Method for combining height maps and profilometer for combining height maps

Abstract

To provide a method for combining height maps and a profilometer for combining height maps.SOLUTION: A method includes: a step 101 of measuring first and second height maps with a sensor of a profilometer; a step 102 of determining a first overlapping area of the first and second height maps; a step 103 of determining first similarity between the first height map and the second height map; a step 104 of determining a second overlapping area of the first height map and the second height map; a step 105 of determining second similarity between the first height map and the second height map; a step 106 of comparing the first and second similarities; a step 107 of combining the first and second height maps; and a step 108 of outputting a composite height map of a sample surface.SELECTED DRAWING: Figure 2

Description

Summary of the Invention

[0001] The present invention relates to a method of measuring a first height map and a second height map of a sample surface using a surface shape measuring device, and combining the first and second height maps into a composite height map. The present invention further relates to a surface shape measuring device configured to measure a first height map and a second height map and combine the first and second height maps into a composite height map.

[0002] Known methods of obtaining a composite height map include measuring a first and a second height map and selecting at least one subsurface of the height map, also known as a template, wherein the at least one subsurface is then moved relative to the other subsurface of the 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, for example, in US8447561B2, to correlate the two subsurfaces. In other words, known methods rely on determining recognizable features of the height maps and matching these features between them.

[0003] Known methods have several problems that the present invention seeks to alleviate. In particular, one or more templates must be selected such that the height maps overlap within the region of the template. For example, multiple templates may have to be tested to prevent inaccurate combinations of height maps due to the presence of similar features on the height maps.

[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 obtaining a composite height map by determining overlapping regions and thereby 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 of measuring a first height map and a second height map of a sample surface of a sample with a surface shape measuring device, for example, an optical surface shape measuring device, and combining the first and second height maps into a composite height map. The surface shape measuring device can be any suitable surface shape measuring device that enables measurement of a plurality of fields of view of the sample surface to obtain two or more height maps that may need to be combined to obtain a composite height map of the sample surface. The first and second height maps may be two of the plurality of height maps of the sample surface. For example, the obtained composite height map may be further combined with a third height map to obtain a larger composite height map.

[0007] The method includes the step of measuring the first and second height maps using a sensor of the surface shape measuring device. The sensor may be an optical sensor, but any suitable type of sensor may be used. The sensor may include a plurality of pixels for obtaining pixel data related to the height of the sample surface within 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 of the sensor, and as a result, the first and second height maps 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 along those regions, the first height map and the second height map are stitched to obtain a composite height map of a part of the sample surface.

[0008] The method further includes combining the first and second height maps to generate a composite height map of the sample surface. The step of combining the height maps includes determining a first overlapping region between the first height map and the second height map by partially overlapping the first height map and the second height map, wherein in the first overlapping region, the first height map and the second height map overlap. In contrast to known methods, a template of the height map is selected and then the template is moved over the other template of the height map. The method of the present invention includes directly obtaining both the first and second height maps and partially overlaying them to define a 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, based on, for example, the sum of correlations or absolute differences, is determined by using a similarity measure to determine the similarity, for example, 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 measure, and this similarity provides a value of the similarity between the first height map and the second height map in the overlapping region. For example, the first similarity value may be based on the sum of the squares of the differences between the height values of the first height map and the height values of the second height map in the first overlapping region.

[0010] After determining the first similarity, the second overlapping region of the first and second height maps is determined by shifting the first and second height maps relative to each other as compared to the first overlapping region. For example, the first height map can be shifted by a pixel distance in the x direction relative to the second height map. Thus, rather than 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 and moving templates relative to each other. The first and second overlapping regions may generally have different surface areas due to the relative movement of the height maps.

[0011] The second similarity is determined between the first height map and the second height map by determining the similarity between the height of the first height map and the height of the second height map within the second overlapping region using a similarity measure. 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 and second overlapping regions. Preferably, the first similarity and the second similarity are based on the same similarity measure.

