Measurement techniques for correcting images with extended depth of field

A computer-implemented method comprising:

• receiving a focal image stack, wherein:
• the focal image stack includes a plurality of images of a measurement object,
• each of the plurality of images captures a region of a surface of the measurement object with a defined focal plane position in a depth direction, and
• the defined focal plane positions of the plurality of images are different from each other;
• generating an initial image with an extended depth of field in the depth direction based on the focal image stack;
• and
• generating a corrected image by correcting a set of imaging errors in the initial image, wherein:
• the set of imaging errors includes a distortion error,
• correcting the distortion error includes, for each point of the initial image:
• assigning at least one distortion value to the point, and
• correcting the point perpendicular to the depth direction based on the at least one distortion value, and
• correcting the distortion error includes, for each point of the initial image:
• assigning a first distortion value and a second distortion value to the point;
• and
• correcting a position of the point in (i) a first direction based on the first distortion value and (ii) a second direction based on the second distortion value.

A computer-implemented method comprising:

• receiving a focal image stack, wherein:
• the focal image stack includes a plurality of images of a measurement object,
• each of the plurality of images captures a region of a surface of the measurement object with a defined focal plane position in a depth direction, and
• the defined focal plane positions of the plurality of images are different from each other;
• generating an initial image with an extended depth of field in the depth direction based on the focal image stack;
• and
• generating a corrected image by correcting a set of imaging errors in the initial image, wherein:
• the set of imaging errors includes a distortion error,
• the set of imaging errors includes an astigmatism error, and
• correcting the astigmatism error includes:
• generating an angle map of the region of the surface of the measurement object;
• and
• for each point of the initial image:
• assigning a first correction value and a second correction value to the point, and
• correcting a depth value of the point based on the first correction value, the second correction value, and the angle map.

A computer-implemented method comprising:

• receiving a focal image stack, wherein:
• the focal image stack includes a plurality of images of a measurement object,
• each of the plurality of images captures a region of a surface of the measurement object with a defined focal plane position in a depth direction, and
• the defined focal plane positions of the plurality of images are different from each other;
• generating an initial image with an extended depth of field in the depth direction based on the focal image stack;
• generating a corrected image by correcting a set of imaging errors in the initial image, wherein:
• the set of imaging errors includes a distortion error, and
• the set of imaging errors includes an astigmatism error,
• generating the focal image stack by capturing the plurality of images in the focal stack using an optical sensor, wherein:
• each of the plurality of images captures the region of the surface of the measurement object with a respective focal plane position, and
• the respective focal plane positions of the plurality of images are different,
• determining first and second correction values for each image point;
• and
• recording a calibration image of a calibration object, wherein:
• respective ones of the first and second correction values are determined based on deviations of the initial image or determined depth values of the object points of the calibration object with respect to a known surface profile of the calibration object,
• the calibration image includes a point grid, and
• determining the first and second correction values includes:
• for each point of the point grid, determining a first point correction value and a second point correction value based on a cost function between an astigmatism model and depth values of the point, and
• interpolating the first and second correction values based on the first and second point correction values of each point of the point grid.

A measuring apparatus comprising:

• a measurement object holder for a measurement object;
• an optical sensor;
• and
• a control device, wherein:
• the optical sensor and the measurement object are spaced apart from one another in a depth direction,
• the optical sensor is configured to capture a plurality of images of a region of a surface of a measurement object,
• the plurality of images form a focal image stack and have defined focal plane positions that are different in the depth direction,
• the control device is configured to:
• generate an initial image with an extended depth of field in the depth direction based on the focal image stack;
• and
• generate a corrected image by correcting a set of imaging errors in the initial image,
• the set of imaging errors includes a distortion error,
• image points of the plurality of images are assigned to corresponding object points on the surface of the measurement object;
• the control device is configured to:
• determine a sharpness value of each of the image points, and
• ascertain a depth value of each of the object points in the depth direction based on the determined sharpness values;
• the initial image is generated based on the ascertained depth values and the focal image stack,
• the control device is configured to:
• for each subset of the image points that is assigned to a common point of the object points, fit a function for the common point along the depth direction to the sharpness values of the subset of the image points, and
• for each object point of the object points, ascertaining the depth value of the object point includes:
• in response to a residual of the fitted function that corresponds to the object point being greater than a threshold value, ascertaining the depth value of the object point based on a maximum of the fitted function;
• and
• in response to the residual of the fitted function being less than or equal to the threshold value, interpolating the depth values of at least two neighboring ones of the object points.

