DE102022118586A1 - Computer-implemented method, procedure, measuring device and computer program product - Google Patents

Abstract

The present invention relates to a computer-implemented method (200) for localizing an edge position of an edge (166) in an image area (162) of an image (160) with an extended depth of field, with the following steps: determining (206) an image gradient for each image point in the Image area (162), wherein the determined image gradients form an image gradient map; determining (210) at least one edge parameter of a modeled, curved edge gradient based on the image gradient map; determining (212) an edge profile (172) of the edge (166) based on a projection of the image points of the image area (162) along the edge profile using the at least one edge parameter; and determining (214) the edge position based on the edge profile (172). The present invention further relates to a method (220) for edge localization in an image with an extended depth of field, a measuring device (10) and a computer program product.

Description

The present invention relates to a computer-implemented method for locating an edge position of an edge in an image region of an image. The present invention further relates to a method for edge localization in an image. The present invention further relates to a measuring device, in particular a coordinate measuring machine or a microscope. The present invention further relates to a computer program product.

Measuring devices for measuring the surface of a workpiece, also called measuring object, are well known in the art. Industrial measurement technology generally requires measuring devices that can measure 3D information on a workpiece. For this purpose, different types of sensors can be used in such measuring devices in order to record the coordinates of a workpiece to be measured.

For example, optical measuring devices are also known in which optical sensors are used. The optical sensors enable contactless detection of the coordinates of a workpiece. In optical measuring devices, the workpiece to be measured is clamped on a table that serves as a workpiece holder. The table forms an X-Y plane. The optical sensor is spaced perpendicular to this plane, i.e. in the Z direction of a Cartesian coordinate system, from the workpiece to be measured.

Since conventional optical measuring devices, such as microscopes or coordinate measuring machines, can only record 2D data, the image depth or depth information in the Z direction is determined using an additional technique.

A non-invasive and inexpensive solution is to determine the depth information in the Z direction using a number of optical measurements. Image blur caused by optical defocus changes in a predictable manner. The optical system of the optical sensor has a focal plane, which is a plane of greatest sharpness. If an object point that lies on the surface of the workpiece is moved towards the focal plane, the image of the object point becomes sharper. If the object point is moved away from the focal plane, the image of the object point becomes blurrier. If the object point is located in the focal plane, the image of the object point is sharpest. The image blur can therefore be controlled by varying the distance between the workpiece and the optical system. Taking images as the workpiece moves through focus creates a focal image stack. Based on the focal image stack, depth information of the object points can be extracted using a technique called Shape from Focus (SFF).

With the SFF technique, the recorded focal image stack is first evaluated using an autofocus metric, which defines a local sharpness measure for each individual image in pixel resolution. A sharpness value is determined for each pixel of each image. The sharpness values are saved in a 3D sharpness matrix. Each individual pixel is therefore assigned a sharpness profile along the z-direction. Then the maximum of each sharpness profile is determined. The maximum therefore indicates at which z position the sharpest image of an object point onto the image point occurs. From this, depth information can then be determined for each object point on the workpiece. Based on the depth information determined, a depth map of the area of the workpiece can be generated. Based on the depth map and the focal image stack, an image with an extended depth of field, a so-called “extended depth of field” (EDOF) image, can then be generated.

Methods that use the SFF technique are known in microscopy. For example, the publication shows EP 2 598 836 A1 a method for compensating for illumination deficiencies in the microscopic Shape from Focus (SFF), first estimating the reflectivity of the scene using a projector camera system and then applying the microscopic Shape from Focus (SFF) to a stack of reflectance cards rather than the original ones Image data is applied.

Furthermore, such procedures are also in the article "Shape From Focus Sytem" by Shree K. Nayar, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 1992, 302-308 as well as in the article “Focus Variation Instruments” by Franz Helmli, Chapter 7 from the book “Optical Measurement of Surface Topography”, pages 131-166, Springer Verlag.

Based on an image that depicts a structure, further information about the structure depicted in the image can be obtained. In particular, it is desirable to obtain further information about the contour of the imaged structure, in particular about edges of the structure. For example, the structure can be a workpiece. In this case, the image can be evaluated to determine the position of edges of the workpiece.

The image to be evaluated can, for example, be a recorded single image or an image with an extended depth of field. The measurement inside half of an image with extended depth of field allows a variety of edge positions to be evaluated from different z positions. In contrast, single-image measurement allows an assessment of edges that are within the sharply imaged focal area. Edges that are out of focus cannot then be evaluated in the image. It is therefore particularly advantageous to carry out edge evaluations in images with an extended depth of field.

Various methods are already known in the prior art for localizing these edges, in particular their subpixel-precise edge position, in an image.

bestimmt. Darin entspricht [x₀,y₀] dem Suchstrahlursprung, [n_x,n_y] der Suchstrahlrichtung und l dem freien Suchstrahlparameter. Die zugehörige Bildinformation I(x_Suchstrahl,y_Suchstrahl) wird hierbei mit Hilfe einer Interpolation aus dem aufgenommenen Bild errechnet. Im nächsten Schritt wird beispielsweise mit Hilfe eines „Canny-Edge-Algorithmus“ oder einer alternativen Technik, insbesondere eines Schwellwert-Verfahren, die Kantenposition bestimmt. Ein derartiges Schwellwert-Verfahren ist beispielsweise in dem Fachartikel „Edge Detection with Sub-pixel Accuracy Based on Approximation of Edge with Erf Function“, HAGARA et al, RADIOENGINEERING, VOL. 20, NO. 2 beschrieben. Zentraler Nachteil eines solchen Kantenbestimmungsverfahrens liegt in der Rauschanfälligkeit der verwendeten Algorithmen. Da die Kanteninformation nur entlang einer einzelnen Suchstrahllinie bekannt ist, führt ein etwaiges Rauschen während der Messung zu einer direkten Beeinflussung der Messergebnisse und vermindert entsprechend deren Qualität.So-called search beam methods are usually used to determine a subpixel-precise edge position. For this purpose, the image information is evaluated along the search beam line along an arbitrarily selected search beam that contains the edge to be measured. The search beam line in the image is represented by the straight line equation $$\left(\begin{array}{l}{x}_{SucHstraHl}\\ y_{SucHstraHl}\end{array}\right)=\left(\begin{array}{l}{x}_0\\ y_0\end{array}\right)+l\left(\begin{array}{l}{n}_x\\ n_y\end{array}\right)$$

certainly. Therein, [x ₀ ,y ₀ ] corresponds to the search beam origin, [n _x ,n _y ] corresponds to the search beam direction and l corresponds to the free search beam parameter. The associated image information I(x _{search beam} , y _{search beam} ) is calculated from the recorded image using interpolation. In the next step, the edge position is determined, for example, with the help of a “canny edge algorithm” or an alternative technique, in particular a threshold value method. Such a threshold value method is described, for example, in the specialist article “Edge Detection with Sub-pixel Accuracy Based on Approximation of Edge with Erf Function”, HAGARA et al, RADIOENGINEERING, VOL. 20, NO. 2 described. The main disadvantage of such an edge determination method is the susceptibility of the algorithms used to noise. Since the edge information is only known along a single search beam line, any noise during the measurement has a direct influence on the measurement results and accordingly reduces their quality.

Alternatively, it is also conceivable, instead of a single search beam, to consider the edge information for a flat area, a so-called region of interest (Rol), and to project it relative to the surface normal with respect to a straight edge. The ROI is therefore an image area of the image, particularly a small one. This procedure is known in the literature as the “slanted edge method” and enables the extraction of a super-resolved and better sampled edge profile. An edge position is then determined using an edge localization method. The slanted edge method is, for example, in the specialist articles "Robust edge-spread function construction methods to counter poor sample spacing uniformity in the slanted-edge method", F. van den Bergh, J. Opt. Soc. Am. A 36, pages 1126-1136 (2019), DOI: 10.1364/JOSAA.36.001126 and "Comparison of MTF measurements using edge method: towards reference data set", Viallefont-Roninet et al, Opt. Express 26, 33625-33648 (2018), DOI: 10.1364/OE.26.033625.

Compared to the search beam method, the “slanted edge method” has an improved signal-to-noise ratio and allows higher localization accuracy due to the over-resolution sampling properties.

However, the methods known from the prior art for edge localization in images with an extended depth of field still leave room for improvements, particularly with regard to the accuracy of determining an edge position.

Against this background, it is a technical object of the present invention to provide a method and a device by means of which edges in an image can be better localized.

• - Bestimmen eines Bildgradienten für jeden Bildpunkt in dem Bildbereich, wobei die bestimmten Bildgradienten eine Bildgradientenkarte bilden;
• - Bestimmen mindestens eines Kantenparameters eines modellierten, gekrümmten Kantenverlaufs basierend auf der Bildgradientenkarte;
• - Bestimmen eines Kantenprofils der Kante auf Basis einer Projektion der Bildpunkte des Bildbereichs entlang des Kantenverlaufs unter Verwendung des mindestens einen Kantenparameters; und
• - Bestimmen der Kantenposition auf Basis des Kantenprofils.

In a first aspect of the present invention, a computer-implemented method for locating an edge position of an edge in an image region of an image is provided. The procedure has the following steps:

• - determining an image gradient for each pixel in the image area, the determined image gradients forming an image gradient map;
• - Determine at least one edge parameter of a modeled, curved edge profile based on the image gradient map;
• - determining an edge profile of the edge based on a projection of the image points of the image area along the edge profile using the at least one edge parameter; and
• - Determine the edge position based on the edge profile.

The image can be a captured still image or an image with an extended depth of field. An image plane of the image can be described using a two-dimensional coordinate system. This can be, for example, a Cartesian coordinate system with an x-direction and a y-direction. The image has a plurality of pixels. The pixels are in the x and y Direction distributed at regular intervals. Each pixel has a gray or RGB value, which describes the brightness or intensity of the pixel. The intensity values form an intensity field φ(x,y) of the image. The intensity field assigns an intensity value to each location in the image. When using an image with an extended depth of field, each pixel can also be assigned a depth value (see for example 6D ), which will not be used for edge localization in the following.

The image can, for example, depict an area of a surface of a workpiece. The workpiece has a surface structure that has edges. Edges of the surface contour therefore also lie in the area of the surface of the workpiece that is shown in the image. In other words, the edges depicted in the image may be edges of the workpiece depicted. The edge position indicates the location of an edge in the image.

The intensities of image points that depict the same, in particular flat, surface of the workpiece are similar. In other words, these intensities differ only slightly from one another. The surfaces of a workpiece adjacent to an edge are displayed in the image with different intensities. This results in a larger change in intensity in the edge area. In other words, the intensity deviation at an edge is greater than in an area without an edge.

In order to localize the position of an edge, at least an image area of the image in which the edge runs is considered. This area can also be referred to as the “Region of Interest” (ROI). The image area can be selected by a user, for example. Alternatively, the image area can be determined based on image analysis. For this purpose, for example, image areas can be selected that have large intensity deviations.

der den Betrag des Vektors angibt und einem Maß für die Stärke der Intensitätsänderung entspricht.To localize an edge position of an edge in the image area, an image gradient is first determined for each pixel. The image gradient indicates how the intensity, i.e. the brightness of the pixels, changes at one location of a pixel compared to surrounding pixels. The image gradient is determined in particular by a change in the brightness of surrounding pixels. The image gradient is therefore the gradient of the intensity field of an image and can be described using the formula [G _x ,G _y ] = ∇φ(x,y). For example, a finite difference approximation of the derivative operator can be used to calculate the gradient. The image gradient is therefore a vector that indicates the change in intensity at an image point, i.e. at a location (x,y) of the image. The image gradient has a direction, which indicates the direction of greatest intensity change at that location, and a gradient value $\text{G}=\sqrt{{\text{G}}_{\text{x}}^2+{\text{G}}_{\text{y}}^2},$

which indicates the magnitude of the vector and corresponds to a measure of the strength of the change in intensity.

beispielsweise durch direktionale Sobelfilter oder numerische Finite-Differenzen Ableitungsverfahren ermittelt werden.The image gradient may be determined for each point based on the image or all or part of the focal image stack of the area of the workpiece. For this purpose, an image gradient is calculated for each pixel. For this purpose, the numerical approximation of the image gradient can be used in the image area $$\left[{\text{G}}_{\text{x}},{\text{G}}_{\text{y}}\right]=\left[{\partial }_{\text{x}}\mathrm{\phi }\left(\text{x},\text{y}\right),{\partial }_{\text{y}}\mathrm{\phi }\left(\text{x},\text{y}\right)\right]$$

can be determined, for example, by directional Sobel filters or numerical finite difference derivation methods.

In order to suppress influences caused by image noise, it is particularly advantageous to calculate the image gradients as a weighted average over several images from a focal image stack, ie $$\left[{\text{G}}_{\text{x}},{\text{G}}_{\text{y}}\right]=\frac{1}{\text{N}}{\displaystyle \sum _{\text{i}=1}^{\text{N}}\left[{\partial }_{\text{x}}{\mathrm{\phi }}_{\text{i}}\left(\text{x},\text{y}\right),{\partial }_{\text{y}}{\phi }_{\text{i}}\left(\text{x},\text{y}\right)\right]}$$

In other words, the image gradient [G _x ,G _y ] indicates how the brightness of surrounding pixels changes. The image gradient [G _x ,G _y ] at an image point is therefore a vector that points in the direction of the greatest change in brightness.

The determined image gradients together form an image gradient map. The image gradient map therefore contains an image gradient [G _x ,G _y ] for each pixel. In other words, the image gradient map assigns a corresponding image gradient [G _x ,G _y ] to each pixel position [x,y].

Basically, an edge in the image area has an edge gradient. The edge course describes the course of the edge in the xy plane. The edge profile therefore describes a curve in the xy plane. The edge course can also be referred to as edge geometry. Each point on the edge has an edge tangent and an edge normal. The edge tangent is a tangent to the edge at the respective point. The edge normal is a normal to the edge at the respective point. The edge tangent and the edge normal lie in the xy plane. The edge tangent runs in a tangential direction to the edge. The tangential direction describes the direction of the tangent to the edge in the xy plane at the respective point on the edge. The tangential direction therefore describes the direction of the edge at the respective point. The tangential direction can also be called the edge direction be referred to. The edge normal runs in a normal direction to the edge. The normal direction describes the direction of the normal to the edge in the xy plane at the respective point on the edge. At each point, the normal direction and the edge direction are perpendicular to each other.

The edge can be curved as desired. “Curved” means the local deviation of a curve from a straight line. Curved therefore does not mean linear. With a linear, i.e. not curved, edge, the normal direction and the edge direction are the same for all points on the edge. With a curved edge, the direction of the edge, i.e. the direction of the edge, changes in the x-y plane along the edge, i.e. when you follow the edge. If the edge is curved, the normal direction also changes along the edge.

The edge course of the edge can be modeled or described using a model of a curved edge course. The modeled, curved edge course serves to describe or approximate the actual edge course of the edge. The modeled, curved edge has at least one edge parameter that is used to describe the edge using the underlying model. In other words, the modeled, curved edge profile has one or more edge parameters. In particular, the modeled, curved edge profile can have more than one edge parameter.

The edge course of the edge can thus be described or modeled using the at least one edge parameter. The edge parameter can, for example, be one parameter or several parameters by means of which the edge direction, the normal direction and/or the curvature of the edge path are described. The edge profile can preferably be described using any function, whereby each edge parameter can be a parameter of the function. If the curvature is constant, the edge parameter can, for example, indicate the location of the center of curvature.

As explained previously, the intensity changes in the area of the edge. The change in intensity runs essentially perpendicular to the edge, i.e. in the normal direction. In other words, the image gradients in the edge region are essentially aligned in the direction normal to the edge. The at least one edge parameter can thus be determined using the modeled, curved edge profile and the specific image gradients.

The determined at least one edge parameter is then used to carry out a projection of the image points of the image area along the edge path, i.e. along the edge path direction, onto the normal direction. Each pixel is assigned a position in the normal direction. With others, the projection determines the position of each pixel relative to the edge.

Based on this projection, an edge profile is then determined or constructed. The edge profile can also be referred to as an edge transfer profile or edge spread function. The edge profile is an intensity profile. The intensity profile indicates the intensity of each pixel at the respective position in the normal direction. The edge profile thus indicates an intensity distribution or an intensity curve in the normal direction. In other words, the edge profile describes the intensity distribution relative to the edge. In this context, one also speaks of an over-resolved edge profile.

