White light interferometer and method for determining height map using white light interferometer

Abstract

To provide an improved method for determining a height map of a sample surface of a sample having reduced vibration dependency compared to a known method.SOLUTION: A method for determining a height map includes: performing a Hilbert transform on an eigenvector of a covariance matrix associated with the biggest eigenvalue to obtain a complex Hilbert transformed eigenvector; determining a reference phase for a reference pixel of a plurality of pixels, on the basis of a ratio of a vector component of a real part and a vector component of an imaginary part of the Hilbert transformed eigenvector associated with the reference pixel; determining if the measured phase of the reference pixel corresponds to the reference phase of the reference pixel; and when the measured phase of the reference pixel does not correspond to the reference phase, reversing a global sign of the determined phase.SELECTED DRAWING: None

Description

Technical Field

[0001] The present invention relates to a method for determining a height map of the surface of a sample by white light interferometry, which uses a white light interferometer comprising a broadband light source and an optical sensor having a plurality of pixels. The present invention further relates to a white light interferometer comprising a broadband light source, an optical sensor having a plurality of pixels, and a processor configured to execute the method of the present invention. The present invention further relates to a digital data carrier comprising a computer program which, when executed on a processor of a white light interferometer according to the present invention, causes the white light interferometer to execute the method according to the present invention.

Background Art

[0002] White light interferometry is a standard technique for determining a height map of the surface of a sample. White light interferometry can enable a very high accuracy of about 1 nm. An example of white light interferometry for determining a height map can be found in European Patent No. 2314982, in which the zero-crossing method is used.

Summary of the Invention

Problems to be Solved by the Invention

[0003] With the increasing requirements for measurement accuracy in the measurement of height maps, there is a need to improve the accuracy of white light interferometry, for example when used to determine a height map. The disadvantage of using a white light interferometer to determine the height map of a sample is that vibrations of the sample relative to the white light interferometer can cause inaccuracies in the determined height map. A white light interferometer relies on determining the phase difference of the reflected light due to differences in the optical path lengths of the light traveling along the optical path within the interferometer. The optical path length can be affected by vibrations of the sample, which in turn affects the phase difference and thus results in an inaccurate height map.

[0004] Vibration of the sample with respect to the white light interferometer can occur due to the instability of the sample holder. The sample holder may be affected by various types of vibrations from the surroundings of the white light interferometer, for example, caused by the movement of a vehicle or a person. The sample holder can also be affected by vibrations that can arise from the presence of other equipment typically present in a laboratory or manufacturing environment.

[0005] If sufficient care is not taken to eliminate the influence of vibrations on the sample, the accuracy of the determined height map may be adversely affected. In some cases, the determined height map may be useless because its error is too large. Vibrations can affect the overall accuracy, reliability, and reproducibility of the results of the white light interferometer.

[0006] As a known method for reducing the influence of vibrations on the results of the white light interferometer, there is a method of using a vibration damper to isolate the white light interferometer from the influence of environmental vibrations. The drawback of these known methods is the increase in the overall cost. Also, depending on the type of damper and the type of vibration, the influence of vibrations may not be reduced sufficiently.

[0007] There is a need for a method for determining a height map of the sample surface of a sample with reduced dependence on vibrations.

[0008] An object of the present invention is to provide an improved method for determining a height map of the sample surface of a sample having reduced vibration dependence as compared with known methods. A further object of the present invention is to provide an alternative method for determining a height map of the sample surface of a sample having reduced vibration dependence as compared with known methods.

Means for Solving the Problem

[0009] The object of the present invention is achieved by the method according to claim 1. The present invention relies on the insight that using an algorithm based on principal component analysis of a stack of interferograms makes it possible to determine a height map for reducing the dependence on random phase shifts in the interferograms used, such as random phase shifts caused by vibrations. The method based on principal component analysis makes it possible to separate the random phase shifts from the phase shifts related to the height of the sample. The phase shifts related to the height of the sample are referred to herein as the measured phase. As a result, the present invention enables an improved or alternative method for determining a height map compared to known methods for determining a height map using known methods for reducing the influence of vibrations.

[0010] The present invention relates to a method for determining a height map of a sample surface of a sample by white light interferometry. The height map of the sample surface can be determined to determine the roughness of the sample surface. The height map of the sample surface may further be determined, for example, to provide quality control of a manufacturing process. White light interferometry is a non-contact optical method for measuring the surface height of a surface having a surface profile.

