Method for determining height map using white light interferometer and white light interferometer therefor

Abstract

The invention relates to a method for determining a height map of a surface of a sample by white light interferometry, wherein a white light interferometer with a broadband light source and an optical sensor comprising pixels is used. The invention also relates to a white light interferometer comprising a broadband light source, an optical sensor comprising pixels and a processor configured to perform the method of the invention. The invention also relates to a digital data carrier comprising a computer program which, when executed on a processor of a white light interferometer according to the invention, causes the white light interferometer to execute the method according to the invention.

Description

Technical Field

[0001] The present invention relates to a method for determining a height map of a surface of a sample by white light interferometry, wherein a white light interferometer comprising a broadband light source and an optical sensor having a plurality of pixels is used. The present invention also relates to a white light interferometer comprising a broadband light source, an optical sensor having a plurality of pixels, and a processor configured to perform the method of the present invention. The present invention also relates to a digital data carrier comprising a computer program which, when run on a processor of a white light interferometer according to the present invention, causes the white light interferometer to perform the method according to the present invention. Background Art

[0002] White light interferometry is a standard technique for determining a height map of a surface of a sample. White light interferometry can allow a very high precision of about 1 nm. An example of a method of white light interferometry for determining a height map can be found in EP2314982B1, where a zero phase crossing method is used.

[0003] As the requirements for measurement accuracy continue to increase, for example, in the measurement of a height map, it is necessary to increase the accuracy of white light interferometry, for example, when used to determine a height map. A disadvantage of using white light interferometry to determine a height map of a sample is that vibrations of the sample relative to the white light interferometer may result in an inaccurate determined height map. White light interferometry relies on determining the phase difference of the reflected light caused by the difference in the path lengths of the light traveling along the optical path in the interferometer. The path length may be affected by vibrations of the sample, which in turn affects the phase difference and thus results in an inaccurate height map.

[0004] Vibrations of the sample relative to the white light interferometer may be caused by instability of the sample holder. The sample holder may be affected by various vibrations from around the white light interferometer, such as vibrations caused by the movement of a vehicle or a person. The sample holder may also be affected by vibrations that may be caused by the presence of other instruments (such as those typically present in a laboratory or manufacturing environment).

[0005] If sufficient attention is not paid to eliminating the influence of vibrations on the sample, the accuracy of the determined height map may be negatively affected. In some cases, the determined height map may be useless due to excessive errors therein. Vibrations may affect the overall accuracy, reliability, and repeatability of the results of the white light interferometer.

[0006] Known methods for reducing the influence of vibrations on the results of white light interferometry include using vibration dampers to isolate the white light interferometer from the vibration effects of the environment. The disadvantages of these known methods are the increase in the total cost. Additionally, depending on the type of damper and the type of vibration, the damper may not be sufficient to reduce the influence of vibrations.

[0007] A method for determining a height map of a sample surface of a sample with reduced susceptibility to vibrations is required. SUMMARY OF THE INVENTION

[0008] The object of the present invention is to provide an improved method for determining a height map of a sample surface of a sample, which method has a reduced susceptibility to vibrations on the sample compared to known methods. Another object of the present invention is to provide an alternative method for determining a height map of a sample surface of a sample, which method has a reduced susceptibility to vibrations on the sample compared to known methods.

[0009] The object of the present invention is achieved by the method according to claim 1.

[0010] The present invention relies on the insight that using an algorithm based on principal component analysis of an interferogram stack allows a method for determining a height map with reduced susceptibility to random phase shifts (e.g., random phase shifts such as those caused by vibrations) of the interferograms used. The principal component analysis-based method allows separation of 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. Thus, compared to known methods for determining a height map using known methods, the present invention allows an improved or alternative method for determining a height map to reduce the influence of vibrations.

[0011] The present invention relates to a method for determining a height map of a sample surface of a sample by white light interferometry. A height map of the sample surface can be determined to determine the roughness of the sample surface. A height map of the sample surface can further be determined to provide, for example, quality control of a production process. White light interferometry is a non-contact optical method for surface height measurement of a surface having a surface profile.