The edge position of the edge can then be determined based on this specific edge profile. The intensity of the pixels usually changes the most in the edge area. For example, the position in the normal direction at which the edge profile has the greatest change or slope can be determined as the edge position. Alternatively, the threshold value at which the edge contrast reaches 50% is often defined as the edge position. In other words, this corresponds to the edge position in which the intensity or gray value corresponds to the average of the maximum & minimum intensity or gray value of the edge transfer function.

• - Erfassen einer Mehrzahl von Bildern des Bereichs der Oberfläche des Werkstücks mittels des optischen Sensors, wobei die Bilder jeweils den Bereich der Oberfläche des Werkstücks mit in der Tiefenrichtung unterschiedlichen, definierten Fokalebenenpositionen abbilden, und wobei die erfassten Bilder einen Fokalbildstapel bilden;
• - Erzeugen des Bildes mit erweiterter Schärfentiefe in der Tiefenrichtung basierend auf dem Fokalbildstapel; und
• - Lokalisieren einer Kantenposition einer Kante in einem Bildbereich des Bildes mit erweiterter Schärfentiefe mittels des Verfahrens nach dem ersten Aspekt der Erfindung.

According to a second aspect of the invention, there is provided a method for edge localization in an image with an extended depth of field, the image depicting a region of a surface of a workpiece, comprising the following steps:

• - Acquiring a plurality of images of the area of the surface of the workpiece by means of the optical sensor, the images each imaging the area of the surface of the workpiece with defined focal plane positions that are different in the depth direction, and the acquired images forming a focal image stack;
• - Generate the image with extended depth of field in the depth direction based on the focal image stack; and
• - Locating an edge position of an edge in an image area of the image with an extended depth of field using the method according to the first aspect of the invention.

• - Steuern des optischen Sensors derart, dass eine Mehrzahl von Bildern eines Bereichs der Oberfläche des Werkstücks mittels des optischen Sensors erfasst wird, wobei die Bilder jeweils den Bereich der Oberfläche des Werkstücks mit in der Tiefenrichtung unterschiedlichen, definierten Fokalebenenpositionen abbilden, und wobei die erfassten Bilder einen Fokalbildstapel bilden;
• - Erzeugen eines Bildes mit erweiterter Schärfentiefe in der Tiefenrichtung basierend auf dem Fokalbildstapel; und
• - Lokalisieren von zumindest einer Kantenposition einer Kante in einem Bildbereich des Bildes mit erweiterter Schärfentiefe mittels des Verfahrens nach dem ersten Aspekt der Erfindung.

According to a third aspect of the invention, a measuring device, in particular a coordinate measuring machine or a microscope, wherein the measuring device has a workpiece holder for a workpiece, an optical sensor and a control device, wherein the optical sensor is designed to produce images of a region of a surface of the workpiece detect, the optical sensor and the workpiece being spaced apart from one another in a depth direction, the control device being adapted to carry out the following steps:

• - Controlling the optical sensor such that a plurality of images of a region of the surface of the workpiece are captured by means of the optical sensor, the images each imaging the region of the surface of the workpiece with defined focal plane positions that are different in the depth direction, and wherein the captured images form a focal image stack;
• - Generate an image with extended depth of field in the depth direction based on the focal image stack; and
• - Localizing at least one edge position of an edge in an image area of the image with an extended depth of field using the method according to the first aspect of the invention.

According to a fourth aspect of the invention, a computer program product is provided with a computer program that has program code means for carrying out a method according to the first aspect of the invention when the computer program is executed on a measuring device. Furthermore, a computer program product can also be provided which includes instructions which, when the program is executed by a computer, cause it to carry out the steps of the method according to the first aspect of the invention.

Advantageously, the new method is implemented using a processing unit or a control device, which may be a general purpose computer or a special purpose computer, storing and executing an appropriate computer program or computer program product, the computer program or computer program product for locating an edge position of an edge in an image area of an Image or for edge localization in an image with extended depth of field is designed and designed according to the aforementioned methods.

A workpiece is understood to mean an object, in particular a measurement object, that is being measured. The workpiece has a surface. Images of an area of the surface can be captured using an optical sensor on a measuring device. The measuring device can in particular be a coordinate measuring machine or a microscope. The optical sensor can, for example, have an image sensor and an optical system. The image sensor can be, for example, a charge-coupled semiconductor element sensor, which is also called a CCD (charge-couple device) sensor. The CCD sensor can be a monochrome sensor or a color sensor. The optical system can image the area of the workpiece surface on the image sensor. The optical system can in particular have a lens that is telecentric at least on the object side.

An image captured with the optical sensor has a plurality of pixels. Each pixel represents an object point of the area of the surface of the workpiece. The number of image points therefore corresponds to the number of object points imaged. Current optical sensors can have resolutions of several megapixels. The number of pixels of a captured image and correspondingly the number of object points imaged correspond to the number of pixels of the optical sensor. The captured images can therefore have several million pixels.

While capturing the images, the focal plane position of the optical sensor is changed in a depth direction relative to the workpiece to capture each image with a different, defined focal plane position.

Preferably, the optical sensor and the workpiece are movable relative to one another in the depth direction, so that a distance in the depth direction between the workpiece and the optical sensor can be changed. For example, the measuring device can have a drive device which is designed to move the optical sensor and the workpiece relative to one another in the depth direction. While capturing the images, the distance of the optical sensor to the workpiece in the depth direction can then be changed to change the focal plane position for each image. The depth direction may be a Z direction of a Cartesian coordinate system, where the captured images are a map of the area of the surface of the workpiece in the X and Y directions. In other words, the mapping of the images is perpendicular to the depth direction. The pictures will recorded at different, defined distances from the workpiece. “Defined” in this context means that the distances at which the images are captured are determined in advance and therefore known. For example, the images can be recorded in 50µm steps.

Since the images are taken from different distances from the workpiece, the focal plane or the plane of greatest sharpness of the optical sensor varies between the images. The optical setting of the optical sensor, in particular the focus distance of the lens, can remain constant. Each image is captured with a different focal plane. The images thus together form a focal image stack. A defined distance is assigned to each image in the focal image stack. The distance of an image corresponds to a depth value in the depth direction, particularly a Z position in the Z direction. In other words, the captured images each image the area of the surface of the workpiece from different, defined distances from the workpiece in a depth direction, with a distance being assigned to each image of the focal image stack.

Alternatively, the focal plane position can be changed during the capture of the images by refocusing the optics or changing the focus distance of the lens of the optical sensor. This means that each focus setting on the lens is assigned a corresponding distance between the optical sensor and the set focal plane in the depth direction. In this way, the focal plane or the plane of greatest sharpness of the optical sensor can be varied optically between the images in order to form the focal image stack. The distance between the workpiece and the optical sensor can then remain constant.

Each image has the same number of pixels. Each pixel of an image represents a corresponding object point of the workpiece from the area of the surface of the workpiece. Each pixel of an image is therefore assigned to a corresponding object point on the surface of the workpiece. An object point can also be referred to as a measurement point. Each object point on the surface of the workpiece has a position in the Cartesian coordinate system, in particular an X position in the X direction, a Y position in the Y direction and a Z position in the Z direction. The Z position in the Z direction can also be called the depth value in the depth direction. Since the captured images each depict the same area of the surface of the workpiece, the image points of the images are assigned to the same object points. In particular, the pixels of the images with the same X and Y coordinates are assigned to the same object point. This means that one image point is assigned to each object point from each image.

Based on the recorded focal image stack, an image with an extended depth of field is then generated in the depth direction. For this purpose, the focused areas of the individual images of the focal image stack are combined to form a sharp overall image. As explained previously, an object point is in focus if it lies in the focal plane when the image is taken. In other words, every object point is imaged sharpest in a certain focal plane position. The focal plane position in which an object point is imaged most sharply can be determined using the images from the recorded focal image stack. The image with an extended depth of field can then be composed, for example, of the image points of the images of the focal image stack that depict the object points most sharply. The image with extended depth of field can also be called a measurement image. The described procedure for generating an image with an extended depth of field thus leads to a measurement recording in the best adjustment plane.

The drive device of the measuring device can adjust the distance between the workpiece and the optical sensor. For this purpose, the drive device can move the workpiece holder and/or the optical sensor in the depth direction. The drive device can have, for example, a piezo-electric drive, a direct drive or a spindle drive. A spindle drive is particularly suitable because it has high resolution, can move large loads and has a large detection range in the depth direction.

The drive device and the optical sensor can be controlled using the control device of the measuring device. For this purpose, the control device can, for example, have a control unit that can send control commands to the optical sensor and the drive device. The calculation steps for generating the corrected image with extended depth of field can also be carried out using the control device of the measuring device. For this purpose, the control device can, for example, have a data processing unit that carries out the steps for generating the corrected image with an extended depth of field.

The “slanted edge method” known in the prior art has a central disadvantage. It is based on the assumption that there is a straight edge within the examined image area (Rol) and the edge information is orthogonal can be projected over the edge normal. In other words, the slanted edge method approximates any shaped edge geometry in the sense of a first Taylor approximation by a linear function, ie with a straight line. However, during metrological investigations, edge profiles are often not measured, but rather round or arbitrarily curved, and the corresponding assumptions of the “slanted edge method” are violated.

The present invention provides a method that can specifically address and circumvent the limitations of the slanted edge method. For this purpose, the edge profile is approximated with an arbitrarily curved profile (for example a circular arc) instead of a straight line. In other words, in contrast to the slanted edge methodology, the proposed method allows the approximation of the local edge profile within the image region (Rol) using an improved second or higher order Taylor approximation instead of a less accurate first order Taylor approximation.

This makes it possible to extend the general advantages of the slanted edge methodology for edge localization in its applicability specifically to round or arbitrarily curved edges that are often relevant for measurement technology. In this way, the edge position of edges, in particular those with curved edges, can be determined better, in particular more precisely, in an image with an extended depth of field.

The technical task posed at the beginning is thus completely solved.

• - Filtern der Bildgradientenkarte, wobei die Bildgradienten verworfen werden, die unterhalb eines definierten Schwellwerts liegen.

In a first embodiment of the first aspect, the method further comprises the following step:

• - Filtering the image gradient map, whereby the image gradients that are below a defined threshold are discarded.

In particular, the image gradients whose gradient values G are below a defined threshold value are rejected. As already explained, the intensity of the image points changes more in the edge area than on flat areas or surfaces. In the filtering step, all small image gradients are therefore discarded. In this way, image gradients of pixels that are not in the edge area can be rejected. This reduces the image gradient map to the image gradients of those pixels that are in the edge area, i.e. close to or on the edge.

In a further embodiment of the first aspect, the at least one edge parameter is one or more parameters of an edge profile model for describing the edge profile, wherein the at least one edge parameter is determined based on the edge profile model and the image gradient map.

The edge profile model is used to describe or approximate the actual edge profile of the edge. In other words, the curved edge profile is modeled using the edge profile model. The modeled, curved edge profile is thus described using the edge profile model, wherein the at least one edge parameter is one or more parameters of the edge profile model and is used to describe the edge profile based on the underlying edge profile model. The edge profile model therefore describes or models the curved edge profile. The at least one edge parameter can then be determined based on the edge gradient model and the image gradient map. In particular, the image gradients [G _x ,G _y ] at pixel positions [x,y] are known from the image gradient map. The at least one edge parameter can then be determined based on these known variables and the edge profile model.

In a further embodiment of the first aspect, the at least one edge parameter is determined by compensation calculation based on the edge profile model and the image gradient map, in particular wherein the least squares method is used for the compensation calculation.

By inserting the known variables from the image gradient map, i.e. the image gradients [G _x ,G _y ] at pixel positions [x,y], into the edge gradient model, an overdetermined system of equations is obtained. This system of equations can then be solved using balancing calculations. In particular, the least squares method can be used for the compensation calculation.

In a further embodiment of the first aspect, the edge parameter is determined by optimization based on the edge profile model and the image gradient map, in particular wherein for optimization the edge profile model is minimized with regard to the local edge roughness.

The edge roughness is an edge roughness of the edge profile. Edge roughness describes the local deviation of the intensity values in an edge profile. As already explained at the beginning, the edge profile is generated using the at least one edge parameter. In other words, the edge profile is generated using one or more edge parameters. The edge roughness ultimately depends on that specific value of each of the one or more edge parameters. The more each edge parameter deviates from its actual value, the greater the roughness of the edge profile generated. The edge roughness can be determined, for example, by comparing a low-pass filtered edge profile and an unfiltered edge profile. Using an optimization algorithm, the at least one edge parameter can then be determined by minimizing the edge roughness. In other words, the edge parameter to be determined is optimized in such a way that the edge roughness of the edge profile becomes minimal.

For example, an initial value can first be set for each edge parameter of the edge profile model. The initial value of each edge parameter can basically be any value. Preferably, the initial value is a first, rough estimate for the respective edge parameter. The edge roughness of the corresponding edge profile can then be determined for the initial value of each edge parameter. By optimizing the value of each edge parameter, the at least one edge parameter with minimal edge roughness of the edge profile can then be determined.

For example, the method of simulated annealing could be used. In particular, the initial value of each edge parameter can, as already explained above, be determined by compensation calculation based on the edge gradient model and the image gradient map.

In a further embodiment of the first aspect, a polynomial function is used as the edge profile model, in particular where the polynomial function is a polynomial of at least second degree

In other words, the polynomial function is a polynomial of second degree or higher. A polynomial function can also be called a polynomial function. The polynomial function can be described, for example, by a Taylor series. In principle, only a linear edge profile can be modeled with a first degree polynomial (e.g. a first degree Taylor approximation). A polynomial of at least second degree also allows the description, i.e. modeling, of curved edges. In this way, the position of a curved edge can be determined very precisely.

In a further embodiment of the first aspect, the curved edge profile has a constant curvature, wherein the at least one edge parameter defines the center of curvature of the edge profile with constant curvature, in particular wherein the projection is a projection of the image points onto a radial direction with respect to the center of curvature.

$$\text{y}={\text{y}}_0+\frac{1}{\rho }\frac{{\text{G}}_{\text{y}}}{\sqrt{G_x^2+G_y^2}}$$

Constant curvature means that the curvature is circular. A curve that has constant curvature has a center of curvature. The center of curvature can also be called the center of curvature. In particular, each point of such a curve has the same distance from the center of curvature. In other words, the curve is curved around the center of curvature. A curved edge run with constant curvature is therefore also curved around a center of curvature. In particular, the at least one edge parameter has the coordinates [x ₀ ,y ₀ ] of the center of curvature. The edge gradient model for constant curvature can be described using two equations: $$\text{x}={\text{x}}_0+\frac{1}{\rho }\frac{{\text{G}}_{\text{x}}}{\sqrt{G_x^2+G_y^2}}$$

$$\text{y}={\text{<figure-callout id="0" label="y" filenames="DE102022118586A1\_0053.png,DE102022118586A1\_0059.png" state="{{state}}">y</figure-callout>}}_0+\frac{1}{\rho }\frac{{\text{G}}_{\text{y}}}{\sqrt{G_x^2+G_y^2}}$$

Here x,y,G _x, G _y are known quantities from the image gradient map and x ₀ ,y ₀ ,ρ are unknown quantities to be determined.

The edge progression model can be simplified to the following equation: $$\left(\text{x}-{\text{x}}_0\right){\text{G}}_{\text{y}}=\left(\text{y}-{\text{y}}_0\right){\text{G}}_{\text{x}}$$

Based on this edge profile model and the known sizes from the image gradient map, the coordinates [x ₀ ,y ₀ ] of the center of curvature can then be determined. In particular, the values x, y, G _x ,G _y of each pixel from the image gradient map can be inserted into the model. This results in an overdetermined system of equations. The overdetermined system of equations can then be solved, as described above, by balancing calculation, in particular using the least squares method, in order to determine the coordinates [x ₀ ,y ₀ ] of the center of curvature.

zum Krümmungszentrum zugeordnet. Das Kantenprofil wird dann basierend auf dieser Projektion bestimmt. Das Kantenprofil gibt somit die Intensitätsverteilung I(r) der Bildpunkte in der radialen Richtung bezüglich des Krümmungszentrums an.With respect to the center of curvature, a radial direction and a tangential direction perpendicular thereto are defined. The tangential direction can also be referred to as the direction of rotation around the center of curvature. With regard to the edge course with constant curvature, the radial direction corresponds to the normal direction and the tangential direction corresponds to the edge course direction. In other words, it runs Cant along the tangential direction with respect to the center of curvature. The projection is thus a projection along the tangential direction with respect to the center of curvature onto or in the radial direction with respect to the center of curvature. In other words, each pixel in the image area is given a radial distance for projection $\text{r}=\sqrt{{\left(\text{x}-{\text{x}}_0\right)}^2+{\left(\text{y}-{\text{y}}_0\right)}^2}$

assigned to the center of curvature. The edge profile is then determined based on this projection. The edge profile thus indicates the intensity distribution I(r) of the image points in the radial direction with respect to the center of curvature.

