Method for combining height maps and contourgraph therefor

Abstract

The invention relates to a method for measuring a first height map and a second height map of a surface of a sample with a contourgraph and combining the first height map and the second height map into a composite height map. The invention also relates to a contourgraph configured to measure a first height map and a second height map and to combine the first height map and the second height map into a composite height map.

Description

Technical Field

[0001] The present invention relates to a method for measuring a first height map and a second height map of a sample surface with a profilometer and combining the first height map and the second height map into a composite height map. The present invention also relates to a profilometer configured to measure the first height map and the second height map and combine the first height map and the second height map into a composite height map. Background Art

[0002] Known methods for obtaining a composite height map include measuring a first height map and a second height map and selecting a subsurface (also referred to as a template) of at least one of the height maps, which is then moved onto a subsurface of the other height map to determine the similarity between the two subsurfaces. Generally, the subsurface can be selected based on the presence of recognizable features that can be used to correlate the two subsurfaces, for example, as in US8447561B2. In other words, the known methods rely on determining the recognizable features of the height maps and matching these features between them. Summary of the Invention

[0003] The known methods have a number of problems that the present invention aims to solve. In particular, one or more templates must be selected such that the height maps overlap in the region of the template. To prevent incorrect combination of the height maps, for example due to the presence of similar features on the height maps, multiple templates may have to be tested.

[0004] A first aspect of the present invention aims to overcome the above problems. The present invention also aims to provide an alternative method for determining the overlapping region, so as to obtain a composite height map by stitching the height maps.

[0005] The object of the first aspect of the present invention is achieved by the method according to claim 1.

[0006] The present invention relates to a method for measuring a first height map and a second height map of a sample surface of a sample with a profilometer (e.g., an optical profilometer) and combining the first height map and the second height map into a composite height map. The profilometer can be any suitable profilometer that allows measuring multiple fields of view of the sample surface to obtain two or more height maps, which may need to be combined to obtain a composite height map of the sample surface. The first height map and the second height map can be two of the multiple height maps of the sample surface. For example, the obtained composite height map can also be combined with a third height map to obtain a larger composite height map.

[0007] The method includes measuring a first height map and a second height map with a sensor of a profiler. The sensor can be an optical sensor, however, any suitable type of sensor can be used. The sensor can include a plurality of pixels for obtaining pixel data related to the height of a sample surface in the field of view of the sensor. The sensor is moved relative to the sample surface, for example, by moving a holder for holding the sample surface relative to the objective lens of the sensor, such that the first height map and the second height map are measured in partially overlapping fields of view of the sensor. As a result, the first height map and the second height map include regions containing the same height information, and the first height map and the second height map can be stitched along this region to obtain a composite height map of a portion of the sample surface.

[0008] The method further includes combining the first height map and the second height map to produce a composite height map of the sample surface. Combining the height maps includes determining a first overlapping region of the first height map and the second height map by partially overlapping the first height map and the second height map, and the first height map and the second height map overlap in the first overlapping region. Compared with a known method in which a template of a height map is selected and then the template is moved on top of a template of another height map, the method of the present invention includes directly acquiring both the first height map and the second height map and partially overlapping them to define the first overlapping region. The template in the known method corresponds to a portion of the measured height map.

[0009] A first similarity between the first height map and the second height map in the first overlapping region is determined by using a similarity metric to determine a similarity (e.g., the correlation between the first height map and the second height map in the overlapping region). Thus, after overlapping the first height map and the second height map, a similarity is assigned to the first overlapping region based on the similarity metric, and the similarity provides a value of a similarity measure between the first height map and the second height map in the overlapping region. For example, the first similarity value can be based on the sum of the squares of the differences between the height values of the first height map and the second height map in the first overlapping region.

[0010] After determining the first similarity, a second overlapping region of the first height map and the second height map is determined by shifting the first height map and the second height map relative to each other compared to the first overlapping region. For example, the first height map can be shifted a pixel distance in the x direction relative to the second height map. Thus, instead of moving a template of the height map, the complete height maps are shifted relative to each other, which increases the amount of information available for determining the correct overlapping region and does not require selecting a template and moving the template relative to each other. Due to the relative movement of the height maps, the first overlapping region and the second overlapping region can generally have different surface areas.