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

[0013] Next, the first and second height maps are combined by stitching the first and second height maps in one of the first and second overlapping regions based on the comparison of the first and second similarities. For example, the stitching can be performed by converting the coordinate frame of one of the height maps to the coordinates from the other of the height maps based on the comparison of the first height map and the second height map. For example, stitching the height maps into a composite height map may be performed by taking 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 each height map. For example, the first and second height maps may be stitched in the overlapping region having the higher or highest similarity. For example, when comparing the similarities of a plurality of overlapping regions, the highest similarity among the similarities may be used to determine which overlapping region to use for stitching the height maps.

[0014] The present invention enables more efficient stitching of the first and second height maps because there is no need to determine a template for the height map or perform a preliminary analysis of the height map to determine related features that can be used to determine the template. Further, the method of the present invention can be more accurate because more information about the height maps is used in determining the similarity compared to using only the information available in the template.

[0015] In an embodiment, the method further includes determining a plurality of overlapping regions of the first and second height maps by successively shifting the first and second height maps relative to each other, preferably, the current overlapping region has a different surface area than the preceding overlapping region, The method determines each similarity by using a similarity measure to determine the similarity between the heights of the first and second height maps in each overlapping region after each shift of the first and second height maps, Comparing a plurality of similarities by normalizing the similarity based on the respective surface areas of the overlapping regions; Based on the comparison of the plurality of similarities, for example, based on one overlapping region having a higher similarity, combining the first and second height maps by stitching the first and second height maps in one of the overlapping regions (for example, the one overlapping region having the highest similarity).

[0016] In these embodiments, a plurality of overlapping regions are determined. Each of the overlapping regions may have a different surface area compared to the previous overlapping region. For each of the overlapping regions, a similarity is determined and normalized, and this can then be used to combine the first height map and the second height map by stitching the height maps within the overlapping region having the highest similarity.

[0017] In an embodiment, the sensor comprises a plurality of pixels, and the first and second height maps are shifted relative to each other by only one pixel of the sensor, for example, in the x - direction and / or y - direction of the first and second height maps. Preferably, the first overlapping region has a surface area corresponding to one pixel of the sensor. In other embodiments, the first and second height maps may be shifted relative to each other by a number of pixels, for example, in the x - direction and / or y - direction. The first overlapping region may have a surface area corresponding to one pixel, that is, the first and second height maps overlap at a one - pixel overlapping region at their corners, and after the determination of the similarity, the first and second height maps are shifted relative to each other by, for example, only one 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 part of a pixel.

[0018] In an embodiment, the step of determining the similarity between the height of the first height map and the height of the second height map includes determining the correlation between the height of the first height map and the height of the second height map using a correlation measure, and the first height map and the second height map are combined based on the correlation.

[0019] In an embodiment, the correlation is the zero-normalized cross-correlation function: [Number] and is determined based on:

[0020] where N is the surface area of each overlapping region, sV is the standard deviation of the height in each overlapping region of the first height map, sW is the standard deviation of the height in each overlapping region of the second height map, Vi is the height in each overlapping region of the first height map, and Wi is the height in each overlapping region of the second height map. meanV is the average height in each overlapping region of the first height map, and meanW is the average height in each overlapping region of the second height map. For example, the correlation value thus obtained can be used to determine a correlation matrix, which can be used to determine the overlapping regions used for stitching. The correlation value is normalized with respect to the surface area N of each overlapping region, as well as the standard deviations sV and sW, enabling a direct comparison between correlations.

[0021] A further problem associated with combining height maps to obtain a composite height map is that systematic errors in the surface shape measurement device and / or measurement technique can introduce measurement artifacts in the height map that can artificially increase or distort the similarity between regions of the height map. For example, the measurement artifacts can result from vibrations and / or illumination changes during measurement. For example, the first and second height maps may be stitched based on a similarity that depends on the measurement artifacts. This can result in an incorrect combination of the first and second height maps. The following embodiments of the present invention aim to overcome this problem.