Alternatively, the coordinates [x ₀ ,y ₀ ] of the center of curvature can also be determined, as described above, by optimization, in particular by minimizing the local edge roughness. If the position of the center of curvature is shifted compared to the actual position, in particular compared to its nominal value, the extracted edge profile has a higher edge roughness. Through optimization, coordinates for the center of curvature can then be determined for which the edge roughness of the corresponding edge profile is minimal.

In this way, the position of a curved edge can be determined precisely and easily.

In a further embodiment of the first aspect, in the step of determining the edge position, the edge position is determined based on a turning point of the edge profile.

In particular, the position at which the edge profile has the greatest change or gradient can be determined as the edge position. In other words, derivation-based methods can be used in particular, which analyze points of maximum slope or turning points of the edge profile (e.g. Canny Edge method). As explained previously, there is a change in intensity at an edge transition. In particular, the intensity of the image points changes more in the edge area than on the adjacent areas. The edge position of the edge in the normal direction then corresponds to the position in the normal direction at which the edge profile has the greatest slope or change in intensity. This position can also be referred to as the turning point of the edge profile. The turning point is therefore a global extremum, in particular a maximum, of the first derivative of the edge profile. In particular, to determine the turning point, a function can first be fitted or adjusted to the specific edge profile. Then the inflection point of this function can be determined. The position of the turning point is then determined as the edge position of the edge.

In a further embodiment of the first aspect, in the step of determining the edge position, the edge position is determined based on reaching a defined threshold value of the edge profile.

In other words, threshold methods can be used, for example, to determine the edge position. Here, a threshold value is defined as the edge position at which the edge contrast reaches this threshold value. A commonly used threshold value corresponds to an edge contrast of 50%. In other words, the edge position in this case corresponds to the position at which the intensity or gray value corresponds to the mean of the maximum & minimum intensity or gray value of the edge transfer function. In particular, to determine the edge position, a function can first be fitted or adjusted to the specific edge profile. Then the argument of this function can be determined at which the function reaches the defined edge contrast or threshold. The specific argument then corresponds to the edge position.

• - Empfangen des Bildes mit erweiterter Schärfentiefe.

In a further embodiment of the first aspect, the method further comprises the following step:

• - Receive the image with extended depth of field.

The image with extended depth of field can be recorded, for example, using a measuring device or other suitable device. The image is then received with an extended depth of field so that edge localization can be carried out based on the received image.

• - Empfangen eines Fokalbildstapels, wobei der Fokalbildstapel eine Mehrzahl von Bildern des Werkstücks aufweist, wobei die Bilder den Bereich der Oberfläche des Werkstücks mit in einer Tiefenrichtung unterschiedlichen, definierten Fokalebenenpositionen abbilden, wobei jedem Bild des Fokalbildstapels eine Fokalebenenposition zugeordnet ist; und
• - Erzeugen des Bildes mit erweiterter Schärfentiefe in der Tiefenrichtung basierend auf dem Fokalbildstapel.

In a further embodiment of the first aspect, the image with an extended depth of field images a region of a surface of a workpiece, the method further comprising the following steps:

• - Receiving a focal image stack, the focal image stack having a plurality of images of the workpiece, the images imaging the area of the surface of the workpiece with defined focal plane positions that are different in a depth direction, a focal plane position being assigned to each image of the focal image stack; and
• - Generate the image with extended depth of field in the depth direction based on the focal image stack.

Instead of receiving the image with an extended depth of field already generated, the image with an extended depth of field can also be generated directly in the process. As already explained previously, the image with an extended depth of field can be generated based on the focal image stack, which images an area of a surface of the workpiece. In this generated image, an edge position of an edge in an image area of the image can then be localized.

• - Bestimmen eines Schärfewerts jedes Bildpunkts jedes Bildes des Fokalbildstapels;
• - Bestimmen eines Tiefenwerts jedes Objektpunkts auf der Oberfläche des Werkstücks in der Tiefenrichtung basierend auf den bestimmten Schärfewerten,

wobei in dem Schritt des Erzeugens das Bild mit erweiterter Schärfentiefe basierend auf den ermittelten Tiefenwerten und dem Fokalbildstapel erzeugt wird.In a further embodiment of the first or second aspect, the pixels of the images of the focal image stack are each assigned to a corresponding object point on the surface of the workpiece, the method further comprising the following steps:

• - determining a sharpness value of each pixel of each image of the focal image stack;
• - determining a depth value of each object point on the surface of the workpiece in the depth direction based on the determined sharpness values,

wherein in the generating step, the image with extended depth of field is generated based on the determined depth values and the focal image stack.

A sharpness value is determined for each pixel. The sharpness value can also be called the focus value. The sharpness value indicates how sharp the respective pixel is. To determine the sharpness value, for example, the brightness, a contrast value or a gray value of a pixel can be considered. In particular, to determine the focus value, a gradient of the brightness, the contrast value or the gray value to the surrounding pixels can be determined. The larger the gradient, the sharper the pixel is and the larger the focus value. The sharpness values are stored in a 3D sharpness matrix.

In order to determine the depth value of an object point, the respective image points of the focal image stack that are assigned to the corresponding object point are considered together. Each of these pixels is from different images. Each pixel is therefore assigned a different distance and, accordingly, a different depth value in the depth direction. Based on this, a depth value can then be determined for each object point at which the object point is imaged most sharply. The depth values of all object points form a depth map.

Once a depth value is determined for each object point from the captured area of the surface of the workpiece, the image with extended depth of field can be generated based on the determined depth values of the object points and the focal image stack. In other words, the image with extended depth of field is generated based on the depth map and the focal image stack. For this purpose, for each object point, for example, the image point from the set of image points assigned to the object point can be taken from the focal image stack, the depth value of which comes closest to the determined depth value of the object point. In other words, for each object point, the image point that provides the sharpest image of the object point can be taken from the focal image stack.

• - Einpassen jeweils einer Funktion entlang der Tiefenrichtung an die Schärfewerte derjenigen Bildpunkte der Bilder, die demselben Objektpunkt zugeordnet sind,

wobei der Tiefenwert jedes Objektpunkts auf der Oberfläche des Werkstücks in der Tiefenrichtung basierend auf einem Maximum der entsprechenden, eingepassten Funktion bestimmt wird.In a further embodiment of the first or second aspect, the method further comprises the following step:

• - Adjusting a function along the depth direction to the sharpness values of those pixels of the images that are assigned to the same object point,

wherein the depth value of each object point on the surface of the workpiece in the depth direction is determined based on a maximum of the corresponding fitted function.

To determine the depth value of the object point, a function in or along the depth direction is adapted to the sharpness values of the corresponding image points that are assigned to the object point. The function can also be called the sharpness function. As described previously, the sharpness value is maximum when the object point lies in the focal plane of the optical sensor. If the distance to the workpiece is shortened or lengthened, the sharpness value decreases. The depth value of the object point can thus be determined from the maximum of the fitted function to the sharpness values of the image points of a corresponding object point. Particularly suitable functions are those that are axially symmetrical to a maximum, in particular to a global maximum.

• - Einpassen jeweils einer Funktion entlang der Tiefenrichtung an die Schärfewerte derjenigen Bildpunkte der Bilder, die demselben Objektpunkt zugeordnet sind,

wobei der Tiefenwert jedes Objektpunkts auf der Oberfläche des Werkstücks in der Tiefenrichtung basierend auf einem Maximum der eingepassten Funktion und einem Residuum der eingepassten Funktion bestimmt wird.In a further embodiment of the first or second aspect, the method further comprises the following step:

• - Adjusting a function along the depth direction to the sharpness values of those pixels of the images that are assigned to the same object point,

wherein the depth value of each object point on the surface of the workpiece in the depth direction is determined based on a maximum of the fitted function and a residual of the fitted function.

In particular, the depth value of an object point on the surface of the workpiece in the depth direction is determined based on a maximum of the corresponding fitted function when the residual of the corresponding fitted function is greater than a defined threshold, where the depth value of an object point on the surface of the workpiece in the depth direction is determined by interpolating the depth values of at least two neighboring object points if the residual of the corresponding fitted function is equal to or smaller than the defined threshold value.

The residual is a measure of how much the function deviates from the determined sharpness values. The residual therefore indicates the quality of the fit. For each object point, a function is adapted to the corresponding sharpness values. The maximum and the residual are determined for this function. It is then determined whether the residual exceeds the threshold value. If the residual does not exceed the threshold value, the depth value of the corresponding object point is determined based on the maximum of the function. When the residual exceeds the threshold value, the depth value of the corresponding object point is determined by interpolation. At least two, in particular all, neighboring object points for which a depth value has already been determined are used for interpolation. In this way, artifacts in the image with an extended depth of field are suppressed, which can be caused, for example, by defocused object points or scattered light.

In particular, for each object point for which the residual exceeds the threshold value, the depth value can first be determined based on the corresponding maximum of the fitted function. Then the depth values of the remaining object points whose residuals do not exceed the threshold value and for which no depth value has yet been determined are determined by interpolating the depth values of the other object points for which a depth value has already been determined. Alternatively, the depth values can first be determined for all object points based on the maxima of the fitted functions. The depth values of the object points for which the calculated residual is below the threshold value are then discarded. For the object points for which the depth value was rejected again, the depth value is then determined by interpolation, as described above.

In a further embodiment of the first or second aspect, the function to be fitted is a Gaussian function, whereby the depth value of each object point corresponds to the expected value, also called the median or central value, of the respective Gaussian function.

A Gaussian function basically has a global maximum at its expected value. If a Gaussian function is adapted to the sharpness values of the image points of an object point, the depth value of the object point can be determined based on the expected value. Furthermore, the intensity profile or the sharpness profile in the depth direction essentially follows a Gaussian curve when the distance to the workpiece is varied in the depth direction. Therefore, if a Gaussian curve is fitted to every point of the area to be imaged, in particular for every object point, the accuracy and reproducibility of the depth map and thus also of the image with an extended depth of field can be further improved.

In a further embodiment of the first or second aspect, each image of the focal image stack is assigned a depth value in the depth direction.

Based on the depth values of the images, the function for the image points of an object point can be adjusted accordingly and the depth value for the corresponding object point can be determined. The depth value of the object point, in particular the z position, results directly from the depth value at which the fitted function is maximum. In particular, the depth values of the images can follow one another in discrete steps. For example, the images can be recorded in 50µm steps. This means that the distance between the images in the depth direction to the workpiece changes by 50 μm from image to image, in particular becomes larger or smaller.

In a further embodiment of the first or second aspect, the sharpness value of each pixel is determined based on a sharpness of the pixel.

As already explained above, the sharpness value of a pixel can be determined, for example, based on a gradient to the surrounding pixels of the corresponding image.

• - Korrigieren eines oder mehrerer Abbildungsfehler in dem erzeugten Bild mit erweiterter Schärfentiefe, wobei die zu korrigierenden Abbildungsfehler mindestens einen der folgenden Fehler aufweisen: einen Verzeichnungsfehler und/oder einen Astigmatismus-Fehler.

In a further embodiment of the first or second aspect, the method further comprises the following step:

• - Correcting one or more imaging errors in the generated image with extended depth of field, the imaging errors to be corrected having at least one of the following errors: a distortion error and / or an astigmatism error.

Correcting one or more aberrations produces a corrected image with increased depth of field. The one or more imaging errors to be corrected are a distortion error and/or an astigmatism error.

When capturing the focal image stack, imaging errors may occur that result from the optical system used to capture the focal image stack. All optical systems have imaging errors, also known as optical aberrations, within the manufacturing tolerances. These lead to a systematic measurement error in the calculated depth values. Astigmatism is particularly problematic because it distorts the depth values. At least the first and second order aberrations can be taken into account and corrected in the Zernike aberration scheme. To correct the astigmatism error, the calculated depth values are corrected for each object point. Based on the corrected depth values, a corrected image with an extended depth of field can then be generated. The proposed correction mechanism allows digital aberration correction to be carried out, which further increases the accuracy.

In addition to the astigmatism error, a distortion error may also occur. Distortion is a geometric imaging error in optical systems that leads to a local change in the imaging scale in the lens equation. This results in an image of the object to be examined that is not true to length or scale. In other words, distortion affects dimensional measurement ability. The distortion can have a center of distortion that can lie on the optical axis. The center of distortion is a point of symmetry of the distortion. The distortion can be rotationally symmetrical about this point of symmetry. In other words, the distortion leads to an image that is not true to length and/or not true to angle. A radial direction and a tangential direction can be defined with respect to the center of distortion. Radial direction and tangential direction are perpendicular to each other.

The distortion error of an optical system therefore leads to a change in scale in the x and y directions, i.e. perpendicular to the depth direction. In other words, each pixel has an imaging error in the x and y directions caused by the distortion. This imaging error can increase as the distance between an image point and the optical axis increases.

The distortion may generally include radial distortion and/or tangential distortion. The radial distortion and the tangential distortion can be described, for example, by the Brown-Conrady model. Radial distortion describes the distortion, i.e. change in scale, in the radial direction. With radial distortion, the image points are distorted in the radial direction. Tangential distortion describes the distortion, i.e. change in scale, in the tangential direction. With tangential distortion, the image points are distorted in the tangential direction.

In order to now obtain a corrected image with an extended depth of field without distortion errors, the distortion error is thus corrected in the image with an extended depth of field. For this purpose, for example, each pixel of the image can be offset/equalized in the x and y directions with an extended depth of field in order to compensate for the distortion error. In particular, each pixel of the image with extended depth of field can be offset/equalized in the radial and optionally the tangential direction with respect to the center of distortion in order to compensate for the distortion error.

By correcting imaging errors, in particular distortion errors and astigmatism errors, a corrected image with an extended depth of field is obtained, in which edges can be localized better.

In a further embodiment of the first or second aspect, in order to correct the distortion error, at least one distortion value is assigned to each point of the image with extended depth of field, wherein a position of each point of the image with extended depth of field perpendicular to the depth direction is corrected based on the at least one distortion value.

The distortion value is a correction value for the distortion of the respective pixel. The at least one distortion value is preferably predetermined. The at least one distortion value determines how the position of a point in the image with an extended depth of field should be changed perpendicular to the depth direction, i.e. in the x and y directions. In other words, the distortion value indicates how the point should be moved in the x and/or y direction for correction. In particular, the at least one distortion value can determine how the point is to be moved in the radial and/or tangential direction with respect to the distortion center to correct radial distortion and tangential distortion. By correcting (i.e., equalizing) the location of each point in the image with expanded depth of field Based on the at least one distortion value, a true-to-scale, measurable measurement recording is generated.

In a further embodiment of the first or second aspect, each point of the image with extended depth of field is assigned a first distortion value and a second distortion value, the location of each point of the image with extended depth of field in a first direction based on the first distortion value and in a second direction is corrected based on the second distortion value.

In this way the distortion of the point can be corrected in two different directions. The first and second directions are perpendicular to the depth direction. Preferably, the first and second directions are not parallel to one another, in particular perpendicular to one another. For example, the first direction can be the x-direction and the second direction can be the y-direction. In this case, the first distortion value is used to correct distortion in the x direction and the second distortion value is used to correct distortion in the y direction. Alternatively, the first direction can also be the radial direction and the second direction can be the tangential direction with respect to the center of distortion. In this case, the first distortion value is used to correct the radial distortion and the second distortion value is used to correct the tangential distortion.

In a further embodiment of the first or second aspect, the astigmatism error is corrected before the distortion error.