[0011] A second similarity between the first height map and the second height map is determined by using a similarity metric to determine the similarity between the heights of the first height map and the second height map in the second overlapping region. The second similarity is comparable to the first similarity in the sense that the relative difference between the two provides information about the difference in similarity between the height maps in the first overlapping region and the second overlapping region. Preferably, the first similarity and the second similarity are based on the same similarity metric.

[0012] The first similarity and the second similarity are compared by normalizing the first similarity and the second similarity based on the corresponding surface areas of the overlapping regions. For example, the first similarity and the second similarity can be normalized by the number of pixels present in each of the overlapping regions. Normalizing the first similarity and the second similarity allows for a direct comparison of the first similarity and the second similarity, which allows for a comparison of the amount of similarity in the first overlapping region with the amount of similarity in the second overlapping region.

[0013] Then, the first height map and the second height map are combined by stitching the first height map and the second height map in one of the first overlapping region and the second overlapping region based on a comparison of the first similarity and the second similarity. For example, the stitching can be accomplished by transforming the coordinate system of one of the height maps to the coordinates from the other height map based on a comparison of the first height map and the second height map. For example, the height maps can be stitched into a composite height map by performing a weighted average of the heights from the height maps, where the weights are determined based on the distance between the pixel and the center of the corresponding height map. For example, the first height map and the second height map can be stitched in the overlapping region having the higher or highest similarity. For example, in the case of comparing multiple similarities of multiple overlapping regions, the highest similarity can be used to determine which overlapping region to use for stitching the height maps.

[0014] The present invention allows for more efficient stitching of the first height map and the second height map because it is not necessary to determine a template of the height map or perform a preliminary analysis of the height map to determine the relevant features that can be used to determine the template. In addition, the method of the present invention can be more accurate because more information about the height map is used in determining the similarity compared to using only the information available in the template.

[0015] In an embodiment, the method further includes:

[0016] - determining a plurality of overlapping regions between the first height map and the second height map by subsequently shifting the first height map and the second height map relative to each other, and wherein, preferably, the current overlapping region has a different surface area than the previous overlapping region;

[0017] - After each shift of the first height map and the second height map, determine the corresponding similarity by using a similarity metric to determine the similarity between the heights of the first height map and the second height map in the corresponding overlapping region;

[0018] - Compare the multiple similarities by normalizing the similarity based on the corresponding surface area of the overlapping region; and

[0019] - Combine the first height map and the second height map by stitching the first height map and the second height map in one of the overlapping regions (e.g., based on an overlapping region with a higher similarity, e.g., in an overlapping region with the highest similarity) in the overlapping region.

[0020] In these embodiments, multiple overlapping regions are determined. Each of the overlapping regions may have a different surface area compared to the previous overlapping regions. For each of the overlapping regions, determine the similarity and normalize it, and then it can be used to combine the first height map and the second height map by stitching the height maps in the overlapping region with the highest similarity.

[0021] In an embodiment, the sensor includes a plurality of pixels, and wherein, the first height map and the second height map are shifted relative to each other by a single pixel of the sensor, for example, in the x-direction and / or y-direction of the first height map and the second height map, and preferably, wherein, the first overlapping region has a surface area corresponding to a single pixel of the sensor. In other embodiments, the first height map and the second height map may be shifted relative to each other by a plurality of pixels, for example, in the x-direction and / or y-direction. The first overlapping region may have a surface area corresponding to a single pixel, that is, the first height map and the second height map overlap with the overlapping region of a single pixel at their corners, and after determining the similarity, the first height map and the second height map are shifted relative to each other by, for example, a single pixel to obtain a second overlapping region. The first overlapping region may also have a surface area corresponding to a plurality of pixels or a fraction of a pixel.

[0022] In an embodiment, determining the similarity between the heights of the first height map and the second height map includes: using a correlation metric to determine the correlation between the heights of the first height map and the second height map, and wherein, the first height map and the second height map are combined based on the correlation.