[0022] In an embodiment, the method further includes classifying the features of two height maps into sharp features and smooth features, and determining the similarity, such as correlation, for each of the overlapping regions by using a weighted similarity measure, such as weighted correlation, where the weights are based on the classification of the features into sharp and smooth features. The inventors have recognized that measurement artifacts predominantly result in relatively smooth features as compared to sharper features. In determining the similarity, i.e., the weighted similarity measure, the influence of measurement artifacts on the matching of height maps can be reduced by increasing the relevance of sharper features as compared to smooth features. The features of the height map may be classified by determining their sharpness, for example, based on the gradient or height with respect to its base region. A feature may be classified as sharp if it belongs to the sharpest 50%, for example 40%, for example 20% of the features. A feature may be classified as smooth if it is not sharp. For example, the weights may be determined on a per-pixel basis, for example based on the gradient associated with the pixel, or on a per-feature basis. Alternatively, the weights may be binary. For example, all sharp features are assigned a weight above a threshold. In an embodiment, sharp features have a greater weight than smooth features. The classification of features may depend on a particular application, such as sample characteristics, sample type, or the characteristics of the optical measurement device.

[0023] In an embodiment, the features are classified based on their gradient and / or the weights are gradient-based.

[0024] A further problem related to combining height maps to obtain a composite height map is that regions having features that appear in two different measurements, for example, for determining the first and second height maps, may differ slightly from each other such that they have less similarity than two flat regions, so that different flat regions of the sample surface may appear similar to, and more similar to, regions having features. If there are two different flat regions, the height maps can be stitched along the flat regions due to the high similarity between them. The following embodiments of the present invention aim to overcome this problem.

[0025] In these embodiments, the method further includes determining one or more flat regions in the first and / or second height map, and determining the first and second height maps modified by providing a change, for example a random change, in the height values of the flat regions, and determining the similarity, for example the correlation, between the first height map and the second height map by determining the similarity between the height of the first modified height map and the height of the second modified height map in the first overlapping region.

[0026] The influence of the flat regions on the similarity between the height maps is suppressed by adding a change, preferably a random change, for example random noise, to at least one flat region of the height map in order to obtain a modified height map. The flat regions in the modified height map will appear less flat due to the added change. Preferably, the change is added to only one of the two height maps, and the similarity is determined for one modified height map and one unmodified height map.

[0027] A flat region can be an area lacking features. The flat regions may also be determined by looking at their deviations from a plane, for example by comparing different parts of a height map with the plane, and the deviation from the plane provides a measure of flatness. The flat regions can be determined by determining the change between the normal vectors to the surface region, such that, for example, little change in the normal vector can indicate that the region is a flat region.

[0028] In an embodiment, one or more flat regions are determined based on the classification of features in the height map. For example, a flat region is a region having a substantially flat feature, for example, a region having a gradient below a predetermined threshold.

[0029] The problem associated with combining height maps to obtain a composite height map is that systematic errors in the surface shape measuring device and / or the measuring technique can introduce measurement artifacts in the height map that can artificially increase or distort the similarity between regions of the height map. For example, measurement artifacts can occur due to vibrations and / or illumination changes during measurement. For example, a first height map and a second height map can be stitched based on a similarity measure that depends on the measurement artifacts. This can result in an inaccurate combination of the first and second height maps. A second aspect of the present invention aims to overcome this problem.

[0030] A second aspect of the present invention relates to a method of measuring a first height map and a second height map of a sample surface of a sample using a surface shape measuring device and combining the first and second height maps into a composite height map, the method including the step of measuring the first and second height maps using a sensor of the surface shape measuring device, the sensor being moved relative to the sample surface such that the first and second height maps are measured within a partially overlapping field of view of the sensor, the method including the step of combining the first and second height maps to generate a composite height map of the sample surface, the step of combining the first and second height maps comprises classifying the features of the first and second height maps into distinct features and smooth features; for a plurality of sub-regions of the first and second height maps, determining the similarity between each sub-region of the first and second height maps by using a weighted similarity measure between the first height map and the second height map in each sub-region; the weights are based on the classification of features into distinct features and smooth features; the step of combining the first and second height maps includes: comparing the similarity between the first height map and the second height map in a plurality of sub-regions; based on the comparison of the similarity, for example, based on one sub-region having a higher similarity (e.g., the sub-region having the highest similarity), combining the first and second height maps by stitching the first and second height maps in one of the sub-regions (e.g., the sub-region having the highest similarity). The sub-region is a part of the region of the height map and is a region of an overlapping region or a part of an overlapping region.