As already explained at the beginning, the distances measured in the image (i.e. the scale) change depending on the edge orientation-dependent autofocus. This error becomes larger the larger the telecentricity deviation of the system is. In other words, astigmatism of the optical system causes the scale to change depending on the edge orientation. This means that due to astigmatic image influences, the specific best (sharpest) image point will no longer be on the best adjustment plane according to Petzval, but will instead be located between the sagittal and tangential best adjustment plane depending on the edge orientation. In order to minimize telecentricity-related measurement influences, an astigmatically compensated (corrected) image with an extended depth of field can be determined. For this purpose, an image with extended depth of field is calculated on the edge orientation-independent best adjustment plane according to Petzval and the distortion correction is then carried out for this image with extended depth of field.

In a further embodiment of the first or second aspect, in order to correct the astigmatism error, an angle map of the area of the surface of the workpiece is generated, with each point of the image with extended depth of field being assigned a first correction value and a second correction value, the depth value of each point of the Image with extended depth of field is corrected based on the first correction value, the second correction value and the angle map.

Astigmatism is an aberration of the “crooked” rays. An obliquely incident beam of rays is refracted to different degrees in the meridional and sagittal planes. In the direction of the meridional plane, a lens is foreshortened, resulting in a shorter focal length than in the sagittal plane. In other words, astigmatism is direction-dependent, particularly dependent on directions of the edges in the images of the images. The astigmatism can be described for each point using an angle-dependent function, in particular a model or fit function, with at least two parameters that have the first and second correction values. In other words, the astigmatism model is an adaptation of the depth value deviation represented via the circular azimuth. In particular, astigmatism can be modeled as a linear combination of two radially symmetrical sine functions. The first correction value corresponds to the coefficient in the first sine function and the second correction value corresponds to the coefficient in the second sine function. The two sine functions are preferably shifted by π/2. The first correction value and the second correction value thus represent two correction values in two mutually perpendicular directions. To correct the astigmatism, an angle map of the area of the surface of the workpiece is generated. The angle map is determined based on an image gradient. The image gradient may be determined for each point based on the extended depth of field image or all or part of the focal image stack of the area of the workpiece. To do this, an image gradient is calculated for each point. The image gradient is determined by a change in the brightness of surrounding pixels. The direction of the image gradient can be represented using an angle. Thus, in the angle map, each point is assigned an angle that indicates the direction of the image gradient. In other words, the angle map represents the corresponding angle of the image gradient for each point of the corrected image with an extended depth of field. Based on this angle, the proportion of the first and second correction values can then be calculated to correct the depth value of the respective object point. The proportion of the first correction value can in particular be determined by the product of the first correction value can be determined by the sine of the angle of the respective point. Accordingly, the proportion of the second correction value can also be determined by the product of the second correction value with the cosine of the angle of the respective point. The correction of the respective depth value can be carried out in particular by subtracting the sum of the components of the first and second correction values from the respective depth value. The first correction value and the second correction value can in particular be precalculated or predetermined. In this way, an astigmatism error in the depth values can be corrected. Based on the corrected depth values of the object points, the image can then be corrected, in particular regenerated, with an extended depth of field. By correcting the astigmatism error, the accuracy of the image is further increased with extended depth of field. The calculation of the image with extended depth of field based on the corrected depth values corresponds to the evaluation of the image with extended depth of field on the astigmatically compensated best adjustment plane according to Petzval.

• - Verändern des Abstands zwischen dem Werkstück und dem optischen Sensor,

wobei in dem Schritt des Erfassens die Mehrzahl von Bildern erfasst wird, während der Abstand zwischen dem Werkstück und dem optischen Sensor verändert wird, wobei die Bilder jeweils den Bereich der Oberfläche des Werkstücks aus unterschiedlichen, definierten Abständen zu dem Werkstück in der Tiefenrichtung abbildenIn a further embodiment of the second aspect, the optical sensor and the workpiece are movable relative to one another in the depth direction, so that a distance in the depth direction between the workpiece and the optical sensor can be changed, the method further comprising the following step:

• - changing the distance between the workpiece and the optical sensor,

wherein in the step of capturing, the plurality of images are captured while changing the distance between the workpiece and the optical sensor, the images each imaging the area of the surface of the workpiece from different, defined distances from the workpiece in the depth direction

In this way, the focal plane position of the optical sensor is changed in a depth direction relative to the workpiece while capturing the images that form the focal image stack.

In a further embodiment of the second aspect, the measuring device has a workpiece holder, wherein the workpiece is arranged on the workpiece holder for measurement.

The workpiece holder can in particular be a work table, a measuring table or an object table. The workpiece holder is designed to hold the workpiece in a defined position during the measuring process. For this purpose, the workpiece holder can, for example, have a flat surface on the top on which the workpiece can be arranged with an extended depth of field while the image is being recorded.

In a further embodiment of the second aspect, the measuring device has a drive device, wherein the drive device moves the optical sensor relative to the workpiece holder in the depth direction and / or moves the workpiece holder relative to the optical sensor in the depth direction in order to increase the distance between the workpiece and to change the optical sensor.

In other words, the drive device is designed to move the workpiece holder and the optical sensor relative to one another and to change the distance between the workpiece and the optical sensor. For this purpose, the drive device can either move the workpiece holder in the depth direction or move the optical sensor in the depth direction or move the workpiece holder and the optical sensor in the depth direction.

In a further embodiment of the second aspect, the distance between the workpiece and the optical sensor is changed in discrete steps.

The distance can be increased or decreased step by step. For example, the distance can be changed in 50µm increments.

• - Beleuchten des Werkstücks mittels der Beleuchtungseinrichtung während des Erfassens der Bilder des Fokalbildstapels.

In a further embodiment of the second aspect, the measuring device has a lighting device, the method further comprising the following step:

• - Illuminating the workpiece using the lighting device while capturing the images of the focal image stack.

The lighting device is used to illuminate at least the area of the surface of the workpiece. The reflected light is then used to create an image in the optical sensor. In this way, the area of the workpiece can be illuminated evenly and the depth values of the surface area can be determined with essentially the same accuracy. The illumination can be, for example, coaxial illumination, ring illumination, dark field illumination, diffuse illumination or point source illumination. The lighting device can in particular be a monochromatic light source, for example a monochromatic laser. A monochromatic light source has the advantage that no chromatic aberrations can occur.

• - Bestimmen des mindestens einen Verzeichnungswerts für jeden Bildpunkt des Bildes mit erweiterter Schärfentiefe, wobei initial ein Bild mit erweiterter Schärfentiefe eines Kalibrationsobjekts, insbesondere eines Punktgitters, aufgenommen wird, wobei der mindestens eine Verzeichnungswert basierend auf einer Abweichungen des Bildes mit erweiterter Schärfentiefe zu einem bekannten Oberflächenprofil des Kalibrationsobjekts bestimmt wird.

In a further embodiment of the second aspect, the method further comprises the following step:

• - Determining the at least one distortion value for each pixel of the image with extended depth of field, wherein initially an image with extended depth of field of a calibration object, in particular a point grid, is recorded, the at least one distortion value being based on a deviation of the image with extended depth of field from a known surface profile of the calibration object is determined.

In this way, in an initial step, the distortion values for the pixels of the image with an extended depth of field are determined. “Initial” means that the step of determining the distortion values occurs before the step of acquiring the plurality of images of the area of the surface of the workpiece. To determine the distortion values, an image with an extended depth of field of a calibration object is first recorded. The calibration object can also be called a calibration mask. The calibration object preferably has round structures. In particular, the calibration object can be a point grid or a shadow mask. A dot grid is a regular arrangement of points. In particular, a point grid is a geometric structure in which points are arranged at equal distances from one another in two or three spatial directions. In the case of two spatial directions, they are perpendicular to each other. In the case of three spatial directions, these are arranged in pairs at an angle of 60° to each other. Each point of the point grid has a spatial extent and is preferably circular. Each point of the point grid can be represented by a plurality of pixels of a captured image. Each point has a flat surface. The surface profile of the point grid is therefore already known in advance. In particular, the point grid can be arranged on the workpiece holder in such a way that the points of the point grid lie in a horizontal plane. The image with an extended depth of field of the calibration object, in particular the point grid, is generated in accordance with the method for generating a corrected image with an extended depth of field, but without the distortion error being corrected. The captured image of the calibration object is then analyzed using distortion routines to determine the distortion, in particular the distortion values. In particular, the distortion values can be determined by comparing the recorded image of the calibration object and/or the associated specific depth values with the known surface profile of the calibration object. Each specific distortion value can be stored in particular in an electronic storage unit. The measuring device can have this storage unit. In particular, the distortion values can be saved in the form of a table (“look-up table”). Once the distortion values have been determined, the corrected image can then be captured with an extended depth of field of the workpiece. The depth values of the object points can be corrected using the specific distortion values. In this way, the distortion values of the pixels can be easily determined and corrected.

• - Bestimmen des ersten Korrekturwerts und des zweiten Korrekturwerts für jeden Bildpunkt des Bildes mit erweiterter Schärfentiefe, wobei initial ein Bild mit erweiterter Schärfentiefe eines Kalibrationsobjekts, insbesondere eines Punktgitters, aufgenommen wird, wobei der jeweilige Korrekturwert basierend auf Abweichungen des Bildes mit erweiterter Schärfentiefe oder der bestimmten Tiefenwerte der Objektpunkte des Kalibrationsobjekts zu einem bekannten Oberflächenprofil des Kalibrationsobjekts bestimmt wird.

In a further embodiment of the second aspect, the method further comprises the following step:

• - Determining the first correction value and the second correction value for each pixel of the image with extended depth of field, initially an image with extended depth of field of a calibration object, in particular a point grid, being recorded, the respective correction value being based on deviations of the image with extended depth of field or the specific one Depth values of the object points of the calibration object are determined to a known surface profile of the calibration object.

To determine the first correction value and the second correction value, each point of the point grid is considered individually. The first and second correction values can then be determined based on a deviation of the calculated depth profile from the actual depth profile of the respective point, which is a flat surface. To determine the correction values, an image with an extended depth of field of a point grid is recorded in advance, i.e. initially. The generation of the image with an extended depth of field of the calibration object, in particular the point grid, is carried out in accordance with the method for generating a corrected image with an extended depth of field, but without the step of correcting the one or more imaging errors. Each specific correction value can be stored in particular in an electronic storage unit. The measuring device can have this storage unit. After the desired correction values have been determined, the corrected image can then be recorded with an extended depth of field of the workpiece. The depth values of the object points can be corrected using the specific correction values. In this way, the correction values can be easily determined and corrected.

• - Bestimmen des ersten Korrekturwerts und des zweiten Korrekturwerts für jeden Punkt des Punktgitters basierend auf einer Kostenfunktion zwischen einem Astigmatismus-Modell und den Tiefenwerten des jeweiligen Punkts; und
• - Interpolieren der ersten und zweiten Korrekturwerte basierend auf den ersten und zweiten Korrekturwerten jedes Punkts des Punktgitters.

In a further embodiment of the second aspect, determining the first and second correction values comprises the following steps:

• - determining the first correction value and the second correction value for each point of the point grid based on a cost function between an astigmatism model and the depth values of the respective point; and
• - Interpolating the first and second correction values based on the first and second correction values of each point of the point grid.

As previously described, each point of the point grid is imaged using a plurality of pixels of a captured image. The depth values of each individual point can be segmented after generating the corrected image with extended depth of field of the point grid. First, the points of the corrected image with an extended depth of field are determined, each of which is assigned to a point on the point grid and depicts it. As previously described, the astigmatism model is an adaptation of the depth value deviation represented by the circular azimuth. The adapted fit function, described by the fit parameters, correspond to the first correction value and the second correction value of the respective point of the point grid. In particular, the astigmatism model can be a linear combination of two radially symmetrical sine functions. The cost function is then minimized according to the coefficients of the sine functions. The coefficients of the sine functions correspond to the first correction value and the second correction value of the respective point of the point grid. Based on the determined first and second correction values for each point of the point grid, the first and second correction values for each point of the corrected image with extended depth of field are determined by interpolation based on the first and second correction values of each point of the point grid.

• - Ausgeben des Bildes mit erweiterter Schärfetiefe und/oder der Kantenposition der Kante in dem Bildbereich des Bildes mit erweiterter Schärfentiefe mittels einer Ausgabeeinrichtung.

In a further embodiment of the second aspect, the method further comprises the following step:

• - Outputting the image with extended depth of field and/or the edge position of the edge in the image area of the image with extended depth of field by means of an output device.

The output device can, for example, have a display, whereby the corrected image can be shown on the display with an extended depth of field. Furthermore, the output device can be designed to output the corrected image with an extended depth of field to an electronic storage device, to another device or to an external display. The electronic storage device can be, for example, a storage medium, in particular a hard drive, a flash memory or a cloud. The further device can, for example, use the corrected image with extended depth of field to carry out further processes. The external display can, for example, be designed to display the corrected image with an extended depth of field.

In a further embodiment of the third aspect, the measuring device further has a drive device, wherein the drive device is designed to move the optical sensor and the workpiece holder relative to one another in the depth direction in order to change a distance between the workpiece and the optical sensor.

By means of the drive device, the focal plane position of the optical sensor can thus be adjusted in the depth direction relative to the workpiece.

• - Steuern der Antriebseinrichtung derart, dass ein Abstand zwischen dem Werkstück und dem optischen Sensor verändert wird,

wobei der optischen Sensor derart gesteuert wird, dass die Mehrzahl von Bildern erfasst wird, während der Abstand zwischen dem Werkstück und dem optischen Sensor verändert wird, wobei die Bilder jeweils den Bereich der Oberfläche des Werkstücks aus unterschiedlichen, definierten Abständen zu dem Werkstück in der Tiefenrichtung abbilden.In a further embodiment of the third aspect, the control device is further set up to carry out the following steps, in particular before the step of generating the corrected image with an extended depth of field:

• - Controlling the drive device in such a way that a distance between the workpiece and the optical sensor is changed,

wherein the optical sensor is controlled such that the plurality of images are captured while changing the distance between the workpiece and the optical sensor, the images each representing the area of the surface of the workpiece from different, defined distances from the workpiece in the depth direction depict.

In this way, the focal plane position of the optical sensor is changed in the depth direction relative to the workpiece while the images forming the focal image stack are captured.

It is understood that the features mentioned above and those to be explained below can be used not only in the combination specified in each case, but also in other combinations or alone, without departing from the scope of the present invention.