[0012] The 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 method (e.g., according to the method of the present invention). The light source can emit light to a beam splitter, which splits the light into a reference beam and a measurement beam. The reference beam can travel along a first path towards the optical sensor, and the measurement beam can travel along a second path reflected from the sample surface to the optical sensor. The two beams interfere with each other, which produces an interference pattern and allows the interferometer to measure an interferogram associated with 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 of different parts of the measurement beam, which is converted into fringes in the interferogram via the resulting relative phase difference. This allows extraction of the height of the sample surface by correlating the height of the sample surface with the resulting relative phase difference. The interferometer may further comprise a sample holder or a sample stage, for example, which can be moved in a direction parallel to the measurement beam to allow different measurement positions relative to the focal plane of the optical sensor.

[0013] The method includes obtaining a stack of interferograms by vertically scanning a sample surface with a focal plane of an optical sensor, where each interferogram includes the measured light intensity of each pixel of the optical sensor at a corresponding height relative to the surface. Thus, each interferogram in the stack is associated with the height of the sample surface relative to the optical sensor and / or an optical plane. To obtain the stack, for example, the sample surface is vertically moved by vertical scanning, where the vertical direction is understood to be parallel to the direction of the measurement beam at the sample surface. The sample surface can be moved between different measurement positions, and an interferogram is determined at each measurement position. The interferogram can be represented by an M×N matrix, for example, when the optical sensor has M×N pixels, where each entry of the M×N matrix includes the intensity of the associated pixel. The intensity contains information related to the relative phase of the measured light at that pixel of the associated interferogram. Thus, by obtaining a stack of Z interferograms, a total of Z M×N matrices can be obtained. 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 interferogram stack can be reshaped into a two-dimensional M*N×Z matrix A M*N×Z , where each column is associated with one interferogram in the interferogram stack. It can be shown that the two-dimensional M*N×Z matrix A M*N×Z can be written as and:

[0014] A M*N×Z = a Z u M*N + b Z v M*N

[0015] where and where is the measured phase, which is 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 rather than

[0016] It can be shown that the two signals u M*N and v M*N are approximately uncorrelated, such that A M*N×Z can be decomposed into u M*N and v M*N , thereby removing the dependence on the random phase shift associated with random vibrations of the sample relative to the interferometer.

[0017] The signals u M*N and v M*N can be obtained by performing operations on the interferogram stack (e.g., the matrix A representing the interferogram stack M*N×Z)Perform principal component analysis to obtain. To this end, the method also includes determining the covariance matrix of the interferogram stack. The covariance matrix can be a square symmetric matrix, which can be obtained by multiplying the matrix by its own transpose. The reshaped two-dimensional matrix A M*N×Z can be multiplied by its transpose in order to obtain the M*N×M*N covariance matrix of the interferogram stack.

[0018] To determine the principal components of the interferogram stack, perform singular value decomposition on the associated covariance matrix. Singular value decomposition allows a square matrix to be decomposed into an orthogonal matrix and a diagonal matrix. Then the principal components of the covariance matrix can be obtained by calculating the projection of matrix A M*N×Z onto the orthogonal matrix of the singular value decomposition, for example

[0019] Y = ΦA M*N×Z

[0020] Here Y includes the principal components of A M*N×Z (i.e., the interferogram stack), and Φ is the orthogonal matrix of the singular value decomposition.

[0021] It can be shown that the principal component associated with the largest eigenvalue and the principal component associated with the second largest eigenvalue correspond to the signals u M*N and v M*N (which are vectors whose each entry is associated with a pixel of the optical sensor and is proportional to the sine and cosine of the measured phase). Therefore, by taking the ratio of the components of u M*N and v M*N , the ratio of the sine and cosine can be obtained. Thus, for example, taking the tangent of such a ratio can result in obtaining the measured phase at the corresponding pixel.

[0022] Therefore, the method includes: 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, and taking 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 measured phase of each pixel (e.g., based on the average wavelength of the broadband light source).