[0031] The inventors have recognized that measurement artifacts result mainly in relatively smooth features as compared to more distinct features. In the use of a similarity measure, i.e., in the use of a weighted similarity measure, the influence of measurement artifacts on the matching of height maps can be reduced by increasing the relevance of more distinct features as compared to smooth features. The features of a height map may be classified, for example, by determining their distinctness based on the gradient or height relative to its base region. A feature may be classified as distinct if it belongs to the 50%, for example 40%, for example 20% most distinct features. A feature may be classified as smooth if it is not distinct. For example, the weight may be determined for each pixel, for example based on the gradient associated with the pixel, or may be determined for each feature. Alternatively, the weight may be binary. For example, all distinct features are assigned a weight that is twice as large as that of smooth features. In an embodiment, distinct features have a larger weight than smooth features. The second aspect of the present invention can be combined with any other aspect of the present invention disclosed herein.

[0032] A problem associated with combining height maps to obtain a composite height map is that different flat regions of the sample surface may appear similar or may appear more similar than regions having features. If two different flat regions are present, the height maps can be stitched along the flat regions due to the high similarity between them. The third aspect of the present invention aims to overcome this problem.

[0033] The third aspect of the present invention relates to a method of measuring a first height map and a second height map of a sample surface of a sample using a surface shape measuring device and combining the first and second height maps into a composite height map, the method including the step of measuring the first and second height maps using a sensor of the surface shape measuring device, the sensor including a plurality of pixels, the sensor being moved relative to the sample surface such that the first and second height maps are measured within a partially overlapping field of view of the sensor, In order to generate a composite height map of the sample surface, including the step of combining the first and second height maps, The step of combining the first height map and the second height map is Determining one or more flat regions in the first and / or second height maps, Determining the modified first and second height maps by providing a change in the height value of the flat region, for example a random change, For a plurality of sub-regions of the first modified height map and the second modified height map, in each sub-region, using a similarity measure to determine the similarity between the first modified height map and the second modified height map, Comparing the similarity between the first modified height map and the second modified height map in a plurality of sub-regions, Based on the comparison of the similarity, for example, based on one sub-region having a higher similarity, combining the first and second height maps by stitching the first and second height maps in one of the sub-regions (for example, the one sub-region having the highest similarity). The influence of the flat region on the similarity between the height maps is suppressed by adding a change, preferably a random change, for example random noise, to at least one flat region of the height map in order to obtain a modified height map. The flat regions in the modified height map will appear less flat due to the added change. Preferably, the change is added to only one of the two height maps, and the similarity measure is determined for one modified height map and one unmodified height map.

[0034] The flat regions can be regions lacking features. The flat regions may also be determined by looking at their deviations from a plane, for example by comparing different parts of the height map with the plane, and the deviation from the plane provides a measure of flatness.

[0035] In an embodiment of the third aspect, the one or more flat regions are determined based on the classification of features in the height map. For example, the flat region has a substantially flat feature, for example, a region having a gradient below a predetermined threshold value.

[0036] The third aspect of the present invention can be combined with any other aspect of the present invention disclosed herein.

[0037] The present invention also relates to a surface shape measuring device, for example, an optical surface shape measuring device, including 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 execute a method according to any aspect of the present invention.