• 1 eine schematische Ansicht eines Messgeräts;
• 2 eine schematische Ansicht eines Verfahrens zum Erzeugen eines korrigierten Bildes mit erweiterter Schärfentiefe;
• 3 eine schematische Ansicht eines Verfahrens zum Aufnehmen eines korrigierten Bildes mit erweiterter Schärfentiefe;
• 4 eine schematische Ansicht von Verfahrensschritten zur Bestimmung von Korrekturwerten;
• 5 eine schematische Ansicht von Verfahrensschritten zur Bestimmung von Verzeichnungswerten;
• 6A eine beispielhafte Ansicht eines Fokalbildstapels;
• 6B eine Ansicht eines Diagramms zur Darstellung von bestimmten Schärfewerten entlang der Tiefenrichtung;
• 6C eine Ansicht eines Diagramms zur Darstellung des Einpassens einer Funktion an bestimmte Schärfewerte entlang der Tiefenrichtung;
• 6D eine beispielhafte Ansicht eines Bildes mit erweiterter Schärfetiefe;
• 7 eine beispielhafte Ansicht zur Darstellung einer Abbildung auf eine gekrümmte Bildebene unter dem Einfluss von Bildfeldkrümmung;
• 8 eine beispielhafte Ansicht zur Darstellung von Astigmatismus einer Linse;
• 9 eine beispielhafte Ansicht zur Darstellung einer Abbildung auf gekrümmte Bildebenen unter dem Einfluss von Astigmatismus;
• 10 eine beispielhafte Ansicht zur Darstellung einer Abbildung auf gekrümmte Bildebenen unter dem Einfluss von Bildfeldkrümmung und Astigmatismus;
• 11 eine beispielhafte Ansicht zur Darstellung von verschiedenen Bildebenen bei der Aufnahme eines Bildes mit erweiterter Schärfentiefe unter dem Einfluss von Bildfeldkrümmung;
• 12 eine beispielhafte Ansicht zur Darstellung von verschiedenen Bildebenen bei der Aufnahme eines Bildes mit erweiterter Schärfentiefe unter dem Einfluss von Bildfeldkrümmung und Astigmatismus;
• 13A eine Ansicht einer Tiefenkarte ohne Korrektur des Astigmatismus-Fehlers;
• 13B eine Ansicht eines Bildes mit erweiterter Schärfentiefe ohne Korrektur des Astigmatismus-Fehlers;
• 14A eine Ansicht einer Tiefenkarte mit Korrektur des Astigmatismus-Fehlers;
• 14B eine Ansicht eines Bildes mit erweiterter Schärfentiefe mit Korrektur des Astigmatismus-Fehlers;
• 15A eine Ansicht einer Darstellung eines Punktgitters;
• 15B eine Ansicht eines 3D-Diagrams zur Darstellung der schärfsten Bildpunkte des Randes eines Punktes des Punktgitters aus 15A;
• 15C eine Ansicht eines Diagramms zur Darstellung der Tiefenwerte der schärfsten Bildpunkte aus 15B über dem jeweiligen Kantenorientierungswinkel.
• 16A eine Ansicht eines ersten Diagramms gemäß einem ersten Beispiel, in dem das Einpassens einer Fit-Funktion an die Tiefenwerte der schärfsten Bildpunkte des Randes eines Punktes eines Punktgitters dargestellt ist;
• 16B eine Ansicht eines zweiten Diagramms gemäß dem ersten Beispiel, in dem die räumliche Verteilung der Tiefenwerte in der Bildebene (x-y Ebene) dargestellt ist;
• 16C eine Ansicht eines dritten Diagramms gemäß dem ersten Beispiel, in dem die räumliche Verteilung von korrigierten Tiefenwerten in der Bildebene (x-y Ebene) dargestellt ist;
• 17A eine Ansicht eines ersten Diagramms gemäß einem zweiten Beispiel, in dem das Einpassens einer Fit-Funktion an die Tiefenwerte der schärfsten Bildpunkte des Randes eines Punktes eines Punktgitters dargestellt ist;
• 17B eine Ansicht eines zweiten Diagramms gemäß dem zweiten Beispiel, in dem die räumliche Verteilung der Tiefenwerte in der Bildebene (x-y Ebene) dargestellt ist;
• 17C eine Ansicht eines dritten Diagramms gemäß dem zweiten Beispiel, in dem die räumliche Verteilung von korrigierten Tiefenwerten in der Bildebene (x-y Ebene) dargestellt ist;
• 18 eine erste beispielhafte Ansicht eines Bildbereichs eines Bildes mit erweiterter Schärfentiefe, in dem eine gerade Kante verläuft, die Projektion der Bildpunkte des Bildbereichs auf eine Normalen-Richtung, und ein darauf basierendes Kantenprofil;
• 19 eine zweite beispielhafte Ansicht eines Bildbereichs eines Bildes mit erweiterter Schärfentiefe, in dem eine gekrümmte Kante verläuft;
• 20A eine dritte beispielhafte Ansicht eines Bildbereichs eines Bildes mit erweiterter Schärfentiefe, in dem eine gekrümmte Kante mit konstanter Krümmung verläuft;
• 20B eine beispielhafte Ansicht eines Diagramms, in dem ein Kantenprofil der Kante aus dem Bild aus 20 in radialer Richtung dargestellt ist;
• 21 eine schematische Ansicht eines Verfahrens zum Lokalisieren einer Kantenposition einer Kante in einem Bildbereich eines Bildes mit erweiterter Schärfentiefe;
• 22 eine schematische Ansicht eines Verfahrens zur Kantenlokalisierung in einem Bild mit erweiterter Schärfentiefe;
• 23 Ansichten von Diagrammen eines ersten Beispiels zur Kantenlokalisierung in einem Bild mit erweiterter Schärfentiefe;
• 24 Ansichten von Diagrammen eines zweiten Beispiels zur Kantenlokalisierung in einem Bild mit erweiterter Schärfentiefe;
• 25A eine Ansicht einer Kantenmessung in einem Bild mittels der Slanted-Edge-Methode;
• 25B einen Ausschnitt eines Kantenbereichs aus 25A;
• 26A eine Ansicht einer Kantenmessung in einem Bild mittels der erfindungsgemäßen Methode;
• 26B einen Ausschnitt eines Kantenbereichs aus 26A;
• 27 eine Darstellung eines Bildes eines Werkstücks mit mehreren Kreisstrukturen;
• 28 eine Darstellung der Rundheitsmessung der einzelnen Kreisstrukturen aus dem Bild der 27 auf Basis eines korrigierten Bildes mit erweiterter Schärfentiefe;
• 29A eine Darstellung der Rundheitsmessung der einzelnen Kreisstrukturen aus dem Bild der 27 auf Basis eines unkorrigierten Bildes in der sagittalen Einstellebene; und
• 29B eine Darstellung der Rundheitsmessung der einzelnen Kreisstrukturen aus dem Bild der 27 auf Basis eines unkorrigierten Bildes in der tangentialen Einstellebene.

Exemplary embodiments of the invention are shown in the drawing and are explained in more detail in the following description. Show it:

• 1 a schematic view of a measuring device;
• 2 a schematic view of a method for generating a corrected image with extended depth of field;
• 3 a schematic view of a method for capturing a corrected image with extended depth of field;
• 4 a schematic view of method steps for determining correction values;
• 5 a schematic view of process steps for determining distortion values;
• 6A an exemplary view of a focal image stack;
• 6B a view of a diagram showing certain sharpness values along the depth direction;
• 6C a view of a diagram showing the fitting of a function to certain sharpness values along the depth direction;
• 6D an exemplary view of an image with extended depth of field;
• 7 an exemplary view for displaying an image on a curved image plane under the influence of image field curvature;
• 8th an exemplary view showing astigmatism of a lens;
• 9 an exemplary view for displaying an image on curved image planes under the influence of astigmatism;
• 10 an exemplary view for displaying an image on curved image planes under the influence of field curvature and astigmatism;
• 11 an exemplary view for displaying different image planes when recording an image with an extended depth of field under the influence of field curvature;
• 12 an exemplary view for displaying different image planes when recording an image with an extended depth of field under the influence of field curvature and astigmatism;
• 13A a view of a depth map without astigmatism error correction;
• 13B a view of an image with extended depth of field without correction of astigmatism error;
• 14A a view of a depth map with astigmatism error correction;
• 14B a view of an image with extended depth of field with astigmatism error correction;
• 15A a view of a representation of a dot grid;
• 15B a view of a 3D diagram to display the sharpest image points of the edge of a point on the point grid 15A ;
• 15C a view of a diagram showing the depth values of the sharpest image points 15B over the respective edge orientation angle.
• 16A a view of a first diagram according to a first example, in which the fitting of a fit function to the depth values of the sharpest image points of the edge of a point of a point grid is shown;
• 16B a view of a second diagram according to the first example, in which the spatial distribution of the depth values in the image plane (xy plane) is shown;
• 16C a view of a third diagram according to the first example, in which the spatial distribution of corrected depth values in the image plane (xy plane) is shown;
• 17A a view of a first diagram according to a second example, in which the fitting of a fit function to the depth values of the sharpest image points of the edge of a point of a point grid is shown;
• 17B a view of a second diagram according to the second example, in which the spatial distribution of the depth values in the image plane (xy plane) is shown;
• 17C a view of a third diagram according to the second example, in which the spatial distribution of corrected depth values in the image plane (xy plane) is shown;
• 18 a first exemplary view of an image area of an image with an extended depth of field in which a straight edge runs, the projection of the image points of the image area onto a normal direction, and an edge profile based thereon;
• 19 a second exemplary view of an image region of an extended depth of field image in which a curved edge extends;
• 20A a third exemplary view of an image region of an extended depth of field image in which a curved edge of constant curvature extends;
• 20B an example view of a diagram showing an edge profile of the edge from the image 20 is shown in the radial direction;
• 21 a schematic view of a method for locating an edge position of an edge in an image region of an extended depth of field image;
• 22 a schematic view of a method for edge localization in an image with extended depth of field;
• 23 Views of diagrams of a first example of edge localization in an image with extended depth of field;
• 24 Views of diagrams of a second example of edge localization in an image with extended depth of field;
• 25A a view of an edge measurement in an image using the slanted edge method;
• 25B a section of an edge area 25A ;
• 26A a view of an edge measurement in an image using the method according to the invention;
• 26B a section of an edge area 26A ;
• 27 a representation of an image of a workpiece with multiple circular structures;
• 28 a representation of the roundness measurement of the individual circular structures from the image 27 based on a corrected image with extended depth of field;
• 29A a representation of the roundness measurement of the individual circular structures from the image 27 based on an uncorrected image in the sagittal adjustment plane; and
• 29B a representation of the roundness measurement of the individual circular structures from the image 27 based on an uncorrected image in the tangential adjustment plane.

In the 18 until 26 Examples of embodiments for edge localization of edges in an image are described. In the 1 until 17 Various exemplary embodiments for generating and recording an image with an extended depth of field are described, on the basis of which edge localization can then be carried out. The described method for edge localization of edges in an image can in principle also be applied to individual images, i.e. to images without an extended depth of field.

1 shows a measuring device 10. The measuring device can be a microscope or a coordinate measuring machine. The measuring device 10 is used to measure a workpiece 12. For this purpose, the measuring device 10 has an optical sensor 14. In addition to the optical sensor 14, other sensors can of course be provided, for example tactile sensors, which, however, are not shown in the present schematic view.

The optical sensor 14 may include an optical system 30 and an image sensor. The optical system 30 images a region of the surface of the workpiece 12 onto the image sensor. The optical sensor 14 can capture an image of the area of the surface of the workpiece 12 using the image sensor.

Furthermore, the measuring device 10 can have a lighting device 32. The lighting device is designed to illuminate at least the area of the surface of the workpiece 12.

The workpiece 12 to be measured is arranged on a workpiece holder 16. The workpiece holder 16 can be a measuring table, a work table or an object table. In the view shown, the workpiece holder 16 is aligned in an XY plane of a coordinate system 18. A Z direction 20 extends perpendicular to the workpiece holder 16. The Z direction 20 is a depth direction. A distance between the optical sensor 14 and the workpiece 12 in the depth direction 20 is marked with a reference numeral 22. A distance between the optical sensor 14 and the workpiece holder 16 in the depth direction 20 is marked with a reference number 34. The optical sensor 14 and the workpiece holder 16 are movable relative to one another. In this way, the distance 34 can be changed. Since the workpiece 12 is arranged on the workpiece holder 16, the distance 22 changes according to the distance 34. In principle, it can be provided for this that the workpiece holder 16 is movable in the depth direction 20 and / or the optical sensor 14, for example by means of a suitable mechanism 24, is movable in the depth direction 20.

The measuring device 10 can also have a drive device 28. The drive device 28 is designed to move the workpiece holder 16 and the optical sensor 14 relative to one another in the depth direction 20. The drive device 28 is preferably designed to move the workpiece holder 16 relative to the optical sensor 14 in the depth direction 20. Alternatively, the drive device 28 can also be designed to move the optical sensor 14 relative to the workpiece holder 16 in the depth direction 20. Of course, the drive device 28 can also be designed to move both the optical sensor 14 and the workpiece holder 16 in the depth direction 20.

The measuring device 10 also has a control device 26. The control device 26 is set up to control the individual components of the measuring device and to process data. For this purpose, the control device 26 can, for example, have various subunits, each of which controls a component and/or processes data. For example, the control device 26 can have a control unit that controls the drive device 28, the optical sensor 14 and/or the lighting device 32. Furthermore, the control device 26 can have a data processing unit that is set up to carry out the evaluation of captured images of the optical sensor. The data processing unit can, for example, generate an image with an extended depth of field of a region of the surface of the workpiece 12 based on a plurality of images that form a focal image stack. Furthermore, the data processing unit can, for example, localize or determine an edge position of an edge in an image area of the generated image with an extended depth of field.

The control device 26 can be connected to or have a non-volatile data memory in which a computer program is stored. In some embodiments, the controller 26 is a general-purpose computer, such as a commercially available personal computer running Windows®, Linux, or MacOS, and the computer program in memory includes program code used to implement embodiments of the new method in combination with the optical Sensor 14 and the drive device 28 are designed and formed. In an alternative embodiment, the controller 26 is a logic circuit, such as a field programmable gate array (FPGA), an application-specific integrated circuit (ASIC), a microcontroller, or any other appropriate programmable electrical circuit. Therein, the embodiments of the new method, in particular control and determination steps, can be implemented with the logic circuit, so that the logic circuit is designed and designed to implement embodiments of the new method in combination with the optical sensor 14 and the drive device 28. Any suitable programming language or hardware description language may be used to implement embodiments of the new method in the logic circuit, such as C, VHDL, and the like.

Furthermore, the measuring device 10 can have an output device 36. The output device 36 is set up to output the image with extended depth of field, the generated edge profile and/or the localized edge position. In particular, the output device 36 can be set up to output the localized edge position. The output device 36 can, for example, have a display on which the image with an extended depth of field, the generated edge profile and/or the localized edge position can be displayed. Alternatively or additionally, the output device 36 can be designed to output the image with extended depth of field, the generated edge profile and/or the localized edge position to an electronic storage device, to another device or to an external display.

In addition, the measuring device 10 can also have an input device with which a user can, for example, enter the number and distances or step sizes of the images to be captured into the coordinate measuring device 10 or can move the optical sensor 14 manually.

Before an area of a surface of the workpiece 12 is recorded, it can be provided that a user enters the number of images to be captured as well as the step size or distances 22 at which the images are to be captured. Alternatively, the number of images to be captured and the step size or distances 22 at which the images are to be captured can be predefined or fixed. To record the area of the surface of the workpiece 12, the control device 26 then controls the drive device 28 in such a way that the distance 22 between the workpiece 12 and the optical sensor 14 is changed in accordance with the presetting. At the same time, the control device 26 controls the optical sensor 14 such that a plurality of images of the area of the surface of the workpiece 12 are captured according to the presetting while the distance 22 is changed. Each image is captured at a different distance 22 from the workpiece 12. The majority of images then form a focal image stack. The focal image stack is then evaluated by the control device 26 to generate the image with an extended depth of field of the area of the surface of the workpiece 12. In this image with extended depth of field, an edge position of an edge in an image area of the image can then be localized.

2 shows a computer-implemented method 40 for generating an, in particular corrected, image with an extended depth of field of a region of a surface of the workpiece 12. The method can be carried out using the control device 26, for example.

In a first step 42 of the method 40, a focal image stack is received. The focal image stack has a plurality of images of the workpiece 12, the images imaging the area of the surface of the workpiece 12 with defined focal plane positions that are different in a depth direction, a focal plane position being assigned to each image of the focal image stack. Each image has pixels. The pixels of the images are each assigned to a corresponding object point on the surface of the workpiece 12.

Preferably, the images each depict the area of the surface of the workpiece 12 from different, defined distances 22 from the workpiece 12 in the depth direction 20. A distance 22 is assigned to each image of the focal image stack. Since the images are captured at different distances 22 from the workpiece 12 in the depth direction 20, each image of the focal image stack is assigned a depth value in the depth direction 20. In particular, the depth values of the images follow one another in discrete steps.

Alternatively, the images each depict the area of the surface of the workpiece 12 with different, defined focus positions, i.e. different focal image planes. Each focus position or setting of the focus distance of the lens of the optical sensor can be assigned a depth value in the depth direction 20, which corresponds to the distance to the focal plane in the respective focus position or setting. The distance between the optical sensor 14 and the workpiece 12 can remain constant.

In 6A Four images of a focal image stack are shown as an example, with different depth values (position in the z direction) being assigned to the images.

In a further optional step 44 of method 40, a sharpness value of each pixel of each image of the focal image stack is determined. The sharpness values of the pixels are determined based on a sharpness of each pixel. For this purpose, a gradient of brightness, a gray value or a contrast value relative to the surrounding pixels of the corresponding image is determined for each pixel. In this way, each pixel of each image from the focal image stack is assigned a sharpness value. Since each image is assigned a depth value in the depth direction 20, the same depth value is assigned to each pixel of the respective image. In other words, each pixel is assigned a depth value and a sharpness value.