[0023] The present invention is also based on the following understanding that the measured phase of the obtained pixels has an undetermined global sign. This global sign is the result of the singular value decomposition of the covariance matrix and the use of the orthogonal matrix Φ when determining the principal components. As can be understood, the orthogonal matrix Φ appears twice in the singular value decomposition of the covariance matrix and is thus not uniquely determined due to its possible global sign change. Therefore, the determined principal components also depend on the sign and are not uniquely determined, which leads to an unknown global sign of the measured phase. The inventors have recognized that the correct global sign can be determined by looking at the phases of the first principal component and the second principal component. When the first principal component lags behind the second principal component by π / 2, the first principal component and the second principal component, regarded as vectors, always have a phase difference of ±π / 2 from the correct global sign of the height map. If this is not the case, the global sign must be inverted relative to the sign used when determining the eigenvectors after Hilbert transform to obtain the correct height map.

[0024] To determine whether the global sign of the measured phase is correct, the method further includes performing a Hilbert transform on the eigenvector associated with the largest eigenvalue of the covariance matrix to obtain the eigenvector after complex Hilbert transform. The real part of the eigenvector after Hilbert transform lags behind the imaginary part of the eigenvector after Hilbert transform by exactly a factor of π / 2.

[0025] Therefore, by determining the reference phase of the reference pixel of the pixel based on the ratio of the vector components of the real part and the imaginary part of the eigenvector after Hilbert transform (for example, by taking the arctangent of the ratio of the vector components of the real part and the imaginary part of the eigenvector after Hilbert transform), where the corresponding vector components are associated with the reference pixel, and determining whether the measured phase of the reference pixel corresponds to the reference phase of the reference pixel, it is possible to check whether the global sign of the measured phase is correct by checking whether the measured phase of the reference pixel corresponds to the reference phase. And if the measured phase does not correspond to the reference phase, the global sign of the height map (for example, the measured phase) is inverted. Therefore, this allows the determination of the height map of the sample surface with the correct global sign.

[0026] In an embodiment, determining whether the measured phase of the reference pixel corresponds to the reference phase of the reference pixel includes:

[0027] - calculating the magnitude of the sum of the measured phase and the reference phase of the reference pixel, and

[0028] calculating the magnitude of the difference between the measured phase and the reference phase of the reference pixel;

[0029] and

[0030] - If the magnitude of the difference is less than the magnitude of the sum, determine that the measured phase of the reference pixel corresponds to the reference phase, and if the magnitude of the difference is greater than the magnitude of the sum,

[0031] then determine that the measured phase of the reference pixel does not correspond to the reference phase.

[0032] This provides a definitive step for determining whether the measured phase of the reference pixel corresponds to the reference phase of the reference pixel.

[0033] The object of the present invention is also achieved by the method of claim 3, which obtains the measured phase in the same manner as the method of claim 1, but differs in determining the correct global sign. The method according to claim 3 includes:

[0034] - Performing a Fourier transform on the first eigenvector associated with the largest eigenvalue of the covariance matrix, and performing a Fourier transform on the second eigenvector associated with the second largest eigenvalue of the covariance matrix;

[0035] - Determining the highest magnitude frequency of the Fourier-transformed first eigenvector;

[0036] - Calculating a first Fourier phase of the Fourier-transformed first eigenvector and a second Fourier phase of the Fourier-transformed second eigenvector associated with the determined highest magnitude frequency;

[0037] - Determining the difference between the first Fourier phase and the second Fourier phase by subtracting the second Fourier phase from the first Fourier phase; and

[0038] - If the difference between the first Fourier phase and the second Fourier phase is between 0 and π modulo 2π, invert the global sign of the determined height map.

[0039] Accordingly, thus, the phase difference between the first principal component and the second principal component is examined by looking at the phase difference of the associated Fourier-transformed vectors. If the difference between the Fourier phases is between 0 and π modulo 2π, the global sign of the height map is inverted with respect to the sign used to examine the difference between the Fourier phases.

[0040] In an embodiment, the ratio of the vector components of the first principal component and the second principal component is proportional to the vector component of the second principal component divided by the vector component of the first principal component. This can allow the use of the arctangent to determine the measured phase.

[0041] In an embodiment, determining the covariance matrix includes removing the average intensity of the interferogram stack. The average intensity can be determined by determining the average value of the intensities of the interferogram stack. The thus determined average intensity can be removed from each entry of the matrix representation of the interferogram stack.