[0023] In an embodiment, the correlation is determined based on a zero-normalized cross-correlation function:

[0024]

[0025] where N is the surface area of the corresponding overlapping region, sV is the standard deviation of the height in the corresponding overlapping region of the first height map, sW is the standard deviation of the height in the corresponding overlapping region of the second height map, V i is the height in the corresponding overlapping region of the first height map, W i is the height in the corresponding overlapping region of the second height map, meanV is the average height in the corresponding overlapping region of the first height map, and meanW is the average height in the corresponding overlapping region of the second height map. For example, the correlation values obtained in this way can be used to determine a correlation matrix, which can be used to determine the overlapping regions for stitching. The correlation values are normalized with respect to the surface area N of the corresponding overlapping region and the standard deviations sV and sW, thus allowing a direct comparison between correlations.

[0026] Another problem related to combining height maps to obtain a composite height map is that systematic errors in the profilometer and / or measurement technique may cause measurement artifacts in the height maps, which may artificially increase or distort the similarity between regions of the height maps. For example, measurement artifacts may be caused by vibrations and / or illumination changes during measurement. For example, the first height map and the second height map may be stitched based on a similarity that depends on measurement artifacts. This may result in an incorrect combination of the first height map and the second height map. The following embodiments of the present invention aim to overcome this problem.

[0027] In an embodiment, the method further includes:

[0028] - classifying the features of the two height maps as sharp features and smooth features;

[0029] and

[0030] - determining the similarity (e.g., correlation) for each overlapping region by using a weighted similarity metric (e.g., weighted correlation), where the weights are based on the classification of the features as sharp features and smooth features.

[0031] The inventors have recognized that measurement artifacts mainly result in relatively smooth features compared to sharper features. By increasing the relevance of sharper features compared to smooth features when determining similarity (i.e., determining a weighted similarity metric), the impact of measurement artifacts on the matching of height maps can be reduced. The features of a height map can be classified, for example, based on the gradient or height relative to the base area of the height map to determine the sharpness of the features. If a feature belongs to 50%, for example 40%, for example 20% of the sharpest features, then the feature can be classified as sharp. If a feature is not sharp, it can be classified as smooth. For example, the weights can be determined on a pixel-by-pixel basis (e.g., based on the gradient associated with the pixel) or on a feature-by-feature basis. Alternatively, the weights can be binary. For example, all sharp features are assigned a weight higher than a threshold. In an embodiment, sharp features have a higher weight than smooth features. The classification of features can depend on the specific application, for example, depending on the sample properties, sample type, or the nature of the optical measurement instrument.

[0032] In an embodiment, the features are classified based on their gradients and / or wherein the weights are gradient-based.

[0033] Another problem related to combining height maps to obtain a synthetic height map is that different flat regions of the sample surface may look similar and may be even more similar than regions with features. For example, because, for example, to determine the first height map and the second height map, regions with features that appear in two different measurements may be slightly different from each other, such that they have a lower similarity than two flat regions. If there are two different flat regions, the height maps can be stitched along the flat regions due to their high similarity between them. The following embodiments of the present invention aim to overcome this problem.

[0034] In these embodiments, the method further comprises:

[0035] - determining one or more flat regions in the first height map and / or the second height map;

[0036] - determining modified first and second heightmaps by providing a variation (e.g., a random variation) of the height values of the flat regions; and

[0037] - determining the similarity between the first height map and the second height map, e.g., the correlation, by determining the similarity between the heights of the modified first and second height maps in the first overlapping region.

[0038] The influence of flat regions on the similarity between height maps is suppressed by adding variations (preferably random variations, such as random noise) to the flat regions of at least one of the height maps to obtain a modified height map. Due to the added variations, the flat regions in the modified height map will appear less flat. Preferably, variations are added only to one of the two height maps, and the similarity is determined for one modified height map and one unmodified height map.

[0039] Flat regions can be regions lacking features. Flat regions can also be determined by looking at their deviation from a plane, for example, by comparing different parts of the height map with a plane, and the deviation from the plane provides a measure of flatness. Flat regions can be determined by determining the variation between the normal vectors of the surface area, such that for example a small variation in the normal vectors can indicate a flat region.