As explained at the beginning, one image point is assigned to each object point from each image. In 6B the sharpness values f(z) of the image points that are assigned to the same object point are shown. Since the pixels come from different images of the focal image stack, the pixels (and thus also their sharpness values) are assigned different depth values. 6B shows the distribution of these sharpness values along the depth direction (z-direction).

In a further optional step 46 of the method 40, a function along the depth direction 20 is fitted to the sharpness values of those pixels of the images that are assigned to the same object point. The function describes an assignment in which each depth value in the depth direction is assigned a corresponding sharpness value. Preferably the function is a Gaussian function. Alternatively, other functions such as a parabolic function can also be used for fitting. Preferably the function is axisymmetric with respect to a maximum. A maximum and a residual can be determined from the fitted function.

Fitting a function along the depth direction 20 to the sharpness values of those pixels of the images that are assigned to the same object point is in 6C shown. 6C shows in particular the diagram of 6B , whereby a function along the depth direction is also adapted to the sharpness values. 6D shows an example of an image with an extended depth of field, which is based on the 6A until 6C is generated.

In a further optional step 48 of the method 40, the depth value of each object point on the surface of the workpiece 12 in the depth direction 20 is determined based on the determined sharpness values.

For example, the depth value of each object point can be determined based on the maximum of the respective fitted function. The maximum has a position, i.e. a depth value, in the depth direction, this depth value being determined as the depth value for the object point.

Alternatively, the depth value of each object point can be determined based on the maximum and residual of the respective fitted function. The residual is a measure of how much the function deviates from the determined sharpness values. The residual therefore indicates the quality of the fit. For each object point for which the residual of the corresponding fitted function is greater than a defined threshold, the depth value determined based on a maximum of the corresponding fitted function. For each object point for which the residual of the corresponding fitted function is equal to or smaller than the defined threshold value, the depth value is determined by interpolating the depth values of at least two neighboring object points. In particular, the depth value can first be determined for all object points based on the maxima of the fitted functions, with the depth values being discarded again for the object points for which the residual of the corresponding fitted function is equal to or smaller than the defined threshold value and by interpolation the depth values of neighboring object points can be determined.

The determined depth values of the object points form a depth map of the area of the surface of the workpiece 12.

In a further step 50 of the method 40, an image with extended depth of field of the area of the surface of the workpiece 12 is generated based on the determined depth values of each object point and the images of the focal image stack. In other words, the image with extended depth of field is generated based on the depth map and the focal image stack. The extended depth of field image created based on the 6A until 6C is generated is in the 6D shown as an example

In a further, optional step 52 of method 40, one or more imaging errors in the image are corrected with extended depth of field. The imaging errors to be corrected can include a distortion error and an astigmatism error. To correct the imaging errors, the position of the image points perpendicular to the depth direction and/or the depth values of the object points, i.e. the depth map, can be corrected. When the depth values of the object points are corrected, the image with extended depth of field is then corrected or regenerated based on the corrected depth values and the focal image stack. Preferably, the distortion error is corrected after the astigmatism error has been corrected. In other words, the astigmatism error can be corrected before the distortion error.

To correct the distortion error, at least one distortion value is assigned to each point of the extended depth-of-field image, wherein a position of each point of the extended depth-of-field image perpendicular to the depth direction is corrected based on the at least one distortion value. The distortion value indicates how the point of the image with extended depth of field is to be moved/equalized in the x and/or y direction or in the radial and/or tangential direction to correct the distortion of the point. In particular, each point of the image with extended depth of field can be assigned a first distortion value and a second distortion value, wherein the position of each point of the image with extended depth of field is corrected in a first direction based on the first distortion value and in a second direction based on the second distortion value . The first and second directions can be, for example, the x and y directions or the radial and tangential directions.

The correction of the astigmatism error depends on the edge direction or the astigmatism error is angle-dependent. An angle map is therefore first determined for the area of the surface of the workpiece 12. The angle map assigns an angle θ to each point in the image with extended depth of field. The angle θ results from an image gradient to surrounding pixels. Each point of the extended depth of field image is associated with a first correction value and a second correction value, wherein the depth value of each point of the extended depth of field image is corrected based on the first correction value, the second correction value and the angle map.

In general, the astigmatism for each of the corrected image with extended depth of field can be described via a function dependent on the angle θ, in particular a model or fit function, with at least two parameters. For a function with two parameters, these parameters correspond to the first and second correction values. In particular, astigmatism can be modeled as a linear combination of two radially symmetrical sine functions. The first correction value corresponds to the coefficient of the first sine function and the second correction value corresponds to the coefficient of the second sine function. For example, astigmatism can be modeled with the formula α sin θ + β cos θ (first-order development) or α sin 2θ + β cos 2θ (second-order development).

Since the angle θ is determined from the angle map for each point of the corrected image with extended depth of field, an effective correction value can be obtained for each point of the corrected image with extended depth of field using the formula α sin θ + β cos θ or α sin 2θ + β cos 2θ can be calculated. The respective depth value is then corrected by subtracting the corresponding effective correction value from the respective depth value. With the help of the corrected depth values (depth map), a corrected image with an extended depth of field can then be generated in which the astigmatic imaging error is corrected.

The correction values and distortion values for correcting the respective imaging errors can be as shown in 4 and 5 can be determined in advance as described below.

3 shows a method 60 for recording an, in particular corrected, image with an extended depth of field of a region of a surface of the workpiece 12 with the optical sensor 14 of the measuring device 10. The workpiece 12 is arranged on the workpiece holder 16 for measurement. The optical sensor 14 can then detect an area of the surface of the workpiece 12. The optical sensor 14 and the workpiece 12 are movable relative to one another in a depth direction 20, so that the distance 22 in the depth direction 20 between the workpiece 12 and the optical sensor 14 is changeable.

In a step 66 of the method 60, the distance 22 between the workpiece and the optical sensor is changed. For this purpose, the drive device can move the optical sensor 14 relative to the workpiece holder 16 in the depth direction 20 and/or move the workpiece holder 16 relative to the optical sensor 14 in the depth direction 20 in order to increase the distance 22 between the workpiece 16 and the optical sensor 14 change. In particular, the distance 22 can be changed in discrete steps, for example in steps of 50 μm.

In a further step 68 of the method 60, a plurality of images of a region of the surface of the workpiece are captured by means of the optical sensor while the distance 22 between the workpiece and the optical sensor is changed, the images each covering the region of the surface of the workpiece 12 from different, defined distances 22 to the workpiece 12 in the depth direction 20, each image point of each image being assigned to a corresponding object point on the surface of the workpiece 12, and the captured images forming a focal image stack.

In a further step 70 of the method 60, the particularly corrected image with an extended depth of field of the area of the surface of the workpiece 12 is produced using the method 2 generated.

In a further optional step 72 of the method 60, the generated, in particular corrected, image with an extended depth of field is output by means of the output device 36.

In a further optional step 64 of the method 60, the workpiece 12 is illuminated by means of the lighting device 32 while capturing the images of the focal image stack.

In a further optional step 62 of the method 60, the first correction value and the second correction value are determined for each object point/pixel of the image with extended depth of field. In other words, the correction values for correcting the astigmatism error are determined. For this purpose, an image with an extended depth of field of a calibration object, in particular a point grid, is initially recorded, i.e. before recording the corrected image with an extended depth of field of the area of the surface of the workpiece 12, in particular before steps 64 to 72. The image with extended depth of field of the calibration object is generated according to steps 64 to 70 with a calibration object as a workpiece, no correction of imaging errors being carried out when generating this image. 15A shows an exemplary representation of a calibration object in the form of a dot grid. Since the surface profile of the calibration object is known, the correction values to be determined can then be determined based on deviations of the image with extended depth of field of the calibration object from the known surface profile of the calibration object.

In a further optional step 63 of method 60, preferably after step 62, at least one distortion value is determined for each point of the image with extended depth of field. For this purpose, an image with an extended depth of field of a calibration object, in particular a point grid, is initially recorded, i.e. before recording the corrected image with an extended depth of field of the area of the surface of the workpiece 12, in particular before steps 64 to 72. The same calibration object can be used in steps 62 and 63. In particular, in step 63, the image of the calibration object, in particular of the point grid, recorded in step 62 can be used. Since the surface profile of the calibration object is known, the at least one distortion value of each point of the extended depth of field image may then be determined based on a deviation of the extended depth of field image from a known surface profile of the calibration object. Preferably, an offset in the x and/or y direction or in the radial and/or tangential direction is determined for each point of the image with an extended depth of field, the correction value indicating the displacement in the corresponding direction. In particular, if a first and a second distortion value are assigned to each point of the image with an extended depth of field, the first distortion value indicates the offset in the first direction (for example x- or radial Direction) and the second distortion value indicates the offset in the second direction (e.g. y or tangential direction).

Steps 62 and 63 are therefore to be understood as calibration steps in which systematic measurement errors of the optical sensor are determined and corresponding correction values are determined. In particular, a point grid can be used for calibration.

4 shows an example of method steps by means of which the correction values in step 62 of method 60 can be determined.

In a first step 80, an image with an extended depth of field of a point grid is generated as a calibration object. The image with extended depth of field of the point grid is generated according to steps 64 to 70 with a point grid as workpiece 12. An exemplary representation of a point grid as a calibration object is 15A shown.

In a further step 82, the image points of the image with an extended depth of field of the point grid are segmented, which represent each individual point of the point grid. In this way, the pixels of the image with an extended depth of field of the point grid are determined, each of which is assigned to a point of the point grid and depicts it. A circular Hough transformation can be used for segmentation, which can be used to detect circles. For example, the circular Hough transform can be applied to the image with extended depth of field of the point grid in order to detect the position of the individual points of the point grid. In particular, the circular Hough transform can be used to determine, for each point of the point grid, the positions of the image points (edge points) which are arranged on the edge of each point grid circle. These edge points are then the image points that are assigned to the respective point of the point grid.

In a further step 84, a first correction value and a second correction value are determined for each point of the point grid based on a cost function L between an astigmatism model and the corrected depth values of the respective point of the point grid. A linear combination of two radially symmetrical sine functions can be used as an astigmatism model. The astigmatism model can be defined, for example, by the formula α sin 2θ + β cos 2θ. Here α and β are the coefficients of the sine functions and θ is an angle in the XY plane around the center of the respective point of the point grid. The cost function L is defined according to the following equation: L(α,β) = Σ|f(r,θ) - (α sin2θ + β cos 2θ)| ²

In the cost function, a sum is formed over those points of the corrected image with an extended depth of field that are assigned to the corresponding point of the point grid or map and/or represent it. The location of these points in the X-Y plane can be specified in polar coordinates r and θ with respect to the center of the respective point of the point grid. f(r, θ) indicates the deviation of the depth value of these points of the corrected image with extended depth of field compared to the average depth value of the point of the point grid. The cost function is then minimized according to the coefficients of the sine functions. The first and second correction values of the point of the point grid can then be determined based on the minimized coefficients α and β. In particular, the first and second correction values of the point of the point grid correspond to the minimized coefficients.

In a further step 86, the first and second correction values of the pixels of the image with extended depth of field, in particular the first and second correction values for the depth values of the object points, are interpolated over the entire area based on the first and second correction values of each point of the point grid. In this way, a first and second correction value can be assigned to each pixel of the image with an extended depth of field, in particular to each object point.

5 shows method steps by means of which the distortion values of the points of the image with extended depth of field are determined in step 63 of method 60.

In a first step 110, an image with an extended depth of field of a point grid is generated as a calibration object. The image with extended depth of field of the dot grid is preferably generated according to steps 64 to 70 with a dot grid as workpiece 12. In particular, in step 110, the image recorded in step 62 or 80 can be used with an extended depth of field of the point grid.

In particular, one or more of the imaging errors, with the exception of the distortion error, can already be corrected in the recorded image with an extended depth of field of the point grid. In particular, the astigmatism error can be corrected.

In a further step 112, the at least one distortion value is determined for each pixel of the image with extended depth of field based on the captured image with extended depth of field of the point grid and the known shape of the point grid, in particular the known arrangement or position of the points of the point grid.

For example, a segmentation of the points of the point grid can first be carried out again, as in step 82, in order to determine the pixels of the image with an extended depth of field of the point grid, which are each assigned to a point of the point grid and represent it. The position of the points of the dot grid can then be determined from the segmented image points. The determined location of each point on the dot grid can then be compared with the known location of each point on the dot grid. In this way, a distortion, i.e. an offset, between the specific and known positions of the points can be determined. From this, at least one distortion value, in particular the first and second distortion value, can then be determined for the point of the dot grid. The distortion values of all pixels of the image with extended depth of field can then be determined by interpolation over the entire area.

With reference to the 7 until 10 The following explains how the measuring influences of field curvature and astigmatism affect the image of an object.

Due to image tilt and curvature, real optical systems image a flat measurement object onto a curved image plane. In addition, real optical systems have a location-dependent telecentricity error, i.e. a location-dependent change in magnification depending on the defocusing. This generally leads to a change in image status, i.e. edge movement, or a dimensional measurement error in the captured image. The interaction between field curvature and telecentricity errors can lead to unexpected and complex measurement influences. In particular, measurement results can change depending on a selected autofocus position, for example on the optical axis or at the edge of the field. This is explained in more detail below.

7 shows the imaging beam path from the exit pupil 120 to the curved image plane 126 for a flat object that is imaged in focus on a curved image plane 126 under the influence of Petzval aberration (image field curvature). This plane is also referred to as the best adjustment plane according to Petzval. The reference number 122 indicates the emerging main ray of an edge point of the object under consideration to be imaged and the reference number 124 indicates an emerging edge ray of the central point of the object under consideration to be imaged. A single autofocus point in the image focuses the image on a single area of the Petzval plane, so that the entire image is not in focus at the same time. Distances/positions (e.g. L1, L2) that are measured in the image change depending on the selected autofocus position (B1, B2), for example in the center of the image or at the edge of the image. For measurement features that are close to each other, assuming that the telecentricity error α (angle of the main beam direction under consideration relative to the optical axis or the image field normal for B1 or B2) is the same for both points, the change in the autofocus position results in a shift (“walking ") lead. For more distant measurement features, assuming that the telecentricity error is different for both points, changing the autofocus position will result in a systematic measurement error.

In addition to the curvature of the image field, real optical systems also have an astigmatic influence. 8th shows an example of the astigmatism of a lens. This has a tangential focus 130 and a sagittal focus 132. These are offset from each other by a delta 134 in the depth direction (z direction). The tangential focus 130 is closer to the lens than the sagittal focus 132. This results in a changing best adjustment plane depending on the edge orientation. In particular, horizontal and vertical edge orientations in the object are imaged most sharply in a different best adjustment plane. The interaction between astigmatism and telecentricity errors also leads to unexpected and complex measurement influences. In particular, measurement results can change depending on an autofocus position on a horizontal or vertical edge. This is explained in more detail below.

9 shows an example of a flat object to be depicted 7 the imaging beam path from the exit pupil 120 in two different image planes 140 and 142, which are created by the fact that the astigmatism of the imaging optics is imaged in different best adjustment planes depending on the edge orientation. In general, these adjustment planes, which are referred to in English as sagittal and tangential and in German as sagittal and meridional, are in contrast to the representation of the 9 does not show a simple progression across the image field. For better explanation, however, the extreme cases of the tangentially best adjustment plane 140 and the sagittally best adjustment plane 142 are in the 9 shown as opposing spherical shells. Depending on the actual edge orientation 144, however, there is also any best adjustment level in between possible. This means that the autofocus will focus in different adjustment planes depending on the local edge orientation. This means that at the same image position, the best autofocus position depends on the edge orientation. Distances (e.g. L1, L2, D1, D2) that are measured in the image change depending on the edge orientation-dependent autofocus in the image. This means in particular that measurement results change depending on the autofocus on a horizontal or vertical line. The error becomes larger the larger the telecentricity deviation α of the system is.

Field curvature and astigmatism can occur simultaneously. This is in 10 shown. A measuring lens that has Petzval curvature and astigmatism will produce the sharpest image in a best adjustment plane 126 between the sagittal and tangential best adjustment plane. The exact position between the image shells depends on the edge orientations in the measurement object. Ie, in general, a telecentricity-related measurement influence is influenced by both Petzval and astigmatic autofocus influences.