[0042] In an embodiment, determining the covariance matrix includes reshaping a three-dimensional M×N×Z matrix representing the interferogram stack into a two-dimensional M*N×Z matrix, where the optical sensor has M×N pixels and the stack includes Z interferograms.

[0043] In an embodiment, determining the height map based on the determined measured phase for each pixel includes multiplying the determined measured phase by the central wavelength of the broadband light source.

[0044] The present invention also relates to a white light interferometer, which includes a broadband light source, an optical sensor including pixels, and a processor for obtaining a height map of the surface of a sample, wherein the white light interferometer (e.g., its processor) is configured to perform the method according to the present invention.

[0045] In an embodiment, the white light interferometer is configured to:

[0046] - obtain an interferogram stack by vertically scanning the surface at the focal plane of the optical sensor, wherein each interferogram includes the measured light intensity of each pixel of the optical sensor at a corresponding height relative to the surface,

[0047] and wherein the processor is configured to:

[0048] - determine the covariance matrix of the interferogram stack;

[0049] - determine the principal components of the interferogram stack by performing a singular value decomposition of the covariance matrix;

[0050] - select 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;

[0051] - for each pixel among the pixels, determine the measured phase by taking the arctangent of the ratio of the vector components of the first principal component and the second principal component, wherein the vector components are associated with the corresponding pixel; and

[0052] - determine the height map based on the determined measured phase for each pixel,

[0053] wherein the processor is further configured to:

[0054] - perform a Hilbert transform on the eigenvector of the covariance matrix associated with its largest eigenvalue to obtain a complex Hilbert-transformed eigenvector;

[0055] - Determine the reference phase of the reference pixel of the pixel by taking the arctangent of the ratio of the real and imaginary vector components of the eigenvector obtained by Hilbert transform, where the vector components are associated with the reference pixel;

[0056] - Determine whether the measured phase of the reference pixel corresponds to the reference phase; and - if the measured phase of the reference pixel does not correspond to the reference phase, invert the global sign of the determined height map.

[0057] In an embodiment of the white light interferometer, the processor is configured to:

[0058] - Calculate the magnitude of the sum of the measured phase and the reference phase of the reference pixel, and calculate the magnitude of the difference between the measured phase and the reference phase of the reference pixel; and

[0059] - If the magnitude of the difference is less than the magnitude of the sum, determine that the measured phase of the reference pixel corresponds to the reference phase, and if the magnitude of the difference is greater than the magnitude of the sum, determine that the measured phase of the reference pixel does not correspond to the reference phase.

[0060] In an embodiment, the white light interferometer is configured to:

[0061] - Obtain a stack of interferograms by vertically scanning the surface through the focal plane of the optical sensor, where each interferogram includes the measured light intensity of each pixel of the optical sensor at a corresponding height relative to the surface,

[0062] And where the processor is configured to:

[0063] - Determine the covariance matrix of the stack of interferograms;

[0064] - Determine the principal components of the stack of interferograms by performing a singular value decomposition of the covariance matrix;

[0065] - Select 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;

[0066] - For each pixel among the pixels, determine the measured phase by taking the arctangent of the ratio of the vector components of the first principal component and the second principal component, where the vector components are associated with the corresponding pixel; and

[0067] - Determine the height map based on the determined measured phase of each pixel,

[0068] wherein the processor is further configured to:

[0069] - perform a Fourier transform on a first eigenvector of the covariance matrix associated with the largest eigenvalue, and perform a Fourier transform on a second eigenvector of the covariance matrix associated with the second largest eigenvalue;

[0070] - determine the highest magnitude frequency of the Fourier-transformed first eigenvector;

[0071] - calculate a first Fourier phase of the Fourier-transformed first eigenvector and a second Fourier phase of the Fourier-transformed second eigenvector associated with the determined highest magnitude frequency;

[0072] - determine the difference between the first Fourier phase and the second Fourier phase by subtracting the second Fourier phase from the first Fourier phase; and

[0073] - if the difference between the first Fourier phase and the second Fourier phase is between 0 and π modulo 2π, invert the global sign of the determined height map.

