or interpolation methods can also be chosen to adjust the above-mentioned extremum points and transition points in order to determine the zero-level extremum point Z0(x). i , y j ) to obtain.

[0048] S5: Based on the zero-level extremum point Z0(x i , y j ) a height position Z d (x i , y j ) of the object to be measured. Zd(xi,yj)=Δl(xi,yj)+Z0(xi,yj)

[0049] In an actual solution process, the extremum point Z0(x) i , y j Due to the zero-level partial envelope curve, an offset can occur in the solution; that is, there is a risk that the potential zero-level partial envelope curve will be incorrectly used instead of the actual zero-level partial envelope curve to regenerate the measurement data. Therefore, step S4 includes: S42. Adjustment of the zero-level extremum point Z0'(xi,yj) Z0 (x i , y j ) of the potential zero-level partial envelope curve, using preconditions to replace erroneous zero-level extremum point Z0(x) i , y j ).

[0050] The prerequisites can be set as needed and can be based on the requirement that continuous height data of the object to be measured does not exhibit any jumps.

[0051] In accordance with step S5, the procedure is applied to the first extremum point P. e (n a , x i , y j ) and the third extremum point P e (n c , x i , y j ) of the potential zero-level partial envelope curve applied to determine the zero-level extrema Z0'(xi,yj) and Z0''(xi,yj) to obtain the potential zero-level partial envelope curve.

[0052] This means that an adjustment to the first extreme value point P e (n a , x i , y j ) and their four adjacent transition points P e (n a-2 , x i , y j ), P e (n a-1 , x i , y j ), P e (n a+1 , x i ,y j ) and P e (n a+2 , x i , y j ) is carried out to determine the zero-level extrema Z0'(xi,yj) to obtain the potential zero-level partial envelope curve;

[0053] The same applies to an adjustment to the third extreme value point P. e (n c , x i , y j ) and its four adjacent transition points P e (n c-2 , x i , y j ), P e (n c-1 , x i , y j ), P e (n c+1 , x i , y j ) and P e (n c+2 , xi , y j ), to reach the zero-level extreme value point Z0''(xi,yj) to obtain the potential zero-level partial envelope curve.

[0054] Assuming that the surface of the step to be measured is smooth and that the determined three-dimensional shape data exhibit a clip-like jump, consideration is given to using the zero-level extremum Z0'(xi,yj) or Z0''(xi,yj) the potential zero-level envelope instead of the erroneous zero-level extremum point Z0(x) i , y j ) to use. Using equation (1), the height position of the object to be measured Z is determined. d (x i , y j ) recalculated.

[0055] Therefore, the method proposed by the present invention for calculating three-dimensional surface profiles by interference has, on the one hand, a lower computational complexity, since no Gaussian functions are used for filtering.

[0056] On the other hand, it does not require filtering all sample points, which increases the real-time capability of the algorithm. At the same time, the algorithm's high fit accuracy is achieved through the use of the steeper partial envelopment curve.

[0057] On the other hand, the present invention is also suitable for interferometers with narrowband laser sources, such as Fabry-Pérot interferometers, Michelson interferometers, Mach-Zehnder interferometers, Sagnac interferometers, Fizeau interferometers, etc.

[0058] In a preferred embodiment of the present inventory, the interferometer is calibrated in step S1 to obtain the peak space displacement Δl of the interferometer. This comprises the following steps: S11. Calibration of the interferometer using a standard mirror with known surface shape, calculation of the standard surface distribution Z(x i , y j ) of the standard mirror, which is obtained by the interferometer.

[0059] In another preferred embodiment of the present invention, an ideal standard planar reflector is selected as the standard mirror, and the interferometer is used with a standard planar reflector having a known surface shape and an ideal plane for the calibration of a broadband white light interferometer.

[0060] Due to the strong reflection signal and high contrast of the standard mirror, conventional methods such as the wavelet transformation method can be used to determine the surface distribution Z(x). i , y j ) of the standard plan mirror. This is considered the standard value.

[0061] In a further embodiment of the present invention, a spherical or non-spherical mirror with a known surface shape can also be selected as the standard mirror. By selecting a standard mirror with the same spectral reflection properties as the object to be measured, the similarity between the interferometric image and the actually measured interferometric image can be improved during calibration, thus increasing the measurement accuracy.

[0062] S12. Performing a temporal interference image series at each pixel measurement point on the standard mirror with the interferometer to determine a deformation distribution Z(x) i , y j ) of the standard mirror to calculate.