Below we will refer again to the 11 until 17C explains how a measurable measurement image, i.e. a corrected image with an extended depth of field, can be taken of an area of the surface of a workpiece.

First, the case is considered in which the astigmatism is assumed to be vanishingly small and only field curvature significantly influences the image. For this purpose, the image quality of the entire focal image stack is evaluated and the corresponding measurement image is calculated on the best adjustment plane, which can be curved as desired. This measurement recording is independent of the autofocus position. However, in addition to the classic distortion, it also has an additional distortion caused by telecentricity errors. This distortion influence must be calibrated and compensated.

To do this, a calibration process is first carried out, as previously described in 5 described, a focal image stack of a calibration object was recorded. A calibration recording is then calculated at the best setting level. An image with an extended depth of field of the calibration object is created as a calibration recording. The distortion of the image is then evaluated at the best adjustment level. At least one distortion value is determined for each point. The distortion values can then be saved in a look-up table.

The measurable image, i.e. the corrected image with an extended depth of field, of an area of a surface of a workpiece can then be recorded in a measuring process. First, a focal image stack of the workpiece is recorded. A measurement recording is then calculated on the arbitrarily curved best adjustment plane according to Petzval. This is exemplary 11 shown. An image with an extended depth of field is generated as a measurement recording, for example using steps 42 to 50 of the method 2 . A distortion correction of the image is then carried out in the best adjustment level based on the distortion values determined in the calibration process. In this way, an autofocus-independent and telecentric error-corrected measurement recording, i.e. a corrected image with an extended depth of field, can be generated. The correction of the distortion can, for example, be carried out as in step 52 of the method 2 described.

The procedure described in this way enables the compensation of autofocus-dependent measurement errors and the creation of a measurable recording with an extended depth of field.

Next, the case in which both astigmatism and field curvature affect the image is considered. Due to these influences, the determined best image point will no longer be on the best adjustment plane according to Petzval, but will mediate between the sagittal and tangential best adjustment plane depending on the edge orientation. In order to minimize telecentricity-related measurement influences, an astigmatically compensated (i.e. corrected) image with an extended depth of field should be determined. For this purpose, the image is not evaluated in the sharpest image plane depending on the edge orientation, but in the best adjustment plane (Petzval shell) that is free of astigmatism. This is exemplary 12 shown.

For this purpose, in an initial step, the astigmatic influences are evaluated and calibrated using a suitable calibration object, i.e. both the best adjustment plane and the astigmatic shell positions are determined.

To calculate an astigmatically compensated image with an extended depth of field of an area of a surface of a workpiece, the sharpest image plane is then first determined and in a subsequent correction step, this image position is shifted into the astigmatically compensated adjustment plane depending on the edge orientation. With the help of the astigmatically compensated depth values of the adjustment plane, an astigmatically compensated image with an extended depth of field is then generated.

Below we will use a point grid as an example as a workpiece to explain how the correction is made of astigmatism is carried out. The dot grid is flat. In 13B An uncorrected image with an extended depth of field of the dot grid is shown as an example. 13A shows an example of a depth map of the depth values of the object points on which the image is based 13B was generated. Due to the astigmatic error, the depth map is not flat.

In 14B As an example, an image with an extended depth of field of the point grid is shown, which is opposite the image from 13B is astigmatically compensated. 14A shows an example of a depth map of the astigmatically corrected depth values of the object points on which the image is based 14B was generated. The corrected depth map shows that the point grid is essentially flat.

An image calculation or image analysis in the sharpest image plane according to the autofocus criterion, i.e. based on the uncorrected depth values, is difficult because a calculated image with an extended depth of field has edge orientation-dependent distortion (“edge walking”) due to astigmatic influences.

The situation is different when calculating or analyzing an image in the astigmatically compensated best adjustment plane, i.e. based on the astigmatically compensated image with an extended depth of field. This results from a shift in the determined image position to the best adjustment level. In this case, the astigmatic walking effects are suppressed. Distortion correction in the astigmatically compensated image with an extended depth of field thus creates a measurable image that is focused everywhere.

To calculate the astigmatically compensated adjustment plane, an astigmatic correction value is determined based on the local edge orientation in the image and subtracted from the depth value of the sharpest adjustment plane. The local edge orientation is approximated here by numerical approximation of the image gradient, for example using directional Sobel filters in a single image or as a weighted averaging of the gradients through several images of the focal image stack.

errechnet und hiervon der Kantenorientierungswinkel $$\theta =arctan\left(\frac{G_x}{G_y}\right)$$

bestimmt.For example, to find the edge orientation within an image, a gradient vector field is created using discrete derivative operators $$\left[G_x,G_y\right]=\left[{\partial }_{x}bild\left(x,y\right),{\partial }_{y}bild\left(x,y\right)\right]$$

calculated and from this the edge orientation angle $$\theta =arctan\left(\frac{G_x}{G_y}\right)$$

certainly.

The numerical determination of the gradient in the image is susceptible to noise and possible interference. This sensitively influences the calculated angle map and can falsify the astigmatic correction. In the worst case, an incorrectly determined angle can imply an incorrect correction step that increases the astigmatic measurement error.

A robust method is to average the gradient vector fields across several image planes in a range of 1-10 Rayleigh units around the sharpest image point and to calculate the angle map from the averaged gradient vector field.

For correction, the astigmatic offset to the best adjustment plane is generally determined as follows using the specific edge orientation angle: $$d\mathrm{e.g}\left(\theta ,x,y\right)={\displaystyle \sum a_m\left(x,y\right)\text{sin}\left(m\theta \right)}+b_m\left(x,y\right)\text{cos}\left(m\theta \right)$$

Here m is a natural number and indicates the order of development. The offset dz therefore indicates the effective correction value for each object point (x, y). If you look at the development up to the Nth order, N third correction values and N fourth correction values are assigned to each object point. The development is preferably only viewed in the second order. The astigmatic offset to the best adjustment plane is then determined as follows: $$d\mathrm{e.g}\left(\theta ,x,y\right)=a_2\left(x,y\right)\text{sin}\left(2\theta \right)+b_2\left(x,y\right)\text{cos}\left(2\theta \right)$$

The first correction value then corresponds to the coefficient a ₂ and the second correction value then corresponds to the coefficient b ₂ .

The effective correction value is then subtracted from the specific position of maximum sharpness, i.e. the determined depth value of the object point. The newly determined position, i.e. the astigmatically corrected depth value of the object point, is not in the direction-dependent absolute focus point, but is compensated for astigmatically caused telecentricity influences.

The astigmatically compensated image with extended depth of field can then be generated based on the astigmatically corrected depth values of the object points. In this way, the recording is no longer in the sharpest image plane, but evaluated at the best setting level. This causes a slightly reduced image sharpness in the astigmatically compensated image with an extended depth of field, but compensates for shifts or measurement errors caused by telecentricity errors. In order to obtain a measurable recording, the distortion is corrected in a final step. The correction of the distortion can, for example, be carried out as in step 52 of the method 2 described.

In the 15A until 17C The procedure in a calibration process for determining the astigmatic correction values, i.e. the first and second correction values, is described again as an example.

First, an image is captured with an extended depth of field of a point grid. 15A shows an exemplary representation of a point grid. The dot grid is flat. However, the astigmatism causes the image points that represent a point of the point grid to be shifted in the depth direction depending on the angle in the direction of the tangential or sagittal focus depending on the angle, i.e. depending on the orientation of the image point to the center of the point of the point grid. This is for example in 15B and 15C shown. 15B shows a 3D diagram to display the sharpest image points of the edge of a point on the point grid 15A . 15C shows a diagram showing the depth values of the sharpest image points 15B over the respective edge orientation angle. In the 15B and 15C It can be seen that the tangential focus 130 and the sagittal focus 132 are shifted in the depth direction 134.

A sum of sine functions Σa _m (x,y) sin(mθ) + b _m (x,y) cos(mθ), preferably a 2nd order sine function a ₂ (x,y) is applied to the determined depth values. sin(2θ) + b ₂ (x,y) cos(2θ), fitted according to the astigmatism model. The development coefficients a _m and b _m are determined using the fit. The development coefficients describe the astigmatic, i.e. tangential and sagittal, best adjustment planes depending on the local edge orientation. The development coefficients therefore correspond to astigmatic correction values for the position of the respective points of the point grid in the image space. If one considers the development only in the first order, the development coefficients a ₁ and b ₁ correspond to the first and second correction values at the location of the point of the point grid in the image space. If one considers the development only in the second order, the development coefficients a ₂ and b ₂ correspond to the first and second correction values at the location of the point of the point grid in the image space. The first and second correction values for the pixels of the image with extended depth of field (for all pixels in the image space) are then determined by interpolation over the entire area (the entire image space).

In the 16A until 16C A first example is shown in which a sum of sine functions (as a fit function) is fitted to the angle-dependent distribution of the depth values of a point on the point grid. 16 A shows a diagram in which the adjustment of the fit function to the depth values of the sharpest image points of the edge of a point of a point grid is shown. In other words shows 16A the fit of the fit function to the angle-dependent distribution of the depth values. 16B shows a diagram showing the spatial distribution of the depth values in the image plane (xy plane). 16C shows a diagram in which the spatial distribution of corrected depth values in the image plane (xy plane) is shown. The corrected depth values result from the difference between the depth values and the fit.

In the 17A until 17C A second example is shown in which a sum of sine functions (as a fit function) is fitted to the angle-dependent distribution of the depth values of a point on the point grid. 17A shows a diagram in which the fitting of the fit function to the depth values of the sharpest image points of the edge of a point of a point grid is shown. In other words shows 17A the fit of the fit function to the angle-dependent distribution of the depth values. 17B shows a diagram in which the spatial distribution of the depth values in the image plane (xy plane) is shown. 17C shows a diagram in which the spatial distribution of corrected depth values in the image plane (xy plane) is shown. The corrected depth values result from the difference between the depth values and the fit.

With reference to the 18 until 19 The following explains how to locate an edge in an image with an extended depth of field.

In the simplest case, an edge can at least be locally approximated as a straight line. The “Slanted Edge” method follows this approach. In 18 is shown as an example of how an edge position of an edge 166 in an image area 162 of the image 160 is localized using the “slanted edge” method in an image 160 with an extended depth of field.

The image 160 has pixels 164 in the image area 162. An edge 166 runs in the image 160. The edge course of the edge 166 is straight and therefore has no curvature. The edge 166 runs in an edge direction 168. A normal direction 170 runs perpendicular to the edge direction 168.

Using the “slanted edge” method, a tilt angle is now determined by which the edge 160, in particular the edge direction 168, is tilted in the y-direction. The normal direction 170 is also tilted to the x direction by the same tilt angle. This tilt angle can be determined by looking at the intensities of the image points in the edge area.

Using the angle, the image points 164 in the image area 162 can then be projected onto the normal direction 170. This projection is in 18 shown with dashed lines that run parallel to the edge direction 168. The projection is therefore a projection of the image area 162 along the edge direction 168 onto the normal direction 170. Using this projection, an over-resolved edge profile 172 of the edge 166 can then be generated in the normal direction 170. The over-resolved edge profile 172 is an intensity profile I(z) of the image points 164 in the image area 162, where z indicates the position in the normal direction. The position z of each pixel in the normal direction 170 results from the coordinates (x, y) of the pixel and the determined tilt angle.

The turning point of the over-resolved edge profile 172 indicates the edge position of the edge 166 in the normal direction 170. In this way, the edge position of a straight edge can be determined using the “Slanted Edge” method.

During metrological investigations, however, it is often not straight edges that are measured, but rather round or arbitrarily curved edges. The “slanted edge” method is unsuitable for determining the edge position of such curved edges. The following describes a methodology that can be used to model an edge with any curved edge and to precisely determine its edge position.

19 shows, similar to 18 , an image area 162 of an image 160 with extended depth of field. An edge 166 runs in the image 160. In contrast to 18 the edge is 166 in 19 not straight, but curved. The edge 166 thus has a curved edge profile. At each point 174 of edge 166, edge 166 has a tangent and a normal. The tangent runs in an edge direction 168. The normal runs in a normal direction 170. The edge direction 168 and the normal direction 170 change along the edge path of the edge 166. The edge direction 168 and the normal direction 170 thus span a curvilinear coordinate system on.

It is now proposed to carry out a projection of the image points in the image 164 along the curved edge, i.e. a projection onto the normal direction 170 of the curvilinear coordinate system. For this purpose, one or more edge parameters can be determined based on the intensities of the image points, in particular based on the image gradients of these image points, by means of which the curved edge profile can be described or modeled. The position z of each pixel in the normal direction 170 thus results from a coordinate transformation into the curvilinear coordinate system. The specific edge parameters of the modeled, curved edge profile are used for coordinate transformation.

Using this projection, an over-resolved edge profile 172 of the edge 166 in the normal direction 170 is then also generated, on the basis of which the edge position in the normal direction 170 can then be determined.

In the 20A and 20B A special case is shown in which an edge 166 has a constant curvature.

20A shows, similar to 19 , an image area 162 of an image 160 with an extended depth of field, in which a curved edge 166 runs. The edge 166 in 20A has an edge profile with constant curvature. The edge 166 thus runs around a center of curvature 176. With constant curvature, the normal direction 170 corresponds to the radial direction with respect to the center of curvature 176 and the edge direction 168 corresponds to the tangential direction with respect to the center of curvature 176. The curvilinear coordinate system is therefore a two-dimensional polar coordinate system with origin in the center of curvature 176.

The projection along the edge profile with constant curvature is therefore a projection along the tangential direction onto the radial direction. The center of curvature can be determined based on the intensities of the image points, in particular based on the image gradients of these image points.

bestimmt werden.The position z of each pixel in the normal direction 170 then corresponds to the radial distance r to the center of curvature 176 in the radial direction. The radial distance r of an image point with the coordinates (x,y) to the center of curvature 176 with the coordinates (x ₀ , y ₀ ) can be determined using the formula $\text{r}=\sqrt{{\left(\text{x}-{\text{x}}_0\right)}^2+{\left(\text{y}-{\text{y}}_0\right)}^2}$

be determined.

Based on the projection onto the radial direction, the over-resolved edge profile can then be created 172 of the edge 166 are generated in the normal direction 170, i.e. in the radial direction. This is in 20B shown. The over-resolved edge profile 172 is an intensity profile I(r) of the image points 164 in the image area 162. Based on the over-resolved edge profile 172, the edge position in the radial direction with respect to the center of curvature 176 can then be determined.

In 21 is a method 200 for locating an edge position of an edge 166 in an image area 162 of an image 160 with extended depth of field described, which uses the new methodology described above. The method 200 may be a computer-implemented method. The method 200 can be carried out, for example, using a computer. Alternatively, the method 200 can also be carried out using the control device 26 of the measuring device 10.

In an optional step 202 of the method 200, the image 160 is received with an extended depth of field. For this purpose, the image 160 can either be stored or generated in an external device, for example. The image 160 can then be received from the external device for edge localization.

Alternatively, in an optional step 204 of the method 200, the image 160 can be generated with an extended depth of field. To generate the image 160 with an extended depth of field, the method 40 can be used, for example 2 be performed.

In a further step 206 of the method 200, an image gradient is determined for each pixel in the image area 162. The determined image gradients form an image gradient map.

In a further, optional step 208 of method 200, the image gradient map is filtered. The image gradients that are below a defined threshold value are rejected.

In a further step 210 of the method 200, at least one edge parameter of a modeled, curved edge profile is determined based on the image gradient map. The at least one edge parameter can be one or more parameters of an edge profile model for describing the edge profile, wherein the at least one edge parameter is determined based on the edge profile model and the image gradient map. For example, a polynomial function can be used as the edge profile model, in particular where the polynomial function is a polynomial of at least second degree.

The at least one edge parameter can be determined by compensation calculation based on the edge profile model and the image gradient map, in particular where the least squares method is used for the compensation calculation. Alternatively or additionally, the at least one edge parameter can also be determined by optimization based on the edge profile model and the image gradient map, in particular wherein for optimization the edge profile model is minimized with regard to the local edge roughness.