[0074] The invention also relates to a digital data carrier comprising a computer program which, when run on a processor of a white light interferometer according to the invention, causes the white light interferometer to perform the method according to the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Embodiments of the invention will now be described by way of example with reference to the accompanying drawings, in which corresponding reference numerals indicate corresponding parts, and in the drawings:

[0076] - Figure 1 a white light interferometer for determining a height map is depicted; and

[0077] - Figure 2 a flowchart of a method for determining a height map is depicted. DETAILED DESCRIPTION

[0078] Figure 1Depicts an example of a white light interferometer 1 for determining a height map. The interferometer includes a broadband light source 2. Light 3 from the light source 2 can pass through a lens 4a, a beam splitter 4b, and a second lens 4c. After passing through the second lens 4c, the light 3 is split by a beam splitter 5 into a first partial beam 4a and a second partial beam 3b. The first partial beam 3a is directed to the surface 6 of a sample 7. The second partial beam 3b is directed to a reference mirror 8 having a reference surface 9. After being reflected by the mirrors 6 and 8, the partial beams 3a, 3b are combined and propagated to an optical sensor 10 having a plurality of pixels. For example, the optical sensor 10 can be a CCD array camera 10. This setup results in an interference signal on the optical sensor 10.

[0079] The pixels of the optical sensor 10 can correspond to spatial positions on the sample surface 6 and on the reference surface 9. After a vertical scan, each pixel can have an associated intensity signal that can be correlated with the height at the corresponding spatial position of the sample 7.

[0080] The sample 7 can be moved through the focal plane of the second lens 4c, and for a plurality of positions of the sample 7 relative to the interferometer 1, interference patterns are captured by the optical sensor 10. In this way, an interference pattern stack can be obtained 101 by the interferometer 1, and this interference pattern stack can be received by a processor 11 to allow the processor to determine a height map based on the method of the present invention.

[0081] Figure 2 Depicts a flowchart of a method for determining a height map, where the method includes:

[0082] - Obtaining 101 an interference pattern stack by vertically scanning the surface 6 by virtue of the focal plane of the optical sensor 10, where each interference pattern includes the measured light intensity of each pixel of the optical sensor 10 at the corresponding height of the surface 6 relative to the focal plane;

[0083] - Determining 102 the covariance matrix of the interference pattern stack;

[0084] - Determining 103 the principal components of the interference pattern stack by performing a singular value decomposition of the covariance matrix;

[0085] - Selecting 104 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; and

[0086] - For each pixel in the pixels, determining 105 the measured phase based on the ratio of the vector components of the first principal component and the second principal component, for example, by taking the arctangent of the ratio of the vector components of the first principal component and the second principal component, where the corresponding vector components are associated with the corresponding pixels.

[0087] As explained in the above description, and asFigure 2 As can be seen, the present invention allows for determining the correct global sign in front of the measured phase based on two methods, both of which are based on the insight that the correct sign is obtained when the first principal component lags behind the second principal component by π / 2. Accordingly, determining the 106 height map based on the measured phase for each pixel includes:

[0088] - Performing a 110 Hilbert transform on the eigenvector associated with the maximum eigenvalue of the covariance matrix to obtain the complex Hilbert-transformed eigenvector;

[0089] - Determining the reference phase of the reference pixel of the 111 pixel based on the ratio of the vector components of the real and imaginary parts of the Hilbert-transformed eigenvector (e.g., by taking the arctangent of the ratio of the vector components of the real and imaginary parts of the Hilbert-transformed eigenvector), wherein the corresponding vector components are associated with the reference pixel;

[0090] - Determining whether the measured phase of the 112 reference pixel corresponds to the reference phase of the reference pixel; and

[0091] - If the measured phase of the reference pixel does not correspond to the reference phase, then reversing the 113 global sign of the measured phase, e.g., the global sign of the height map.