[0011] This method utilizes a white light interferometer comprising a broadband light source and an optical sensor having a plurality of pixels. The white light interferometer may further comprise a processor for causing the white light interferometer to determine a height map according to a certain method, for example, the method of the present invention. The light source can emit light to a beam splitter that divides the light into a reference light beam and a measurement light beam. The reference light beam can follow a first path towards the optical sensor, and the measurement light beam can follow a second path that reflects on the sample surface and then heads towards the optical sensor. The two light beams interfere with each other to generate an interference pattern, enabling the interferometer to measure the interference wave corresponding to the sample surface at a specific position of the sample surface relative to the interferometer. The height difference of the sample surface results in slightly different travel distances for different portions of the measurement light beam, which is converted into fringes in the interference wave through the resulting relative phase difference. Thus, the height of the sample surface can be extracted by associating the height of the sample surface with the obtained relative phase difference. The interferometer may further comprise a sample holder or a sample stage movable to different measurement positions with respect to the focal plane of the optical sensor in a direction parallel to the measurement light beam, for example.

[0012] This method includes obtaining a plurality of interference waves by performing a vertical scan of the surface of a sample so as to pass through the focal plane of an optical sensor, each interference wave including the light intensity measured for each pixel of the optical sensor at each height with respect to the surface. Thus, each of the plurality of interference waves corresponds to the height of the surface of the sample with respect to the optical sensor and / or the optical plane. To obtain the plurality of interference waves, the sample surface is moved vertically, for example, by vertical scanning. The vertical direction is understood to be the direction parallel to the measurement light beam at the sample surface. The sample surface may be moved between different measurement positions, and the interference wave is determined at each measurement position. The interference wave can be represented, for example, by an M×N matrix when the optical sensor has M×N pixels, and each entry of the M×N matrix includes the intensity of the corresponding pixel. The intensity includes information regarding the relative phase of the light measured at that pixel with respect to the corresponding interference wave. Thus, by acquiring Z plurality of interference waves, a total of Z M×N matrices can be acquired. For example, the Z M×N matrices can be represented by a single three-dimensional M×N×Z matrix. The three-dimensional M×N×Z matrix representing the plurality of interference waves can be transformed into a two-dimensional M*N×Z matrix A M*NxZ can be deformed. The two-dimensional M*NxZ matrix A M*NxZ can be written as a sum as follows. A M*NxZ =a Z u M*N +b Z v M*N

[0013] Here, u M*N =Bcos(Φ M*N ) and v M*N =Bsin(Φ M*N ), where Φ M*N is the measured phase related to the height of the surface at the pixel. B is the modulation amplitude, and a Z and b Z depend on the random phase shift and do not depend on Φ M*N .

[0014] The two signals u M*N and v M*N are AM*NxZ is approximately uncorrelated so as to be decomposable into u M*N and v M*N and thus it can be shown that the dependence on the random phase shift associated with the random vibration of the sample with respect to the interferometer is removed.

[0015] The signals u M*N and v M*N can be obtained by performing principal component analysis on a plurality of interference waves, for example, on a matrix representing a plurality of interference waves A M*N ×Z. For this purpose, the method further includes determining a covariance matrix for the plurality of interference waves. The covariance matrix can be a square matrix and a symmetric matrix that can be obtained by multiplying the matrix by its own transpose matrix. The deformed two-dimensional matrix A M*NxZ may be multiplied by its transpose matrix so that an M*N×M*N covariance matrix of a plurality of interference waves is obtained.

[0016] To determine the principal components of a plurality of interference waves, singular value decomposition is performed on the corresponding covariance matrix. Singular value decomposition makes it possible to decompose a square matrix into an orthogonal matrix and a diagonal matrix. And the principal components of the covariance matrix can be obtained, for example, by calculating the projection of the matrix A M*NxZ onto the orthogonal matrix of the singular value decomposition. Y = ΦA M*NxZ Here, Y includes the principal components of A M*NxZ i.e., the principal components of a plurality of interference waves, and Φ is the orthogonal matrix of the singular value decomposition.

[0017] It can be shown that the principal component corresponding to the largest eigenvalue and the principal component corresponding to the second largest eigenvalue correspond to the signals u M*N and v M*N (which is a vector having each entry associated with a pixel of the optical sensor and is proportional to the sine and cosine of the measured phase). Thus, u M*N and v M*NBy calculating the ratio of the components, the ratios of sine and cosine can be obtained. As a result, for example, by calculating the tangent of such a ratio, it becomes possible to obtain the measured phase at each pixel.