[0040] In an embodiment, one or more flat regions are determined based on the classification of features in the height map, for example, where the flat region is a region having a substantially flat feature (e.g., having a gradient below a predetermined threshold).

[0041] One problem associated with combining height maps to obtain a synthetic height map is that systematic errors in the profilometer and / or measurement technique may result in measurement artifacts in the height maps, which may artificially increase or distort the similarity between regions of the height maps. For example, measurement artifacts may be caused by vibrations and / or illumination changes during measurement. For example, the first height map and the second height map may be stitched based on a similarity metric that depends on the measurement artifacts. This may result in an incorrect combination of the first height map and the second height map. The second aspect of the present invention aims to overcome this problem.

[0042] The second aspect of the present invention relates to a method for measuring a first height map and a second height map of a sample surface of a sample with a profilometer and combining the first height map and the second height map into a synthetic height map, the method comprising:

[0043] - Measuring the first height map and the second height map with a sensor of the profilometer, wherein the sensor is moved relative to the sample surface such that the first height map and the second height map are measured in a partially overlapping field of view of the sensor;

[0044] - Combining the first height map and the second height map to produce a synthetic height map of the sample surface,

[0045] characterized in that combining the first height map and the second height map comprises:

[0046] - Classify the features of the first height map and the second height map into sharp features and smooth features;

[0047] - For a plurality of sub-regions of the first height map and the second height map, determine the similarity between the corresponding sub-regions of the first height map and the second height map by using a weighted similarity metric between the first height map and the second height map in the corresponding sub-region, wherein the weights are based on the classification of the features as sharp features and smooth features;

[0048] - Compare the similarity between the first height map and the second height map in the plurality of sub-regions; and

[0049] - Combine the first height map and the second height map by stitching the first height map and the second height map in one of the sub-regions based on the similarity-based comparison, e.g., based on a sub-region with a higher similarity, e.g., in a sub-region with the highest similarity.

[0050] The inventors have recognized that measurement artifacts mainly result in relatively smooth features compared to sharper features. By increasing the relevance of sharper features compared to smooth features when using a similarity metric (i.e., using a weighted similarity metric), the impact of measurement artifacts on the matching of height maps can be reduced. The features of the height map can be classified by, for example, determining the sharpness of the height map based on the gradient or height relative to the base region of the height map. If a feature belongs to 50%, e.g., 40%, e.g., 20% of the sharpest features, then the feature can be classified as sharp. If the feature is not sharp, it can be classified as smooth. For example, the weights can be determined on a pixel-by-pixel basis (e.g., based on the gradient associated with the pixel) or on a feature-by-feature basis. Alternatively, the weights can be binary. For example, all sharp features are assigned twice the weight of smooth features. In an embodiment, sharp features have a higher weight than smooth features. The second aspect of the present invention can be combined with any other aspect of the present invention disclosed herein.

[0051] One problem related to combining height maps to obtain a synthetic height map is that different flat regions of the sample surface may look similar and may even be more similar than regions with features. If there are two different flat regions, the height maps can be stitched along the flat region due to the high similarity between them. The third aspect of the present invention aims to overcome this problem.

[0052] The third aspect of the present invention relates to a method for measuring a first height map and a second height map of a sample surface of a sample using a profilometer and combining the first height map and the second height map into a synthetic height map, the method comprising:

[0053] - Measuring a first height map and a second height map with a sensor of a profiler, wherein the sensor includes a plurality of pixels, and wherein the sensor is moved relative to the sample surface such that the first height map and the second height map are measured in a partially overlapping field of view of the sensor;

[0054] - Combining the first height map and the second height map to generate a composite height map of the sample surface,

[0055] Characterized in that combining the first height map and the second height map includes:

[0056] - Determining one or more flat regions in the first height map and / or the second height map;

[0057] - Determining a modified first height map and a modified second height map by providing a change (e.g., a random change) in the height values of the flat regions; and

[0058] - Using a similarity metric to determine the similarity between the modified first height map and the modified second height map in corresponding sub-regions for a plurality of sub-regions of the modified first height map and the modified second height map;

[0059] - Comparing the similarity between the modified first height map and the modified second height map in the plurality of sub-regions; and

[0060] - Combining the first height map and the second height map by stitching the first height map and the second height map in a sub-region based on the similarity-based comparison, e.g., in a sub-region with a higher similarity, e.g., in a sub-region with the highest similarity.