[0092] Or determining the 106 height map based on the measured phase for each pixel includes:

[0093] - Performing a 120 Fourier transform on the first eigenvector associated with the maximum eigenvalue of the covariance matrix and performing a Fourier transform on the second eigenvector associated with the second largest eigenvalue of the covariance matrix;

[0094] - Determining the highest amplitude frequency of the 121 Fourier-transformed first eigenvector;

[0095] - Calculating the 122 first Fourier phase of the Fourier-transformed first eigenvector associated with the determined highest amplitude frequency and the second Fourier phase of the Fourier-transformed second eigenvector;

[0096] - Determining the 123 difference between the first Fourier phase and the second Fourier phase by subtracting the second Fourier phase from the first Fourier phase; and

[0097] - If the difference between the first Fourier phase and the second Fourier phase is between 0 and π modulo 2π, then reversing the 124 global sign of the measured phase, e.g., the global sign of the height map.

Claims

1. A method for determining a height map of a sample surface by white light interferometry, wherein a white light interferometer including a broadband light source and an optical sensor having a plurality of pixels is used, and the method includes: - obtaining a stack of interferograms by vertically scanning the surface with respect to the focal plane of the optical sensor, wherein each interferogram includes the measured light intensity of each pixel of the optical sensor at a corresponding height of the surface with respect to the focal plane; - determining the covariance matrix of the stack of interferograms; - determining the principal components of the stack of interferograms by performing a 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 the second largest eigenvalue of the covariance matrix; - for each pixel of the pixels, determining a measured phase based on the ratio of the vector components of the first principal component and the second principal component, for example, by taking the arctangent of the ratio of the vector components of the first principal component and the second principal component, wherein the corresponding vector components are associated with the corresponding pixel; and - determining the height map based on the measured phase of each pixel, wherein determining the height map includes: - performing a Hilbert transform on the eigenvector associated with the largest eigenvalue of the covariance matrix to obtain a complex Hilbert-transformed eigenvector; - determining a reference phase of a reference pixel of the pixel based on the ratio of the vector components of the real part and the imaginary part of the Hilbert-transformed eigenvector, for example, by taking the arctangent of the ratio of the vector components of the real part and the imaginary part of the Hilbert-transformed eigenvector, wherein the corresponding vector components are associated with the reference pixel; - determining whether the measured phase of the reference pixel corresponds to the reference phase of the reference pixel; and - if the measured phase of the reference pixel does not correspond to the reference phase, then reversing the global sign of the measured phase, for example, the global sign of the height map.

2. The method according to claim 1, wherein determining whether the measured phase of the reference pixel corresponds to the reference phase of the reference pixel includes: - 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; and - if the magnitude of the difference is less than the magnitude of the sum, then determining that the measured phase of the reference pixel corresponds to the reference phase, and if the magnitude of the difference is greater than the magnitude of the sum, then determining that the measured phase of the reference pixel does not correspond to the reference phase.

3. A method for determining a height map of a surface of a sample by white light interferometry, wherein a white light interferometer including a broadband light source and an optical sensor having a plurality of pixels is used, and the method includes: - obtaining a stack of interferograms by vertically scanning the surface with respect to the focal plane of the optical sensor, wherein each interferogram includes the measured light intensity of each pixel of the optical sensor at a corresponding height with respect to the surface; - determining the covariance matrix of the stack of interferograms; - Determining the principal components of the interferogram stack by performing a 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 the second largest eigenvalue of the covariance matrix; - For each pixel among the pixels, determining a measured phase based on a ratio of vector components of the first principal component and the second principal component, for example, by taking the arctangent of the ratio of the vector components of the first principal component and the second principal component, wherein the corresponding vector components are associated with the corresponding pixel; And - Determining the height map based on the determined measured phase for each pixel, wherein determining the height map includes: - Performing a Fourier transform on a first eigenvector of the covariance matrix associated with the largest eigenvalue, and performing a Fourier transform on a second eigenvector of the covariance matrix associated with 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 associated with 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; And - If 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, for example, the global sign of the height map.

4. The method according to one or more of the preceding claims, wherein the ratio of the vector components of the first principal component and the second principal component is proportional to the vector component of the second principal component divided by the vector component of the first principal component.

5. The method according to one or more of the preceding claims, wherein determining the covariance matrix includes removing the average intensity of the interferogram stack.

6. The method according to one or more of the preceding claims, wherein determining the covariance matrix includes reshaping a three-dimensional M×N×Z matrix representing the interferogram stack into a two-dimensional M*N×Z matrix, wherein the optical sensor has M×N pixels and the stack includes Z interferograms.