[0038] In an embodiment of the surface shape measuring device, the processor is configured to perform a step of determining a first overlapping region of the first and second height maps by partially overlapping the first and second height maps. In the first overlapping region, the first and second height maps overlap. The processor determines a first similarity between the first height map and the second height map by determining a similarity between the height of the first height map and the height of the second height map in the first overlapping region using a similarity measure. The processor is configured to perform a step of determining 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. The second overlapping region preferably has a surface area different from that of the first overlapping region. The processor determines a second similarity between the first height map and the second height map by determining a similarity between the height of the first height map and the height of the second height map in the second overlapping region using a similarity measure. The processor compares the first and second similarities by normalizing the first and second similarities based on the surface area of each of the overlapping regions. Based on the comparison of the first and second similarities, in one of the overlapping regions (e.g., the overlapping region with higher similarity), combining the first and second height maps by stitching the first and second height maps; Based on the combined first and second height maps, outputting a composite height map of the sample surface, and is configured to perform.

[0039] In an embodiment, the processor is configured to cause the surface shape measuring device to measure the first and second height maps using a sensor of the surface shape measuring device, and the sensor is moved relative to the sample surface such that the first and second height maps are measured within a partially overlapping field of view of the sensor; configured to perform combining the first and second height maps to generate a composite height map of the sample surface; The step of combining the first height map and the second height map includes classifying the features of the first and second height maps into distinct features and smooth features; determining the similarity between respective sub-regions of the first and second height maps by using a weighted similarity measure between the first and second height maps in each sub-region, wherein the weight is based on the classification of the features into distinct features and smooth features; The step of combining the first height map and the second height map includes comparing the similarity between the first and second height maps in a plurality of sub-regions; based on the comparison of the similarity, for example, based on one sub-region with higher similarity, combining the first and second height maps by stitching the first and second height maps in one of the sub-regions (e.g., the sub-region with the highest similarity).

[0040] In an embodiment, the processor is configured to cause the surface shape measuring device to perform a step of measuring first and second height maps using a sensor of the surface shape measuring device, and the sensor is moved relative to the sample surface such that the first and second height maps are measured within a partially overlapping field of view in the sensor. The processor is configured to perform a step of combining the first and second height maps to generate a composite height map of the sample surface. The step of combining the first height map and the second height map includes determining one or more flat regions in the first and / or second height maps, determining first and second height maps corrected by providing a change in the height value of the flat region, for example a random change, determining the similarity in respective sub-regions of the first corrected height map and the second corrected height map for a plurality of sub-regions of the first corrected height map and the second corrected height map, comparing the similarity between the first corrected height map and the second corrected height map in the plurality of sub-regions, and combining the first and second height maps by stitching the first and second height maps in one of the sub-regions (e.g., the sub-region having the highest similarity), for example, based on one sub-region having a higher similarity, based on the comparison of the similarities.

[0041] The present invention also relates to a digital data storage medium including software for causing a surface shape measuring device according to the present invention to execute the method according to the present invention when executed on a processor of the surface shape measuring device according to the present invention.

[0042] Here, embodiments of the present invention will be described by way of example with reference to the accompanying drawings in which corresponding reference symbols indicate corresponding parts:

Brief Description of the Drawings

[0043]

Figure 1

Figure 2

Figure 3

Figure 4

[0044] FIG. 1 shows a surface shape measuring device 1 including a sensor 2 having pixels for measuring a first height map and a second height map of the sample surface of a sample 3, for example, an optical surface shape measuring device 1. The surface shape measuring device 1 may be an interferometer such as a white light interferometer configured to measure the height map of the sample 3 using an interference pattern.

[0045] The surface shape measuring device may further include a sample holder 4 for holding the sample 3. The sample holder 4 can enable relative movement between the sample 3 and the sensor 2 and enable measurement of the first and second height maps in a partially overlapping field of view of the sensor 2.