[0061] The influence of the flat regions on the similarity between the height maps is suppressed by adding a change (preferably a random change, e.g., random noise) to the flat regions of at least one of the height maps to obtain a modified height map. Due to the added change, the flat regions in the modified height map will appear less flat. Preferably, the change is added only to one of the two height maps, and the similarity metric is determined for one modified height map and one unmodified height map.

[0062] The flat regions can be regions lacking features. The flat regions can also be determined by looking at their deviation from a plane, e.g., by comparing different parts of the height map with a plane, and the deviation from the plane provides a measure of flatness.

[0063] In an embodiment of the third aspect, one or more flat regions are determined based on the classification of features in the height map, e.g., where the flat regions are regions having substantially flat features (e.g., having a gradient below a predetermined threshold).

[0064] The third aspect of the present invention can be combined with any other aspect of the present invention disclosed herein.

[0065] The present invention also relates to a profiler, for example, an optical profiler, comprising: a sensor having pixels for measuring a first height map and a second height map of a sample surface of a sample, a sample holder for holding the sample, and a processor configured to perform a method according to any aspect of the present invention.

[0066] In an embodiment of the profiler, the processor is configured to:

[0067] - Determine a first overlapping region of the first height map and the second height map by partially overlapping the first height map and the second height map, wherein the first height map and the second height map overlap in the first overlapping region;

[0068] - Determine a first similarity between the first height map and the second height map by using a similarity metric to determine the similarity between the heights of the first height map and the second height map in the first overlapping region;

[0069] - Determine a second overlapping region of the first height map and the second height map by shifting the first height map and the second height map relative to each other compared to the first overlapping region, wherein the second overlapping region preferably has a surface area different from that of the first overlapping region;

[0070] - Determine a second similarity between the first height map and the second height map by using a similarity metric to determine the similarity between the heights of the first height map and the second height map in the second overlapping region;

[0071] - Compare the first similarity and the second similarity by normalizing the first similarity and the second similarity based on the respective surface areas of the overlapping regions;

[0072] - Combine the first height map and the second height map by stitching the first height map and the second height map in one of the overlapping regions based on the comparison of the first similarity and the second similarity, for example, in the overlapping region having a higher similarity; and

[0073] - Output a composite height map of the sample surface based on the combined first height map and second height map.

[0074] In an embodiment, the processor is configured to:

[0075] - Cause the profiler to measure the first height map and the second height map with the sensor of the profiler, wherein the sensor moves relative to the sample surface such that the first height map and the second height map are measured in a partially overlapping field of view of the sensor;

[0076] - Combine a first height map and a second height map to generate a synthetic height map of the sample surface,

[0077] characterized in that combining the first height map and the second height map comprises:

[0078] - Classify the features of the first height map and the second height map as sharp features and smooth features;

[0079] - For a plurality of sub-regions of the first height map and the second height map, determine the similarity between the corresponding sub-regions of the first height map and the second height map by using a weighted similarity metric between the first height map and the second height map in the corresponding sub-region, wherein the weights are based on the classification of the features as sharp features and smooth features;

[0080] - Compare the similarity between the first height map and the second height map in the plurality of sub-regions; and

[0081] - Combine the first height map and the second height map by stitching the first height map and the second height map in one of the sub-regions based on the similarity-based comparison, for example, in a sub-region with a higher similarity, for example, in a sub-region with the highest similarity.