7. The method according to one or more of the preceding claims, wherein determining the height map based on the determined measured phase for each pixel includes multiplying the determined measured phase by the central wavelength of the broadband light source.

8. A white light interferometer, comprising a broadband light source, an optical sensor including pixels, and a processor for obtaining a height map of the surface of a sample, wherein the white light interferometer, for example, its processor, is configured to perform the method according to one or more of the preceding claims.

9. The white light interferometer according to claim 8, wherein the white light interferometer is configured to: - Obtaining an interference pattern stack by vertically scanning the surface with the focal plane of the optical sensor, where each interference pattern includes the measured light intensity of each pixel of the optical sensor at a corresponding height relative to the surface, and where the processor is configured to: - Determine the covariance matrix of the interference pattern stack; - Determine the principal components of the interference pattern stack by performing singular value decomposition of the covariance matrix; - Select 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 among the pixels, determine the measured phase based on the ratio of the vector components of the first principal component and the second principal component, for example, by taking the arctangent of the ratio of the vector components of the first principal component and the second principal component, where the vector components are associated with the corresponding pixel; and - Determine the height map based on the determined measured phase of each pixel, where determining the height map includes: - Performing a Hilbert transform on the eigenvector associated with the largest eigenvalue of the covariance matrix to obtain a complex Hilbert-transformed eigenvector; - Based on the ratio of the vector components of the real part and the imaginary part of the Hilbert-transformed eigenvector, for example, by taking the arctangent of the ratio of the vector components of the real part and the imaginary part of the Hilbert-transformed eigenvector, determine the reference phase of the reference pixel of the pixel, where the vector components are associated with the reference pixel; - Determine whether the measured phase of the reference pixel corresponds to the reference phase; and - If the measured phase of the reference pixel does not correspond to the reference phase, invert the global sign of the measured phase, for example, the global sign of the height map.

10. The white light interferometer according to claim 9, wherein the processor is configured to: - Calculate the magnitude of the sum of the measured phase of the reference pixel and the reference phase, and calculate the magnitude of the difference between the measured phase of the reference pixel and the reference phase; and - If the magnitude of the difference is less than the magnitude of the sum, determine that the measured phase of the reference pixel corresponds to the reference phase, and if the magnitude of the difference is greater than the magnitude of the sum, determine that the measured phase of the reference pixel does not correspond to the reference phase.

11. The method according to claim 8, wherein the white light interferometer is configured to: - Obtaining an interference pattern stack by vertically scanning the surface with the focal plane of the optical sensor, where each interference pattern includes the measured light intensity of each pixel of the optical sensor at a corresponding height relative to the surface, and where the processor is configured to: - Determine the covariance matrix of the interference pattern stack; - Determine the principal components of the interference pattern stack by performing singular value decomposition of the covariance matrix; - Select 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 of the pixels, a measurement phase is determined based on a ratio of vector components of the first principal component and the second principal component, for example by taking an arctangent of the ratio of the vector components of the first principal component and the second principal component, wherein the vector components are associated with respective pixels; And - A height map is determined based on the determined measurement phase for each pixel, wherein determining the height map includes: - Performing a Fourier transform on a first eigenvector associated with the largest eigenvalue of the covariance matrix and performing a Fourier transform on a second eigenvector associated with the second largest eigenvalue of the covariance matrix; - Determining a highest magnitude frequency of the Fourier-transformed first eigenvector; - Calculating a first Fourier phase of the Fourier-transformed first eigenvector associated with the determined highest magnitude frequency and a second Fourier phase of the Fourier-transformed second eigenvector; - Determining a difference between the first Fourier phase and the second Fourier phase by subtracting the second Fourier phase from the first Fourier phase; And - If the difference between the first Fourier phase and the second Fourier phase is between 0 and π modulo 2π, reversing a global sign of the measurement phase, e.g., a global sign of the height map.

12. A digital data carrier comprising a computer program which, when run on a processor of a white light interferometer according to one or more of claims 8 - 11, causes the white light interferometer to perform the method according to one or more of claims 1 - 7.

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