[0018] Therefore, the method includes a step of selecting a first principal component related to the maximum eigenvalue of the covariance matrix and a second principal component related to the second maximum eigenvalue of the covariance matrix, and a step of calculating the ratio of the vector components of the first principal component and the second principal component. The measured phase can be determined based on this ratio. The height map is obtained based on the phase measured for each pixel, for example, based on the average wavelength of a broadband light source.

[0019] The present invention is further based on the insight that the measured phase obtained for a pixel has an undetermined global sign. This global sign is due to the result of using the orthogonal matrix Φ in the singular value decomposition of the covariance matrix and the determination of the principal components. As can be understood, since the orthogonal matrix Φ appears twice in the singular value decomposition of the covariance matrix, it is not uniquely determined due to the possible global sign change. As a result, the determined principal components are also not uniquely determined up to the sign, so the global sign of the measured phase becomes unknown. The inventors have recognized that the correct global sign can be determined by looking at the phases of the first and second principal components. The first principal component and the second principal component, viewed as vectors, always have a phase difference of ±π / 2 when the first principal component lags the second principal component by π / 2, and have the correct global sign of the height map. If this is not the case, the global sign must be inverted with respect to the sign used when determining the Hilbert-transformed eigenvector in order to obtain the correct height map.

[0020] To determine whether the global sign of the measured phase is correct, the method further includes performing a Hilbert transform on the eigenvector of the covariance matrix associated with the maximum eigenvalue of the covariance matrix to obtain a complex Hilbert transform eigenvector. The real part of the Hilbert transform eigenvector lags behind the imaginary part of the Hilbert transform eigenvector by exactly π / 2.

[0021] Accordingly, based on the ratio of the vector components of the real and imaginary parts of the eigenvector in which each vector component of the Hilbert-transformed eigenvector is associated with a reference pixel, for example, by calculating the arctangent of the inverse of the ratio, the reference phase of the reference pixel of the pixel is determined, and by determining whether the measured phase of the reference pixel corresponds to the reference phase of the reference pixel, it is checked whether the measured phase of the reference pixel corresponds to the reference phase. If the measured phase does not correspond to the reference phase, for example, by inverting the global sign of the measured phase, it is possible to check whether the global sign of the measured phase is correct. Accordingly, this makes it possible to determine a height map of the sample surface having the correct global sign.

[0022] In an embodiment, determining whether the measured phase of the reference pixel corresponds to the reference phase of the reference pixel includes the following processing. - Calculating the magnitude of the sum of the measured phase and the reference phase of the reference pixel, and calculating the magnitude of the difference between the measured phase and the reference phase of the reference pixel - If the magnitude of the difference is smaller than the magnitude of the sum, determining that the measured phase of the reference pixel corresponds to the reference phase, and if the magnitude of the difference is larger than the magnitude of the sum, determining that the measured phase of the reference pixel does not correspond to the reference phase This provides an explicit step for determining whether the measured phase of the reference pixel corresponds to the reference phase of the reference pixel.

[0023] The object of the present invention is also achieved by the method of claim 3, which obtains the phase measured in the same way as the method of claim 1, but differs in determining the correct global sign. The method according to claim 3 includes the following processes. - performing a Fourier transform on the first eigenvector of the covariance matrix associated with the largest eigenvalue and performing a Fourier transform on the second eigenvector of the covariance matrix associated with the second largest eigenvalue - determining the highest amplitude frequency of the Fourier-transformed first eigenvector - calculating the first Fourier phase of the Fourier-transformed first eigenvector and the second Fourier phase of the Fourier-transformed second eigenvector associated with the determined highest amplitude frequency - determining the difference between the first Fourier phase and the second Fourier phase by subtracting the second Fourier phase from the first Fourier phase - when the difference between the first Fourier phase and the second Fourier phase is between 0 and π modulo 2π, inverting the global sign of the determined height map

[0024] Thus, the phase difference between the first principal component and the second principal component is checked by examining a plurality of phase differences of the Fourier-transformed vectors associated with each other. The global sign of the height map is inverted with respect to the sign used to check the difference between the Fourier phases when those differences are between 0 and π modulo 2π.