[0082] In an embodiment, the processor is configured to:

[0083] - Cause a profiler to measure the first height map and the second height map with a sensor of the profiler, wherein the sensor moves relative to the sample surface such that the first height map and the second height map are measured in a partially overlapping field of view of the sensor;

[0084] - Combine the first height map and the second height map to generate a synthetic height map of the sample surface,

[0085] characterized in that combining the first height map and the second height map comprises:

[0086] - Determine one or more flat regions in the first height map and / or the second height map;

[0087] - Determine a modified first height map and a modified second height map by providing a change (e.g., a random change) in the height values of the flat regions; and

[0088] - For a plurality of sub-regions of the modified first height map and the modified second height map, determine the similarity between the corresponding sub-regions of the modified first height map and the modified second height map;

[0089] - Compare the similarity between the modified first height map and the modified second height map in the plurality of sub-regions; and

[0090] - Combine the first height map and the second height map by stitching the first height map and the second height map in one of the sub-regions in the similarity-based comparison, for example, in a sub-region with a higher similarity, for example, in a sub-region with the highest similarity.

[0091] The invention also relates to a digital data carrier comprising software which, when run on a processor of a profiler according to the invention, causes the profiler to perform the method according to the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] 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 which:

[0093] Figure 1 A profiler is depicted;

[0094] Figure 2 A flowchart of a method according to a first aspect is depicted;

[0095] Figure 3 A flowchart of a method according to a second aspect is depicted;

[0096] Figure 4 A flowchart of a method according to a third aspect is depicted. DETAILED DESCRIPTION

[0097] Figure 1 A profiler 1 is depicted, for example, an optical profiler 1, which includes a sensor 2 having pixels for measuring a first height map and a second height map of a sample surface of a sample 3. The profiler 1 can be an interferometer, for example, a white light interferometer, which is configured to measure the height map of the sample 3 using interference patterns.

[0098] The profiler may further include a sample holder 4 for holding the sample 3. The sample holder 4 may allow relative movement of the sample 3 and the sensor 2 to allow measurement of the first height map and the second height map in partially overlapping fields of view of the sensor 2.

[0099] The profiler includes a processor 5 which is connected to the sensor 2 to allow reception of the measured height maps of the sample surface from the sensor 2. The processor 5 is configured to perform the method of the invention. For example, according to the first aspect, the processor 5 may be configured to:

[0100] - Cause 101 the sensor 2 to measure the first height map and the second height map, wherein the sensor 2 moves relative to the sample surface such that the first height map and the second height map are measured in partially overlapping fields of view of the sensor 2;

[0101] - Combine the first height map and the second height map to generate a synthetic height map of the sample surface; and

[0102] - Output the synthetic height map of the 108 sample surface based on the combined first height map and second height map,

[0103] wherein combining the first height map and the second height map includes:

[0104] - Determine a first overlapping region of the 102 first height map and the second height map by partially overlapping the first height map and the second height map, and the first height map and the second height map overlap in the first overlapping region;

[0105] - Determine a first similarity between the 103 first height map and the second height map by using a similarity metric to determine the similarity between the heights of the first height map and the second height map in the first overlapping region;

[0106] - Determine a second overlapping region of the 104 first height map and the second height map by shifting the first height map and the second height map relative to each other compared to the first overlapping region, wherein the second overlapping region preferably has a surface area different from that of the first overlapping region;

[0107] - Determine a second similarity between the 105 first height map and the second height map by using a similarity metric to determine the similarity between the heights of the first height map and the second height map in the second overlapping region;

[0108] - Compare the 106 first similarity and the second similarity by normalizing the first similarity and the second similarity based on the respective surface areas of the overlapping regions; and

[0109] - Combine the 107 first height map and the second height map to generate a synthetic height map by splicing the first height map and the second height map in one of the overlapping regions based on the comparison of the first similarity and the second similarity, for example, in the overlapping region with the higher similarity.