A non-transitory computer-readable medium comprising computer-executable instructions including:

• receiving a focal image stack, wherein:
• the focal image stack includes a plurality of images of a measurement object,
• each of the plurality of images captures a region of a surface of the measurement object with a defined focal plane position in a depth direction, and
• the defined focal plane positions of the plurality of images are different from each other;
• generating an initial image with an extended depth of field in the depth direction based on the focal image stack;
• generating a corrected image by correcting a set of imaging errors in the initial image, wherein:
• the set of imaging errors includes a distortion error, and
• image points of the plurality of images are assigned to corresponding object points on the surface of the measurement object:
• determining a sharpness value of each of the image points;
• ascertaining a depth value of each of the object points in the depth direction based on the determined sharpness values, wherein the initial image is generated based on the ascertained depth values and the focal image stack;
• and
• for each subset of the image points that is assigned to a common point of the object points, fitting a function for the common point along the depth direction to the sharpness values of the subset of the image points, wherein, for each object point of the object points, ascertaining the depth value of the object point includes:
• in response to a residual of the fitted function that corresponds to the object point being greater than a threshold value, ascertaining the depth value of the object point based on a maximum of the fitted function;
• and
• in response to the residual of the fitted function being less than or equal to the threshold value, interpolating the depth values of at least two neighboring ones of the object points.

A measuring apparatus comprising:

• a measurement object holder for a measurement object;
• an optical sensor;
• and
• a control device, wherein:
• the optical sensor and the measurement object are spaced apart from one another in a depth direction,
• the optical sensor is configured to capture a plurality of images of a region of a surface of a measurement object,
• the plurality of images form a focal image stack and have defined focal plane positions that are different in the depth direction,
• the control device is configured to:
• generate an initial image with an extended depth of field in the depth direction based on the focal image stack;
• and
• generate a corrected image by correcting a set of imaging errors in the initial image,
• the set of imaging errors includes a distortion error,
• correcting the distortion error includes, for each point of the initial image:
• assigning at least one distortion value to the point;
• and
• correcting the point perpendicular to the depth direction based on the at least one distortion value, and
• correcting the distortion error includes, for each point of the initial image:
• assigning a first distortion value and a second distortion value to the point;
• and
• correcting a position of the point in (i) a first direction based on the first distortion value and (ii) a second direction based on the second distortion value.

A measuring apparatus comprising:

• a measurement object holder for a measurement object;
• an optical sensor;
• and
• a control device, wherein:
• the optical sensor and the measurement object are spaced apart from one another in a depth direction,
• the optical sensor is configured to capture a plurality of images of a region of a surface of a measurement object,
• the plurality of images form a focal image stack and have defined focal plane positions that are different in the depth direction,
• the control device is configured to:
• generate an initial image with an extended depth of field in the depth direction based on the focal image stack;
• and
• generate a corrected image by correcting a set of imaging errors in the initial image,
• the set of imaging errors includes a distortion error,
• the set of imaging errors includes an astigmatism error, and
• correcting the astigmatism error includes:
• generating an angle map of the region of the surface of the measurement object;
• and
• for each point of the initial image:
• assigning a first correction value and a second correction value to the point, and
• correcting a depth value of the point based on the first correction value, the second correction value, and the angle map.