[0025] In an embodiment, the ratio of the vector component of the first principal component to the vector component of the second principal component is proportional to the quotient of dividing the vector component of the second principal component by the vector component of the first principal component. This may make it possible to calculate the arctangent to determine the measured phase.

[0026] In an embodiment, determining the covariance matrix includes removing the average intensity of a plurality of interfering waves. The average intensity can be determined by determining the average of the intensities of the plurality of interfering waves. The average intensity so determined can be removed from each entry of the matrix representation of the plurality of interfering waves.

[0027] In an embodiment, determining the covariance matrix includes transforming a three-dimensional M×N×Z matrix representing a plurality of interfering waves into a two-dimensional M*N×Z matrix, where the optical sensor has M×N pixels and the stack includes Z interfering waves.

[0028] In an embodiment, determining the height map based on the measured phases determined for each pixel includes multiplying the determined measured phases by the center wavelength of the broadband light source.

[0029] The present invention further relates to a white light interferometer comprising a broadband light source, an optical sensor comprising pixels, and a processor for acquiring a height map of the surface of a sample, wherein the white light interferometer, for example its processor, is configured to execute the method according to the present invention.

[0030] In an embodiment, the white light interferometer is configured to perform the following processes. - A step of acquiring a plurality of interfering waves by performing a vertical scan of the surface so as to pass through the focal plane of the optical sensor, each interfering wave including the measured light intensity for each pixel of the optical sensor at each height with respect to the surface The processor is configured as follows. - A step of determining a covariance matrix for a plurality of interfering waves - A step of determining the principal components of the plurality of interfering waves by performing a singular value decomposition of the covariance matrix - A step of selecting a first principal component associated with the largest eigenvalue of the covariance matrix and a second principal component associated with the second largest eigenvalue of the covariance matrix - For each pixel of the pixels, determining the measured phase by calculating the arctangent of the inverse ratio of the vector components of the first and second principal components, wherein the vector components correspond to the respective pixels - Determining a height map based on the measured phase determined for each pixel

[0031] The processor is further configured to perform the following processing. - Performing a Hilbert transform on the eigenvector of the covariance matrix associated with the largest eigenvalue to obtain a complex Hilbert-transformed eigenvector - Determining the reference phase of a pixel with respect to a reference pixel by calculating the arctangent of the inverse ratio of the vector component of the real part and the vector component of the imaginary part of the Hilbert-transformed eigenvector, wherein the vector components correspond to the reference pixel - Determining whether the measured phase of the reference pixel corresponds to the reference phase - If the measured phase of the reference pixel does not correspond to the reference phase, inverting the global sign of the determined height map

[0032] In an embodiment of the white light interferometer, the processor is configured to perform the following processing. - Calculating the magnitude of the sum of the measured phase and the reference phase of the reference pixel and calculating the magnitude of the difference between the measured phase and the reference phase of the reference pixel - If the magnitude of the difference is smaller than the magnitude of the sum, determining that the measured phase of the reference pixel corresponds to the reference phase, and if the magnitude of the difference is larger than the magnitude of the sum, determining that the measured phase of the reference pixel does not correspond to the reference phase

[0033] In an embodiment, the white light interferometer is configured to perform the following processing. - Obtaining a plurality of interference waves by performing a vertical scan of the surface so as to pass through the focal plane of the optical sensor, wherein each interference wave includes the measured light intensity for each pixel of the optical sensor at each height with respect to the surface The processor is configured to perform the following processes. - Determining a covariance matrix for a plurality of interfering waves - Determining principal components of the plurality of interfering waves by performing singular value decomposition of the covariance matrix - Selecting a first principal component related to the maximum eigenvalue of the covariance matrix and a second principal component related to the second maximum eigenvalue of the covariance matrix - For each pixel of the pixels, determining the measured phase by calculating the arctangent of the ratio of the vector components of the first and second principal components, wherein the vector components correspond to the respective pixels - Determining a height map based on the measured phases determined for each pixel

[0034] The processor is further configured to perform the following processes. - Performing a Fourier transform on a first eigenvector of the covariance matrix related to the largest eigenvalue and performing a Fourier transform on a second eigenvector of the covariance matrix related to the second largest eigenvalue - Determining the highest amplitude frequency of the Fourier-transformed first eigenvector - Calculating a first Fourier phase of the Fourier-transformed first eigenvector and a second Fourier phase of the Fourier-transformed second eigenvector related to the determined highest amplitude frequency - Determining the difference between the first Fourier phase and the second Fourier phase by subtracting the second Fourier phase from the first Fourier phase - If the difference between the first Fourier phase and the second Fourier phase is between 0 and π modulo 2π, inverting the global sign of the determined height map

[0035] The present invention further relates to a digital data carrier including a computer program that causes a white light interferometer to execute the method according to the present invention when executed on a processor of the white light interferometer according to the present invention.