[0046] The surface shape measuring device includes a processor 5 connected to the sensor 2 to enable receiving the measured height map of the sample surface from the sensor 2. The processor 5 is configured to execute the method of the present invention. For example, according to the first aspect, the processor 5 may be configured to perform step 101 of causing the sensor 2 to measure the first height map and the second height map. The sensor 2 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 2. The processor 5 combines the first and second height maps to generate a composite height map of the sample surface. Based on the combined first and second height maps, step 108 of outputting a composite height map of the sample surface can be performed. The step of combining the first height map and the second height map is including step 102 of determining a first overlapping region of the first and second height maps by partially overlapping the first and second height maps, in which the first and second height maps overlap in the first overlapping region, The step of combining the first height map and the second height map is determining a first similarity between the first height map and the second height map by determining the similarity between the height of the first height map and the height of the second height map in the first overlapping region using a similarity measure, step 103; including step 104 of determining 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, the second overlapping region preferably having a surface area different from that of the first overlapping region, The step of combining the first height map and the second height map is determining a second similarity between the first height map and the second height map by determining the similarity between the height of the first height map and the height of the second height map in the second overlapping region using a similarity measure, step 105; comparing the first and second similarities by normalizing the first and second similarities based on the surface area of each of the overlapping regions, step 106; combining the first and second height maps by stitching the first and second height maps in one of the overlapping regions (e.g., the overlapping region with higher similarity) based on the comparison of the first and second similarities to generate a composite height map, step 107.

[0047] For example, according to the second aspect, the processor 5 may be configured to perform step 201 of causing the sensor 2 to measure a first height map and a second height map. The sensor 2 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 2, The processor 5 combines the first and second height maps to generate a composite height map of the sample surface, and is configured to perform step 206 of outputting a composite height map of the sample surface based on the combined first and second height maps. Combining the first height map and the second height map includes step 202 of classifying the features of the first and second height maps into sharp features and smooth features, and for a plurality of sub-regions of the first and second heavy maps, by using a weighted similarity measure between the first height map and the second height map in each sub-region, determining the similarity between the respective sub-regions of the first and second height maps in step 203, where the weights are based on the classification of the features into sharp features and smooth features, The processor 5 compares the similarity between the first height map and the second height map in a plurality of sub-regions in step 204, and based on the comparison of the similarities, for example, based on one sub-region having a higher similarity, combining the first and second height maps by stitching the first and second height maps in one of the sub-regions (e.g., the one sub-region having the highest similarity) in step 205.

[0048] For example, according to the third aspect, the processor 5 may be configured to perform step 301 of causing the sensor 2 to measure a first and a second height map. The sensor 2 is moved relative to the sample surface such that the first and second height maps are measured in a partially overlapping field of view of the sensor 2, The processor 5 combines the first and second height maps to generate a composite height map of the sample surface, and configured to perform step 302 of outputting a composite height map of the sample surface based on the combined first and second height maps, The step of combining the first height map and the second height map includes step 303 of determining one or more flat regions in the first and / or second height maps, step 304 of determining modified first and second height maps by providing a change in the height value of the flat region, such as a random change, step 305 of determining the similarity in each sub-region of the first modified height map and the second modified height map for a plurality of sub-regions of the first modified height map and the second modified height map, step 306 of comparing the similarity between the first modified height map and the second modified height map in the plurality of sub-regions, and step 307 of combining the first and second height maps by stitching the first and second height maps in one of the sub-regions (e.g., in the one sub-region having the highest similarity) based on the comparison of the similarity, for example, based on one sub-region having a higher similarity.

Claims

1. 1. A method of measuring a first height map and a second height map of a sample surface of a sample with a surface profilometer and combining the first and second height maps into a composite height map, the method comprising: measuring the first and second height maps with a sensor of a surface profilometer, the sensor being moved relative to the sample surface such that the first and second height maps are measured within overlapping fields of view of the sensor; combining the first and second height maps to generate a composite height map of the sample surface; Including, The step of combining the first and second height maps comprises: determining a first overlap region of the first and second height maps by partially overlapping the first and second height maps, where the first and second height maps overlap; determining a first similarity between the first and second height maps by determining a similarity between the first and second height maps in the first overlap region using a similarity measure; determining a second overlap region of the first and second height maps by shifting the first and second height maps relative to one another compared to the first overlap region; determining a second similarity between the first and second height maps by determining a similarity between heights of the first and second height maps in the second overlap region using the similarity measure; comparing the first similarity and the second similarity by normalizing the first and second similarities based on a surface area of ​​each of the first overlap region and the second overlap region; combining the first and second height maps by stitching the first and second height maps in one of the first overlap region and the second overlap region based on a comparison of the first similarity measure and the second similarity measure. method.