A measuring apparatus comprising:

• a measurement object holder for a measurement object;
• an optical sensor;
• and
• a control device, wherein:
• the optical sensor and the measurement object are spaced apart from one another in a depth direction,
• the optical sensor is configured to capture a plurality of images of a region of a surface of a measurement object,
• the plurality of images form a focal image stack and have defined focal plane positions that are different in the depth direction,
• the control device is configured to:
• generate an initial image with an extended depth of field in the depth direction based on the focal image stack;
• and
• generate a corrected image by correcting a set of imaging errors in the initial image,
• the set of imaging errors includes a distortion error,
• the set of imaging errors includes an astigmatism error,
• the control device is configured to generate the focal image stack by capturing the plurality of images in the focal stack using an optical sensor,
• each of the plurality of images captures the region of the surface of the measurement object with a respective focal plane position,
• the respective focal plane positions of the plurality of images are different,
• the control device is configured to:
• determine first and second correction values for each image point;
• and
• record a calibration image of a calibration object,
• respective ones of the first and second correction values are determined based on deviations of the initial image or determined depth values of the object points of the calibration object with respect to a known surface profile of the calibration object,
• the calibration image includes a point grid, and
• determining the first and second correction values includes:
• for each point of the point grid, determining a first point correction value and a second point correction value based on a cost function between an astigmatism model and depth values of the point, and
• interpolating the first and second correction values based on the first and second point correction values of each point of the point grid.

A non-transitory computer-readable medium comprising computer-executable instructions including:

• receiving a focal image stack, wherein:
• the focal image stack includes a plurality of images of a measurement object,
• each of the plurality of images captures a region of a surface of the measurement object with a defined focal plane position in a depth direction, and
• the defined focal plane positions of the plurality of images are different from each other;
• generating an initial image with an extended depth of field in the depth direction based on the focal image stack;
• and
• generating a corrected image by correcting a set of imaging errors in the initial image, wherein:
• the set of imaging errors includes a distortion error,
• correcting the distortion error includes, for each point of the initial image:
• assigning at least one distortion value to the point;
• and
• correcting the point perpendicular to the depth direction based on the at least one distortion value, and
• correcting the distortion error includes, for each point of the initial image:
• assigning a first distortion value and a second distortion value to the point;
• and
• correcting a position of the point in (i) a first direction based on the first distortion value and (ii) a second direction based on the second distortion value.

A non-transitory computer-readable medium comprising computer-executable instructions including:

• receiving a focal image stack, wherein:
• the focal image stack includes a plurality of images of a measurement object,
• each of the plurality of images captures a region of a surface of the measurement object with a defined focal plane position in a depth direction, and
• the defined focal plane positions of the plurality of images are different from each other;
• generating an initial image with an extended depth of field in the depth direction based on the focal image stack;
• and
• generating a corrected image by correcting a set of imaging errors in the initial image, wherein:
• the set of imaging errors includes a distortion error,
• the set of imaging errors includes an astigmatism error, and
• correcting the astigmatism error includes:
• generating an angle map of the region of the surface of the measurement object;
• and
• for each point of the initial image:
• assigning a first correction value and a second correction value to the point, and
• correcting a depth value of the point based on the first correction value, the second correction value, and the angle map.

A non-transitory computer-readable medium comprising computer-executable instructions including:

• receiving a focal image stack, wherein:
• the focal image stack includes a plurality of images of a measurement object,
• each of the plurality of images captures a region of a surface of the measurement object with a defined focal plane position in a depth direction, and
• the defined focal plane positions of the plurality of images are different from each other;
• generating an initial image with an extended depth of field in the depth direction based on the focal image stack;
• generating a corrected image by correcting a set of imaging errors in the initial image, wherein:
• the set of imaging errors includes a distortion error, and
• the set of imaging errors includes an astigmatism error;
• generating the focal image stack by capturing the plurality of images in the focal stack using an optical sensor, wherein:
• each of the plurality of images captures the region of the surface of the measurement object with a respective focal plane position, and
• the respective focal plane positions of the plurality of images are different;
• determining first and second correction values for each image point;
• and
• recording a calibration image of a calibration object, wherein:
• respective ones of the first and second correction values are determined based on deviations of the initial image or determined depth values of the object points of the calibration object with respect to a known surface profile of the calibration object,
• the calibration image includes a point grid, and
• determining the first and second correction values includes:
• for each point of the point grid, determining a first point correction value and a second point correction value based on a cost function between an astigmatism model and depth values of the point, and
• interpolating the first and second correction values based on the first and second point correction values of each point of the point grid.