[0036] Here, embodiments of the present invention will be described by way of example with reference to the accompanying drawings in which corresponding reference numerals indicate corresponding parts.

Brief Description of the Drawings

[0037]

Figure 1

Figure 2

Mode for Carrying Out the Invention

[0038] FIG. 1 shows an example of a white light interferometer 1 for determining a height map. The interferometer includes a broadband light source 2. The light 3 from the light source 2 can pass through a lens 4a, a beam splitter 4b, and a second lens 4c. The light 3 that has passed through the second lens 4c is split by a beam splitter 5 into a first partial light beam 3a and a second partial light beam 3b. The first partial light beam 3a is directed toward the surface 6 of the sample 7. The second partial light beam 3b is directed toward a reference mirror 8 having a reference surface 9. After reflection by the mirrors 6 and 8, the partial light beams 3a, 3b are combined and propagated to an optical sensor 10 having a plurality of pixels. For example, the optical sensor 10 may be a CCD array camera. This setting generates an interference signal on the optical sensor 10.

[0039] The pixels of the optical sensor 10 can correspond to spatial positions on the sample surface 6 and the reference surface 9. After vertical scanning, each pixel can have an intensity signal associated with the height at the corresponding spatial position of the sample 7.

[0040] The sample 7 may be moved so as to pass through the focal plane of the second lens 4c, and for a plurality of positions of the sample 7 with respect to the interferometer 1, interference waves are captured by the optical sensor 10. In this way, a plurality of interference waves can be acquired (110) by the interferometer 1, and the plurality of interference waves can be received by a processor 11, enabling the processor to determine a height map based on the method of the present invention.

[0041] FIG. 2 shows a flowchart of a method for determining a height map. The method includes the following processes.

[0042] Step 101 of obtaining a plurality of interference waves by vertically scanning the surface 6 through the focal plane of the optical sensor 10. Each interference wave includes the light intensity measured for each pixel of the optical sensor 10 at each height of the surface 6 with respect to the focal plane.

[0043] Step 102 of determining a covariance matrix for the plurality of interference waves.

[0044] Step 103 of determining the principal components of the plurality of interference waves by performing singular value decomposition of the covariance matrix.

[0045] Step 104 of selecting a first principal component related to the maximum eigenvalue of the covariance matrix and a second principal component related to the second maximum eigenvalue of the covariance matrix.

[0046] Step 105 of determining the measured phase for each pixel of the plurality of pixels based on the ratio of the vector component of the first principal component and the vector component of the second principal component (for example, by calculating the arctangent of the inverse of the ratio). Here, each vector component corresponds to each pixel.

[0047] As described above and as can be seen from FIG. 2, the present invention is based on both insights that the correct sign is obtained when the first principal component lags the second principal component by π / 2, enabling the determination of the correct global sign before measuring the phase based on two methods. Thus, step 106 of determining a height map based on the phase measured for each pixel includes any of the following: - Obtaining a complex Hilbert transform eigenvector by performing a Hilbert transform on the eigenvector of the covariance matrix related to the maximum eigenvalue of the covariance matrix in step 110. Step 111 of determining the reference phase of a pixel with respect to a reference pixel based on the ratio of the real and imaginary vector components of the Hilbert-transformed eigenvector (e.g., based on calculating the arctangent of the ratio). Here, each vector component is associated with the reference pixel. Step 112 of determining whether the measured phase of the reference pixel corresponds to the reference phase of the reference pixel. Step 113 of inverting the global sign of the measured phase, e.g., in the height map, if the measured phase of the reference pixel does not correspond to the reference phase.

[0048] Alternatively, step 106 of determining a height map based on the phase measured for each pixel includes the following processing. Step 120 of performing a Fourier transform on the first eigenvector of the covariance matrix associated with the largest eigenvalue and performing a Fourier transform on the second eigenvector of the covariance matrix associated with the second largest eigenvalue. Step 121 of determining the highest amplitude frequency of the Fourier-transformed first eigenvector. Step 122 of calculating a first Fourier phase of the Fourier-transformed first eigenvector corresponding to the determined highest amplitude frequency and a second Fourier phase of the Fourier-transformed second eigenvector. Step 123 of determining the difference between the first Fourier phase and the second Fourier phase by subtracting the second Fourier phase from the first Fourier phase. Step 124 of inverting the global sign of the measured phase, e.g., in the height map, if the difference between the first Fourier phase and the second Fourier phase is between 0 and π modulo 2π.