2. The method comprises: determining a plurality of overlap regions of the first and second height maps by subsequently shifting the first and second height maps relative to one another; determining a similarity between the first and second height maps by determining a similarity between heights of the first and second height maps in respective overlap regions by using the similarity measure after each shift of the first and second height maps; comparing the plurality of similarities by normalizing the similarities based on a surface area of ​​each of the overlapping regions; combining the first and second height maps by stitching the first and second height maps at an overlap region based on a plurality of similarity comparisons. The method of claim 1.

3. the sensor comprises a plurality of pixels, and the first and second height maps are shifted relative to one another by one pixel of the sensor. The method according to claim 1 or 2.

4. the similarity measure is based on a correlation between heights of the first and second height maps in their respective overlap regions, and the first and second height maps are combined based on the correlation. The method according to claim 1 or 2.

5. The correlation is calculated using the zero-normalized cross-correlation function: [0010] is determined based on where N is the surface area of ​​each of the first and second overlapping regions, sV is the standard deviation of heights in each overlapping region of the first height map, sW is the standard deviation of heights in each overlapping region of the second height map, Vi is the height in each overlapping region of the first height map, Wi is the height in each overlapping region of the second height map, meanV is the average height in each overlapping region of the first height map, and meanW is the average height in each overlapping region of the second height map. The method according to claim 4.

6. The method comprises: classifying the features of the two height maps into sharp and smooth features; determining a similarity for each of the overlapping regions by using a weighted similarity measure; The weights are based on classifying features into sharp and smooth features. The method according to claim 1 or 2.

7. The sharp features have a higher weight than the smooth features. The method according to claim 6.

8. The features are classified based on their gradients and / or the weights are based on gradients. The method according to claim 6.

9. The method comprises: determining one or more flat regions in the first height map and / or the second height map; determining the first and second height maps modified by providing a change in height values ​​of the one or more flat regions; and using the similarity measure to determine a similarity between the first and second height maps within the first overlap region. The method according to claim 1 or 2.

10. the one or more flat regions are determined based on classification of features in a height map.

10. The method of claim 9.

11. 3. A surface profilometer comprising a sensor having pixels for measuring first and second height maps of a sample surface of a sample, and a processor configured to carry out the method according to claim 1 or 2.

12. The processor, causing the sensor to measure the first and second height maps, the sensor being moved relative to a sample surface such that the first and second height maps are measured within overlapping fields of view of the sensor; combining the first and second height maps to generate a composite height map of the sample surface; outputting a composite height map of the sample surface based on the combined first and second height maps; The step of combining the first and second height maps comprises: determining a first overlap region of the first and second height maps by overlapping the first and second height maps, where the first and second height maps overlap; determining a first similarity between the first and second height maps by determining a similarity between heights of the first and second height maps within the first overlap region using a similarity measure; determining a second overlap region of the first and second height maps by shifting the first and second height maps relative to one another compared to the first overlap region; determining a second similarity between the first and second height maps by determining a similarity between heights of the first and second height maps in the second overlap region using the similarity measure; comparing the first similarity and the second similarity by normalizing the first and second similarities based on a surface area of ​​each of the first overlap region and the second overlap region; combining the first and second height maps by stitching the first and second height maps in one of the overlapping regions based on a comparison of the first similarity and the second similarity. The surface shape measuring apparatus according to claim 11.

13. A computer program product, when executed on the processor of a surface profile measuring apparatus according to claim 11, causing the surface profile measuring apparatus to carry out the method according to claim 1.

Images