[0063] This includes the following steps: S121. Conservation of the zero-level partial envelope curve of the temporal interference image series of the standard mirror. S122. Use of the zero-level partial envelope of the temporal interference image series of the standard mirror to determine the extremum points and transition points of the zero-level partial envelope of the standard mirror. S123. Use of the extremum points and transition points of the zero-level partial envelope of the standard mirror to determine the height position of the extremum points of the zero-level partial envelope for each pixel measurement point on the standard seal. S124. Calculation of the deformation distribution Z(x) i , y j) of the standard mirror based on the altitude position.

[0064] The method for determining the extremum points and transition points of the zero-level partial envelopment curve of the standard mirror in step S12 is the same as the method for determining the extremum points and transition points of the zero-level partial envelopment curve of the stage in the embodiments described above, therefore it will not be explained again here.

[0065] S13. Calculation of the peak space shift Δl(x) caused by the light path incompatibility inside the interferometer i , y j ): Δl(xi,yj)=Z(xi,yj)−Z¯(xi,yj)

[0066] The Fig. 4a, Fig. 5a and Fig. Figures 6a show the three-dimensional surface profile at the same stair landing, obtained using the method of the present invention, the Fourier transformation method and the center of gravity method. Fig. 4b, Fig. 5b and Fig.Figure 6b shows the corresponding focus area cross-sectional diagrams.

[0067] It is evident that the use of the present invention results in a surface roughness (RMS value) of 0.038 µm for the upper surface and 0.009 µm for the lower surface. The height is 1.755 µm, with a difference of 6 nm from the standard value of 1.761 µm.

[0068] Compared to the conventional Fourier transformation method (RMS value for the upper surface is 0.045 µm, RMS value for the lower surface is 0.015 µm), the RMS value for the upper surface is reduced by 15.6% and for the lower surface by 40%.

[0069] Compared to the conventional center of gravity method (RMS value for the upper surface is 0.045 µm, RMS value for the lower surface is 0.017 µm), the RMS value for the upper surface is reduced by 15.6% and for the lower surface by 47%.

[0070] The data above demonstrate that the method of the present invention exhibits more accurate surface characteristics. The measured height measurement errors are in the range of ±0.01 µm (standard stair tread defines the error range), which represents a very high level of reliability.

[0071] On the other hand, the step sample consists of silicon as a base, produced by chemical etching. The silicon material tends to be black and exhibits relatively low spectral reflectance, resulting in a relatively low signal-to-noise ratio, and therefore the solution result is not ideal. Nevertheless, the use of the method presented here allows for significant improvements in surface roughness (RMS value) and keeps the height difference within the calibration range. It can be applied to samples with low reflectance and offers prospects for use in industrial measurements, scientific investigations, and other practical applications.