In particular, the modeled, curved edge profile can have a constant curvature. This case was made with reference to 20A and 20B already explained in detail. The at least one edge parameter then defines the center of curvature 176 of the edge profile with constant curvature. The projection is then a projection of the image points onto the radial direction with respect to the center of curvature 176.

In a further step 212 of the method 200, an edge profile 172 of the edge 166 is determined based on a projection of the image points of the image area (162) along the edge profile using the at least one edge parameter.

In a further step 214 of the method 200, the edge position of the edge 166 is determined based on the edge profile 172. The edge position can be determined, for example, based on a turning point of the edge profile 172.

In 22 is a method 220 for edge localization in an image 160 with extended depth of field, the image 160 depicting a region of a surface of a workpiece 12. The method 200 can be carried out, for example, by means of the control device 26 of the measuring device 10.

In a first step 222 of the method 220, an image 160 is recorded with an extended depth of field. To capture the image 160 with an extended depth of field, for example, the method 60 can be used 3 be performed.

In a further step 224 of the method 220, an edge position of an edge 166 in an image area 162 of the image 160 with an extended depth of field is then determined using the method 200 21 generated.

The case of constant curvature of the edge will be discussed in more detail below. The edge geometry is displayed relative to a common center of curvature [x ₀ ,y ₀ ]. This can be called a Taylor approximation Order can be understood. Determining the common center of curvature 176 meets the central challenge and there are several options here. in the 23 and 24 Two examples are shown of how the center of curvature 176 and on the basis of this the over-resolved edge profile 172 can be determined in the radial direction with constant curvature of the edge profile.

In 23 A first example of edge localization is shown in an image with an extended depth of field. The picture shows a circular structure (see 23(A) ). To locate the edge, an image area is selected in which part of the circular edge runs (see 23(B) ).

bspw. durch direktionale Sobelfilter oder numerische Finite-Differenzen Ableitungsverfahren ermittelt. Um Einflüsse durch Bildrauschen zu unterdrücken ist es besonders vorteilhaft die Bildgradienten als gewichtete Mittelung über mehrere Bilder aus einem Fokalbildstapel zu errechnen. Dies kann mit folgender Formel erfolgen: $$\left[{\text{G}}_{\text{x}},{\text{G}}_{\text{y}}\right]=\frac{1}{\text{N}}{\displaystyle \sum _{\text{i}=1}^{\text{N}}\left[{\partial }_{\text{x}}{\mathrm{\phi }}_{\text{i}}\left(\text{x},\text{y}\right),{\partial }_{\text{y}}{\mathrm{\phi }}_{\text{i}}\left(\text{x},\text{y}\right)\right]}$$

In a first step, the local edge orientation is determined. For this purpose, the numerical approximation of the image gradient is used in the selected image area $$\left[{\text{G}}_{\text{x}},{\text{G}}_{\text{y}}\right]=\left[{\partial }_{\text{x}}\mathrm{\phi }\left(\text{x},\text{y}\right),{\partial }_{\text{y}}\mathrm{\phi }\left(\text{x},\text{y}\right)\right]$$

for example, determined by directional Sobel filters or numerical finite difference derivation methods. In order to suppress influences caused by image noise, it is particularly advantageous to calculate the image gradients as a weighted average over several images from a focal image stack. This can be done using the following formula: $$\left[{\text{G}}_{\text{x}},{\text{G}}_{\text{y}}\right]=\frac{1}{\text{N}}{\displaystyle \sum _{\text{i}=1}^{\text{N}}\left[{\partial }_{\text{x}}{\mathrm{\phi }}_{\text{i}}\left(\text{x},\text{y}\right),{\partial }_{\text{y}}{\mathrm{\phi }}_{\text{i}}\left(\text{x},\text{y}\right)\right]}$$

Furthermore, it is advantageous to additionally filter the calculated image gradients. Calculated image gradients, which are located away from the edge, are predominantly influenced by pure image noise due to the lack of edge contrast and are correspondingly distorted. It makes sense to discard all image gradients whose gradient value is below a threshold value to be defined.

$$\text{y}={\text{y}}_0+\frac{1}{\rho }{\text{G}}_{\text{y}}$$

In a next step, the center of curvature of the edge is calculated using the calculated image gradient map [G _x ,G _y ] (see 23(C) ). Assuming that the edge path within the image area can be approximated as a circle, there is a common center of curvature [x ₀ ,y ₀ ] at which the calculated vector field [G _x ,G _y ] of the local edge orientation has a common origin. One way to determine this common origin is to solve the overdetermined system of equations from the known quantities x,y,G _x ,G _y within the selected image area for the unknown quantities x ₀ ,y ₀ ,ρ in the sense of a least-square optimization $$\text{x}={\text{x}}_0+\frac{1}{\rho }{\text{G}}_{\text{x}}$$

$$\text{y}={\text{<figure-callout id="0" label="y" filenames="DE102022118586A1\_0053.png,DE102022118586A1\_0059.png" state="{{state}}">y</figure-callout>}}_0+\frac{1}{\rho }{\text{G}}_{\text{y}}$$

zugeordnet (siehe 23(D)). Dann wird die Intensität der Bildpunkte (siehe 23(E)) in radialer Richtung betrachtet. Dazu wird das überaufgelöste Katenprofil $\text{I}(\text{r}=\sqrt{({\left(\text{x}-{\text{x}}_0\right)}^2+\left(\text{y}-{\text{y}}_0\right){}^2)})$

$$

in der radialen Richtung erzeugt.This means that the best center of curvature across all image gradients in the image gradient map is calculated. With the help of the center of curvature [x ₀ ,y ₀ ] calculated in this way, the over-resolved edge profile can be extracted. For this purpose, each pixel of the image area is assigned the radial distance to the center of curvature $\text{r}=\sqrt{({\left(\text{x}-{\text{x}}_0\right)}^2+\left(\text{y}-{\text{y}}_0\right){}^2)}$

assigned (see 23(D) ). Then the intensity of the image points (see 23(E) ) viewed in the radial direction. The over-resolved cat profile is used for this purpose $\text{I}(\text{r}=\sqrt{({\left(\text{x}-{\text{x}}_0\right)}^2+\left(\text{y}-{\text{y}}_0\right){}^2)})$

$$

generated in the radial direction.

Based on this edge profile, the edge position in the radial direction can then be determined, i.e. the distance from the edge to the center of curvature [x ₀ ,y ₀ ].

In 24 A second example of edge localization is shown in an image with an extended depth of field. In the second example, the center of curvature is calculated using an optimization that minimizes the local edge roughness. If the local edge origin is shifted compared to its nominal value, the extracted edge profile has a higher roughness (a possible measure for the roughness is, for example, the comparison between the low-pass filtered edge transfer function and the unfiltered edge transfer function).

This comparison makes it possible to determine a center of curvature by optimizing the position [x ₀ ,y ₀ ] in such a way that the determined roughness of the edge profile is minimized. This is schematic in the 24(A) to (C) shown. 24(A) shows an edge profile, for the creation of which the position of the center of curvature is estimated or using a different procedure, such as that from 23 , was determined. 24(B) shows an enlarged view of the intensity values of the edge profile 24(A) in the edge area. 24(C) shows the intensity values of an optimized edge profile in the edge region, where the position of the center of curvature [x ₀ ,y ₀ ] was optimized to the roughness of the edge profile to reduce. The edge roughness in 24(C) is significantly lower than in 24(B) .

In the 25A until 26B A comparison is shown for an edge measurement based on the extracted edge profiles of the slanted edge method in comparison to the proposed new method.

Shown is a recorded measurement image of a Siemens star superimposed on a calibration mask with its nominal diameter and the determined edge positions based on the slanted edge method (see 25A and 25B) and the proposed methodology (see 26A and 26B) . The extracted edge localization results using the slanted edge method show significantly increased measurement errors compared to the proposed methodology.

In the following, a workpiece with several circular structures will be considered as another example. In 27 a picture of this workpiece is shown. There are 30 circular structures in the area shown. From this area, method 60 is used 3 a corrected image is recorded with an extended depth of field, in which the distortion error and the astigmatism error are corrected. Then, for example, using the method 200 21 the edges of the circular structures are localized.

For comparison purposes, in the example under consideration, the edge localization of the circular structures is carried out once in the corrected image with an extended depth of field and further in individual image measurements, i.e. in individual images of the focal image stack. The roundness of the circular structures can then be determined based on the localized edges.

In the 28 , 29A and 29B Roundness measurements of the circular structures are shown in various images. 28 shows the roundness measurement in a corrected image with extended depth of field. The 29A and 29B show roundness measurements in images for which image planes were selected that lie in the maximum points of astigmatism, i.e. one image each in the best sagittal and tangential image plane. 29A shows a roundness measurement in an uncorrected image in the best sagittal plane. 29B shows a roundness measurement in an uncorrected image in the best tangential plane.

The comparison of the roundness measurement 28 with them 29A and 29B illustrates the measurement error that can arise from an autofocus measuring point on a horizontal or vertical edge. It becomes clear that both the center and shape within the roundness measurements change depending on the images chosen. This deviation is in the range of 1-1.5 µm and is therefore significantly larger compared to the deviation of around 200 nm in the corrected image with extended depth of field. This illustrates the improvement in accuracy achieved by a corrected image with extended depth of field.

QUOTES INCLUDED IN THE DESCRIPTION

This list of documents listed by the applicant was generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• EP 2598836 A1 [0007]

Non-patent literature cited

• "Shape From Focus Sytem" by Shree K. Nayar, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 1992, 302-308 [0008]
• "Robust edge-spread function construction methods to counter poor sample spacing uniformity in the slanted-edge method", F. van den Bergh, J. Opt. Soc. Am. A 36, pages 1126-1136 [0013]
• "Comparison of MTF measurements using edge method: towards reference data set", Viallefont-Roninet et al, Opt. Express 26, 33625-33648 [0013]

Claims (21)

Computer-implemented method (200) for locating an edge position of an edge (166) in an image area (162) of an image (160), comprising the following steps: - determining (206) an image gradient for each pixel in the image area (162), the determined image gradients forming an image gradient map; - Determining (210) at least one edge parameter of a modeled, curved edge profile based on the image gradient map; - Determining (212) an edge profile (172) of the edge (166) based on a projection of the image points of the image area (162) along the edge profile using the at least one edge parameter; and - Determine (214) the edge position based on the edge profile (172). Procedure according to Claim 1 , wherein the method (200) further comprises the following step: - filtering (208) of the image gradient map, wherein the image gradients that are below a defined threshold value are rejected. Procedure according to Claim 1 or 2 , wherein the at least one edge parameter is one or more parameters of an edge profile model for describing the edge profile, wherein the at least one edge parameter is determined based on the edge profile model and the image gradient map. Procedure according to Claim 3 , wherein the at least one edge parameter is determined by compensation calculation based on the edge profile model and the image gradient map, in particular wherein the least squares method is used for the compensation calculation. Procedure according to Claim 3 or 4 , wherein the at least one edge parameter is determined by optimization based on the edge profile model and the image gradient map, in particular wherein for optimization the edge profile model is minimized with regard to the local edge roughness. Procedure according to one of the Claims 3 until 5 , whereby a polynomial function is used as the edge profile model, in particular where the polynomial function is a polynomial of at least second degree. Procedure according to one of the Claims 1 until 6 , wherein the curved edge profile has a constant curvature, and wherein the at least one edge parameter defines the center of curvature (176) of the edge profile with constant curvature, in particular wherein the projection is a projection of the image points onto a radial direction with respect to the center of curvature (176). Procedure according to one of the Claims 1 until 7 , wherein in the step of determining (214) the edge position, the edge position is determined based on a turning point of the edge profile (172). Procedure according to one of the Claims 1 until 7 , wherein in the step of determining (214) the edge position, the edge position is determined based on reaching a defined threshold value of the edge profile (172). Procedure according to one of the Claims 1 until 9 , wherein the method further comprises the following step: - receiving (202) the image, in particular wherein the image is an image with an extended depth of field. Procedure according to one of the Claims 1 until 9 , wherein the image is an extended depth of field image, wherein the extended depth of field image images a region of a surface of a workpiece (12), the method (200) further comprising the following steps: - receiving (42) a focal image stack, wherein the focal image stack has a plurality of images of the workpiece (12), the images imaging the area of the surface of the workpiece (12) with different, defined focal plane positions in a depth direction (20), with each image of the focal image stack being assigned a focal plane position; - Generating (50) the image with extended depth of field in the depth direction based on the focal image stack. Method (220) for edge localization in an image with an extended depth of field, the image depicting a region of a surface of a workpiece (12), with the following steps: - Acquiring (68) a plurality of images of the region of the surface of the workpiece (12) by means of the optical sensor (14), wherein the images each image the area of the surface of the workpiece (12) with different, defined focal plane positions in the depth direction (20), and wherein the captured images form a focal image stack; - Generating (50) the image with extended depth of field in the depth direction (20) based on the focal image stack; and - locating an edge position of an edge (166) in an image area (162) of the image (160) with extended depth of field using the method (200) according to one of the Claims 1 until 10 . Procedure according to Claim 11 or 12 , wherein the method further comprises the step: - correcting (52) one or more imaging errors in the generated image with extended depth of field, the imaging errors to be corrected having at least one of the following errors: a distortion error and / or an astigmatism error. Procedure according to Claim 12 or 13 , wherein the optical sensor (14) and the workpiece (12) can be moved relative to one another in the depth direction (20), so that a distance (22) in the depth direction (20) between the workpiece (12) and the optical sensor (14 ) can be changed, the method further comprising the following step: - changing (66) the distance between the workpiece (12) and the optical sensor (14), the plurality of images being captured in the capture step (68). , while the distance (22) between the workpiece (12) and the optical sensor (14) is changed, the images each showing the area of the surface of the workpiece (12) from different, defined distances (22) to the workpiece (12). in the depth direction (20). Procedure according to one of the Claims 12 until 14 , wherein the measuring device (10) has a workpiece holder (16), the workpiece (12) being arranged on the workpiece holder (16) for measurement. Procedure according to Claim 15 , wherein the measuring device (10) has a drive device (28), wherein the drive device (28) moves the optical sensor (14) relative to the workpiece holder (16) in the depth direction (20) and / or the workpiece holder (16) relative to the optical sensor (14) moves in the depth direction (20) to change the distance (22) between the workpiece (12) and the optical sensor (14). Procedure one of the Claims 12 until 16 , wherein the measuring device (10) has an illumination device (32), the method further comprising the following step: - illuminating (64) the workpiece (12) by means of the illumination device (32) while capturing the images of the focal image stack. Measuring device, in particular a coordinate measuring machine or a microscope, wherein the measuring device (10) has a workpiece holder (16) for a workpiece (12), an optical sensor (14) and a control device (26), the optical sensor (14) being designed for this purpose is to capture images of a region of a surface of the workpiece (12), the optical sensor (14) and the workpiece (12) being spaced apart from one another in a depth direction (20), the control device (26) being set up to do the following To carry out steps: - Controlling the optical sensor (14) in such a way that a plurality of images of a region of the surface of the workpiece (12) are captured by means of the optical sensor (14), the images each representing the region of the surface of the workpiece (12). image with defined focal plane positions (22) that are different in the depth direction (20), and wherein the captured images form a focal image stack; - Generating an image (160) with extended depth of field in the depth direction (20) based on the focal image stack; and - locating at least one edge position of an edge (166) in an image area (162) of the image (160) with an extended depth of field using the method (200) according to one of Claims 1 until 10 . measuring device Claim 18 , wherein the measuring device (10) further has a drive device (28), wherein the drive device (28) is designed to move the optical sensor (14) and the workpiece holder (16) relative to one another in the depth direction (20), in order to to change a distance (22) between the workpiece (12) and the optical sensor (14). measuring device Claim 19 , wherein the control device (26) is further set up to carry out the following steps, in particular before the step of generating the corrected image with an extended depth of field: - Controlling the drive device (28) such that a distance (22) between the workpiece (12) and the optical sensor (14), the optical sensor (14) being controlled such that the plurality of images are captured while the distance (22) between the workpiece (12) and the optical sensor (14 ) is changed, the images each depicting the area of the surface of the workpiece (12) from different, defined distances (22) from the workpiece (12) in the depth direction (20). Computer program product with a computer program, the program code means for carrying out a method according to one of the Claims 1 until 11 when the computer program is executed on a measuring device (10).

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