[0110] For example, according to the second aspect, the processor 5 may be configured to:

[0111] - Cause the 201 sensor 2 to measure the first height map and the second height map, wherein the sensor 2 moves relative to the sample surface such that the first height map and the second height map are measured in the partially overlapping field of view of the sensor 2;

[0112] - Combine the first height map and the second height map to generate a synthetic height map of the sample surface; and - Output the synthetic height map of the 206 sample surface based on the combined first height map and second height map,

[0113] Among them, combining the first height map and the second height map includes:

[0114] - Classifying the features 202 of the first height map and the second height map into sharp features and smooth features; - For multiple sub-regions of the first height map and the second height map, determining 203 the similarity between the corresponding sub-regions of the first height map and the second height map by using a weighted similarity metric between the first height map and the second height map in the corresponding sub-region, where the weights are based on the feature classification as sharp features and smooth features;

[0115] - Comparing 204 the similarity between the first height map and the second height map in multiple sub-regions;

[0116] And

[0117] - Combining 205 the first height map and the second height map by stitching the first height map and the second height map in one of the sub-regions based on the similarity-based comparison, for example, in a sub-region with a higher similarity, for example, in a sub-region with the highest similarity.

[0118] For example, according to the third aspect, the processor 5 can be configured to:

[0119] - Cause 301 the sensor 2 to measure the first height map and the second height map, where the sensor 2 moves relative to the sample surface such that the first height map and the second height map are measured in the partially overlapping fields of view of the sensor 2;

[0120] - Combine the first height map and the second height map to generate a synthetic height map of the sample surface; and - Output 302 the synthetic height map of the sample surface based on the combined first height map and the second height map,

[0121] It is characterized in that combining the first height map and the second height map includes:

[0122] - Determining 303 one or more flat regions in the first height map and / or the second height map;

[0123] - Determining 304 a modified first height map and a modified second height map by providing a change (e.g., a random change) in the height values of the flat regions; and

[0124] - For multiple sub-regions of the modified first height map and the modified second height map, determining 305 the similarity between the corresponding sub-regions of the modified first height map and the modified second height map;

[0125] - Comparing 306 the similarity between the modified first height map and the modified second height map in multiple sub-regions; and

[0126] - Combine the first height map and the second height map by splicing the first height map and the second height map in one of the sub-regions based on a similarity-based comparison, for example, in a sub-region with a higher similarity, for example, in a sub-region with the highest similarity.

Claims

1. A method for measuring a first height map and a second height map of a sample surface of a sample using a profilometer and combining the first height map and the second height map into a synthetic height map, wherein the profilometer is, for example, an optical profilometer, the method comprising: - measuring the first height map and the second height map with a sensor of the profilometer, wherein The sensor is moved relative to the sample surface such that the first height map and the second height map are measured in partially overlapping fields of view of the sensor; - combining said first height map and said second height map to generate said composite height map of said sample surface, Characterized in that combining the first height map and the second height map comprises: - determining a first overlapping region of the first height map and the second height map by partially overlapping the first height map and the second height map, the first height map and the second height map overlapping in the first overlapping region; - determining a first similarity between the first height map and the second height map by determining a similarity between heights of the first height map and the second height map in the first overlapping area using a similarity metric; - determining a second overlapping area of ​​the first height map and the second height map by shifting the first height map and the second height map relative to each other compared to the first overlapping area, wherein preferably the second overlapping area has a different surface area than the first overlapping area; - determining a second similarity between the first height map and the second height map by determining a similarity between heights of the first height map and the second height map in a second overlapping region using the similarity metric; - comparing the first similarity and the second similarity by normalizing the first similarity and the second similarity based on the respective surface areas of the overlapping regions; and - combining the first height map and the second height map by stitching the first height map and the second height map in one of the overlapping areas based on a comparison of the first similarity measure and the second similarity measure, (e.g., in an overlapping area with a higher similarity, such as a highest similarity).

2. The method according to claim 1, wherein: The method further comprises: - determining a plurality of overlapping regions of the first height map and the second height map by subsequently shifting the first height map and the second height map relative to each other, and wherein, preferably, a current overlapping region has a different surface area than a previous overlapping region; - determining a similarity between the first height map and the second height map by determining a similarity between heights of the first height map and the second height map in respective overlapping regions using the similarity metric after each shift of the first height map and the second height map; - comparing said plurality of similarities by normalizing said similarities based on said respective surface areas of said overlapping regions; and - combining the first height map and the second height map by stitching the first height map and the second height map in one of the overlapping areas based on a comparison of multiple similarities, for example, based on one of the overlapping areas with a higher similarity, for example, in one of the overlapping areas with the highest similarity.