Claims

[1] A method for calculating three-dimensional surface profiles by interference, characterized by that includes the following steps: S1. Calibration of an interferometer using a standard mirror to determine a peak space displacement Δl of the interferometer; S2. Use of the interferometer to acquire a temporal interference image series for each pixel measurement point P(x) i , y j ) on an object to be measured, wherein the temporal interference image series consists of N interference images with interference fringes; S3. Obtaining a zero-level partial envelope and a potential zero-level partial envelope of the temporal interference image series; S4. Use of the zero-level partial envelope curve to determine a zero-level extremum point Z0(x) i , y j ) of the zero-level partial envelope curve; S5. Calculation of an altitude position Z d (x i , yj ) of the object to be measured based on the zero-level extremum point Z0(x i , y j ): Zd(xi,yj)=Δl(xi,yj)+Z0(xi,yj) [2] The method for calculating three-dimensional surface profiles by interference according to claim 1, characterized by that the standard mirror is an ideal standard plan reflector or a spherical or non-spherical mirror; wherein the standard mirror has the same spectral reflection properties as the object to be measured. [3] The method for calculating three-dimensional surface profiles by interference according to claim 1, characterized by , that step S3 comprises the following steps: S31. Determine if N. Sample points P(n, x) i , y j ) at the same pixel position (x i , y j ) of the temporal interference pattern series extrema P e (n, x i , y j ) or transition points P t (n, x i , y j) are, where n ∈ [1, M], M is a given value; S32. Obtaining the zero-level partial envelope curve and the potential zero-level partial envelope curve of the temporal interference image series based on the determined extreme value points P e (n, x i , y j ). [4] The method for calculating three-dimensional surface profiles by interference according to claim 3, characterized by , that step S31 includes the following steps: S311. Exposure of each sample point P(n, x) i , y j ) on N. Interference patterns for recording intensity values ​​I(n, x) i , y j ) of each sample point P(n, x i , y j ) on the interference patterns; S312. Construction of a data cube S based on the intensity values ​​I(n, x) i ,y j ) of the N. test points P(n, x i , y j) on interference patterns, the N. sample points are located at the same position in the temporal interference pattern sequence, The model for constructing the data cube S is as follows: S(n,i,j)=[I(n+1,xi,yj)−I(n,xi,yj)]×[I(n,xi,yj)−I(n−1,xi,yj)] where, I(n, x i , y j ) the intensity value of the sample point P(n, x) i , y j ) represented on the No. n image of the temporal interference pattern series; I(n+1, x i , y j ) the intensity value of the sample point P(n+1, x i , y j ) represented on the No. n+1 image of the temporal interference image series; I(n -1, x i , y j ) the intensity value of the sample point P(n-1, x i , y j ) represented on the No. n-1 image of the temporal interference image series; S313. Determine whether the sample point P(n, x) i , y j) an extreme point of the temporal interference pattern series is: if S(n, i, j) ≤ 0 , then the test point is P(n, x) i , y j ) an extremum point P e (n, x i , y j ); If S(n, i, j) > 0, then the test point is P(n, x). i , y j ) a transition point P t (n, x i , y j ). [5] The method for calculating three-dimensional surface profiles by interference according to claim 3, characterized by , that step S32 is the following method: Sorting of each pixel measurement point P(x i , y j ) corresponds to an extremum point on the temporal interference pattern series, where at least three intensity values ​​are selected in descending order: a first extremum point P e (n a , x i , y j ), a second extremum point P e (n b , x i , y j) and a third extremum point P e (n c , x i , y j ), where the following relationship exists: Ie(na,xi,yj) <Ie(nb,xi,yj); Ie(nb,xi,yj)>Ie(nc,xi,yj); where, I e (n a , x i , y j ) the intensity value of the first extreme value point P e (n a , x i , y j ) is, I e (n b , x i , y j ) the intensity value of the second extreme point P e (n b , x i , y j ) is, I e (n e , x i , y j ) the intensity value of the third extreme point P e (n c , x i , y j ) is; then lies P e (n b , x i , y j ) on the zero-level partial envelope curve; The first extreme value point P e (na , x i , y j ) and the third extremum point P e (n c , x i , y j ) lie on the potential zero-level partial envelope curve. [6] The method for calculating three-dimensional surface profiles by interference according to claim 1, characterized by , that step S4 comprises the following steps: S41. Use of the extremum points P e (n a , x i , y j ) and transition points P t (n k , x i , y j ) on the zero-level partial envelope curve to determine the zero-level extremum point Z0(x i , y j ) of the zero-level partial envelope curve. [7] The method for calculating three-dimensional surface profiles by interference according to claim 6, characterized by , that the method for determining the zero-level extremum point Z0(x i , y j ) includes the following steps: Selection of at least two first transition points P t (n k+1 , x i , y j ) and second transition points P t (n k-1 , x i , y j ), which are located near the extremum point P e (n k , x i , y j ) of the zero-level partial envelope curve; use of a fitting method to fit the extremum point P e (n a , x i , y j ), of the first transition point P t (n k+1 , x i , y j ) and the second transition point P t (n k-1 , x i , y j ) of the zero-level partial envelope curve to determine the zero-level extremum point Z0(x i , y j ). [8] The method for calculating three-dimensional surface profiles by interference according to claim 7, characterized bythat the adjustment method includes at least one of the following methods: adjustment, center of gravity method or interpolation method. [9] The method for calculating three-dimensional surface profiles by interference according to claim 1, characterized by , that step S4 further includes the following steps: S42. Adjustment of the zero-level extremum point Z0'(xi,yj) of the potential zero-level partial envelope curve, using preconditions to replace erroneous zero-level extremum point Z0(x) i , y j ); The prerequisite is: Continuous surface measurement data of the object to be measured show no height jumps. [10] The method for calculating three-dimensional surface profiles by interference according to claim 1, characterized by , that step S1 comprises the following steps: S11. Use of a standard mirror with known surface shape for calibrating the interferometer and obtaining the standard surface distribution Z(x) i , y j ) of the standard mirror; S12. Performing a temporal interference image series at each pixel measurement point on the standard mirror with the interferometer to determine a deformation distribution Z(x) i , y j ) of the standard mirror to calculate; S13. Calculation of the peak space shift Δl(x) caused by light path inequality inside the interferometer i , y j ): Δl(xi,yj)=Z(xi,yj)−Z¯(xi,yj) [11] The method for calculating three-dimensional surface profiles by interference according to claim 1 or 10, characterized by that the interferometer is a broadband white light interferometer or a narrowband laser interferometer.

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