Claims

1. A method for determining a height map of a sample surface by white light interference using a white light interferometer comprising a broadband light source and an optical sensor having a plurality of pixels, comprising: acquiring a plurality of interference waves by vertically scanning the sample surface so as to pass through the focal plane of the optical sensor, each of the interference waves including the light intensity measured for a corresponding pixel of the optical sensor at each height of the sample surface with respect to the focal plane; determining a covariance matrix for the plurality of interference waves; determining principal components of the plurality of interference waves by performing singular value decomposition of the covariance matrix; selecting a first principal component associated with the largest eigenvalue of the covariance matrix and a second principal component associated with a second largest eigenvalue of the covariance matrix; determining the phase measured for each of the plurality of pixels based on a ratio of a vector component of the first principal component and a vector component of the second principal component corresponding to each pixel of the plurality of pixels; determining the height map based on the phase measured for each of the respective pixels; comprising: the step of determining the height map comprises: obtaining a complex Hilbert-transformed eigenvector by performing a Hilbert transform on an eigenvector of the covariance matrix associated with the largest eigenvalue; determining a reference phase of a reference pixel among the plurality of pixels, the reference phase being determined based on a ratio of a vector component of a real part and a vector component of an imaginary part of the Hilbert-transformed eigenvector corresponding to the reference pixel; determining whether the measured phase of the reference pixel corresponds to the reference phase of the reference pixel; a method comprising, when the measured phase of the reference pixel does not correspond to the reference phase, reversing the global sign of the measured phase.

2. The step of determining whether the measured phase of the reference pixel corresponds to the reference phase of the reference pixel comprises: calculating a magnitude of a sum of the measured phase and the reference phase of the reference pixel and calculating a magnitude of a difference between the measured phase and the reference phase of the reference pixel. When the magnitude of the difference is smaller than the magnitude of the sum, determining that the measured phase of the reference pixel corresponds to the reference phase, and when the magnitude of the difference is larger than the magnitude of the sum, determining that the measured phase of the reference pixel does not correspond to the reference phase; The method according to claim 1, comprising:

3. A method for determining a height map of a surface of a sample by white light interferometry using a white light interferometer including a broadband light source and an optical sensor having a plurality of pixels, acquiring a plurality of interference waves by vertically scanning the surface so as to pass through a focal plane of the optical sensor, each of the interference waves including an optical intensity measured for a corresponding pixel of the optical sensor at each height with respect to the surface; determining a covariance matrix for the plurality of interference waves; determining principal components of the plurality of interference waves by performing singular value decomposition of the covariance matrix; selecting a first principal component corresponding to a maximum eigenvalue of the covariance matrix and a second principal component corresponding to a second maximum eigenvalue of the covariance matrix; determining a phase measured for each of the plurality of pixels based on a ratio of a vector component of the first principal component and a vector component of the second principal component corresponding to each pixel of the plurality of pixels; and determining the height map based on the phase measured for each of the pixels, The step of determining the height map includes performing a Fourier transform of a first eigenvector of the covariance matrix corresponding to the maximum eigenvalue and performing a Fourier transform of a second eigenvector of the covariance matrix corresponding to the second maximum eigenvalue; determining a highest amplitude frequency of the Fourier-transformed first eigenvector; calculating a first Fourier phase of the Fourier-transformed first eigenvector and a second Fourier phase of the Fourier-transformed second eigenvector corresponding to the determined highest amplitude frequency; determining a difference between the first Fourier phase and the second Fourier phase by subtracting the second Fourier phase from the first Fourier phase; A method having a step of inverting the global sign of the measured phase when the difference between the first Fourier phase and the second Fourier phase is between 0 and π modulo 2π.

4. The ratio of the vector component of the first principal component to the vector component of the second principal component is proportional to the value obtained by dividing the vector component of the second principal component by the vector component of the first principal component. The method according to any one of claims 1 to 3.

5. The method according to any one of claims 1 to 3, wherein the step of determining the covariance matrix includes a step of removing the average intensity of the plurality of interference waves.