3. The method according to one or more of the preceding claims, wherein: The sensor comprises a plurality of pixels, and wherein the first height map and the second height map are shifted relative to each other by a single pixel of the sensor, and preferably wherein the first overlapping region has a surface area corresponding to a single pixel of the sensor.

4. The method according to one or more of the preceding claims, wherein: The similarity metric is based on a correlation for determining a correlation between heights of the first height map and the second height map in respective overlapping regions, and wherein the first height map and the second height map are combined based on the correlation.

5. The method according to claim 4, wherein: The correlation is determined based on a zero-normalized cross-correlation function: Where N is the surface area of ​​the corresponding overlapping region, sV is the standard deviation of the height in the corresponding overlapping region of the first height map, sW is the standard deviation of the height in the corresponding overlapping region of the second height map, and V i is the height in the corresponding overlapping area of ​​the first height map, W i is the height in the corresponding overlapping area of ​​the second height map, meanV is the average height in the corresponding overlapping area of ​​the first height map, and meanW is the average height in the corresponding overlapping area of ​​the second height map.

6. The method according to one or more of the preceding claims, wherein: The method further comprises: - classifying the features of the two height maps into sharp features and smooth features; and - determining the similarity for each overlapping region by using a weighted similarity measure, such as a weighted correlation, wherein the weights are based on the classification of features into sharp features and smooth features, wherein the similarity is such as a correlation.

7. The method according to claim 6, wherein: The sharp features have higher weights than the smooth features.

8. The method according to one or more of claims 6-7, wherein: The features are classified based on gradients of the features and / or wherein the weights are based on the gradients.

9. The method according to one or more of the preceding claims, wherein: The method further comprises: - determining one or more flat areas in the first height map and / or the second height map; - determining a modified first height map and a modified second height map by providing a variation of the height values ​​of the flat area, the variation being, for example, a random variation; and - using the similarity measure to determine a similarity between the first height map and the second height map in a first overlapping region, the similarity being for example a correlation.

10. The method according to claim 9, wherein: The one or more flat regions are determined based on a classification of features in the height map, for example, where a flat region is a region having substantially flat features, for example, a region having a gradient below a predetermined threshold.

11. A profilometer comprising a sensor having pixels for measuring a first height map and a second height map of a sample surface of a sample, the profilometer being, for example, an optical profilometer, and a processor configured to perform the method according to one or more of the preceding claims, wherein the profilometer preferably comprises a sample holder for holding the sample.

12. The profiler according to claim 11, wherein: The processor is configured to: - causing the sensor to measure the first height map and the second height map, wherein the sensor is moved relative to the sample surface such that the first height map and the second height map are measured in partially overlapping fields of view of the sensor; - combining the first height map and the second height map to produce a composite height map of the sample surface; and - outputting a composite height map of the sample surface based on the combined first height map and the second height map, Wherein, combining the first height map and the second height map comprises: - determining a first overlapping region of the first height map and the second height map by partially overlapping the first height map and the second height map, the first height map and the second height map overlapping in the first overlapping region; - determining a first similarity between the first height map and the second height map by determining a similarity between heights of the first height map and the second height map in the first overlapping area using a similarity metric; - determining a second overlapping area of ​​the first height map and the second height map by shifting the first height map and the second height map relative to each other compared to the first overlapping area, wherein the second overlapping area preferably has a different surface area than the first overlapping area; - determining a second similarity between the first height map and the second height map by determining a similarity between heights of the first height map and the second height map in the second overlapping area using the similarity metric; - comparing the first similarity and the second similarity by normalizing the first similarity and the second similarity based on the respective surface areas of the overlapping regions; and - combining the first height map and the second height map by stitching the first height map and the second height map in one of the overlapping areas based on a comparison of the first similarity and the second similarity, for example in the one with the higher similarity.

13. A digital data carrier comprising software which, when run on a processor of a profiler according to one or more of claims 11-12, causes the profiler to perform the method according to one or more of claims 1-10.

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