6. The step of determining the covariance matrix includes transforming a three-dimensional M×N×Z matrix representing the plurality of interference waves into a two-dimensional M*N×Z matrix, the optical sensor has M×N pixels, and the plurality of interference waves includes Z interference waves. The method according to any one of claims 1 to 3.

7. The step of determining the height map based on the phase measured for each pixel includes a step of multiplying the determined measured phase by the central wavelength of the broadband light source. The method according to any one of claims 1 to 3.

8. A white light interferometer comprising a broadband light source, an optical sensor having pixels, and a processor for obtaining a height map of the surface of a sample, wherein the processor is configured to execute the method according to any one of claims 1 to 3.

9. The white light interferometer is configured to perform a step of obtaining a plurality of interference waves by vertically scanning the surface so as to pass through the focal plane of the optical sensor, each of the interference waves including the light intensity measured for the corresponding pixel of the optical sensor at each height with respect to the surface. The processor is configured to perform a step of determining a covariance matrix for the plurality of interference waves, a step of determining the principal components of the plurality of interference waves by performing singular value decomposition of the covariance matrix, and a step of selecting a first principal component associated with the maximum eigenvalue of the covariance matrix and a second principal component associated with the second maximum eigenvalue of the covariance matrix. By calculating the arctangent of the inverse ratio of the vector component of the first principal component and the vector component of the second principal component corresponding to each pixel of the plurality of pixels, determining the phase measured for each pixel of the plurality of pixels; Determining the height map based on the phase measured for each pixel; and is configured to execute, The step of determining the height map includes: Obtaining a complex Hilbert-transformed eigenvector by performing a Hilbert transform on the eigenvector of the covariance matrix associated with the largest eigenvalue; Determining a reference phase of a reference pixel among the plurality of pixels, the step of determining the reference phase based on the ratio of the vector component of the real part and the vector component of the imaginary part of the Hilbert-transformed eigenvector corresponding to the reference pixel; Determining whether the measured phase of the reference pixel corresponds to the reference phase of the reference pixel; When the measured phase of the reference pixel does not correspond to the reference phase, reversing the global sign of the measured phase. The white light interferometer according to claim 8.

10. The processor is configured to: Calculating the magnitude of the sum of the measured phase of the reference pixel and the reference phase, and calculating the magnitude of the difference between the measured phase of the reference pixel and the reference phase; When the magnitude of the difference is smaller than the magnitude of the sum, determining that the measured phase of the reference pixel corresponds to the reference phase, and when the magnitude of the difference is larger than the magnitude of the sum, determining that the measured phase of the reference pixel does not correspond to the reference phase. The white light interferometer according to claim 9.

11. The white light interferometer is configured to: Vertically scanning the surface so as to pass through the focal plane of the optical sensor to obtain a plurality of interference waves, each of the interference waves including the light intensity measured for the corresponding pixel of the optical sensor at each height with respect to the surface; The processor is configured to: Determining a covariance matrix for the plurality of interference waves; Determining the principal components of the plurality of interference waves by performing a singular value decomposition of the covariance matrix; selecting a first principal component related to the maximum eigenvalue of the covariance matrix and a second principal component related to the second maximum eigenvalue of the covariance matrix; determining the phase measured for each of the plurality of pixels based on a ratio of a vector component of the first principal component and a vector component of the second principal component corresponding to each of the plurality of pixels; configured to execute a step of determining the height map based on the phase measured for each of the pixels; the step of determining the height map includes: performing a Fourier transform on a first eigenvector of the covariance matrix corresponding to the maximum eigenvalue and performing a Fourier transform on a second eigenvector of the covariance matrix corresponding to the second maximum eigenvalue; determining a highest amplitude frequency of the Fourier-transformed first eigenvector; calculating a first Fourier phase of the Fourier-transformed first eigenvector and a second Fourier phase of the Fourier-transformed second eigenvector corresponding to the determined highest amplitude frequency; determining a difference between the first Fourier phase and the second Fourier phase by subtracting the second Fourier phase from the first Fourier phase; when the difference between the first Fourier phase and the second Fourier phase is between 0 and π modulo 2π, reversing the global sign of the measured phase; The white light interferometer according to claim 8.

12. A computer program for causing the white light interferometer to execute the method according to any one of claims 1 to 3 when executed on a processor of the white light interferometer according to claim 8.

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